CORRELATION BETWEEN TEAM POINTS, CORSI
(July 2009)
I have been looking at the Corsi Number as an alternative to +/- ratings. Its appeal is that it includes a lot more events than +/- (as it is the difference between shots directed at the goal for and against when a player is on the ice in 5 on 5 situations). The drawback is that it includes missed shots and blocked shots as being equivalent to goals. Any systematic reason why a player or team might take or allow an excessive number of shots that miss that net (or some other anomaly like that) would skew the ratings.
Some teams have Corsi Numbers that do not correlate well with their regular season success. For the most part this can be explained: Corsi is only calculated in 5 on 5 situations, while +/- is calculated to include even strength and short handed goals. Power play success shows up in neither +/- nor Corsi.
In general teams with good +/- ratings also have good Corsi Numbers and vice versa.
Corsi Numbers vary from +/- largely for three reasons. The inclusion of shorthanded goals in +/- can change things significantly in a few cases. Teams with goaltending that is worse than or better than average will see different results in their shots allowed and goals allowed and similarly teams with better than or worse than average shooting percentages will see the same results, but in reverse.
The idea behind looking at +/- ratings and Corsi Numbers comes from an attempt to follow baseball sabermetrics. It is well known in baseball that runs scored and allowed is a better predictor of future success than win loss records. Similarly, it is true that goals scored and allowed (which is essentially the idea of +/-) better predict future success than win loss records.
Corsi is a first attempt to find a sub-element of goals scored. It isn’t successful in being a better predictor of success than +/-, but it may be a step in the right direction.
Hockey makes the distinctions between special teams and even strength play in these numbers (where baseball has nothing similar) to try to compare between teams and players in similar situations. If we are looking at trying to predict the future success of teams, these distinctions are not so important, but for now they remain in my data. We can look at how team Corsi and +/- ratings correlate with the point totals that teams get.
Team +/- ratings have a very strong correlation with points of 0.880. Team Corsi Numbers have a strong (but lower) correlation of 0.626. A significant part of the better correlation from +/- comes from the fact that it includes shorthanded goals and Corsi does not. What is interesting is that both Corsi and +/- ratings correlate better with points than they do with EACH other. This shows that they are somewhat complimentary measures of team success. It is usually true that if a team has a high Corsi and low +/- (or vice versa) the results of the team are somewhere in the middle of both.
Corsi Numbers are useful to show team success. They do not do as good a job as +/- ratings, but they offer some complimentary information that +/- does not. This shows a significant value in studying Corsi Numbers.
DOMINATING TERRITORY & GAMES WON
(Aug 2009)
One widely-held notion on the Oilogosphere is that a team that has more shots at net than the opposition is also very likely dominating the game territorially. This notion is almost certainly true. How many shots at net come from the defensive end of the ice? Not many.
But does that dominance, that positive Corsi plus/minus number, also lead to victory?
Essentially, Ballentine finds that good Corsi numbers have some relationship to winning hockey games, but it’s no slam dunk
It makes sense that the teams that dominate territorially tend to be winning teams. But territorial dominance isn’t a stranglehold on winning, certainly not in one game, nor in a short playoff series, and not even over the length of an entire season, not for all NHL teams.
More than half of all goals come because of some mistake in the offensive or neutral zones of the rink, where a giveaway or a missed check will lead to a deadly rush up ice, even an uneven man rush up ice, and a goal will result. That adds up to only one shot at net, only one plus mark in the Corsi plus/minus file, but it adds up to one big goal against on the scoreboard.
A team that gives up more than its share of these types of rushes and goals will tend to lose, even if it otherwise holds its own when it comes to territorial play.
On an individual level, a player gets a minus or a plus Corsi number when a shot on net occurs, but that player is just one of ten position players on the ice, and he may have had little or no impact on the play. Some players, saddled with weak linemates, might well have a bad Corsi plus/minus through little fault of their own.
