Understanding What The Different GAR Models Favour
· Ian’s WAR Model
· Strongly Values:
· What players are going to do (Expected point production)
· Doesn’t Value:
· What players have done
· Players who put up more points than “Expected”
· Players who drastically outperform their career Sh
· DTMAboutHeart’s WAR Model
· Strongly Values
§ Penalty Differential
· Doesn’t Value
§ Players who drive play drastically better/worse than in prior seasons
§ Bases play-driving ability on a multi-year sample
· Manny’s WAR Model
§ Strongly Values
· In-Season Shooting Talent
· How many more Goals than Expected Goals a player has scored
§ Doesn’t Value
· Point Production
· Especially empty calorie points (players who produce points but don’t drive play)This is because his model literally doesn’t look at Points
§ Dom Luszczyszyn’s Game Score and EvolvingWild’s Weighted Points Above Replacement
· Strongly Value
· Point Production
· Don’t Value
· Play-drivers with mediocre point production, especially defencemen (ie. Tanev & Hjalmarsson)
· Keep this all in mind when you see a player whose WAR or Game Score doesn’t pass the smell test.
§ Sometimes it simply has to do with the model’s weights, sometimes that player is genuinely more valuable than public perception (this is often the case), and sometimes….
GOALS ABOVE REPLACEMENT
GAR/WAR DEFINITION
Goals Above Replacement (GAR, WAR, and SPAR) is a metric that attempts to assign a total value to each player, which represents how much that player contributed to their team in a single number. This single number is comprised of multiple components that are ratings for each area of play within a given sport.
GAR is then converted to wins and WAR is the result.
INTERPRETING AND REDEFINING GAR/xGAR MODELS
it’s very difficult to evaluate these models at the individual player level. There is no agreed upon way to measure the performance/impact of a player.
In many ways, player evaluations are just subjective opinions. This is why, my approach is slightly different: How well does the GAR and xGAR models describe team performances?
I’m going to use goal differential to measure team performance. This gives us a stat that we can compare with team GAR/xGAR.
Just because team GAR correlates well with goal differential at the team level, doesn’t mean it’s necessarily a great descriptive model at the player level. A model can’t be great at the player level and bad at the team level, but it can be great at the team level and bad at the player level.
Surprisingly, xGAR describes team results better than GAR does. This is a bit surprising since GAR is supposed to be more of a descriptive model whereas xGAR is supposed to be more predictive in its nature. The difference is not huge, but it’s still interesting.
WAR – WHAT IS IT GOOD FOR
The concept is a simple one: we can measure the contribution of each player quantitatively by comparing them to a replacement level player, which is a player who is available for a nominal cost via free agency, waivers, or in trade.
The goal is to create a single currency to compare all parts of the game, with the best level of data available.
GAR is a statistic that not only had a very high correlation with goal differential and team points, but was also reasonably predictive of future performance.
Basically GAR attempts to quantify the impact a player has on their teams goal differential by expressing all of their contributions in one number – the goals above (or below) a replacement level NHL player. It’s an attempt – and, of course, a rough one – to combine multiple factors like scoring, goal tending, face offs, penalty differentials, shot differential, and scoring to create a measured value of a player’s season.
Here are some key aspects they considered in designing the metric, especially as is relates to shot metrics for skaters an example:
· Adjust for teammates and competition simultaneously, including replacement level players.
· Separate offensive and defensive contributions.
· Adjust for usage, including whether a faceoff was won or lost, and score situation.
· Model separately for each shot danger (low, medium, high), because we know that forwards and defensemen contribute differently between and within these groups.
· Distinguish between performance (what happened) and talent (what would be most likely in future).
GAR is currently the best publicly available tool we have to work with.
The sum of player GAR for a team has a strong correlation to both goal differential, and team points.
This intuitively makes sense. The higher the goals against replacement of the players on that team, the more likely the team will win, which effectively means that the stat does what we want it to do, at least retrospectively.
There’s a strong relationship between regular season points and GAR. The higher your team GAR, the more likely you’ll outscore your opponent, the more games you win.
Looking at playoff success, the vast majority of playoff contenders in recent years have excelled by this metric, usually as a result of having two to three players who achieve an elite GAR rating.
