INTRODUCTION TO HOCKEY ANALYTICS
Possession is the building block. Once you can fake an understanding of that, you’re halfway home. But you can also expect to encounter a whole lot of additional stats that sound much more complicated. They are, but in a way that makes enough sense that they shouldn’t trip you up.
Opponents of advanced stats sometimes try to dismiss the numbers by talking about context — you have to watch the game, man! But the advanced stats crowd is one step ahead of them, and has already developed plenty of stats that at least try to factor context into the equation.
Don’t teams take more shots when they’re trailing and fewer when they’re protecting a lead? Yes, which is why we have Fenwick Close. What if a good player is just stuck on a crappy team? Let’s check his Relative Corsi. What if he’s stuck with bad linemates? Let’s look at Quality of Teammates. Does he always line up against the best players? Quality of Competition. But his coach uses him as more of a defensive type of … Zone Starts! You get the idea.
Most statistics in hockey is based on shots. I think the best way to describe shot statistics is through a shot hierarchy. At the top you have the result, and then you can use shot data to describe how the result occurred.
Shooting And Goaltending
(Counting Stats):
In the NHL data there are 4 types of shot events:1. Goal2. Shot (on goal)3. Miss4. Block
These shot types are then categorized in 4 statistical groups. It’s a bit confusing that the event “shot” doesn’t include goals, but the statistic “shot” does:
Goals
Shots: Goals + Shots
Fenwick: Goals + Shots + Misses
Corsi: Goals + Shots + Misses + Blocks
Goals, shots, fenwick and corsi are what we call simple counting stats. This means that you’re simply counting the number of shot attempts. There’s no modelling involved.
If we look at the shot hierarchy, we see that offense and defense is split into shooting/generation and goaltending/prevention respectively. At first, we’re going to focus on shooting and goaltending. You would typically define shooting as Sh% and goaltending as Sv%. However, you could also define shooting/goaltending based on fenwick or corsiGeneration And Prevention
(Counting stats):You often talk about shot differentials. The goal is to generate more shots than you allow. You can either look at normal differentials or you can look at percentagesThe difference between shots generated and shots allowed is called play driving. So, when someone talks about play driving, they are likely referring to CF% or xGF% (more on that below).Shooting And Goaltending (Modelling):
Until this point, we’ve only focused on counting stats. Let’s now look at modelling stats (the stats below the dashed line in the shot hierarchy image).All the modelling stats in the shot hierarchy are connected to expected goals3 different ways of measuring shooting and goaltending:
· GAx and GSAx
· dFSh% and dFSv%
· GF/xGF and GA/xGA
GAx and GSAx is simply goals scored above expected and goals saved above expected respectively
This is a way to measure the total shooting/goaltending impact. How many goals have been scored/saved above expected?
It turns out that dFSh% is actually the same as GAx per fenwick and dFSv% is the same as GSAx per fenwick
So, dFSh% and dFSv% are ways to measure shooting and goaltending performance as impact per fenwick (unblocked shot attempt). This is often how you see goaltender performance being measured
The 3rd option is to measure GF/xGF and GA/xGA. How many goals are scored/allowed per expected goal? Here we are measuring performance in regard to expected goals instead of fenwicks. If GF/xGF is above 1, you’re scoring more than expected. If GA/xGA is above 1, your goaltending is below expected.
It’s preferable to measure performance in regard to xG instead of fenwicks, because it’s fairer.
So, I think GF/xGF and GA/xGA are the best ways to measure shooting/goaltender performance… But dFSh% and dFSv% are the consensus metrics. In other words, you will need to understand both metrics.
Generation And Prevention (Modelling):The final part of the shot hierarchy is the advanced generation/prevention part.
Generation is simply xGF, whereas prevention is xGA. Unlike the counting stats, these metrics combine shot quantity and shot quality. In fact, you can split up generation/prevention into quality and quantity.
Shot quality is defined as xG per fenwick – the average shot-value. Shot quantity is just the total number of shots. We’re using fenwicks, because xG-models are fenwick-based.
Like mentioned earlier, the combination generation and prevention is called play driving:SHOT FORMULAS
Here’s the formulas connected to each step of the shot hierarchy. All the formulas are equal to the goal differential (G+/-), so it’s a way to calculate the result
G+/- = GA - GF
G+/- = (GF/xGF)×(xGF/FF)×FF - FA×(xGA/FA)×(GA/xGA)
So, results equal:shooting * shot quality for * shot quantity for – shot quantity against * shot quality against * goaltending
ADVANCED HOCKEY STATS PRIMER
INDIVIDUAL vs ON-ICE vs TEAM STATISTICS
Before we get into specific advanced statistics, let me mention the overriding concept of individual statistics vs on-ice statistics vs team statistics.
Individual Statistics
are exactly what they sound like: Statistics an individual puts up. These are goals, assists, points and shots that the individual player produces
While these are called ‘individual statistics,’ they can still be heavily influenced by one’s teammates and an individual player can also influence his teammates’ individual statistics. As a result, it is often better to look at on-ice statistics.
On-Ice Advanced Statistics
Are what the player and his team mates produce when the player is on the ice.
Both individual and on-ice statistics can be used for individual player evaluation.
Team statistics
are just what they sound like: Statistics related to team performance.
Team statistics are, as you may have guessed, best used in team evaluation.
Per 60 Stats
Rate statistics, also referred to as per-60 minute or per-hour statistics, are a player’s or team’s statistics per-60 minutes of play.
Most of the data-driven analysts in both the basketball and hockey worlds agree that rate statistics provide a more accurate depiction of a player’s talent than raw stat totals.
In addition to the obvious advantage of adjusting for games missed due to injuries, a prominent reason for using rate statistics is that they help account for the effects of a coach who makes terrible deployment decisions.
While cumulative stats are easier to digest for most people, they can severely over or underrate players’ true values due to them getting more or less ice time than deserved
One thing to note when discussing rate stats is that sample size is critical. A player who is called up for one game and puts up a nice performance in only a few minutes of ice time will have tremendous rate stats, so it is important to eliminate players who haven’t garnered enough ice time.
It is also imperative to understand player deployment when discussing rate statistics. A player’s rate statistics can quickly become inflated if they are sheltered by the coach, and therefor often play in the offensive zone and/or against weak opposition.
To truly measure scoring efficiency, the amount of time a player spent on the ice needs to be taken into account.
This is why we use “Per 60” metrics to evaluate scoring efficiency. Essentially, a player’s Points Per 60 (Points/60) rate is how many points were produced on average every sixty minutes a player was on the ice.
Over one-game sample sizes, raw point totals are still the best way to go. But when evaluating efficiency over longer periods of time, Per 60 stats reign supreme.
INDIVIDUAL STATS
Primary Point Production
The concept of primary points is simple. A player is awarded a primary point if he either scores a goal or receives the primary assist.
The primary assist is awarded to the player of the same team who last touched the puck before the goal scorer.
The secondary assist goes to the player of the same team who touched the puck before the primary assister.
Another way to look at this, is primary points are total points (the standard statistic all fans know and love) minus secondary assists.
The reason for using primary point production for player analysis instead of total points is that more often than not, the primary assist served a larger role in the goal being scored than the secondary assist.
Further, multiple leading analysts have proven beyond a shadow of a doubt that primary assists are far more indicative of a player’s talent level and that they are also more repeatable.
In layman’s terms, if a player racks up a high primary assist total, it is far more likely that this is due to his abilities and more likely to occur again in the future, compared to a player that only racks up a lofty secondary assist total.
When analyzing players, using primary assists instead of total assists is a good way to understand which players truly possess high levels of playmaking ability.
Further, you can use secondary assists as a way to identify a player whose point total may be bloated compared to his actual talent level.
If you are a fantasy hockey player, you can use this to your advantage by selling high on a guy that has padded his assist totals with secondary assists, as these are far less repeatable across the remainder of the season than primary assists.
Goals
I’m not going to waste anyone’s time defining what a goal is. However, I do want to point out that we can dissect goal data in the very same manner we do with expected goals and shot attempts.
Broadcasts and box scores use the stat plus/minus as a way to explain goal differential when a player is on the ice. Plus/minus is a horrendous stat that counts goals scored by penalty killers and those on the ice with the opposing goalie pulled, but does not count power play goals. By doing this, plus/minus greatly favors players like Michael Grabner, who play a lot of penalty kill and 5v6 time, and hurts players like Kevin Shattenkirk, who log a lot of minutes on the power play.
However, just because plus/minus is an atrocious statistic, doesn’t mean that we shouldn’t examine goal differential. In fact, it’s quite the opposite. We should treat goal differential like expected goals, in that we should primarily focus at 5v5 data for a truer gauge of a player’s ability, and dissect in use rate and relative versions to help round out our analysis of a player.
Goals For (GF)
The number of goals a team scored across a specified period of time (period, game, season etc.). Similar to expected goals, goals in this context can be applied to illustrate how a whole team does, or the impact a specific player has on the team’s ability to score goals.
Goals Against (GA)
The amount of goals a team allowed across a specified period of time. Similar to goals for, goals against can be used to show how a whole team does, or the impact a specific player has on the team’s ability to prevent goals against.
Goals Scored (G)
This is the statistic you all know and love, the amount of goals a player scored. In the expected goals and shot attempt metric sections, the individual player statistic was designated with an “i” before it, standing for “individual.” Here this is unnecessary, as we simply refer to this as Goals instead of individual goals.
Goals For Per-60 (GF/60)
The amount of goals a team accumulates per-60 minutes of play. Similar to GF and GA, GF/60 can be applied to see how the entire team did or to view the impact a specific player has on the team.
Also, just a reminder, per-60 stats are not the same as per-game stats, so be sure not to confuse the two.
Goals Against Per-60 (GA/60)
The amount of goals a team allows per-60 minutes of play. Similar to GF and GA, GA/60 can be applied to see how the entire team did or to view the impact a specific player has on the team.
Goals For Percentage (GF%)
The percentage of all goals accumulated by both teams that are generated by a specific team.
The formula is:
GF% = GF/(GF+GA).
This statistic is the one that should be used instead of plus/minus if you wish to evaluate a player’s impact on generating goals for and preventing goals against.
GF% can be used to demonstrate the percentage of goals generated by an entire team during a game, or it can be used to illustrate the percentage of goals generated by a team when a specific player is on the ice.
A GF% of 50% means that the team and the opponent generated the exact same number of goals over the specified period of time.
Relative Goals For Percentage (RELGF%)
The difference between a team’s goal differential when a player is on and off the ice.
Relative statistics help us view a player’s impact on a team and mitigate the effects that a team has on a player. Making it easier for us to truly compare players on poor and strong shot attempt differential teams.
A player with a positive RelGF% is one whose team performs better in terms of GF% when the player is on the ice, compared to when he is off the ice.
SHOTS ON GOAL
Shots on goal is the stat that even the most novice hockey fan is familiar with, as this metric is used in all hockey broadcasts and box scores, and is often simply referred to as “shots.”
Shots that hit the post are not included in this shots metric, nor are shots that miss the net or those that get blocked by the opponent. Goals however, are included in this stat (and goals are also included in both Corsi and Fenwick).
The reason I am including shots on goal here, despite its widespread popularity, is because I think it is important to note that shots data is also available in all of the flavors that we just discussed in the previous Corsi and Fenwick sections.
While you will likely only hear broadcasters discuss shots in terms of team or individual player shot attempts, you can break down the data in all of the same ways you can with Corsi and Fenwick.