Corsi numbers have use, which is why I often refer to them in my ratings of players, but that value is somewhat uncertain and it might well be wise not to attach too much weight to the Corsi plus/minus of any individual player
Simply put, Corsi plus/minus is one useful factor to consider about a player, but it’s not definitive. It is best used as possible indicator, as opposed to the last word, on any given player.
SHOTS, FENWICK, CORSI
There doesn’t appear to be a general agreement as to which of shot, fenwick and corsi percentage serves as the best metric to use once score effects have been controlled for.
This raises the question: which of the three measures ought to be looked to for the purpose of team evaluation?
There is a stronger relationship between fenwick and winning percentage than there is between corsi and winning or between shot differential and winning.
In fact, the correlation between corsi and winning percentage was about the same as the correlation between shot differential and winning percentage, even though including blocked shots substantially increased the sample size.
The upshot is that the inclusion of blocked shots in the analysis doesn’t add much information.
However, the weaker relationship between corsi and winning can be partially accounted for by score effects. In particular, the trailing team does better in terms of corsi than it does with respect to either shot percentage or fenwick.
On the other hand, corsi is more reliable than either fenwick or shot ratio at the half-season level, which is a product of the fact that there are simply more corsi events then fenwick or shot events in our sample. Thus, corsi should prima facie be considered the superior metric of the three due to its superior reliability.
In other words, a team’s score tied corsi over a 40 game sample is a better indicator of how it will perform over the remainder of its schedule than is score tied fenwick or score tied shot percentage.
PREDICTIVE VALIDITY OF CORSI
Corsi Tied is the best predictor of how a team will perform over the remainder of its schedule, regardless of the point in the schedule at which the calculation occurs.
Corsi Tied is only marginally more predictive of future success than goal ratio or winning percentage when looking at samples of 60 games or more. In other words, as the sample size becomes increasingly large, there are diminishing returns with respect to the predictive advantage of Corsi. By the end of the season, all three variables seem to predict future success equally well.
The above fact has implications in terms of determining playoff probabilities at the team level, with the results suggesting that a composite metric would work best.
Corsi Tied is a much better predictor early in the schedule, but the two measures have about the same predictive power by the end of the year.
IS FENWICK CLOSE A SIGNIFICANT PREDICTOR OF WINNING
shot differential (which correlates strongly with Fenwick Close) was only predictive of 54.7% of game results.
To put this in perspective, you’re more likely to pick the winner of a game correctly by simply choosing the home team than you are by choosing the team with the better shot differential entering the game.
I calculated single-game Fenwick Close, even-strength shooting and save percentages, and PDO for each team in every game. In order to explore the consistency and predictive utility of each of these measures, I also calculated 1-game, 3-game, 5-game, 10-game, and 20-game “lagged” values prior to each game in the dataset.
The autocorrelation of Fenwick Close is much stronger than that of shooting and save percentages. Not only is single-game Fenwick Close more consistent than single-game Sh% or Sv%, it has a stronger autocorrelation than 3-game and 5-game moving averages of these variables, in which some of the noise has presumably filtered out. A 20-game moving average of puck possession has an autocorrelation of 0.77, while a similar average for Sh% has an autocorrelation of just 0.41, and a 20-game Sv% has a 0.52 autocorrelation. So, if you need more evidence that puck possession is a much more consistent and repeatable measure of team performance than shooting or goaltending, there you go.
But what about the relationship beween these variables and winning?
A few points to note here:
· When the number of observations in your data gets into the hundreds, it’s wise to be somewhat skeptical of statistical significance. Any effect can appear significant if you have enough power to throw at the model. For example, while it’s interesting that the prior game’s PDO is a significant predictor of win probability, the tiny effect size makes this a tough result to interpret.