If you want to compete for the Stanley Cup all you need to do is acquire a cumulative team GAR of over 107. Simple right?
WHAT IS GAR
Player value is decomposed into six categories: even strength offense, even strength defence, power play offense, penalty drawing, penalty taking, and faceoffs.
These are all summed up to get a total value for the player.
The stat straddles the line between being a measure of ‘true talent’ as opposed to ‘the value a player provided’. Parts of the even strength offense and defense are more a measure of ‘true talent’ but the rest tends to be a measure of what happened.
At the very least, GAR is a valuable starting point to get an idea of what a player’s worth is, that can be refined and studied further. At its best, it is far more than that – it’s a concrete expression of how much a player is helping or hurting a team
GOALS ABOVE REPLACEMENT
(Mar 2018)
Even Strength Offense:
For forwards, primary points are king. For defencemen all points are relatively equal, with slightly more focus on assists. And for either position, shot quality (ixFSh%) is slightly more important than shot quantity (iFF/60).
Point production (CBPM) is only half of the equation. That’s because there’s another key input to players offensive output, their ability to drive play.
Some players (especially defencemen) can be elite offensive players without massive point totals. They achieve this by driving shots and scoring chances towards the other teams net. Making sure their team generates goals even though they may not be directly picking up points.
To account for players ability to drive play offensively I use C-XPM
This uses 2 key metrics, Relative to teammate Corsi for, and relative to teammate expected goals for.
With the 2 main metrics defined, C-XPM is simple.
Originally I had corsi and expected goals weighted equally, however with some testing I found XG to be way more volatile (especially for defense-men). As a result, the ratings are skewed to include both but favor corsi.
Even Strength Defense:
Even strength defense uses 2 of the metrics mentioned above, corsi and expected goals. This time it’s relative to teammate corsi (RelTCA) and expected goals against (RelTxGA). It’s the same thing, just the ability to suppress shots and chances relative to your teammates rather than generate them. So the basic equation is the just the inverse everything mentioned above.
Furthermore players don’t have an the ability to influence their goalies save percentage, so preventing quantity against (Corsi) is more important than players ability to suppress quality (XG).
Power Play:
About 30% of goals in the NHL are scored on special teams, so roughly 30% of the value in this model is distributed between these upcoming sections.
People generally put a premium on primary points, however based off the BPM weights being used, either type of assist provides significantly more value than a goal.
Ryan Stimpson’s work illustrates that passing data is more predictive of future goals than shot data at even strength, and since power-play offence is especially reliant on passing to open up the opposing penalty kill, the gap might be even larger on the power-play. These two things help explain why assists are king on the power-play, not primary points.
Penalty Differential:
A significant part of special teams is deciding how much time is spent playing each one
For the model, it’s split into two separate categories. First is players to draw penalties, and second is players ability to stay out of the box.
Conventional wisdom from @EvolvingWild states that a penalty is worth 0.17 goals,
Extras:
The finishing touches of the model, we have face-offs.
Face-offs are a valuable input into a center-mans output.
Weaknesses Of The Model:
First is the inability to quantify short handed impact.
f a player dramatically outperforms their past performance, they will be scaled back towards their career norm. This helps find “true talent” because generally, the more extreme a players results, the more likely luck played a significant role.
LS-GAR (GAR + xGAR)
Let’s start with the GAR model.
The correlation (R-squared = 0.631) with GF% is better than it was for corsi and expected goals, so this bodes well for when we adjust for goaltending.
This shows that GAR Skater combined with GSAx correlates very well team quality. This is interesting.
So far so good. The next thing I want to do, is to combine the two models into one
I’ve called the model LS-GAR, and it combines GAR Skater, xGAR Skater and GSAx.
As hoped the combined model works even better than GAR and xGAR individually
I have made it an average model, meaning if the team is at 0, it is now an average team (bubble playoff team) instead of a replacement team. The model has therefore changed from a GAR model to a GAA model (goals above average).
The second thing I have done is to make sure one goal in my model actually equals one goal in team goal differential. This way we can compare LS-GAA directly to goal differential
LS-GAA is the sum of 5 components: Goaltending, Even strength (consists of an offense and defense component), Powerplay, Shorthanded and Penalties (drawn and taken).