Shots data is not as predictive as Corsi or Fenwick, but it still matters and helps round out the analysis of a team.
Shots For (SF)
The amount of shots on goal a team takes.
Similar to Corsi and Fenwick, shots in this context can be applied to illustrate how a whole team does, or the impact a specific player has on the team’s ability to generate shots on goal.
Specifically, you can use SF to state how many shots on goal a team has had over a specified course of time (period, game, season etc.), or you can use it to convey how many shots on goal a team takes while a specific player is on the ice.
Shots Against (SA)
The amount of shots on goal a team allows. Similar to shots for, shots against can be used to show how many shots on goal an entire team allows over a specified period, or it can be used to illustrate the impact a specific player has on the shots on goal allowed by a team.
Individual Shots For (ISF)
The amount of shots on goal an individual player takes himself.
Shots For Per-60 (SF/60)
The amount of shots on goal a team accumulates per-60 minutes of play. Similar to SF and SA, SF/60 can be applied to see how the entire team did or to view the impact a specific player has on the team.
Shots Against Per-60 (SA/60)
The amount of shots on goal a team allows per-60 minutes of play. Similar to SF and SA, SA/60 can be applied to see how the entire team did or to view the impact a specific player has on the team.
Shots For Percentage (SF%)
The percentage of all shots on goal that are taken by a team.
The formula is
SF% = SF/(SF+SA).
SF% can be used to demonstrate the percentage of shots on goal taken by an entire team during a game, or it can be used to illustrate the percentage of shots on goal taken by a team when a specific player in on the ice.
A SF% of 50% means that the team and the opponent took the exact same number of shots on goal over the specified period of time
Relative Shots For Percentage (RELSF%)
The difference between a team’s shots when a player is on and off the ice.
ON-ICE STATS
POSSESSION STATISTICS: CORSI & FENWICK
Teams that control play by outshooting and outchancing opponents tend to be the most successful at outscoring opponents.
“Driving play,” therefore, directly leads to wins — at the team level, and in turn, the player level as well.
But how does one measure this ability? What are the best ways to determine which players are helping their teams most to win the underlying shot and chance battles that lead to goals and victories?
This is probably the most commonly used concept in hockey analytics and yet often the most controversial.
In many respects possession, Corsi and Fenwick, have almost become synonymous with “hockey analytics,” although there is a lot more to hockey analytics than just these two metrics.
Possession is essentially defined as how much a team possesses or controls the puck. It could be represented as time (i.e. The Maple Leafs possessed the puck for 28:37 in last night’s game) or as a percentage (i.e. the Maple Leafs possessed the puck during 45.8% of the play in last night’s game).
The idea behind possession: The more you control the puck, the more opportunity you have to generate scoring chances as well as less opportunity for your opponents. This is a good thing and something teams should want to do.
Unfortunately, the NHL doesn’t track possession time, which is where Corsi and Fenwick come in. Corsi and Fenwick are shot-based metrics. Corsi considers shots + shots that missed the net + shots that were blocked. Fenwick is the same but does not consider blocked shots.
People generally use Corsi and Fenwick as a proxy for possession or puck control.
Corsi can be presented as a counting stat (i.e. the Maple Leafs had 52 Corsi events for last night), but is more commonly represented as a percentage. If the Maple Leafs had a 52% Corsi percentage it would mean — of all the Corsi events that took place last night by either team — 52% of them were taken by the Leafs. Corsi percentage is often shortened to Corsi% or, as I tend to frequently use, CF% (corsi-for percentage).
Fenwick percentage is the Same but without considering shots that were blocked. In theory one could also just look at shots (ignoring both shots that missed the net and shots that were blocked), but doing so is far less common.
These statistics can also be described as rate statistics split between offense and defense. For example, I use CF20 (or CF/20) as indicating Corsi For per 20 minutes of ice time. CA20 would be corsi against per 20 minutes of ice time. CF/60 and CA/60 are also commonly used as indication per 60 minutes of ice time.
Although some people have preferences for Corsi over Fenwick or vice versa depending on use, I for the most part consider them interchangeable as they are extremely-highly correlated. For the most part I consider them to measure the same thing and using one over the other is unimportant.
That said, whenever I talk about whether I can/could drop one of them from my stats database, there is generally a group of people that want to continue to see both be made available.
Note: You may also see Corsi/Fenwick referred to as shot attempts, which is becoming a more user friendly and intuitive way of describing them.
CORSI
Corsi is the foundational concept behind hockey advanced stats. It may be an odd name for a metric, but it’s actually a fairly straightforward stat to explain. Corsi — at its core — is just plus/minus for shot attempts instead of goals.
Just as a player finishes with a plus/minus of +2 if he was on the ice for two goals by his team at even strength and zero by the other team, a player’s Corsi rating would be +2 if he was on the ice for 10 shot attempts by his team and 8 by the opposition.
A few things must be noted here. “Shot attempts” does not mean just shots on goal — it counts missed shots and blocked shots as well. In addition, no one uses raw plus/minus Corsi to judge players anymore, and the reasons for that will be explained later. Still, it helps to start at the conceptual level first to fully explain how the final, better versions of the metric are derived.
Corsi is simply a fancy word for shot attempts. By shot attempts, we mean all shots directed by a team at a net, including those that miss the net and those that are blocked by the opponent. The reason it is called Corsi, and not just shot attempts, is because goaltender coach Jim Corsi was the first to start tracking it, and he felt the stat served as a much better measure for how much work his goalies have to put in each night than standard shots on goal, because a goalie has to react to all opponent shot attempts, regardless if they barely miss the net or get blocked.
The primary reason why Corsi is so highly regarded within the analytics community is because it has been proven beyond any reasonable doubt to have more predictive power than standard shots and especially goals. This is because shot attempts are more repeatable, and in a sport such as hockey where all goals are precious, the ability to consistently generate chances will drive scoring far more than anything else.
Unfortunately, certain individuals within the hockey universe treated Corsi as a catch-all statistic for a stretch of time. For those unfamiliar with catch-all statistics such as WAR in baseball (or hockey, which I will get to later), they are single metrics based on complex formulas that attempt to encapsulate the overall value of a player, and convey the value against that of an average “replacement player.” Let me make this clear, corsi is not meant to illustrate the overall value of a player.
Corsi comes in many forms, and to understand how to use Corsi in player or team analysis, it is important to learn all of its versions.
But why is Corsi such a key element of advanced stats? It’s because the goal of using stats in hockey is to better predict what will happen next, specifically which teams are likely to outscore their opponents and win more games in the future. The key finding with regards to Corsi was that shot attempt differential — both on the team and player level — does a better job of predicting future goal differential than past goal differential.
This is why a player with a great traditional plus/minus but an awful Corsi is generally expected to “regress” in the future. A player (or team) can only survive being buried in shot differential for so long before the goal battle starts being lost.
Corsi For (CF)
The amount of shot attempts a team takes, including shots on goal, shots that miss the net (or hit the post) and blocked shots.
Corsi in this context can be applied to illustrate how a whole team does, or the impact a specific player has on the team’s ability to generate shot attempts.
Specifically, you can use CF to simply state how many shot attempts a team had over a specified timeframe (period, game, season etc.), or you can use it to convey how many shot attempts a team takes while a specific player is on the ice.
Corsi Against (CA)
The amount of shot attempts a team allows, including shots on goal, missed shots (including those that hit the post) and blocked shots.
Similar to Corsi for, Corsi against can be used to show how many shot attempts an entire team allows over a specified period, or it can be used to illustrate the impact a specific player has on the shot attempts allowed by a team.
Individual Corsi For (ICF)
The amount of shot attempts an individual player takes himself.
There is no individual Corsi against measurement, as it is extremely difficult in many cases to accurately state whether a specific shot attempt was given up by a specific player.
Corsi For Per-60 (CF/60)
The amount of shot attempts a team accumulates per-60 minutes of play.
While team-level CF/60 is not necessarily a per-game statistic, it still helps us account for the differences in games played at any point in the season between teams, as teams do not accumulate games played at the exact same rate.
It also helps us account for differences in the numbers of penalties teams take and draw, and the amount of times they go into overtime, all of which can influence a team’s raw shot attempt totals across all situations.
At an individual level, the stat shows the impact that a player has on his team’s shot attempt rate while he was on the ice, and helps us account for the fact that some players get more ice time than others.
Using rate statistics helps us account for playing time differences to help us understand who truly has the most significant impact on shot generation.
It should be noted that rate statistics can be heavily influenced by deployment as well, so it is important to understand how a player is being utilized by his coach when discussing any rate statistic.
Corsi Against Per-60 (CA/60)
The amount of shot attempts a team allows per-60 minutes of play.
All of the same context provided within the CF/60 definition can be applied to CA/60, with the obvious exception being with CA/60, we are talking about a team’s ability suppress shot attempts or a specific player’s impact on shot attempts against.
Corsi For Percentage (CF%)
The percentage of all shot attempts that are taken by a team.
This is the most common shot attempt-based metric used, and often when a fan or analyst simply refers to a team’s or player’s “Corsi,” they are in fact referencing the Corsi for percentage.
The formula is
CF% = CF/(CF+CA).
Similar to both Corsi for and Corsi against, Corsi for % can be used to demonstrate the percentage of shot attempts taken by an entire team during a game, or it can be used to illustrate the percentage of shot attempts taken by a team when a specific player in on the ice.
A CF% of 50% means that the team and the opponent took the exact same number of shot attempts over the specified period of time.
As I discussed in the beginning of the Corsi section, the bulk of Corsi’s value comes in its predictive ability, particularly compared to goals and standard shots. CF% in particular is the metric that has been used in the various predictably studies. CF% has been proven by multiple renowned analysts to be a better predictor of future goal differential at both the team and player level.
Relative Corsi For Percentage (RELCF%)
The difference between a team’s Corsi when a player is on and off the ice.
Corsi Quality Of Competition (CF.QOC)
The weighted average Corsi for percentage of the opponents that an individual faces over a specified period of time.
In most models, the weight used is ice time, with the theory that, in general, the best players are those that get the most ice time.
Corsi Quality Of Teammates (CF.QOT)
The weighted average Corsi for percentage of the teammates a player shares the ice with over a specified period of time. In most models, the weight used is ice time, with the theory that, in general, the best players are those that get the most ice time.
FENWICK
Another strange name for a metric, but also fairly straightforward when you break it down. Fenwick is nearly identical in definition to Corsi, with one exception — blocked shots are not part of the equation. Only shots on goal and missed shots count when it comes to Fenwick.
Generally speaking, Corsi is more predictive of future goal differential than Fenwick, which raises the question of why the latter is still in use.
There’s a few reasons for that. To start, it’s a good metric to have in the arsenal when evaluating players and teams who tend to block lots of shots as part of an intentional strategy.
The more Important reason, however, is that Fenwick forms the basis for the most widely-used Expected Goals models. Blocked shots are not included in that stat, making xG essentially “Weighted Fenwick” by definition.
Fenwick measures all unblocked shot attempts. Fenwick is very similar to Corsi in that it recognizes the value in shot attempts that miss the net, but it strips out blocked shots. This is because some analysts feel that shot blocking is a skill, or at least a purposeful tactic employed by an opposing team, and therefor they believe that a team should not be given credit for a shot attempt when it is blocked.