· When looking at the large odds ratios that are frequently associated with Fenwick Close, Sh%, and Sv%, keep in mind that these variables only take values between 0 and 1. As such, the effect might not be as dramatic as it looks. For example, the odds ratio for the 5-game lagged Fenwick Close should be interpreted as follows: a team with a 5-game Fenwick Close of 100% is 17.47 times more likely to win than a team with a Fenwick Close of 0%.
· PDO may be useful as shorthand when discussing luck in team performance, but these results suggest that its use can obscure the predictive value of its component parts.
· The consistency of Fenwick Close may actually work against its utility as a predictor of winning. That is, the autocorrelation results suggest that a team’s Fenwick Close converges to a steady-state value fairly quickly, which implies that it doesn’t vary much from game to game. Unfortunately, in a regression-based analysis, a measure that doesn’t vary much isn’t going to be able to explain variation in the outcome of interest.
· On the other hand, Sh% and Sv% are much less consistent variables, yet their greater variability doesn’t translate to a stronger correlation with win probability. This suggests a weaker underlying connection to wins.
Using statistics to predict single-game outcomes is very, very challenging. It’s likely the case that stronger possession play leads to a marginal increase in win probability, and over the course of a long season, this increase translates into additional wins and points. The same, of course, can be said of goaltending and team shooting, but these are less reliable from game to game than controlling the puck. But when it comes to single games, or small numbers of games (i.e., playoff series), no variable, even Fenwick Close, is as predictive as you might expect.
WHAT WE CAN PREDICT AND WHAT WE CANT PREDICT
For one thing, puck possession is correlated with winning, but it’s not a necessary or sufficient condition for it. That is, it’s a correlate of winning, but not a determining cause; regularly controlling a greater share of shots helps to push the math of Goals-For and Goals-Against in a team’s favor, but it doesn’t necessarily translate into a favorable goal differential or standings points. As a feature of teams’ games that’s at least somewhat within their control, possession is more consistently associated with future win probabilities than PDO, but Sh% and Sv% are much stronger explanatory factors in past results than Fenwick numbers. What this suggests is that the random chance, player talent, and other factors underlying goal-scoring are a critical piece of the causality behind hockey outcomes.
This brings us to an important feature of statistical regression: regression is an empirical regularity, but it doesn’t necessarily occur within a specific time frame. When you predict the collapse of a team like the 2013-14 Leafs or the 2011-12 Minnesota Wild, you’re taking a risk when it comes to the timing.
There are always going to be teams for whom the offsetting bad luck never materializes over 82 games.
The question of timing is especially pertinent when it comes to understanding playoff series. As an empirical regularity, teams with strong possession numbers tend to do well in the NHL postseason, but it doesn’t follow that strong puck control causes the playoff success. There’s no evidence that possession differential is a consistent predictor of victories in single games, and for every strong possession team that’s gone on to Stanley Cup glory (e.g., the 2007-08 Red Wings, the 2009-10 Blackhawks), there are teams like the 2011-12 Red Wings, the 2011-12 Penguins, and the 2008-09 Sharks, who failed to advance past the first round despite superlative possession numbers
The reason playoff series are so difficult to predict is that fluctuations in luck can happen at any moment, and the team that experiences the fewest dry spells in April, May and June is the one that ends up hoisting the big trophy.
Whether because of match-ups or low PDO, many, many teams playing strong possession hockey don’t end up winning in the playoffs. For better or worse, what separates the winners from the also-rans is simple puck luck, not possession.
SCORE ADJSTED CORSI IS BEST PREDICTOR OF WINS
Time and again, we’ve been over how the best indicator of future success in the standings is some form of Corsi percentage. First it was score-tied, and thanks to a further application of something we knew five years ago, now it’s score-adjusted. While Corsi, or anything else we have does not measure Matt Cullen’s will to win a race, Tom Wilson’s ability to fire up his teammates, or the fact that Ryan Callahan’s grandmother is in the stands, it does measure, and until somebody comes up with something better, is the best measure of what Pierre’s intangibles hope to achieve.