GAR/xGAR
We know how to define a good team. Good teams outscore their opponents and win hockey games. It’s as simple as that. Therefore, I’m going to use goal differential to measure team performance. This gives us a stat that we can compare with team GAR/xGAR.
Just because team GAR correlates well with goal differential at the team level, doesn’t mean it’s necessarily a great descriptive model at the player level. A model can’t be great at the player level and bad at the team level, but it can be great at the team level and bad at the player level.
My first step is to simply look at the correlation between team GAR/xGAR and team goal differential.
Surprisingly, xGAR describes team results better than GAR does. This is a bit surprising since GAR is supposed to be more of a descriptive model whereas xGAR is supposed to be more predictive in its nature. The difference is not huge, but it’s still interesting.
So, let’s add the goaltender GAR and see what happens
With this addition the correlation in both models increases, but more in the xGAR model. In fact, the xGAR model already correlates really well with team performance. There are two things worth noting though:GK_GAR = GK_xGAR – There’s only one GAR stat for goaltending.GAR > xGAR – In general players have a larger GAR than xGAR.This could indicate that GK_GAR is factored better for the xGAR model than the GAR model.
I also tried using GSAx (based on Evolving-hockey’s xG model) as my goaltender stat. That gave the following result: Now, we see the GAR model being slightly better than the xGAR model.
I will try and redefine GAR and xGAR, so that I can compare them directly to goal differential, which is a zero-sum stat. The sum of the goal differentials for all NHL team will always be zero, so therefore I want to reform the GAR and xGAR models into zero-sum models. I’m going to call the models goals above average (GAA) and expected goals above average (xGAA), because that’s what they are.
Going forward I will be using GSAx as my goaltending component. I don’t necessarily think GSAx is a better stat than GK_GAA, but it fits better with the GAA and xGAA models.
Now, we have two models that can be compared directly, so what happens if we combine them? Here’s the combined model, which I have called sGAA.
The combined model correlates better with goal differential than the two models individually.
Discussion:
So, what was the purpose with this exercise? First of all, I wanted to make a descriptive model where you can see the impact of a player directly. If a player has a GAA of +4, he’s simply worth 4 goals more than the average player and he’s worth 4 goals to the goal differential of the team.
Secondly, I want the model to correlate directly to team performance, so that it can be used as the basis in a predictive model, that predicts future team results.
The GAR and xGAR models from Evolving-Hockey are primarily used for player evaluations, but I think these redefined GAA models can be great for team evaluations as well.
WAR
UNDERSTANDING WAR AND ITS PRACTICAL APPLICATIONS TO PLAYER EVALUATION
‘WAR’ tries to take shot rate metrics like Corsi, combine them with other factors, and then tie the result directly to the column on the score-sheet that matters the most: Wins
‘Goals Above Replacement’, or ‘GAR’, is actually easier to interpret than WAR, especially for individual players.
It is very difficult for a player to pass a GAR score of even 10 in a given season.
The first chart shows that fewer than 14% of players achieve this each year, and the second shows that even conference final-reaching teams usually only have ~4.5 players with a GAR of 10+. Even fewer have a GAR of 15+, at approximately 5.9%, or only 1 in 17 players in the league
Goalies and Defensemen are under-represented in the top GAR ranges, when looked at on a three-year average basis. This highlights an important qualifier of the GAR metric: like most NHL player evaluation, it currently best evaluates a player’s offensive contributions.
Looking at the components of GAR (the next section) will explain why: defensemen will largely contribute to just one or two of the six components (e.g. impact on shot rates), while forwards will contribute to shot rates while also providing material contribution through their shooting percentage, face-offs, and penalty drawing.
As a result, when using the current GAR metric to evaluate players, it will be most accurate to compare players within positions, rather than across them.
