Feb 272013

The last several days I have been playing around a fair bit with team data and analyzing various metrics for their usefulness in predicting future outcomes and I have come across some interesting observations. Specifically, with more years of data, fenwick becomes significantly less important/valuable while goals and the percentages become more important/valuable. Let me explain.

Let’s first look at the year over year correlations in the various stats themselves.

Y1 vs Y2 Y12 vs Y34 Y123 vs Y45
FF% 0.3334 0.2447 0.1937
FF60 0.2414 0.1635 0.0976
FA60 0.3714 0.2743 0.3224
GF% 0.1891 0.2494 0.3514
GF60 0.0409 0.1468 0.1854
GA60 0.1953 0.3669 0.4476
Sh% 0.0002 0.0117 0.0047
Sv% 0.1278 0.2954 0.3350
PDO 0.0551 0.0564 0.1127
RegPts 0.2664 0.3890 0.3744

The above table shows the r^2 between past events and future events.  The Y1 vs Y2 column is the r^2 between subsequent years (i.e. 0708 vs 0809, 0809 vs 0910, 0910 vs 1011, 1011 vs 1112).  The Y12 vs Y23 is a 2 year vs 2 year r^2 (i.e. 07-09 vs 09-11 and 08-10 vs 10-12) and the Y123 vs Y45 is the 3 year vs 2 year comparison (i.e. 07-10 vs 10-12). RegPts is points earned during regulation play (using win-loss-tie point system).

As you can see, with increased sample size, the fenwick stats abilitity to predict future fenwick stats diminishes, particularly for fenwick for and fenwick %. All the other stats generally get better with increased sample size, except for shooting percentage which has no predictive power of future shooting percentage.

The increased predictive nature of the goal and percentage stats with increased sample size makes perfect sense as the increased sample size will decrease the random variability of these stats but I have no definitive explanation as to why the fenwick stats can’t maintain their predictive ability with increased sample sizes.

Let’s take a look at how well each statistic correlates with regulation points using various sample sizes.

1 year 2 year 3 year 4 year 5 year
FF% 0.3030 0.4360 0.5383 0.5541 0.5461
GF% 0.7022 0.7919 0.8354 0.8525 0.8685
Sh% 0.0672 0.0662 0.0477 0.0435 0.0529
Sv% 0.2179 0.2482 0.2515 0.2958 0.3221
PDO 0.2956 0.2913 0.2948 0.3393 0.3937
GF60 0.2505 0.3411 0.3404 0.3302 0.3226
GA60 0.4575 0.5831 0.6418 0.6721 0.6794
FF60 0.1954 0.3058 0.3655 0.4026 0.3951
FA60 0.1788 0.2638 0.3531 0.3480 0.3357

Again, the values are r^2 with regulation points.  Nothing too surprising there except maybe that team shooting percentage is so poorly correlated with winning because at the individual level it is clear that shooting percentages are highly correlated with goal scoring. It seems apparent from the table above that team save percentage is a significant factor in winning (or as my fellow Leaf fans can attest to, lack of save percentage is a significant factor in losing).

The final table I want to look at is how well a few of the stats are at predicting future regulation time point totals.

Y1 vs Y2 Y12 vs Y34 Y123 vs Y45
FF% 0.2500 0.2257 0.1622
GF% 0.2214 0.3187 0.3429
PDO 0.0256 0.0534 0.1212
RegPts 0.2664 0.3890 0.3744

The values are r^2 with future regulation point totals. Regardless of time frame used, past regulation time point totals are the best predictor of future regulation time point totals. Single season FF% is slightly better at predicting following season regulation point totals but with 2 or more years of data GF% becomes a significantly better predictor as the predictive ability of GF% improves and FF% declines. This makes sense as we earlier observed that increasing sample size improves GF% predictability of future GF% while FF% gets worse and that GF% is more highly correlated with regulation point totals than FF%.

One thing that is clear from the above tables is that defense has been far more important to winning than offense. Regardless of whether we look at GF60, FF60, or Sh% their level of importance trails their defensive counterpart (GA60, FA60 and Sv%), usually significantly. The defensive stats more highly correlate with winning and are more consistent from year to year. Defense and goaltending wins in the NHL.