The stat is named after Matt Fenwick, who was a writer for an old Calgary Flames blog, The Battle for Alberta. Long story short, Matt Fenwick believed that Corsi’s best application was to gauge scoring chances, and a blocked shot is not something that should be deemed a scoring chance; therefore, stripping out blocked shots would improve the stat when it comes to measuring scoring chances.
Both Fenwick and Corsi have been proven to have more predictive power then shots on goal and there are strong arguments for using each.
Personally, I believe both stats are useful and can be used and dissected in different ways to tell different stories; I do not think you should use one or the other, and instead you should consider both.
In terms of predictive ability, noted hockey statistician Micah Blake McCurdy wrote a piece for Hockey-Graphs a few years ago that, among many things, concluded that score-adjusted Corsi serves as a better predictor than score-adjusted Fenwick (it should be noted this was not the purpose of the article, simply one takeaway from it).
All of the context I provided in the above Corsi section can also be applied to Fenwick. It is NOT meant to be a WAR-like stat, and it can be applied in a variety of ways to help us understand team, player and goalie performance.
Fenwick For (FF)
The amount of unblocked shot attempts a team takes, including shots on goal and shots that miss the net (or hit the post).
Similar to Corsi, Fenwick in this context can be applied to illustrate how a whole team does, or the impact a specific player has on the team’s ability to generate unblocked shot attempts.
Specifically, you can use FF to state how many unblocked shot attempts a team has had over a specified course of time (period, game, season etc.), or you can use it to convey how many unblocked shot attempts a team takes while a specific player is on the ice.
Fenwick Against (FFA)
The amount of unblocked shot attempts a team allows, including shots on goal and shots that miss the net (or hit the post).
Similar to Fenwick for, Fenwick against can be used to show how many unblocked shot attempts an entire team allows over a specified period, or it can be used to illustrate the impact a specific player has on the unblocked shot attempts allowed by a team.
Individual Fenwick For (IFF)
The amount of unblocked shot attempts an individual player takes himself.
There is no individual Fenwick against measurement, as it is extremely difficult in many cases to accurately state whether a specific unblocked shot attempt was given up by a specific player.
Fenwick For Per-60 (FF/60)
The amount of unblocked shot attempts a team accumulates per-60 minutes of play.
While team-level FF/60 is not necessarily a per-game statistic, it still helps us account for the differences in games played at any point in the season between teams, as teams do not accumulate games played at the exact same rate. It also helps us account for differences in the numbers of penalties teams take and draw, and the amount of times they go into overtime, all of which can influence a team’s raw unblocked shot attempts across all situations.
At an individual level, the stat shows the impact a player has on his team’s unblocked shot attempt rate while he was on the ice, and helps us account for the fact that some players get more ice time than others.
Using rate statistics helps us account for playing time differences to help us understand who truly has the most significant impact on shot generation. It should be noted that rate statistics can be heavily influenced by deployment as well, so it is important to understand how a player is being utilized by his coach when discussing any rate statistic.
Fenwick Against Per-60 (FA/60)
The amount of unblocked shot attempts a team allows per-60 minutes of play.
All of the same context provided within the FF/60 definition can be applied to FA/60, with the obvious exception being with FA/60, we are talking about a team’s ability suppress shot attempts or a specific player’s impact on shot attempts against.
Fenwick For Percentage (FF%)
The percentage of all unblocked shot attempts that are taken by a team.
This is the most common Fenwick-based metric used, and often when a fan or analyst simply refers to a team’s or player’s “Fenwick,” they are in fact referencing their Fenwick for percentage.
The formula is
FF% = FF/(FF+FA).
Similar to both Fenwick for and Fenwick against, Fenwick for % can be used to demonstrate the percentage of unblocked shot attempts taken by an entire team during a game, or it can be used to illustrate the percentage of shot attempts taken by a team when a specific player in on the ice.
A FF% of 50% means that the team and the opponent took the exact same number of unblocked shot attempts over the specified period of time.
Relative Fenwick For Percentage (RELFF%)
The difference between a team’s Fenwick when a player is on and off the ice.
Fenwick Quality Of Competition (FF.QOC)
The weighted average Fenwick for percentage of the opponents that an individual faces over a specified period of time.
In most models, the weight used is ice time, with the theory that, in general, the best players are those that get the most ice time.
Fenwick Quality Of Teammates (FF.QOT)
The weighted average Fenwick for percentage of the teammates a player shares the ice with over a specified period of time. In most models, the weight used is ice time, with the theory that, in general, the best players are those that get the most ice time.
SHOT QUALITY, SV%, SH%, PDO
Save And Shooting Accuracy Metrics
Now, I’m not saying that numbers such as gaa and save percentage for goaltenders aren’t useful, they certainly are. What I am saying, however, is that they are flawed, and there are other metrics out there that that help isolate the performance of the actual player, and strip out some of the background noise that may be influencing the more basic numbers.
Further, many of the same principles that make standard save percentage a flawed stat can be applied to standard shooting percentage.
A player’s shooting percentage can be drastically influenced one way or another by the level of goaltending they face, which obviously is not something the skater can control.
For these reasons, advance shooting metrics help us make more informed conclusions on a player’s shooting ability.
Shooting Percentage (SH%)
The percentage of all shots on goal that are goals. This is the standard shooting percentage that is typically being discussed when a broadcaster or beat writer is discussing a team’s or player’s shooting percentage.
Save Percentage (SV%)
The percentage of all shots on goal that are saved. This is the standard save percentage that is typically being discussed when a broadcaster or beat writer is discussing a team’s or player’s save percentage.
Shot Quality
One of the issues many (predominantly non-hockey analytic supporters, but myself to some extent as well) have with Corsi and Fenwick is that they are measuring shot attempts and not the quality of the shot attempt. There have been countless debates over this and to what extent shot quality exists and its relative importance. It is unfortunate, really, because neither side is absolutely right.
Let me first define the notion of shot quality. For me, showing that shot quality is real and is significant starts and ends with showing that a player or a team has the ability to maintain elevated shooting percentages.
If a team year in and year out can maintain an elevated shooting percentage, shot quality exists. If a player year in and year out can maintain an elevated shooting percentage, shot quality exists.
We know that some shots are more difficult than others (i.e. a rebound shot from 8′ is far more difficult than a point shot from 45′), but what we want to know is whether a team or player can have a higher quality shot on average.
Having shots that are, on average, More difficult to save and thus have a higher chance of resulting in a goal is essentially the definition of shot quality. Now, does this exist at either the player or team level?
Let’s start by looking at players. Over the past 7 seasons, the players with the highest on-ice shooting percentage (i.e. the shooting percentage of all shots taken while the player was on the ice) during 5 on 5 play (minimum 4000 minutes of ice time) are Sidney Crosby, Steven Stamkos, Alex Tanguay, Marian Gaborik and Marty St. Louis, all with an on-ice shooting percentage above 10.2%. The five worst players, all with an on-ice shooting percentage below 6%, are Travis Moen, Nate Thompson, Samuel Pahlsson, Shawn Thornton, and Craig Adams.
To not believe in shot quality at the player level one must believe that there is little or no difference between those two groups and they have achieved their elevated (or suppressed) shooting percentages by luck (good or bad) alone. If anyone believes that they are denying reality.
Furthermore, if anyone believes that the difference between shooting 10% and shooting 6% is not significant they are denying reality as well (shooting 10% over 6% means scoring 66% more goals on the same number of shots). Shot quality exists and is an important consideration in player evaluation
At the team level, shot quality is a little more difficult to show because it has generally been difficult for teams to assemble a group of players that can drive shooting percentage up and down the line up.
High shooting percentage players are difficult to acquire and it would be cost prohibitive to assemble a full team of high shooting percentage players (in part because NHL teams have generally paid more for them).
That said, there some teams that have shown an ability to maintain elevated or suppressed shooting percentages.
The differences at the team level are less significant than at the player level, though, and thus Corsi is more effective as a team evaluation tool.
The analytics bear this out.
It is my belief that players have an ability to influence their teams save percentage, although I do believe it is much more difficult to quantify this effect.
Since any given year a player only plays in front of a couple goalies, it is extremely difficult to decouple the player’s impact on save percentage from their goalie’s.
That said, I believe the ability is there, although less so than the ability to drive shooting percentage. I’ll get into this further later on when I discuss score effects.
PDO
PDO is the sum of a team’s shooting percentage and its save percentage, converted from percentages into whole numbers.
This stat is almost always discussed in terms of 5v5 play only, but you can generate it for other situations.
So, if a team has a 92% 5v5 save percentage, and an 8.5% 5v5 shooting percentage, they have a PDO of 100.5.
PDO is often referred to as a measurement of a team’s luck, with 100 being average, anything over 100 being deemed lucky (the higher you go, the luckier the team is) and anything under 100 being deemed unlucky (the lower you go, the unluckier the team is).
The reason that PDO is considered a measurement of luck, is because over very large sample sizes, teams will sport a 5v5 save percentage of about 92%, and a 5v5 shooting percentage of about 8%.
In theory, if a team has a high PDO, that means they are getting an abnormally high shooting or save percentage (or both), and in most cases over large sample sizes, this is unsustainable and you can expect it to eventually regress to the mean.
There are certainly outliers, and certain teams loaded with snipers or elite goalies have been able to sustain above-100 PDOs over multiple seasons.
So, while factors like elite (or dreadful) goaltending and specific systems can cause a team to be able to sustain a high or low PDO over multiple years, when you look at the data for the entire league, a much larger sample, you see that in fact, 5v5 save percentage and 5v5 shooting percentage tend to hover around 8% and 92%, respectively.
PDO is not perfect, but it is one of many tools we can use in our analysis of a team.
Similar to many of the other stats we have already discussed, PDO can also be used in player analysis.
We can look at a team’s PDO when a specific player is on the ice to help round out our analysis, particularly when discussing a player’s goal differential.
We have discussed numerous times so far the role that shot quality has in player and team analysis, and we can include this information into our examination of PDO in a similar manner we do with goalie save percentage
PDO is an interesting statistic; it is essentially on-ice save percentage plus on-ice shooting percentage. Across the league the mean would be 100%, but individual teams and players can fluctuate a little from that point.
Some people use PDO as an indication of luck or good/bad fortune by looking at how much PDO deviates from 100%, but one must take into consideration the quality of goaltending the player plays in front of or the players’ ability to drive on-ice shooting percentage.
A PDO of 102% does not necessarily mean the player is lucky. Gaborik’s PDO over the last 7 seasons is 103.1%, while Crosby’s is 102.8%. So, while PDO can provide some indication of good/bad fortune, one must still consider to what extent the player’s talent or the circumstances play in as a factor.
Expected Pdo (XPDO)
The sum of a team’s expected Fenwick shooting percentage and expected Fenwick save percentage, converted from percentages into whole numbers.
Because most expected goals models use unblocked shot attempts (Fenwick), the expected PDO model also uses Fenwick shooting and save percentages instead of standard.
Like expected goals, expected PDO helps us mitigate goaltender performance, and helps us understand how a team would have fared given league-average goaltending. A high expected PDO indicates that a team is either generating a lot of high quality scoring chances, or suppressing high quality scoring chances against (or both), and can therefore be expected to have a higher PDO than your average team
Adjusted (Delta) PDO (DPDO)
The difference between a team’s actual PDO and their expected PDO.
The formula is:
dPDO = PDO – xPDO.
This serves as a more accurate measure of a team’s (or skater’s) luck than normal PDO, because expected PDO considers the scoring chance quality of teams.