WAR is currently made up of the following six components for skaters, which I have grouped into the three broad categories below:
· Offensive Contributions
· Shot rate for
· Shooting percentage
· Defensive Contributions
· Shot rate against
· ‘Gameplay’ Contributions
· Faceoff win percentage
· Ability to draw penalties
· Ability to avoid taking penalties
USING GAR TO QUANTIFY A PLAYERS VALUE AND SALARY CAP EFFICIENCY
1 win (WAR) = ~6 goals (GAR)
Based on the free agent market and the current cap, every 1 WAR a player contributes is worth $2.8M in contract value.
the market ‘price’ of a 1 WAR or 6 GAR player is approximately $3.4M in player salary per year (2016).
the most legitimate, ‘fair’, and repeatable way for a team to maximize their cap efficiency is to either focus on acquiring young players in the draft, or by trying to trade for prospects early into their tenures as NHLers.
GAR FOR ROSTER CONSTRUCTION AND MAXIMIZING CAP EFFICIENCY
There is a very strong relationship between a team’s total GAR score and its points in the standings – even stronger than Corsi.
80% of conference finalist teams have total GAR scores of 107 or more.
NHL GM’s could reasonably set a target of 107 GAR for their teams. In years where a team is forecasting close to 107 GAR, the GM should consider trading for those last 1-2 key pieces to make a run.
If the team is well off of 107, the GM can instead use it to guide his long term plan by answering (i) how he can acquire a core group of players to reach 107 GAR, and (ii) once acquired, how can he best divide his cap space between those players in order to keep them?
the simplest way a team can effectively manage its salary cap is to be disciplined in contract negotiations, and avoid giving large contracts to high risk or potentially declining players.
· Last, this chart helps to show that the Blackhawks have constructed their roster around a ‘core’ set of 7-8 players that drive their results:
· This core consists largely of the team’s top 4 forwards, top 3 defensemen, and starting goalie (Toews, Kane, Hossa, Sharp, Keith, Seabrook, Hjalmarsson, and Crawford)
· These players collectively earn 64% of the salary cap, and contribute 67% of the team’s GAR
· Interestingly, this directly matches the typical conference finalist team having ~8 or so 10+ GAR players,
THE ART OF WAR
(May 2017)
The underlying theory is simple: measure a player’s value according to the fraction of wins they contribute above what a replacement-level player could provide.
There is no single process in hockey by which players exert an influence on the creation of wins. Just about any event on the ice surface during play can affect the rate of goals – from a faceoff win, to a body check, to a failed pass attempt.
Identifying manners in which players can contribute positively or negatively is not difficult. The challenge lies in avoiding overlap between these categories, such that the sum of the contributions truly represents a player’s total value.
A successful WAR model should capture all major contributions a player might have, without allowing overlap.
The complete list of WAR components is:
· Offensive shot rates
· Defensive shot rates
· Offensive shot quality
· Defensive shot quality
· Shooting
· Penalties taken
· Penalties drawn
· Zonal transitions
With a ninth component unique to goaltenders, measuring the ability to prevent goals.
The full model controls for score effects, zone starts, home ice and skater advantage.
A NEW WAR MODEL
As a reminder, here’s a quick breakdown of what my WAR formula takes into account:
· 5v5 Shot Impact
· Blends Shot Quantity (Corsi) & Shot Quality (Expected Goals)
· Expected Offence
· Expected Point Production for Forwards
· Shooting Talent (‘Goals Above Expected’) for Defencemen
· Penalty Differential
· Faceoff Differential
· Power Play Value
The reason I like single metrics like WAR is because they do what we’re all trying to do when we use statistics – weighting them all against each other in attempt to reach some kind of conclusion on a player.
This is where a metric like WAR can help objectively guide us in the right direction.
I’ve found that the better way to look at these metrics are in “tiers”, in that we can be pretty confident that player ranked in the Top 50 is providing more value to his team than a player ranked in the early 100s.