What is interesting though is that this largely differs from what we see at the individual level. At the individual level there is much more variation in the offensive stats indicating individual players have more control over the offensive side of the game. This might suggest that team philosophies drive the defensive side of the game (i.e. how defensive minded the team is, the playing style, etc.) but the offensive side of the game is dominated more by the offensive skill level of the individual players. At the very least it is something worth of further investigation.

The last takeaway from this analysis is the declining predictive value of fenwick/corsi with increased sample size. I am not quite sure what to make of this. If anyone has any theories I’d be interested in hearing them. One theory I have is that fenwick rates are not a part of the average GMs player personal decisions and thus over time as players come and go any fenwick rates will begin to vary. If this is the case, then this may represent an area of value that a GM could exploit.


Feb 212013

Over the past few years I have had a few discussions with other Leaf fans about the relative merits of Francois Beauchemin. Many Leaf fans argue that he was a good 2-way defenseman who can play tough minutes and is the kind of defenseman the Leafs are still in need of. I on the other hand have never had quite as optimistic view of Beauchemin and I don’t think he would make this team any better.

On some level I think a part of the difference in opinion is that many look at his corsi numbers which aren’t too bad but I prefer to look at his goal numbers which have generally not been so good. So, let’s take a look at Beauchemin’s WOWY numbers and see if there is in fact a divergence between Beauchemin’s corsi WOWY numbers and his goal WOWY numbers starting with 2009-11 5v5 WOWY starting with CF% WOWY.


I have included a diagonal line which is kind of a ‘neutral’ line where players perform equally well with and without Beauchemin. Anything to the right/below the line indicates the player played better with Beauchemin than without and anything to the left/above they played worse with Beauchemin. As you can see, the majority of players had a better CF% with Beauchemin than without. Now, let’s take a look at GF% WOWY.


While a handful of players had better GF% with Beauchemin, the majority were a little worse off. There is a clear difference between Beauchemin’s CF% WOWY and his GF% WOWY. What is interesting is this difference can be observed in 2007-08, 2009-10, 2010-11, and 2011-12 (he was injured for much of 2008-09 so his WOWY data is not reliable due to smaller sample size). Looking at his 5-year WOWY charts you get a clear picture that Beauchemin seemingly has a skill for ‘driving play’ but not ‘driving goals’. Let’s dig a little further to see if we can determine what his ‘problem’ by looking at his 2009-11 two year CF20, GF20, CA20 and GA20 WOWY’s.





As you can clearly see, Beauchemin appears to be much better at generating shots and shot attempts than he is at generating goals. The majority of players have a higher corsi for rate when with Beauchemin than when not with Beauchemin but the majority also have a lower goals for rate. What about ‘against’ rates?





For CA20 and GA20 is is better to be to be above/left of the diagional line because unlike GF%/CF%/GF20/CF20 it is better to have a smaller number than a larger number. There doesn’t seem to be quite as much of a difference between CA20 and GA20 as with CF20 and GF20 so the difference between CF% and GF% is driven by the inability to convert shots and shot attempts into goals as opposed to the defensive side of the game. That said, there is no clear evidence that Beauchemin makes his teammates any better defensively.

There are two points I wanted to make with this post.

  1. Leaf fans probably shouldn’t be missing Beauchemin.
  2. For a lot of players a corsi evaluation of that player will give you a reasonable evaluation of that player but there are also many players where a corsi evaluation of that player will not tell the complete story. Some players can consistently see a divergence between their goal stats and their corsi stats and it is important to take that into consideration.


Using goalies to estimate zone start impact on corsi

 Uncategorized  Comments Off on Using goalies to estimate zone start impact on corsi
Nov 082012

Eric T. over at NHL Numbers had a post last week summarizing the current state of our statistical knowledge with respect to accounting for zone start differences.  If you haven’t read it definitely go read it because it is not only a good read but because it concludes that how the majority of people have been doing is is wrong.

Overall, no two estimates are in direct agreement, but the analyses that are known to derive from looking directly at the outcomes immediately following a faceoff converge in the range of 0.25 to 0.4 Corsi shots per faceoff — one-third to one-half of the figure in widespread use. It is very likely that we have been overestimating the importance of faceoffs; they still represent a significant correction on shot differential, but perhaps not as large as has been previously assumed.

