A Closer Look At Plus-Minus

The object of a hockey game is simple. Score more goals than your opponent. I know earth shattering, right? Anyways, if your team manages to score more goals than it has scored against it, it hopefully will have a chance to compete for Lord Stanley’s Cup in the playoffs. I say hopefully because the teams that outscore the most over the course of a season don’t always end up making the playoffs based on which division they play in, blowouts inflating differentials, or other chance factors. Below in the chart you can see the results from 2006-2012 with each dot representing a team’s goal differential vs. how many points it collected over 82 games. As seen by the high R2 value of 0.87 (on a 0 to 1 scale) this data set has a high predictive value for future outcomes.



Knowing that, the obvious goal for a GM of a team should be to make moves to maximize its goal differential (+/-). How do you do that? There is a lot of great work being done on various blogs on advanced stats such as Corsi, Fenwick and Scoring Chance counting. Counting scoring chances is probably the best of the bunch, but no doubt an onerous task and somewhat subjective based on the counter. Corsi and Fenwick are variations on shot differential factoring in blocks and/or misses. They tell you something about puck and territory possession but don’t necessarily correlate well with +/-. In fact, they are basically in line with Shots differential in terms of explaining +/- as all of them have R2 values in the range of 0.18-0.20. Team shooting % when a player is on the ice does a far better job of explaining +/- than those metrics and so does team save % when the player is on the ice (R2 values of 0.44 and 0.26 respectively).



Since none of these stats alone does a great job of determining +/-, why not use some basic math and put them all together to create something that does explain +/-?

Goal Differential = GF – GA = Shots For * Shooting % - Shots Against * (1 – Save %)

So broken down, you want players who take more shots, score on more of those shots, allow fewer shots and stop more of those shots from going in…or at least maximize the combination. This should be obvious but using this method correlates 100% with +/-. Now the goal is to accurately predict each of these stats for each player, and where better to look than the past. From 2007-2012 the average player who played at least 10 games in a season had an On-Ice SH% of 7.7% and an On-ice SV% of 91.7%. I made no effort to weight these values by time on ice which should explain the values not adding to 100% as would be expected. Looking now at individual players over that time span you would see there is some variability in these percentages, but it is not all over the map. A guy who typically scores over the average often does so in all 5 seasons looked at. Applying an 80% confidence interval shows the average player to vary from his own average by + or – 1.8%/1.7% in SH% and SV% respectively.

Sidney Crosby leads the pack in On-Ice SH% with an average 12.5% over the span. Other top offensive stars include Gaborik (11.4%), Stamkos (11.0%) and Tanguay (11.0%). Beware though, a guy like Kurtis Foster scores a 10.1% buoyed by an 18.8% in 2008/09. Without that season his average drops to 8.0% and he appears to be on the decline with his last two seasons at 7.1 and 6.7%. I would definitely consider consistency and trends very heavily in this analysis.

How about in the d-zone? Something interesting happens here; goons score disproportionately well? My guess is this has to do with coaches typically only using goons against goons. Since they typically have no actual hockey skill, their shots are less likely to go in, thus increasing the perceived goon defensive ability.  I will call this the George Parros rule as he sports a huge 96.1% On-ice SV%. Wade Belak also manages a high rate at 94.7%. Looking at non-goons, UFA  Kent Huskins is a guy you don’t hear much about who sports a 94.4%, Mikkel Boedker has a high 94.5% supported by a couple of high seasons in which he played less than half the games.  Impending UFA Jason Garrison has been remarkably consistent with seasons of 93.5%, 93.7% and 93.6%. Other names of interest include Brad Marchand at 93.6% and Manny Malhotra at 93.0%. Lidstrom and Pronger come in at 92.3%.

I am not going to over analyze the shooting stats as the top guys would probably be discussed often enough in discussions on Corsi. Rolling it all up though here are some of the top players in the league who have played in at least 3 qualifying seasons.


The most valuable players in terms of Expected +-/60 mins then include Crosby (+1.56), Datsyuk (+1.43), the Sedins (+1.31/1.18) and Ovechkin (+1.11). Ben Lovejoy and Keith Aucoin at the top of the list could be a good sign for them, but I caution once again that consistency is key, and note these numbers can be skewed by small sample size seasons.

You will note that I also included columns called “Adj. +-” in the table. It is a known fact that the Sedin’s start a lot in the offensive end (62%/65%) at the expense of the Malhotra’s of the world (34%). Also some players have the fortune of playing for a Detroit or Vancouver instead of a Columbus or Edmonton. Who do you think would have a higher On-ice SV% a guy playing in front of Khabibulin or Luongo? In order to make these adjustments I normalized each player’s team’s SH% and SV% that season to the average and adjusted his On-Ice %’s accordingly. I also graphed Offensive Zone Start vs. +-/60 and adjusted based on the trend line equation. Finally I felt that a guy who takes more penalties than he draws is not really helping his team so I factored that in using the league average 17.3% power play success rate. I was going to adjust for Corsi Realative Quality of Competition, but found it held almost no correlation and showed playing against better players increases players expected +-/60. This did not make logical sense; maybe that just means the best players play mostly against each other but I threw it out none-the-less. I won’t get into the details any further but show below how this changes the top 50 players from above.


Datsyuk and Crosby continue to lead. Perron and Thornton and half of Detroit jump up in the rankings. Parise shows why he is the top UFA this season at +0.99, while Suter doesn’t show as great at only +0.04. I’ve read Guillaume Latendresse may not receive a RFA qualifying offer from Minnesota due to injury concerns. He scores a +0.91 Adj. +-, but his last two injury shortened seasons inflate that number. Small sample sizes, or had a guy who has been battling tough zone starts his whole career started to put things together in his 5th/6th NHL seasons on his way to becoming a dominating power forward? At only 25 years old, 6’2”/230lbs this former 27 goal scorer who averages 2 hits per game could make some GM look very smart for taking that gamble.

*All data used is Even Strength 5 vs.5 courtesy of behindthenet.ca

**The attached excel file provides a look at all players qualifying seasons (min 10 games) from 2007-2012. Sorry the full table is way to big to fit nicely on the page.

07-12 Players Data.xls737.5 KB