Understanding What The Different Models Favour
· Ian’s WAR Model
· Strongly Values:
· What players are going to do (Expected point production)
· Doesn’t Value:
· What players have done
· Players who put up more points than “Expected”Players who drastically outperform their career Sh
· DTMAboutHeart’s WAR Model
· Strongly Values
§ Penalty Differential
· Doesn’t Value
§ Players who drive play drastically better/worse than in prior seasons
§ Bases play-driving ability on a multi-year sample
· Manny’s WAR Model
§ Strongly Values
· In-Season Shooting Talent
· How many more Goals than Expected Goals a player has scored
§ Doesn’t Value
· Point Production
· Especially empty calorie points (players who produce points but don’t drive play)This is because his model literally doesn’t look at Points
§ Dom Luszczyszyn’s Game Score and EvolvingWild’s Weighted Points Above Replacement
· Strongly Value
· Point Production
· Don’t Value
· Play-drivers with mediocre point production, especially defencemen (ie. Tanev & Hjalmarsson)
· Keep this all in mind when you see a player whose WAR or Game Score doesn’t pass the smell test.
§ Sometimes it simply has to do with the model’s weights, sometimes that player is genuinely more valuable than public perception (this is often the case), and sometimes…
Limitations
· Dividing Credit
· The Sedin Problem
· Playing with a Dominant Player
· Playing without a Dominant Player
Closing Thoughts
The reason statistics are used in every walk of life is because we can use them to objectively analyze things. That’s what WAR models like mine are attempting to do by quantifying player value. They try to take all of the important information into account, weight each metric based on its impact on goals, and then spit out a final result.
HOW TO CREATE WAR FOR ANY SPORT
(Dec 28, 2018)
While WAR is wins above REPLACEMENT, the most important part of WAR is the comparison to AVERAGE. Indeed, the replacement step is both an after thought, and in some respects, unnecessary.
What you want to do is measure all the aspects of a player’s performance relative to the league average. Not for the position, but the player, unless that position is very (VERY) distinct, like pitcher in baseball or goalie in hockey
You want to measure in the currency that you can measure in, meaning bases, outs, runs, goals. And eventually, you want to convert into wins. For baseball you can use a standard 10:1 runs to win converter and in hockey 6:1 goals to wins.
THE PATH TO WAR
(June 28, 2016)
A single metric, when properly used, can be used to analyze salaries, trades, roster composition, draft strategy, etc. Though it should be noted that WAR, or any single number rating, is not a magic elixir since it can fail to pick up important differences in skill sets or role, particularly in hockey.
The development of an accurate single comprehensive metric to measure player impact will be an iterative process. However, it seems the framework exists to fuse human input and on-ice performance into something that can lend itself to more complex analysis
WAR PHILOSOPHY & OBJECTIVES
WAR model was set up with a fundamental philosophy – one extremely important to understanding what it measured: the model was intended to be as predictive as possible.
In the field of hockey statistics, the idea of a metric being repeatable or predictive is one that has become foundational. That is to say, metrics are often “validated” on their ability to do one or both. In our opinion, the main reason Corsi (shot attempts) caught on and became such a fundamental idea in hockey work was due to its ability to better predict team wins. Expected Goals used this concept as well
WAR – THE PROCESS
While a goal is scored (and with the RTSS data we have a lot information about each goal), evaluating how much credit a given player should receive for that goal is a much more difficult question.
In hockey, goal scoring is a much more complex system of teammates and opponents and goalies and strength states etc.
This is why we often use “on-ice” metrics to evaluate skaters. If a player scores a goal, it wasn’t just him that contributed to that goal, his teammates (and the defending skaters and the goalie) contributed to the goal as well among a host of other factors. We want to know how much all players are contributing to both offense and defense at all times, not just who actually scored.
The methodology we’re using is directly influenced by the techniques used in basketball for NBA analysis: create individual player ratings using RAPM for a given timeframe, use those values for a separate model that uses RTSS-derived metrics (goals, relative to teammate metrics, zone start percentages, etc.) to create single season values (which we call Statistical Plus Minus or SPM), and convert the SPM output(s) to the eventual WAR components.
RTSS pbp -> RAPM -> SPM -> GAA -> Team Adj -> GAR -> WAR
We’ve reached the end of our modeling processes! We’ve now laid out the “guts” of the RAPM and SPM models, which are the foundation for our WAR model. These together give us the basis for four of the five components of skater WAR (EV Offense, EV Defense, Powerplay Offense, Shorthanded Defense). The last remaining component is penalties – both drawn and taken.