In the article Eric refers to my observation that eliminating the 10 seconds after a zone start effectively removes any effect that the zone start had on the game.  From there he combined my zone start adjusted data found at stats.hockeyanalysis.com with zone start data from behindthenet.ca and came up with an estimate that a zone start is worth 0.35 corsi.  He did this by subtracting the 10 second zone start adjusted corsi from standard 5v5 corsi and then running a regression against the extra offensive zone starts the player had.  In the comments I discussed some further analysis I did on this using my own data (i.e. not the stuff on behindthenet.ca) and came up with similar, though slightly different, numbers.  In any event I figured the content of that comment was worthy of its own post here.

So, when I did the correlation between extra offensive zone starts and difference between 5v5 and 5v5 10 second zone start adjusted corsi I got the following (using all players with >1000 minutes of ice time over last 5 seasons):

My calculations come up with a slope of 0.3043 which is a little below that of Eric’s calculations but since I don’t know the exact methodology he used that might explain the difference (i.e. not sure if Eric used complete 5 years of data, or individual seasons).

What is interesting is that when I explored things further, I noticed that the results varied across positions, but varied very little across talent levels.  Here are some more correlations for different positions and ice time restrictions.

Position Slope r^2
All Players >1000 min. 0.30 0.55
Skaters >1000 min. 0.28 0.52
Forwards >1000 min. 0.26 0.50
Defensemen >1000 min. 0.33 0.57
Goalies >1000 min. 0.44 0.73
Forwards >500 min. 0.26 0.50
Forwards >2500 min. 0.26 0.52
Forwards 500-2500 min. 0.26 0.39

Two observations:

1.  The slope for forwards is less than the slope for defensemen which is (quite a bit) less than the slope for goalies.

2.  There is no variation in slope no matter what restrictions we put on a forwards ice time.

There isn’t really much to say regarding the second observation except that it is nice to see consistency but the first observation is quite interesting.  Goalies, who have no impact on corsi, see the greatest zone start influences on corsi of any position.  It is a little odd but I think it addresses one of the concerns that Eric had pointed out in his article:

The next step would be to remove the last vestige of sampling bias from our analysis. The approaches that focus on the period immediately after the faceoff reduce the impact of teams’ tendency to use their best forwards in the offensive zone, but certainly do not remove it altogether.

I think that is exactly what we are witnessing here, but maybe more importantly teams put out their best defensive players and, maybe more importantly, their best face off guys for defensive zone face offs. If David Steckel, who is an excellent face off guy, is getting all the defensive zone face offs, it is naturally going to suppress the corsi events immediately after the defensive zone face off because he is going to win the draw more often than not.  There is probably more line matching done for the zone face offs than during regular play so the line matching suppresses some of the zone start impact.  It is more difficult to line match when changing lines on the fly so a good coach can more easily get favourable line matches. The result is normal 5v5 play offensive players might see a boost to their corsi (because they can exploit good matchups) and during offensive zone face offs they see their corsi suppressed because they will almost always be facing good defensive players and top face off guys.  Thus, the boost to corsi based on a zone start is not as extreme as should be for offensive players.  The opposite is true for defensive players.

Defensemen are less often line matched so we see their corsi boost due to an offensive zone face off a little higher than that of forwards, but it isn’t near as high as goalies because there are defensemen that are primarily used in offensive situations and others that are primarily used in defensive situations.

Goalies though, tell us the real effect because they are always on the ice and they are not subject to any line matching.  In the table above you will notice that goalies have a significantly higher slope and an impressively high r^2.  I feel I have to post the chart of the correlation because it really is a nice chart to look at.

I have looked at a lot of correlations and charts in hockey stats but very few of them are as nice with as high a correlation as the chart above.