So, if a team has a positive dPDO, it means that their actual PDO is higher than their expected PDO. This indicates that they are getting higher shooting and/or save percentage(s) than what should be expected, given the quality of scoring chances involved.
Expected Shooting Percentage (XSH%)
The shooting percentage that a goalie (or team) should have with a league average performance given the quality of chances he faced. It is important to note that expected shooting percentage is NOT a measure of how well a skater or team has actually shot, it merely serves as a benchmark for the shooting percentage that an average skater or team should have posted, given the quality of chances he faced.
Expected Save Percentage (XSV%)
The save percentage that a goalie (or team) should have with a league average performance given the quality of chances he faced.
It is important to note that expected save percentage is NOT a measure of how the goalie actually performed, it merely serves as a benchmark for the save percentage that an average goalie should have posted, given the quality of chances he faced.
With that said, I once saw a guy on Twitter make the argument that because Halak’s xSv% is greater than Lundqvist’s, that means Halak has had a better season—please don’t be that guy. That is a very false statement. What that does mean, however, is that the Islanders defense has performed better in front of Halak than Lundqvis has, so Halak has faced on average lesser quality scoring chances than Lundqvist.
Adjusted (Delta) Shooting Percentage (DSH%)
The difference between a skater’s (or team’s) actual shooting percentage and his expected shooting percentage.
The formula is
dSh% = Sh% – xSh%.
This stat helps show us whether a skater’s shooting percentage is sustainable or not, given the quality of scoring chances he has generated.
If a player has a high dSh%, then his actual shooting percentage is higher than his expected shooting percentage.
This means that he is shooting at a higher percentage than what would be expected of him given the quality of scoring chances he has generated, meaning that it is likely unsustainable and will regress downwards eventually.
Adjusted (Delta) Save Percentage (DSV%)
This stat is the difference between a goalie’s (or team’s) actual save percentage and his (or its) expected save percentage.
The formula is
dSv% = Sv% – xSv%.
This is a very valuable stat that helps show how much better (or worse) a goalie is doing compared to how an average goalie would have performed given the quality of shots faced.
A dSv% of 0 means that a goalie has performed exactly to the level of an average goalie given the quality of shots faced.
Corsi Shooting Percentage (CSH%)
The percentage of all shot attempts that are goals.
By comparison, standard shooting percentage only counts shots on goal, so a player’s (or team’s) Corsi shooting percentage is always lower than his (or its) standard shooting percentage.
Corsi Save Percentage (CSV%)
The percentage of all shot attempts that are saved.
By comparison, standard save percentage only counts shots on goal, so a goalie’s (or team’s) Corsi save percentage is always higher than his (or its) standard save percentage.
Fenwick Shooting Percentage (FSH%)
The percentage of all unblocked shot attempts that are goals.
By comparison, standard shooting percentage only counts shots on goal, so a player’s (or team’s) Fenwick shooting percentage is always lower than his (or its) standard shooting percentage.
Because it strips out blocked shots, Fenwick shooting percentage is often the preferred calculation when discussing shot quality and individual save metrics by quality, such as low danger save percentage.
Fenwick Save Percentage (FSV%)
The percentage of all unblocked shot attempts that are saved.
By comparison, standard save percentage only counts shots on goal, so a goalie’s (or team’s) Fenwick save percentage is always higher than his (or its) standard save percentage.
Because it strips out blocked shots, Fenwick save percentage is often the preferred calculation when discussing shot quality and individual save metrics by quality, such as low danger save percentage.
Expected Fenwick Shooting Percentage (XFSH%)
The Fenwick shooting percentage (percentage of all unblocked shots that convert to goals) that a player or team would have shot if the opposing goalie performed at a league-average level, given the quality of scoring chances generated.
The formula for the stat is: expected Fenwick shooting percentage = expected goals for/Fenwick for.
Expected Fenwick Save Percentage (XFSV%)
The Fenwick save parentage that a goalie (or team) should have with a league average performance given the quality of chances faced.
The formula for the stat is: expected Fenwick save percentage = 1 – expected goals against/Fenwick against.
Adjusted (Delta) Fenwick Shooting Percentage (DFSH%)
The difference between a skater’s (or team’s) actual Fenwick shooting percentage and his expected Fenwick shooting percentage.
The formula is dFSh% = FSh% – xFSh%.
All of the same context provided in the dSh% definition can be applied here, with the caveat that dFSh% considers all unblocked shot attempts, while dSh% considers only shots on goal.
Adjusted (Delta) Fenwick Save Percentage (DFSV%)
The difference between a goalie’s (or team’s) actual Fenwick save percentage and his expected Fenwick save percentage.
The formula is dFSv% = FSv% – xFSv%.
All of the same context provided in the dSv% definition can be applied here, with the caveat that dFSv% considers all unblocked shot attempts, while dSv% considers only shots on goal.
SAMPLE SIZE
This is probably a good time to bring up the issue of sample size because it is an integral reason why people would choose to use Corsi or Fenwick over goals.
I just told you that shot quality is real right after telling you that possession/Corsi and Fenwick are important and valuable tools in analytics. Here is the issue: Goals are a relatively infrequent event in hockey.
A team will score typically 2-4 goals per game and 200-250 goals per season. They will take between 25 and 35 shots per game and 2200 to 2800 shots per season, and they can have nearly twice as many Corsi events per game. These differences have a major impact in how confident we can be in the conclusions we can make and that has an impact on how we conduct analytics. Let me explain.
Since goals are so rare, a lucky bounce or two or a “hot streak” can have a huge impact on the results of a statistical analysis.
With 20 games of data, goals are a very poor predictor of future performance but Corsi or Fenwick are far better predictors. This is true at both the team and player level. The greater number of events means we can draw conclusions far more quickly, which is a significant reason why people use Corsi and Fenwick.
The significantly greater number of Corsi events that occur mean that we generate large sample sizes far more quickly and we get a better representation of talent far more quickly.
CORSI/FENWICK vs GOALS
Corsi/Fenwick have larger sample sizes and thus “stabilize” closer to true talent levels far faster than goals.
Shooting percentages do vary significantly across players (and to a lesser extent teams) and players likely have some impact on save percentage.
As a result of this, Corsi/Fenwick will never be able to truly represent a players (or to a lesser extent teams) true offensive or defensive value (true value should always measure in terms of ability to boost goals for and suppress goals against because that is what truly matters in hockey).
As explained above, the people that tend to rally against analytics tend to do so on the idea that not all shots are created equal.
The analytics people who fight back tend to argue that, at the team level, possession metrics like Corsi and Fenwick are the better predictor of future performance and thus it is fair to use Corsi and Fenwick as a primary talent evaluator (even if it doesn’t tell the whole story).
Both sides have cases to be made, but as with most disputes the truth is somewhere in the middle.
A team or (especially) a player evaluation that doesn’t include some consideration for the percentages is an incomplete and possibly incorrect evaluation and it is vitally important to be aware of this.
Conversely, a team or player evaluation based largely on goal-based statistics that doesn’t include some consideration for sample size related errors and uncertainty is an incomplete and possibly incorrect evaluation (and we need to be aware of this, too).
GAME STATES & SCORE EFFECTS
Performance By Situation
It doesn’t take a hockey expert to know that there are different situations in a game. Even strength, power plays, penalty kills — all come with distinct strategies and goals for teams. Yet all too often, performance across situations is smushed together when evaluating the performance of a player or even a team.
That’s a trap that the advanced stat community attempts to avoid. In order to provide proper context to performance, I’ll often distinguish between production at 5v5, 5v4, 4v5, and all other situations in my articles.
Why?
Some advanced metrics are only useful in evaluating play during certain situations.
Take Corsi, for example. Generally speaking, when it’s referenced as a stat, it’s only describing results at 5-on-5. There are a couple of reasons for that. To start, 5v5 is the most frequent situation in all of hockey. Last season, about 78% of the total minutes in the NHL were played at 5v5. Second, by nature, the two teams are on equal footing when they are playing five-aside hockey. Therefore, both teams (in theory) have an equal chance to “drive play” in their direction and win the shot and goals battles. This obviously isn’t the case when one team is a player up.
Also, limiting Corsi evaluation to 5-on-5 play removes the complication of power play and penalty kill roles.
Not every player on a team has the benefit of skating on the top power play unit. If we looked at every player’s “all-situations” Corsi For Percentage, obviously the ones who receive power play time (and no penalty kill minutes to drag down his metrics) will look the most impressive.
But it’s not an apples-to-apples comparison.
That’s why 5v5 Corsi For Percentage is the most widely used, because every skater receives ice time in that situation, allowing for fair comparisons.
That’s not to say there isn’t any value in looking at “all-situations” metrics. I’ll often check overall Expected Goals totals after a game because a team should be given credit for drawing penalties or avoiding them when understanding if they “should have” won the game. But for the most part — on both the team and player level — it’s more precise to separate out performance by each individual situation.
Score Effects
A lot of the time score effects aren’t important, but for some occasions and for some teams they can have an impact on a team’s overall 5v5 statistics; therefore, at times they should be taken into consideration.
I mentioned score effects in the section above in reference to a players ability to impact his teams save percentage. Score effects are evidence of this.
Teams and individual players have a worse on-ice save percentage when playing catch up hockey than when protecting a lead. This can only happen if players have the ability to influence save percentage.
The theory goes — when players play more aggressive offensive hockey when trying to play catch up, they give up more odd-man rushes against resulting in higher quality shots against and a lower save percentage. The opposite is true when a team plays more conservative defensive hockey when protecting a lead.
This, to me, is clear evidence that players can and do influence save percentage at least based on style of play, if not by talent differences
“Score-Adjusted” Statistics
Score adjusted statistics are those that are weighted in accordance to the game score in order to account for the fact that at various game states (e.g. a team is winning/losing) teams will be playing differently.
The reason for this is, when a team is trailing, they are likely pressing to try to tie it up, and vice versa.
To account for this, a formula is applied to weigh shot attempts in accordance to the game state; a higher weight is applied to shot attempts taken by the team with the lead and vice versa, and different weights are applied based on how many goals a team is leading or trailing by.
Score adjusting statistics, particularly shot-based metrics, have been proven to better represent how a team/player performed.
You may have taken note that I often qualify a player or team’s Corsi For Percentage in my articles with the caveat that it is “score-adjusted.”
This is actually a relatively new development in the analytics community — Eric Tulsky (now employed by the Carolina Hurricanes) identified a way to account for the impact of the score of the game on Corsi/Fenwick results back in 2012, and Micah Blake McCurdy expanded upon Tulsky’s findings in 2014. They both concluded that such an adjustment serves to improve the existing metrics.
But what does it mean to “score-adjust” metrics like Corsi, Fenwick and Expected Goals? The answer goes back to an aspect of hockey that most fans intuitively understand — score effects.
Generally speaking, teams treat games differently depending upon the score. When down by one goal, a trailing team tends to unleash the hounds, taking more risks to move the puck up ice and attempt to pepper its opponent with shots and tie things up. By the same token, when up by five goals, a team would be forgiven if it let a foot off the gas, resulting in the trailing team gaining the territorial edge on the ice even though its chances of a comeback are minimal at best.
Score-adjustment of metrics like Corsi and xG accounts for these factors, and in turn gives a more accurate measurement of how well play was actually driven.
Essentially, it notes league-average shot results in each score situation, and uses that as a baseline (rather than 50 percent) to judge performance.