WAR – REPLACEMENT LEVEL DECISIONS & FINAL REMARKS
It might be hard to understand why we use replacement level and not average as our baseline – the concept of “average” is very common and well understood by most. But the issue within evaluation here is that an “average” player is valuable; when we baseline our metric around an average player, we lose an ability to apply meaningful context to our evaluation. Replacement level, on the other hand, sets the baseline lower – the baseline now becomes the level at which a player can be determined to be “replaceable” i.e. easily substituted for another readily-available player.
Replacement level players: The line against which a player’s value should be measured is the replacement level. The replacement level is a very real, very tangible place for a baseball team or a baseball player; drop under it and they release you
We used the minimum contract method to determine replacement level. Briefly, we looked at the performance of all players who were paid league-minimum salaries over a given time-span (in our case this is the RTSS era, since 2007).
We determine a threshold where all players below that threshold are considered “replacement players”, and we then average all of those players’ performance to arrive at an aggregate replacement player.
To convert Goals in hockey to Wins, we followed the traditional “Pythagorean Expectation” method. Essentially, we need to find the exponent e in the equation:
Goals Per Win = (4 * League GF per Game) / e
None of the prior hockey WAR models have used Goals. At all. They’ve used some combination of shot attempts, expected goals, and shooting talent. But none have used actual Goals. Yet here we are using Goals For as the target for the RAPM models that make up our offensive components, using those RAPM models’ outputs (EVO/PPO) to create our SPM-component models, and calling that good. This is the biggest difference between our WAR model and those made for hockey in the past.
Shot attempts and xG models are generally more predictive of future scoring than goals are overall because they are more stable and occur at a much higher rate than goals do, among other reasons. But there’s a problem here – while shot attempts and xG are invaluable tools, they don’t measure how teams actually win games. In hockey, goals win games.
No acceptable method has been developed, by us or anyone else, to properly separate skaters from the goalies that play behind them and the actual goals that are scored while they are on the ice.
· Given the often stark differences between a given player’s GF and xGF results and our hope of keeping the model as closely tied to wins as possible, we’ve chosen to use the GF RAPM for the basis of our offensive components. This means a certain amount of luck will be included in the results, and the amount of luck included here will likely be hard to determine.
· We’ve chosen to use xGA for defense because it’s the best way we know how to separate skaters’ impacts on goals allowed from the goalies they play in front of. We feel this is an acceptable approach given the extremely difficult task of separating skaters from goalies and assigning “responsibility” to both using goals given the data we have. It’s important to remember that skaters have little to no control over whether a given shot will result in a goal against
WAR works best as an approximation. A 6 WAR player might be worth between 5.0 and 7.0 WAR, but it is pretty safe to say they are at least an All-Star level player and potentially an MVP.”
WAR – HIGH LEVEL OVERVIEW
(Dec 2020)
The model is built on six components:
· Isolated impact on even strength offense.
· Isolated impact on even strength defense.
· Isolated impact on power play offense.
· Isolated impact on penalty kill defense.Isolated impact on team penalty minutes taken and drawn.
· Isolated shooting and goaltending impact
Penalties are by far the least important component of this model, and over the course of the past three seasons, Samuel Girard is the only player whose net penalty impact has contributed at least one win to his team.
Over the course of these 3 seasons, among all skaters who played at least 200 combined minutes at even strength, on the power play, and shorthanded, exactly 0 wins above replacement is 37th percentile. In other words, my best estimate is that 37% of players with a decent sample size provided contributions below replacement level
Results
11% of the variance in team standings can be explained by some combination of the performance of players who switched teams and external factors like strength of schedule and luck, and the other 89% of that variance is explained by true team impact in that season.
WAR UPDATE
(June 2021)
These numbers bear out my general stance on public expected goal models: In the aggregate, they’re fair, and I would say they’re closer to good than bad. But on the power play in particular, they’re missing a lot of important context.
After testing and validating that my expected goal model is fair in every season, it came time to test my WAR model.
The R² value of 0.82 tells us that the model can explain 82% of the variance in standings points per 82 games. The rest can be explained by some combination of wins contributed by players who played for multiple teams, pure luck, and modeling error
In order to get an idea of how much value we really gain from using WAR, the next step is to compare it to hockey’s current most popular statistic: Points
I have to admit, I’m impressed by how well skater point totals hold their own here. They’re clearly inferior, but not by the massive margin that I’d expected. This evidence suggests that in the absence of a superior metric, there is absolutely nothing wrong with using points descriptively.