I believe that this is telling us that an offensive zone start is worth 0.44 corsi, but only when a player is playing against similarly defensively capable players as he would during regular 5v5 play which I speculate above is not necessarily (or likely) the case.  The 0.44 adjustment really only applies to an idealistic situation that doesn’t normally occur for any players other than goalies.  So where does that leave us?  Should we use a zone start adjustment of 0.44 corsi for all players, or should we use something like 0.33 for defensemen and 0.26 for forwards?  The answer isn’t so simple.  One could argue that we should apply 0.44 to all players and then make some sort of QoC adjustment and that would make some sense.  But if we are not intending to apply a QoC adjustment, does that mean we should use 0.33 and 0.26?  Maybe, but that is a little inconsistent because it would mean you are using a QoC adjustment only for the zone start adjustment of a players stats, and not for all his stats.  The answer for me is what I have been doing the past little while and not even attempt to adjust a players stats based on zone starts differences and rather simply just ignore the the portion of play that is subject to being influenced by zone starts – the 10 seconds after a zone start face off.  To me it seems like the simplest and easiest thing to do.


Jun 262012

I have had a lot of battles with the pro-corsi crowd with regards to the merits of using Corsi as a player evaluation tool.  I still get people dismissing my goal based analysis (which seems really strange since goals are what matters in hockey) so I figured I should summarize my position in one easy to understand post.  So, with that, here are 10 significant reasons why I don’t like to use a corsi based player analysis.

1.  Look at the list of players with the top on-ice shooting percentage over the past 5 seasons and compare it to the list of players with the top corsi for per 20 minutes of ice time and you’ll find that the shooting percentage list is far more representative of top offensive players than the top corsi for list.

2.  Shooting percentage is a talent and is sustainable and three year shooting percentage is as good a predictor of the following 2 seasons goal scoring rates as 3 year fenwick rates and 3 year goal rates are a far better predictor.

2007-10 FF20 vs 2010-12 GF20 0.253
2007-10 SH% vs 2010-12 GF20 0.244
2007-10 GF20 vs 2010-12 GF20 0.363

3.  I have even shown that one year GF20 is on average as good a predictor of  the following seasons GF20 as FF20 is as a predictor of the following seasons FF20 so with even just one full season of data goal rates are as good a metric of offensive talent as fenwick rate is.  Only when the sample size is less than one season (and for almost all NHL regulars we have at least a seasons worth of data) is fenwick rate a better metric for evaluating offensive talent.

4.  Although difficult to identify, I believe I have shown players can suppress opposition shooting percentage.

5.  Zone starts affect shots/corsi/fenwick stats significantly more than they affect goal stats thus the non-adjusted shot/corsi/fenwick data are less useful than the non-adjusted goal data.

6.  Although not specifically a beef with Corsi, much of the corsi analysis currently being done does not split out offensive corsi and defensive corsi but rather looks at them as a percentage or as a +/- differential.  I believe this is a poor way of doing analysis because it really is useful to know whether a player is good because he produces a lot of offense or whether the player is good because he is great defensively.  Plus, when evaluating a player offensively we need to consider the offensive capability of his team mates and the defensive capability of his opposition, not the overall ability of those players.

7.  I have a really hard time believing that 8 of the top 9 corsi % players over the past 5 seasons are Red Wing players because they are all really talented and had nothing to do with the system they play or some other non-individual talent factor.

8.  Try doing a Malkin vs Gomez fenwick/corsi comparison and now do the same with goals.  Gomez actually has a very good and very comparable fenwick rating to Malkin, but Malkin is a far better player at producing goals thanks to his far superior on-ice shooting percentage (FSh% = fenwick shooting percentage = goals / fenwick for).  Gomez every single season has a much poorer on-ice shooting percentage than Malkin and this is why Malkin is the far better player.  Fenwick/Corsi doesn’t account for this.

Malkin Gomez Malkin Gomez Malkin Gomez
Season(s) FF20 FF20 GF20 GF20 FSh% FSh%
2011-12 16.5 14.0 1.301 0.660 7.9% 4.7%
2010-11 16.1 16.4 0.949 0.534 5.9% 3.3%
2009-10 15.3 14.2 1.112 0.837 7.3% 5.9%
2008-09 12.4 16.8 1.163 0.757 9.4% 4.5%
2007-08 14.1 15.9 1.206 0.792 8.5% 5.0%
2007-11 14.7 14.7 1.171 0.745 8.0% 5.1%


So there you have it.  Those are some of the main reasons why I don’t use corsi in player analysis.  This isn’t to say Corsi isn’t a useful metric.  It is a useful metric in identifying which players are better at controlling play. Unfortunately, controlling play is only part of the game so if you want to conduct a complete thorough evaluation of a player, goal based stats are required.