Generally speaking, score-adjustment favors a team that leads in a contest — a club that jumped out to an early 3-0 edge and held it throughout may have finished with an raw 45% Corsi For Percentage, but after score-adjustment, that rate may jump to over 50 percent. Score adjustment also improves the predictivity of future goal differential for metrics like Corsi, confirming its importance.
USAGE – ZONE STARTS, QoC, QoT
Zone Starts
Simply put, a zone start is any time a player is on the ice for a faceoff.
We all know hockey is a fluid sport, with line changes happening all the time during play. This makes it difficult to track how exactly a player is deployed, particularly due to the fact that line changes that occur during an active play often are only partial changes, so the lines get temporarily scrambled and a player might be out in a situation that the coach didn’t necessarily plan.
Because of this, and the general chaotic nature of line changes at times, it isn’t all that valuable to track player deployment in terms of the situation every time they touch the ice.
The reason analysts use zone start to measure deployment is because, with the exception of icings following faceoffs, a coach has the ability to specify exactly which players he wants on the ice for the faceoff.
Coaches take a number of variables into account when deciding who to deploy on a faceoff, including the state of the game and the zone the puck is in (offensive, neutral or defensive). Further, the home team has the benefit of “last change,” which means they can wait for the away team to choose who to deploy before they choose, allowing the home team to also consider the opponents on the ice when choosing who to deploy.
When analyzing zone starts, data sites such as Corsica provide statistics that show the number of zone starts or percentage of zone starts a player takes in each of the three zones: offensive, neutral or defensive.
Typically, if a player has a higher percentage of offensive zone starts than defensive, it means the coach views him as a player he wants on the ice in offensive situations, most likely because he has a relatively strong ability to score or playmake compared to his other teammates.
Conversely, if a player has an disproportionally large amount of defensive zone starts, it means the coach views that player as a defensive-oriented player, who he trusts to prevent the opposition from scoring after a defensive zone faceoff.
For most players it is not a significant factor in on-ice performance.
Quality of Competition (QoC)
Like Zone Starts, QoC is largely overstated when it comes to the impact it has on a players overall statistics.
While a player playing against Sidney Crosby will have worse statistics than when playing against a typical third or fourth liner, the reality is that there are no players so consistently playing against high end players (or low end players) that their statistics will be impacted in a significant way.
The reality is zone starts and QoC metrics are of minimal importance in player evaluation and are best used solely as an indication of how his coach views his skill set.
Quality of Teammates (QoT)
QoT can have a significant impact on a players statistics.
By far the only usage statistic that really needs to be taken under significant consideration in player evaluation is quality of teammates.
WOWY
Where to find it: NaturalStatTrick.com player pages
That brings us to what I consider the most important concept in hockey analytics: WOWY’s.
WOWY stands for With Or Without You and looks at how players perform when playing on the ice together and when playing apart from each other.
The value of WOWY’s is they tell us who is the more important player and who is making who better.
WOWY’s help show who the production drivers are and who are not. To me, that answers the most important question in hockey. You want players who drive results, not those that depend on others to drive results.
The concept behind WOWYs is simple: They measure how well someone drives play, via Corsi or xG differential with a specific teammate, and how well without that teammate.
The goal? Isolate play-driving to figure out who is really doing the most work to help the team control play.
The simplicity of WOWYs help to explain their popularity in online hockey circles. At its core, a WOWY is a straightforward comparison between two players that tells an obvious story. And usually, that story involves showing how one player is “dragging down” another’s results.
The flaws and limitations of WOWYs:
In short, the primary concern is that WOWYs are often presented as an end-all, be-all argument for or against a player, when in reality, they leave out a lot of key information.
For starters, WOWYs focus on only two players. In hockey, of course, each team has five skaters on the ice (during 5-on-5 play). WOWYs inherently ignore the impact of the other three, who are clearly playing a part in driving results
WOWYs can also miss important information about the nature of minutes spent without another player.
There are simply better, more comprehensive stats available in the public sphere that utilize the concept behind WOWY. Individual WOWYs are mere components of those superior stats, in the same way that microstats describe only pieces of the play-driving ability measured by metrics like Corsi or xG.
That’s not to say WOWYs don’t have value, just like exits per 60 minutes or controlled entry percentage do. The “with” side of WOWYs can be a quick check to see if a new defensive pairing is working, for example. And there’s always storytelling value in breaking down a more complex metric into its components to better explain why a player grades out well in it.
But when trying to isolate an individual’s play-driving ability, why use only a piece of the equation when there are accessible ways to look at the whole thing?
WOWY (With or Without You) analysis attempts to help us understand how specific players impact one another on the ice. In essence, WOWY analysis looks at pairs of players and examines how they perform together versus apart.
A common misconception, and one that I fell victim to when I first started examining advanced stats, is that WOWY analysis and relative statistics are the same thing. The key difference is that WOWY analysis examines the impact that one specific player has on another, while relative statistics attempt to illuminate how the entire team does with a specific player on the ice compared to when he is off the ice.
The primary reason why WOWY analysis is important is because it helps us understand how a player performs with or without another player. This sort of analysis helps us to quantify some (true) clichés that you hear bandied about the hockey world such as “good players make others better” and that two players have “chemistry” with one another. With WOWY analysis, we can dig into the data and see that player A in fact always plays better when he is paired with player B. We can also look at how a player impacts each individual player on a team, and if the player usually raises the play of his teammates, you can pretty safely conclude he in fact is an effective player.
HockeyViz is an excellent resource brought to us by Micah Blake McCurdy that, among its many capabilities, offers graphical depictions of WOWY analysis.
IPP, IGP, & IAP
IPP stands for individual points percentage and is calculated by dividing the number of points a player has produced by the number of goals that were scored while the player was on the ice.
This statistic tells us who is most involved in the teams offensive production when they are on the ice.
Like WOWY’s, IPP can help us determine which players are integral to their teams offense when they are on the ice and which players are more bystanders when it comes to offensive production.
IGP stands for individual goals percentage and is calculated almost exactly the same as IPP, but instead of using the points the player has we use the goals the player has scored.
IAP is the same as IGP except that it uses assists instead of goals and can be used to identify play makers rather than goal scorers.
EXPECTED GOALS
Shot Quality
This is a concept that all fans are already aware of, the simple fact that some shots are of “higher quality,” or more likely to lead to a goal, than others.
Shot quality, however, is of particular importance to a number of the key advanced analytics currently permeating hockey discussions.
From ex-Rangers goalie and current MSG studio analyst Steve Valiquette, to hockey statisticians such as Dawson Sprigings (DTMAboutHeart) and Emmanuel Perry (proprietor of Corsica), shot quality plays a vital role in analysis, particularly when it comes to discussing expected goals and adjusted save percentage (both of which are discussed in full in their own dedicated sections later).
Before we get ahead of ourselves and discuss specific stats that incorporate shot quality, we must first understand how shot quality serves as the foundation for these stats. A few different analysts have their own models for stats that incorporate shot quality analysis, but at the core of all of them, they assign weightings to shot attempts based on the quality of the shot. Shot quality is determined by numerous things, including distance from the net, angle of the shot, type of shot (slap shot, one-timer, wrist shot, rebound etc.), whether the shot was on a breakaway and more.
Typically, for simplicity sake when sharing shot quality data with the public, analysts and models organize shots across three buckets: high danger, medium danger and low danger shots.
Different models have different specifications for what qualifies for each shot classification, and it is not a hard and fast science (and all of the analyst will tell you that themselves).
We will discuss Fenwick in greater detail in its own section, but it should be quickly noted that the reason we use Fenwick shooting percentage instead of standard shooting percentage is because Fenwick shooting percentage serves as a far more accurate representation of a player’s actual shooting percentage. This is because standard shooting percentage only accounts for shots on goal and ignores all of the times the player shot the puck and missed the net.
Expected goals is a statistic that considers both shot quantity and quality in order to provide a metric for how many goals a team (or player) should have scored, given the quality of scoring chances generated, if the opposing goalie played at a league-average level.
Expected goals accomplishes this by weighting each unblocked shot attempt by a variety of shot attributes, with heavier weightings applied to shot characteristics with a higher chance of leading to a goal.
The shot characteristics considered by expected goals include shot type (wrist, slap, deflection etc.), distance from the net, shot angle, whether a shot was a rebound or generated off the rush, and if it was taken on the power play, even strength or on the penalty kill.
So, for a quick example of how the model works, a slap shot taken from the slot that was generated off a two-on-one rush would have a much heavier weight applied to it than a weak wrist shot taken by a defenseman from the point.
It should be noted that multiple models for expected goals exist and they have some variations in their calculations.
Expected goals is far from a perfect stat, and quite frankly there is no such thing as a perfect stat.
Nonetheless, expected goals is a valuable tool for evaluating games, players and teams. In fact, expected goals has been proven by multiple leading hockey statisticians to have even more predictive power than Corsi and Fenwick.
Lastly, and least analytically, expected goals just passes the smell test better than any other commonly used advanced metric. You often hear fans say things like “we deserved the win/loss!” after a game. I personally have found that, far more often than not, expected goals totals from a game aligns with these sentiments far more often than Corsi totals do.
Similar to the shot metrics discussed above, expected goals data comes in many forms, and to understand how to use the data in player or team analysis it is important to learn all of its versions.
There’s a common critique of the concept of Corsi, and if you’re a newbie to advanced stats, it may have already crossed your mind while reading the above explanations. “Obviously outshooting your opponent is important, but what if you get outshot but the shots you do create are really good? It might be a good Corsi period if a team racks up 10 shot attempts and allows just five, but what if all five from the opposition were breakaways and all ten from the team in question were weak wrist shots from the point?
These are the problems that Expected Goals addresses.
The models behind xG (shorthand for Expected Goals) weigh each unblocked shot for a number of factors. Shot location is the main one, but the models also recognize events like rebounds and rush chances as well. It then assigns a value to each shot, based on the likelihood of the shot resulting in a goal. A point shot may have an xG value of 0.02, while a rebound chance directly in front of the goalie might be worth 0.40. By accounting for quality, xG responds to the criticism of Corsi that “not all shots are equal.”
It’s Important to note that there remains debate whether xG is actually “better” than Corsi when it comes to evaluating teams and players.
Personally, I use the two metrics — Corsi and xG — in tandem, knowing that the former describes a raw territorial advantage, while the latter describes whether the shot quality battle was won as well.
Expected Goals For (XGF)
The number of goals a team should have scored against league-average goaltending, given the quality of scoring chances they generated across a specified period of time (period, game, season etc.).
Similar to shot attempt metrics, expected goals in this context can be applied to illustrate how a whole team does, or the impact a specific player has on the team’s ability to generate scoring chances.
Expected Goals Against (XGA)
The amount of goals a team should have allowed with league-average goaltending, given the quality of scoring chances they allowed across a specified period of time.
Similar to expected goals for, expected goals against can be used to show how a whole team does, or the impact a specific player has on the team’s ability to suppress scoring chances against.
Individual Expected Goals Created (ixG):
The amount of Expected Goals generated by an individual player. This metric can be filtered by situation and can also be presented in “Per 60” form.
5v4 Corsi For Per 60 (CF60):
The amount of shots generated by a team during 5-on-4 situations per 60 minutes of play.
A good way to evaluate the shot creation efficiency of a power play.
This can be presented as a team-metric, or for individual players (how many shots did the team average when an individual was on the ice).