Similar to aggregate skater points, team standings points alone do a decent job of predicting future standings points, but they don’t stack up to WAR. If you want to determine who the best team is going to be in the following year and you have a good idea of how much everybody is going to play for each team, you’re a lot better off than you would be if you just had last year’s standings points.
Limitations
the model would place less emphasis on shooting and more on play-driving.
play-driving components are much more repeatable than shooting.
WAR – EMMANUEL PERRY
Four ways by which a player can influence the occurrence of goals:
· The rate of shots for or against a team
· The likelihood of a shot becoming a goal
· The rate of penalties taken for or against a team
· The game state or context of imminent play
However, revision led me to separate the second item into two distinct components: impact on shot quality and shooting
I propose a framework for WAR in hockey using the following distinct components:
· Shot Rates
o For
o Against
· Shot Quality
o For
o Against
· Shooting
· Goaltending
· Penalties
o For
o Against
· Zone Transitions
o Offensive
o Neutral
o Defensive
It is important to note that player impact should be independent of contextual factors that may influence results yet fall outside of the player’s control. Such elements in hockey are: zone starts, game state and score effects
The starting assumption might be: the probability of scoring on a shot is a function of the shooter and the goaltender. The coefficient associated with a given player acting as shooter would then give the player’s partial impact on shooting percentage, independent from the role of goaltenders.
NAIVE WAR
This is the the simplest I can make WAR for the NHL. In other words, Naïve WAR.
For this iteration, we start with the absolute core: goals, assists, time on ice, and saves.
I’ll work through the Edmonton Oilers. The Oilers are 36-32, meaning .529 win% on 68 games. We are going to allocate 60% of the games to the forwards (40.8), 30% to the defensemen (20.4), and 10% to the goalies (6.8). Roster sizes are 12 F, 6 D, 2 G (aka, 60/30/10 split).
The forwards total 12,215 minutes played. Since they have 40.8 games, that means each 299 minutes converts to 1 game.
Draisaitl has 1538 minutes, which we divided by 299, to give us 5.1 games. We do that for all the forwards. For defensemen, the conversion is 389 minutes per game. Darnell Nurse has 4.1 games.
For goalies, it’s 602 minutes per game. Mike Smith gets 3.5 games and Mikko Koskinen gets 3.3 games.
Ok, now we’ve established the game shares of each player. The total adds up to 68 games. Since the Oilers won .529 per game, we multiply that to establish the base for each player. Draisaitl base is 2.7 W and 2.4 L. What this base represents is what an average Oilers player would have, given that number of games.
Draisaitl is not average. So, we need to figure out how much above average he is. In this NAÏVE WAR, we can only work with G and A.
The Oilers have 215 goals and 366 assists. If we multiply the assists by 0.5874, we get 215. In other words, our metric will give half the value to goals and half the value to assists. Draisaitl has 43 goals and 39 adjusted assists for a total of 82 goal… something… 82 goal contributions? Whatever. It’s 82.
The average Oilers forward has 35 minutes on ice per goal contribution. Which means that Draisaitl is 38 goal contributions above average. The goal to win conversion is to divide by 6, so we have +6.4 Wins Above Average Oilers. (Again, using only G and A, and not adjusting for PP. We start somewhere and we start here. That’s why it’s NAÏVE WAR.)
Since Draisaitl has a base of 2.7-2.4, we add 6.4 wins and subtract 6.4 losses. That gives Draisaitl 9.1 wins and NEGATIVE 3.9 losses. Because the “-” is already used for the “positive” losses, we will follow the lead from Bill James, flip the sign to “+” for “negative” losses. And so Draisaitl has a 9.1 + 3.9 record.
The two goalies gives up .091 goals per shot faced. Multiply that by each of their shots faced for their baseline. For Mike Smith, that’s 97 goals allowed, compared to the 103 he gave up. So, he’s -6. Mikko is +6.
We convert to wins as noted above, and so, they are -1, and +1 respectively. Which we add to their baselines.
Comments