Apr 192012

Prior to the season Gabe Desjardins and I had a conversation over at MC79hockey.com where I predicted several players would combine for a 5v5 on-ice shooting percentage above 10.0% while league average is just shy of 8.0%.  I documented this in a post prior to the season.  In short, I predicted the following:

  • Crosby, Gaborik, Ryan, St. Louis, H. Sedin, Toews, Heatley, Tanguay, Datsyuk, and Nathan Horton will have a combined on-ice shooting percentage above 10.0%
  • Only two of those 10 players will have an on-ice shooting percentage below 9.5%

So, how did my prediction fair?  The following table tells all.

Player GF SF SH%
SIDNEY CROSBY 31 198 15.66%
MARTIN ST._LOUIS 74 601 12.31%
ALEX TANGUAY 43 371 11.59%
MARIAN GABORIK 57 582 9.79%
JONATHAN TOEWS 51 525 9.71%
NATHAN HORTON 34 359 9.47%
HENRIK SEDIN 62 655 9.47%
BOBBY RYAN 52 552 9.42%
PAVEL DATSYUK 50 573 8.73%
DANY HEATLEY 42 611 6.87%
Totals 496 5027 9.87%

Well, technically neither of my predictions came true.  Only 5 players had on-ice shooting percentages above 9.5% and as a group they did not maintain a shooting percentage above 10.0%.  That said, my prediction wasn’t all that far off.  8 of the 10 players had an on-ice shooting percentage above 9.42% and as a group they had an on-ice shooting percentage of 9.87%.  If Crosby was healthy for most of the season or the Minnesota Wild didn’t suck so bad the group would have reached the 10.0% mark.  So, when all is said and done, while technically my predictions didn’t come perfectly true, the intent of the prediction did.  Shooting percentage is a talent, is maintainable, and can be used as a predictor of future performance.

I now have 5 years of on-ice data on stats.hockeyanalysis.com so I thought I would take a look at how sustainable shooting percentage is using that data.  To do this I took all forwards with 350 minutes of 5v5 zone start adjusted ice time in each of the past 5 years and took the first 3 years of the data (2007-08 through 2009-10) to predict the final 2 years of data (2010-11 and 2011-12).  This means we used at least 1050 minutes of data over 3 seasons to predict at least 700 minutes of data over 2 seasons.  The following chart shows the results for on-ice shooting percentage.

Clearly there is some persistence in on-ice shooting percentage.  How does this compare to something like fenwick for rates (using FF20 – Fenwick For per 20 minutes).

Ok, so FF20 seems to be more persistent, but that doesn’t take away from the fact that shooting percentage is persistent and a reasonable predictor of future shooting percentage.  (FYI, the guy out on his own in the upper left is Kyle Wellwood)

The real question is, are either of them any good at predicting future goal scoring rates (GF20 – goals for per 20 minutes) because really, goals are ultimately what matters in hockey.

Ok, so both on-ice shooting percentage and on-ice fenwick for rates are somewhat reasonable predictors of future on-ice goal for rates with a slight advantage to on-ice shooting percentage (sorry, just had to point that out).  This is not inconsistent with what I  found a year ago when I used 4 years of data to calculate 2 year vs 2 year correlations.

Of course, I would never suggest we use shooting percentage as a player evaluation tool, just as I don’t suggest we use fenwick as a player evaluation tool.  Both are sustainable, both can be used as predictors of future success, and both are true player skills, but the best predictor of future goal scoring is past goal scoring, as evidenced by the following chart.

That is pretty clear evidence that goal rates are the best predictor of future goal rates and thus, in my opinion anyway, the best player evaluation tool.  Yes, there are still sample size issues with using goal rates for less than a full seasons worth of data, but for all those players where we have multiple seasons worth of data (or at least one full season with >~750 minutes of ice time) for, using anything other than goals as your player evaluation tool will potentially lead to less reliable and less accurate player evaluations.