Individual Expected Goals For (IXGF)
The amount of expected goals an individual player generates himself.
Similar to the shot-based metrics, there is no individual expected goals against measurement, as it is nearly impossible in most cases to accurately state whether a specific scoring chance was given up by one specific player.
One way you can use ixGF is to compare a player’s actual goals scored over a period of time to their individual expected goals for, in order to gain an understanding of whether they are under or over-performing in terms of goal production.
Expected Goals For Per-60 (XGF/60)
The amount of expected goals a team accumulates per-60 minutes of play.
Similar to xGF and xGA, xGF/60 can be applied to see how the entire team did or to view the impact a specific player has on the team.
At an individual level, the stat shows the impact that a player has on his team’s ability to accumulate scoring chances while he is on the ice, and helps us account for the fact that some players get more ice time than others.
Using rate statistics helps us account for playing time differences to help us understand who truly has the most significant impact on shot generation.
It should be noted that rate statistics can be heavily influenced by deployment as well, so it is important to understand how a player is being utilized by his coach when discussing any rate statistic.
Expected Goals Against Per-60 (XGA/60)
The amount of expected goals a team allows per-60 minutes of play.
Similar to xGF and xGA, xGA/60 can be applied to see how the entire team did or to view the impact a specific player has on the team.
All of the same context provided within the xGF/60 definition can be applied here, with the obvious exception being with xGA/60, we are talking about a team’s ability suppress scoring chances or a specific player’s impact on expected goals against.
Expected Goals For Percentage (XGF%)
The percentage of all expected goals accumulated by both teams that are generated by a specific team.
The formula is
xGF% = xGF/(xGF+xGA).
xGF% can be used to demonstrate the percentage of expected goals generated by an entire team during a game, or it can be used to illustrate the percentage of expected goals generated by a team when a specific player in on the ice.
An xGF% of 50% means that the team and the opponent generated the exact same number of expected goals over the specified period of time.
When I discussed the predictive power of expected goals in the preamble to this section, it was mainly with this specific stat in mind, expected goals for percentage.
One particularly useful way to use xGF% in team analysis is by examining a team’s standing in the league in xGF% compared to where they stand in terms of Corsi.
Since shot quantity plays a role in accumulating expected goals, one can conclude that if a team has a much higher standing in xGF% than CF%, then a relatively high percentage of their shot attempts are those of a higher quality, and more likely to be converted to a goal.
Relative Expected Goals For Percentage (RELXGF%)
The difference between a team’s expected goal differential when a player is on and off the ice.
MICROSTATS
In the strictest sense, raw “microstats” aren’t much different than secondary metrics tracked by the NHL, such as hits, blocks or faceoffs won. They’re simply events that occur during a game that are recorded by trackers. The key difference between the two? Microstats (also called manually tracked stats) are gathered by a third party, since the NHL doesn’t record them, and these stats tend to focus on the play-driving and offense creation aspects of hockey.
But what are microstats?
Most of them center on two on-ice events: offensive zone entries and defensive zone exits.
In recent years, trackers like Sznajder have expanded their work to include passes all over the ice (largely inspired by Ryan Stimson’s Passing Project), but entries/exits — and the stats derived from them — still are the most widely cited.
These stats allow us to answer intriguing questions. Who is the best defenseman on a team in generating breakouts? Which forwards dump the puck into the offensive zone the most? Which defensemen turn the puck over in the defensive zone the most or least? Before, we had to guess at these answers. Now, as a result of manually tracking, we have cold, hard evidence.
What does this have to do with play-driving, though? It goes to the heart of what it means to “drive play”: moving the puck from defense to offense, pushing play forward. “Transition” actions like zone entries and exits are, by nature, at the root of play-driving.
And so is the nature of those entries and exits. Research has shown that controlled entries (carry-ins) are about twice as valuable as uncontrolled ones (dump-ins) in creating shots. The analytics community also found that controlled defensive zone exits help to create offensive zone entries for the team with the puck far more often than uncontrolled defensive zone exits.
In other words, controlled is good and uncontrolled is not nearly as good. It’s why stats like controlled entry percentage and controlled exit percentage are regularly cited to champion an individual’s “play-driving” ability.
But a note of caution: Microstats (at least in their current form) are only a part of the play-driving puzzle.
It’s the same with hockey. Being able to regularly engineer controlled defensive zone exits is a valuable skill, especially for defensemen. Even novice fans intuitively understand the importance of moving the puck up ice to launch an attack. But the process of play-driving doesn’t stop there. There are still puck battles to be won, passes in the offensive zone to be made, shots to be taken. Excelling at one aspect of play-driving is great — but by itself, it doesn’t make someone a play-driver. There are better, more comprehensive metrics that shed light on who truly deserves that tag.
That doesn’t mean microstats aren’t important — after all, getting a good start in the 100-meter dash is a key part of winning the race. Microstats are vital for deeper hockey research projects that answer pointed questions about tactics or playing styles. They also can be helpful in constructing theories to explain why a player performs well (or poorly) by metrics like Corsi and xG.
But be skeptical if you read that a player is “good” solely because of strong microstats. The core reason metrics like Corsi and xG have value is because, as outlined in Part 1, they predict future goal-based outcomes better than past goal-based results. Think of it this way: Microstats describe actions that are just pieces of the play-driving whole, rather than the entire equation.
Perhaps in the future — maybe when the NHL fully implements its universal tracking package, which is In the works — a comprehensive public metric that accounts for exits, entries, battles won, passes made, turnovers created and God knows what else might exist that proves statistically superior to the Corsi and xG-centric stats of today. But for now, it’s best to view microstats as a supplement to shot and chance differential metrics (and the more complex metrics derived from them), not as a replacement.
TEAM STATS
WHAT STATS ARE MEANINGFUL IN A GIVEN SEASON
GOOD STATS
First let us explore the statistics that show a high correlation to wins and points in the standings:
5v5 Close Corsi For % is quite highly repeatable – it’s the most reliable metric on this list year over year. It is also highly informative of a team’s likelihood of winning games. If you want a stat that tells you if your team is doing well, that is likely to mean anything in the future, this is probably the best statistic you can make use of.
Now look carefully at some of the other “important” yearly statistics. 5v5 PDO and the GF60 and GA60 stats. Notice how low their reliability scores are? That’s because there’s a large amount of variation in how much teams score or how many goals they allow year over year.
This is because SH% and SV% are NOT repeatable, reliable statistics at the team level. Yes one player might be consistently good or consistently bad, but the randomness of all of his team-mates (the guy on the hot streak – the guy in a funk) has a way of balancing all of this out over the course of a season
So while PDO and Goals For and Against mean a LOT in the standings, they aren’t something you can rely upon to remain the same in the future.
MIDDLING STATS
Let’s have a look at the middling stats that do make a difference, but do not correlate quite so highly.
These are the stats that may have more to do with the style of game a team relies upon, that DO affect winning and losing – but they don’t correlate as highly to team Win% or Point% because it is possible for teams to win despite being less strong in one specific area.
What you'll notice in this section are the Face Off statistics, Team 5v5 Sv%, and the component rates that make up Corsi and Fenwick. These are all relevant but they make a difference at the margins.
Meanwhile others – that we classically think of as extremely important – PP% and PK% are very unreliable year to year, and don’t have a major correlation to Win% or Pt% anyway.
5v5 play is obviously far more of a factor to winning than the PP or PK. Not that either aspect doesn’t matter, it’s just possible for teams to win games without those two factors working in their favour.
Face Offs are also noticeably a fairly reliable feature of a team… but they’re getting down in to the lower end of meaning with respect to correlation to winning or pt%.
So yes – it’s nice that we brought Tyler Bozak back to win draws, but his Face Off prowess is unlikely to make us a better team if he makes the team worse at 5 on 5 when he ISN’T taking a draw.
SHITTY STATS
These statistics show virtually no correlation to winning. That means that teams can win and lose whether or not they rate highly or not in these statistics
You’ll notice that team 5v5 Sh% is near the top of this list. It also has very low reliability. Then you’ll see all of the penalty, hit, TK/GV/BKS, and RTSS stats. Virtually none of these matter to teams winning and losing. Teams win with an edge, or win without one. They also lose with an edge and lose without one. Being big and tough is NOT a cure all to a losing franchise… getting better at puck possession and spending more time in the other team’s end is.
ADDING CONTEXT - TURNING THE CONCEPTS INTO USEFUL STATS
Deployment
Whenever you analyze a player, whether you are using the eye test or advanced analytics, it is important to understand the role in which the player is being used by the coach.
Is the player a top-6 scoring wing, whom the coach throws onto the ice for as many offensive zone faceoffs as possible? Is he a shutdown center that the coach throws onto the ice against the opposing team’s top line? Is he a third-paring defenseman that gets sheltered by the coach, or in layman’s terms, is the player primarily used in the offensive zone and is only on the ice against weaker opposition lines?
Understanding a player’s role on the team and how he is deployed by the coach, are critical to understanding how well he is actually playing.
If a forward is commonly used in a defensive role, and his primary responsibility is to prevent the opposing top line from scoring, it would be irresponsible for us as fans to expect him to put up lofty point totals. Conversely, a defenseman who is primarily used against weaker opponents and in the offensive zone (i.e. sheltered) is likely to put up inflated shot metrics and point totals compared to a defenseman tasked with shutting down the opposition’s best players.
There are a number of components that must be considered to fully understand how a player is being deployed:
_____ For Percentage
Fill in the above blank with Corsi, Fenwick, xG, even Goals and the concept remains the same.
I noted earlier that no one uses raw plus/minus counts when presenting advanced stats anymore (when was the last time you read a stat article saying that Claude Giroux was a +4 Corsi on the night?). That’s becausee the hockey community has shifted to presenting advanced metrics in ratio form, and then turning it into an easy-to-read percentage.
A good rule of thumb for these metrics is that anything over 50% is solid performance, both on the team and player level. It means that the team in question outshot the opposition, which is obviously a positive outcome.
Corsi For Percentage isn’t the only usage of this enhancer, of course. Fenwick For Percentage, xG For Percentage, Goals For Percentage — it’s all driven by the same concept.
TEAM RELATIVE STATISTICS
Team relative statistics, which the vast majority of the time are what people are referring to when they mention “relative statistics,” illustrate the difference between a team’s performance when a certain player is on the ice compared to when he is off.
A relative statistic does not illustrate how the player did in a vacuum, per se, but instead illustrates how the player did relative to his teammates.
Relative statistics help demonstrate a player’s impact on their team, and somewhat mitigate the Impact that the team has on the player.
A quick example of this is that a generally poor possession team (such as the Rangers) will generally have a large number of players below 50% in Corsi For Percentage. However, when you look at the relative Corsi figures, it will be a much more level playing field with respect to this in the positives and negatives.
Using relative statistics removes the impact of a poor overall possession team on a player’s numbers, and instead displays the numbers in terms of how much better the team was with a certain player on the ice, compared to when he was off the ice.
It isn’t perfect, as players who play the majority of their minutes with the same players (such as Girardi being anchored to McDonagh for most of the 2016-2017 season) will still be impacted by those teammates, but it is a significant step in the right direction towards isolating a player’s impact on his team.
_____ Relative To Teammates
Teammate relative statistics (abbreviated Rel TM) go a step beyond team relative metrics and attempts to further isolate a player’s performance by benchmarking his numbers against all of his individual teammates, instead of against his entire team in aggregate.