This isn’t to say that what Pierre lists as intangibles aren’t important, or that a good character guy in the room isn’t necessary. The trick is to identify players that possess these traits, and at the same time, drive shot attempts towards the opposing team’s net. You can harp on intangibles all you want, but if the result is utilizing a player like Tanner Glass or Zac Rinaldo for an extended period of time, your process is broken, plain and simple.
Hockey may be the hardest sport to predict on a game-by-game basis. Whether you look at basic models or betting markets, one trend is blatantly obvious: in hockey, even controlling for everything we know, a vast majority of the matchups have odds between 55/45 and 65/35 either way. 3:1 favorites in a single game don’t happen often, which is why in small samples, we see extreme results.
When you start to ask why, it becomes less and less surprising; hockey is a game of razor thin margins anywhere you look.
Still, despite the studies identifying score-adjusted metrics as the best predictor of future team success, fans, analysts, and even teams (see: Ducks, Anaheim) still can’t rationalize the inherent randomness of losing as a 60% favorite in one game or one series.
At the end of the day, the fact that mainstream hockey circles can’t comprehend that 35-45% underdogs can win games and series, but don’t over the long run, doesn’t prove the metrics we have are broken. Instead, it proves that their understanding, and by association the overall understanding of the game, is broken.
25 GAMES IN WHAT DOES CORSI SAY
There’s plenty of more advanced ways to better predict how the rest of the season will go, but Corsi offers a simple baseline in a way that helps explain why it is so important.
The data tells us that the optimal time to make these predictions is 20-25 games into the season. Do it earlier and the sample size would be too small for optimal results. Do it any later and there are too few games left to predict.
PERFORMANCE ON DEC 1ST AND MAKING PLAYOFFS
https://hockey-graphs.com/2016/12/02/how-does-performance-as-of-dec-1-relate-to-making-the-playoffs/
How do early-season shot-based metrics relate to whether a team ultimately makes the playoffs?
“Expected goals” are even better at predicting future performance than shot attempts or goals. Expected goals take into account not only the quantity of shots taken but also the quality of the opportunity based on a variety of factors, including location, shot type, etc.
So instead of simply looking at shot attempts (Corsi), lets look at both of these metrics together and see if there is a relationship to post-season action, and even to post season success.
When plotted, you can see that there is fairly pronounced linear relationship between shot attempts and expected goals. The r² for this relationship is 0.70 over a full season, which indicates that shot attempts predict about 70% of the value in expected goals. This is to be expected since shot attempts go into the calculation for expected goals.
After just 20-25 games, the playoff teams mostly separate themselves from the pack.
Of the 107 teams above 50% in both shot attempts and expected goals on Dec. 1, 81 (or 76%) go on to make the playoffs. Conversely, only a third of teams below 50% in both metrics wind up playing in the post-season.
It appears that the early-season shot attempts ratio is a stronger indicator of whether a team will make the playoffs than expected goals ratio.
That being said, one of the original intentions of this analysis was to determine whether looking at expected goals in addition to shot attempts would improve our ability to determine which teams might make the playoffs.
Early on, at least, it does not appear that expected goals add much to the analysis.
If we were looking at each metric independently, we can see that with a full season of data, expected goals becomes a marginally a better indicator of whether a team will make the playoffs.
And when we combine the two metrics, we can see that success rate increases to 82%. So with a full season of data, the combination of metrics is incrementally better.
Teams that go far in the playoffs typically excel on both scales, but 32 of 36 (or 89%) conference finalists have finished the season with an expected goals ratio above 50%.
Over the last nine NHL seasons, the first 20-25 games of shot attempt data has been a relatively good indicator of whether teams go on to make the playoffs. The addition of expected goals does not significantly improve the our ability to predict playoff teams early on.
However, by the end of the regular season, the strength of expected goals as an indicator builds and even surpasses that of shot attempts. This would appear to indicate that the expected goals metric needs more than 20-25 games before it fully stabilizes.
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