Teammate relative statistics accomplish this by combining principles used in calculating team relative statistics and WOWY analysis (discussed in the next section).
The key in calculating relative teammate statistics is by including the player’s on-ice performance as well as the average of all of his individual teammates’ on-ice performance when the player we are analyzing is not on the ice.
So, for example, if we are discussing Corsi for per-60 (CF/60), the calculation would take the total on-ice CF/60 of the player we are analyzing, but also subtract the average of all his individual teammates’ on-ice CF/60s without the player on the ice. Another key point to the calculation is that the teammates’ portion of the calculation is weighted by individual teammate time on ice percentage (TOI%) with the player being analyzed. Each individual teammate is assigned a weight relative to their TOI% with the player being analyzed in order to properly account for how much of a potential impact that teammate may have on the player.
the biggest issue with both team relative stats and standard teammate relative stats (such as the “RelT” data available on Corsica), simply put, is that It is difficult to isolate the performance of a player who is often deployed with the same teammate(s).
An additional Issue pointed out by the twins is that team strength has an impact on both forms of relative statistics. They note that, “players on the worst teams appear better and players on the best teams appear worse relative to the league.”
In order to account for the impact that both of these issues have on relative teammate statistics, the Solbergs created adjustments
The important thing to note however, is that they explicitly state that they believe the adjustments “do a very good job dealing with the innate problems the Rel TM method poses,” and they provide ample evidence to back up this claim.
The point in me explaining all of their calculations, weightings and adjustments that are involved in their relative teammate statistical model, is to lay the foundation for this claim, which they made in the conclusion of his piece: “for every type of long-term player evaluation, I feel the adjusted Rel TM method is vastly superior to the Rel Team method.” They also state that, “In general, I feel the Rel TM method – when adjusted for its inherent issues – is one of the best single-number “pen and paper” methods we have at our disposal for player evaluation.”
In other words, relative teammate statistics serve as a more reliable way to isolate and analyze single player performance than WOWY analysis or relative team analysis.
Now, relative team and WOWY analysis certainly still are valuable evaluation techniques in their own right, but the new adjusted relative teammate versions serve as better long-term analysis techniques for individual players.
the statistics attempt to measure a player’s total impact on his team, relative to his teammates, for a respective metric (such as Corsi or expected goals).
The impact statistics take into account all 5v5 data and include the adjustments we discussed above. They work similarly to any differential number (plus-minus style), which is important to note because players with more ice time can have a greater variance in their numbers.
As much as we all like to isolate per-60-minute production, total impact statistics are also vitally important, because a player who can produce at a high level while receiving high usage is obviously more valuable and has a larger team impact than a player who produces at a high level but receives minimal ice time.
The reason why looking at the quality of teammates that a player shares large amounts of ice time with is simple: good players make those around them better. This is a very simple concept that we hear across all team sports.
There is much debate within analytical communities across all sports regarding how to quantify just how much a player can improve the play of those around him, but nearly all analysts agree that the quality of the players that an individual plays with will certainly have an impact on his play.
In fact, Connor Tompkins wrote a Hockey-Graphs article a few years back that concluded that “quality of teammate effects are observable in a full season sample size.” In layman’s terms, his study concluded beyond a reasonable doubt that the data shows that the quality of teammates an individual plays with has a measurable impact on his play and production.
WOWY analysis is one way you can view this impact.
Because of these measurable impacts, we can conclude that teammate quality is certainly important, and should be considered when discussing player analysis and deployment.
Just like the first qualifier above, this applies to Corsi, Fenwick, xG and Goals in the same exact way.
Relative metrics answer a simple question — how did a player perform in comparison to his teammates?
We already know that finishing with a Corsi For Percentage over 50% is generally speaking a good outcome, but what if the whole team finished above 50 percent? What if the whole team was below 50%? How do we judge who truly produced the most positive outcomes?
With relative metrics, it all comes down to how the team performs with a player on the ice versus when he sits on the bench.
This context is key to truly understanding which forwards and defensemen qualify as “play-drivers.” Not only do you want your best players to be consistently finishing with Corsi For Percentages over 50%, you also want them possessing positive Corsi Rel rates as well.
RelTM
Where to find it: Evolving-Hockey.com
This brings us to the RelTM metric
A disclaimer: There’s a big difference between relative metrics (explained in Part 1) and RelTM, despite the similarities in name. Relative (or Rel) metrics simply calculate the percentage point difference between how a team drives play when a specific player is on the ice, and how the club performs when he sits on the bench. It’s just an on/off differential.
RelTM, on the other hand, is more like WOWY on steroids.
Remember the problem with individual WOWYs, that they focus on only two players and ignore everyone else? RelTM gets around that issue by measuring how basically every single player on a team performs with the player being evaluated, and then combines all of the information into one comprehensive metric
RelTM answers this question: Do a player’s teammates tend to deliver better results by Corsi and/or xG when playing with him (a positive RelTM) or do they usually produce worse results with him (a negative RelTM)?
Now, not all WOWYs in the RelTM equation are weighted equally — the less time a player spends with a teammate, the less weight it’s given.
Grading out as “plus-3” by Corsi plus/minus per 60 RelTM (or Corsi ±/60 RelTM) means that a player (on average) improves the Corsi differential of his teammates by three shot attempts every 60 minutes of play; a negative-3 Corsi ±/60 RelTM indicates the player deflates his teammates differentials by an average of three shots.
The expected goals version of the metric (xG ±/60 RelTM) functions in the same way.
So what qualifies as a “good” performance by these metrics?
Without getting too mathematical, here’s a rough breakdown of acceptable full-season RelTM ranges for each position, broken down into tiers. (Note: This is a general guide for ease of understanding and should not be taken as gospel.)
Don’t forget that a key underlying goal of advanced metrics is to identify players who help their teams to outshoot and outchance the opposition, because those underlying advantages ultimately lead to goal advantages (which lead to wins).
That’s what positive RelTM players do — acquire a bunch of them, and your team is probably going to win a lot.
Like any metric, however, RelTM has limitations. It doesn’t account for the impact of zone starts, quality of competition or schedule effects on play-driving results. Score effects can be added through after-the-fact adjustment, but there are other stats that account for those more thoroughly by including them in the overarching mathematical model. (RelTM is basically just an equation, not a full-fledged model.) And in small samples, RelTM can spit out some pretty extreme results, so be sure to avoid jumping to concrete conclusions about a player due to a sky-high or basement-level-low RelTM early in a season.
These weaknesses don’t render the metric useless, even though some important variables aren’t fully present. On the whole, however, RelTM is a perfectly acceptable way to get a read on an individual’s play-driving ability at even strength.
Rel vs. RelTM
So, we have both Rel and RelTM. Which is the better metric when trying to determine if (and to what degree) an individual actually drives play?
The diplomatic answer is that both have their uses, so long as it’s clear what is being measured and what question is being answered.
The short answer is that RelTM is usually better.
To be clear, Rel can be useful, especially when RelTM isn’t easily accessible. It’s certainly better than raw Corsi or xG differential in determining which players on a team are truly best at driving play.
And there are rare instances when RelTM unfairly punishes or credits players for team-wide dramatic improvements or drop-offs in play-driving — Rel can be better suited to avoid that trap.
But on the whole, RelTM is the better metric to use when trying to measure individual play-driving ability. Now, go out and buy a teddy bear
QUALITY OF COMPETITION
There is considerably more debate within the analytics community regarding the impact that quality of competition has compared to quality of teammates.
The Connor Tompkins article I shared above offers a second conclusion, with Tompkins stating that he “did not find evidence that coaches can choose the quality of competition their players face over a full season of play.” He goes on to discuss numerous reasons for why he did not find any evidence of this, most notably sample size issues.
He also explicitly states that, just because that the data shows no evidence of the impact, doesn’t mean that quality of competition doesn’t have an impact, and he went on to share that Garret Hohl (whom is the co-founder of both Hockey-Graphs and a data company that professional hockey teams pay for information) has research showing that quality of competition has a greater impact on an Individual game or playoff series than across an entire season.
There have been numerous other studies on the topic, but long story short, while many agree that quality of competition does matter, there is little consensus over exactly how it matters and how to measure its impact.
Various sites, including Corsica, provide statistics that are weighted to demonstrate the quality of competition a skater plays against, and the quality of teammates he plays with, which I will discuss in greater detail within their dedicated sections below.
One thing that is important to note is that most of these models use an opposing player’s ice time as the weight used to account for quality.
By this I mean that a metric such as Corsi Quality of Competition uses the time on ice the opponents received as the weight, with the methodology being that better players receive more ice time.
this is not necessarily the best barometer of the quality of a player. However, it is still a step in the right direction, and more often than not, the best players on a team receive the most ice time
ISOLATED SHOT RATE
(via Threat)
Where to find it: HockeyViz.com
Does the above mean that RelTM is the end-all, be-all of play-driving measurement for players? Maybe a few years ago, but not anymore.
The smartest minds in the public sphere haven’t accepted the inherent weaknesses of RelTM, which at its core, is a relatively simple metric in mathematical terms. More complex models are necessary to account for the missing variables in the RelTM formula.
One such popular model is Micah Blake McCurdy’s isolated shot rate, quantified as “Threat,” which is available for public viewing on HockeyViz.com. It’s often cited by fans on social media when judging players or teams; if you’re active on hockey Twitter, you likely have seen the inimitable visualizations from McCurdy’s model.
Why use isolated shot rate? A weakness of RelTM is that it really only measures the impact one player has on the shot and chance differentials of teammates. Isolated shot rate is far more ambitious in its aims — on the single-player level, it looks to completely isolate an individual’s impact on his team’s ability to create and prevent offense.
It starts out simple enough. McCurdy’s “Threat” model is the starting point, and among quality-adjusted shot models, Threat is about as straightforward as it gets.
It begins with raw shot differential, and then weights every shot based on location, using the league-average shooting percentage from that particular spot. That’s it. No accounting for rebounds, rushes and backhand shots. It’s just location-adjusted shot differential.
If 3 percent of all NHL shots at 5-on-5 taken from the right faceoff dot over a given year go into the net, then the model will give every shot from the right faceoff dot a 3 percent chance of success. Easy to understand, right
The complexity comes later.
Isolated shot rate takes the results from the basic Threat model, and then accounts for a ridiculous amount of outside factors that also affect a player’s weighted shot differential: teammate impact, the effect of competition, shift starts, score effects, schedule-related fatigue and coaching impact on results. It even factors in an Individual’s play-driving results from past seasons. (Remember this distinguishing factor of isolated shot rate — it’ll be important in the next section.)
After gathering all of these variables, a mathematical regression (specifically, a ridge regression) is used, and results in the model’s estimation of a player’s impact on his team’s 5-on-5 offense and defense
The model also provides visualizations alongside the numbers. It’s a key aspect of the presentation — it’s no coincidence that McCurdy’s website is titled HockeyVIZ after all.
The maps show where shots tend to be generated (and allowed) with a player on the ice at even strength — red means more shots than league-average in a particular region; blue indicates fewer shots. This gives insight into the “nuts and bolts” of isolated shot rate in a way that numbers alone fail to do. With this model, a person can actually see where shots tend to originate from with a player on the ice, which helps to quickly identify how the team is succeeding (or failing) when a player skates.
What are isolated shot rate’s limitations?
For starters, it intentionally shies away from placing a single-number grade on a player. While one can roughly combine the offensive and defensive Threat numbers, there’s a reason why the metric is not presented as such by its creator: It’s not meant to “rank” players in a set order, or to measure “total value added” as some metrics (like Wins Above Replacement) try to do. It’s simply a measurement of even-strength play-driving ability that primarily uses visualizations to tell the story
The simplicity of the initial Threat model is another limitation. There’s a reason public standalone xG models account for additional information beyond shot volume and location — such as rebounds, rush chances and shot type. It’s because these layers provide more detail about the quality of the underlying shots. Isolated shot rate assumes every shot taken from a specific location is equal, and that’s not necessarily the case, as a shot from the right faceoff circle on a rush has a better chance of fooling a goaltender than a shot from the same spot generated on the cycle.
Isolated shot rate doesn’t account for shooting talent, either. Some players have the ability to outperform shot- and chance-based expectations, simply because their shooting is just that good or because they have a knack for making their teammates’ shots more dangerous than “expected” due to especially creative passing. The model, by design, doesn’t pick up on either skill.
But if you’re looking solely to evaluate an individual’s play-driving ability at even strength, isolated shot rate will do nicely
RAPM
Where to find it: Evolving-Hockey.com
And now, we come to Regularized-Adjusted Plus Minus, or RAPM.
Even more than isolated shot rate — which stands alone due to its visual element — RAPM is the spiritual successor to RelTM, though RAPM didn’t directly evolve out of RelTM from a mathematical standpoint.
Like RelTM, RAPM results can be presented in Corsi and xG form. And “good” RAPM results usually look very similar to strong RelTM grades.
In fact, when compared directly, individual results by Corsi RelTM and Corsi RAPM were correlated by about 84 percent last season; the correlation between the two metrics by expected goals was even higher — around 87 percent.
Full-population RAPM ranges tend to be less extreme than those of RelTM, but it’s rare to find players who grade out fantastically by one and terribly by the other.
Still, there’s far more “under the hood,” so to speak, with RAPM.
RAPM starts out with raw shot creation (and suppression) results for a player. It then takes almost every outside influence on Corsi or xG differential that a skeptic could possibly fathom — teammates, competition, zone starts, home/road impact, schedule effects — and uses a mathematical model and ridge regression to attempt to account for each one of them.
Sound familiar? It should, if you paid attention to the previous section, ahem.
RAPM and isolated shot rate have many similarities, in both their aims (isolate offensive and defensive impact from all other factors) and how they go about achieving those aims from a math standpoint.
Not all of the add-ons are the same — for example, isolated shot rate attempts to account for the impact of a coach, RAPM does not — but the overarching goal of bringing them all into the statistical party is the same: to successfully isolate play-driving ability.
Yet there are key differences, even beyond the intricacies of the math involved. For starters, RAPM doesn’t share isolated shot rate’s “hesitation” regarding single-number results — the end play-driving stats of the model (Corsi RAPM/60 and xG RAPM/60) take into account offensive and defensive impacts and combine them into one number, which can be used to determine the best play-drivers at a given time
RAPM also splits its results into raw shot differential (Corsi) and quality-adjusted differential (xG), and lets people pick and choose between the two.
Isolated shot rate, as covered earlier, solely uses its underlying Threat model, which is sort of a middle ground between Corsi and xG, since it takes into account shot location but not factors such as rebounds or rushes.
And perhaps the largest functional difference between isolated shot rate and RAPM is their differing approaches to including prior information (before the season being measured). If you’re looking at a player’s single-season RAPM results, that’s all you’re looking at — data from just that season. Every year, RAPM begins with the assumption that each player has an equal talent level — essentially, league-average talent. Isolated shot rate’s formula, on the other hand, accounts for a player’s past results.
There are benefits to both approaches. Isolated shot rate isn’t going to be as “fooled” as RAPM by an early season play-driving hot streak by a historically poor player, since the metric includes past results in its formula. But RAPM is inherently going to be a more on-the-nose description of what a player’s results look like now (the season in question), since it’s almost exclusively looking at just a single year.
The fact that RAPM doesn’t account for past results might qualify as a limitation — especially if you’re trying to zero in on a player’s true talent level as a play-driver — but it shouldn’t necessarily be viewed as a flaw of the model.
So what is the “right” way to use RAPM?
It should be viewed as an upgrade to RelTM as a measurement of individual play-driving ability over a single season, for starters.
Like RelTM, it can be easily presented in single-number form (the results tend to look similar), but it accounts for far more outside factors than the comparatively rudimentary RelTM is capable of including.
Also, RAPM should be used as a play-driving metric, and not one that measures total value.
Like isolated shot rate, it doesn’t account for shooting talent, and it’s not a Wins Above Replacement metric that tries to rank players according to how much value they add to their teams.
RAPM is a fantastic tool if you’re trying to learn which player on a team has pushed play in the right direction most at even strength.
Looking for a list of the best players in hockey? When attempting to answer that question, RAPM results are just a component, not the whole story, of course.
As a single-number metric that measures individual impact on Corsi and xG differential, however, RAPM is probably the best around.
CATCH-ALL STATISTICS
Catch-all statistics like baseball’s now popularized WAR are valuable metrics that help us quantify the overall value a player brings to the ice.
Nobody will argue that these catch-all stats are perfect and that they should be the end all be all in player analysis (well, nobody worth listening to will argue that at least), but they most certainly are valuable analytical tools.
Baseball is by far the easiest sport of the “big four” in the U.S. to have a catch-all statistic for, thanks to the nature of the game; it is more or less a series of individual events, making it much easier to assess exactly what was the cause and effect of a play.
Free flowing sports such as basketball and hockey are much more difficult to assess in this manner, but that hasn’t stopped leading statisticians in each sport from creating their own models for a catch-all statistic.
The now-defunct WAR On Ice hockey stats site (both site creators were hired by NHL teams, so the site has since been shut down) made the first prominent foray into hockey catch all stats with their WAR statistic, which they published a series of posts about.
More recent catch-all models include Dawson Sprigings’ (better known as DTM About Heart) Goals Above Replacement (GAR), Luke Solberg’s (Evolving Wild) Weighted Points Above Replacement (wPAR) and Manny Perry’s (Corsica creator) version of WAR.
Analysts have also come up with catch-all metrics to evaluate entire teams—Manny Perry’s K Rating—and individual game performances: Dom Luszczyszyn’s Game Score.
WAR
Analyzing the individual components is a great way to understand what aspects of the game various players excel at.
WAR is only a player-level statistic, and it aims to quantify the total value a player brings to the team by accounting for a myriad of individual components.
Manny’s WAR model consists of eight total components for skaters: offensive shot rates, defensive shot rates, offensive shot quality, defensive shot quality, shooting, penalties taken, penalties drawn and zonal transitions.
Manny also has a WAR statistic for goalies that attempts to measure their ability to prevent goals. Since WAR measures how much better a player is than a “replacement player,” it should be noted that Manny defines a replacement player as “one who can be signed at the league minimum salary.
GAR
Stands for Goals Above Replacement and was first created by Dawson Sprigings (DTM About Heart).
What GAR does at its core, is it takes the wins above replacement stat (WAR), and converts it to goals above replacement, with the methodology being that scoring a goal is the ultimate goal of any play in hockey.
Because Dawson’s data is not available, I won’t dive into it with the level I did WAR, but it is worth pointing out that it functions similarly to WAR, in that it analyzes individual components of a player’s game in order to generate the single catch-all stat.
WPAR
Stands for Weighted Points About Replacement and was created by Luke Solberg. Luke (better know as EvolvingWild) released the methodology and data for his new aggregated value model in the summer of 2017, and it follows a similar construct to both predecessors, albeit with slightly different components and weights to make it unique.
The biggest difference between wPAR and its predecessors is its linear regression model.
Another difference that is worth noting here is that WAR focuses on wins added by player, GAR focuses on goals added, and wPAR focuses on point totals.
Lastly, wPAR scales the data to consider the season in order to account for the fact that the value of the “replacement” player may differ from one season to the next.
The individual components that wPAR consists of and weights individually include goals, primary assists, secondary assists, tango shots (shots that miss the net; in other words, an individual players Corsi minus their shots on goal), individual expected goals, relative Corsi differential (RelCF%), penalties taken, penalties drawn and faceoff differential.
The model also includes interaction variables, which Luke notes are very useful for accounting for the effect that independent variables may have on one another. Similar to WAR, wPAR is a cumulative stat, and it also comes in the form of wPAR per-60 to provide us with a method of comparing players with varying amounts of ice time.
Analyzing the individual components is a great way to understand what aspects of the game various players excel at.
In terms of the player data that Luke shared, he grouped the components into five categories: Counts (includes goals, primary and secondary assists, tango shots, iXG and the interaction variables), Differential (RelCF%), Penalties Taken, Penalties Drawn and Faceoff Differential.
K RATING
This is “a composite tailored regression model” created by Manny Perry of Corsica.
In layman’s terms, it is a comprehensive model that, similar to the catch-all statistics provided above, accounts for a variety of individual components that are each “optimally accounted for.”
However, unlike WAR, GAR and wPAR, K Rating is a team-level statistic that attempts to gauge the overall quality of a team with one metric.
Think of K Rating as the team-level version of WAR. In Manny’s methodology for K Rating, he demonstrates the predictive power of the metric, and he flat out states in the conclusion, “given its predictive power, I strongly believe K will be the single best publicly available team metric in hockey.”
Similar to the player-level catch-all statistics, there can be a lot of value derived from analyzing the individual components of K Rating.
GAME SCORE
Game Score is a catch-all statistic created by Dom Luszczyszyn that quantifies the total value of a player’s productivity from a single game.
Dom’s NHL version of Game Score incorporates all of the following stats in an attempt to quantify the overall performance of a player: goals, primary assists, secondary assists, shots on goal, blocked shots, penalty differential, faceoffs, 5v5 Corsi differential and 5v5 goal differential.
However, as you all know, not all stats carry the same importance, so Dom assigned weights to each of the aforementioned stats to come up with the following formula for Game Score:
Skater Game Score = (0.75 * G) + (0.7 * A1) + (0.55 * A2) + (0.075 * SOG) + (0.05 * BLK) + (0.15 * PD) – (0.15 * PT) + (0.01 * FOW) – (0.01 * FOL) + (0.05 * CF) – (0.05 * CA) + (0.15 * GF) – (0.15* GA)
Dom also created a Game Score model to assess goaltender performance, which included two stats—goals against and saves—which are also weighted according to importance. The goalie model is as follows:
Goalie Game Score = (-0.75 * GA) + (0.1 * SV)
Game Score has multiple applications, and Dom frequently uses it in his writing when assessing player and team performance across single games as well as entire seasons (and everything in between).
Dom notes in his methodology that, “there’s many applications for Game Score across hockey analysis that I think can further our understanding of the sport and how players work at the game level. Consistency, streakiness, clutchiness; whether they’re real or random is a question a stat like Game Score can help answer and one that we perhaps couldn’t answer properly beforehand.
Dom also recently created another stat based off of Game Score, which he calls Game Score Value Added (GSVA).
GSVA is a three-year version of Game Score that is translated to its value in wins. In other words, GSVA is similar to WAR, GAR and wPAR, in that it communicates player value in terms of wins, as opposed to points or any other production metric. One particularly useful application of GSVA is Dom’s use of the model in the pre-season to project individual player performance, and then aggregating these performances by team to project team performance.
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