As for the defensive side of the game, I have not found a single reasonably good predictor of future goals against rates, regardless of whether I look at corsi, fenwick, goals, shooting percentage or anything else.  This isn’t to suggest that players can’t influence defense, because I believe they can, but rather that there are too many other factors that I haven’t figured out how to isolate and remove from the equation.  Most important is the goalie and I feel the most difficult question to answer in hockey statistics is how to separate the goalie from the defenders. Plus, I believe there are far fewer players that truly focus on defense and thus goals against is largely driven by the opposition.

Note:  I won’t make any promises but my intention is to make this my last post on the subject of sustainability of on-ice shooting percentage and the benefit of using a goal based player analysis over a corsi/fenwick based analysis.  For all those who still fail to realize goals matter more than shots or shot attempts there is nothing more I can say.  All the evidence is above or in numerous other posts here at hockeyanalysis.com.  On-ice shooting percentage is a true player talent that is both sustainable and a viable predictor of future performance at least on par with fenwick rates.  If you choose to ignore reality from this point forward, it is at your own peril.


Jan 282012

I have been having a discussion as to whether shot quality exists over at Pension Plan Puppets and more precisely whether certain players can drive a teams shooting percentage while they are on the ice.  As part of the discussion I brought up the on-ice shooting percentage differences between Scott Gomez and Michael Cammalleri and decided that it would be useful to present that comparison as a post here.

First off, let me define shot quality as how I see it.  Shot quality is an ability for players to systematically drive (or suppress) shooting percentages when they are on the ice.  To me it doesn’t matter whether they can drive shooting percentages because they can get more shots from better shooting locations, or are better shooters, or are better playmakers setting up  changes with the goalie out of position.  Those are interesting things to investigate, but investigating them isn’t necessary to show shot quality exists.  Shot quality, in my mind, is all about a players being able to drive (or suppress) shooting percentage when they are on the ice, regardless of how.

In the past I have used examples such as Henrik Sedin vs Travis Moen and some comments I got were “but those are extreme cases” which is an interesting comment because in essence they person making that argument is admitting that shot quality exists but only in extreme cases.  So, I decided that it might be useful to take a look at two players who generally speaking play similar roles.  Scott Gomez and Michael Cammalleri.  Both Gomez and Cammalleri are top six forwards generally thought of as more offensive players.  What is also interesting is they over the past 4 1/2 seasons they both have switched teams and they have both spent a couple years playing on the same team, sometimes on the same line.    Let’s take a look at their 5v5 on-ice shooting percentages over the past 4 1/2 seasons.

 Sh% Gomez Cammalleri Difference
2007-08 7.09 8.15 1.06
2008-09 6.15 9.25 3.10
2009-10 7.89 9.66 1.77
2010-11 4.50 7.07 2.57
2011-12 7.96 8.11 0.15

In each and every season Cammalleri has had a higher shooting percentage, sometimes much higher.  Only this season have they been close in their on-ice shooting percentages.  If that isn’t a systematic ability by Cammalleri and his linemates to get a higher shooting percentage than Gomez and his linemates, I don’t know what is.  They can do it every singles season.

Now, let’s take a look at their offensive fenwick rates.  Here are their fenwick for per 20 minutes of 5v5 ice time rates.

 FF20 Gomez Cammalleri Difference
2007-08 15.86 14.3 -1.56
2008-09 16.76 15.38 -1.38
2009-10 14.21 13.4 -0.81
2010-11 16.4 14 -2.4
2011-12 16.8 12.06 -4.74

Well now, that tells us a different story.  Gomez and his line mates take far more shots than Cammalleri and his line mates, and they do it every single season.  Gomez and his line mates seem to have a much better skill at taking shots, but Cammalleri and his line mates seem to have a much better skill at capitalizing on shots.  The question now is, which skill results in more goals.  Here are their 5v5 goals for per 20 minute stats.

 GF20 Gomez Cammalleri Difference
2007-08 0.792 0.801 0.009
2008-09 0.757 1.020 0.263
2009-10 0.837 0.927 0.090
2010-11 0.534 0.713 0.179
2011-12 0.854 0.756 -0.098

Now that is interesting.  Cammalleri and his line mates have out produced Gomez and his line mates every year until this season.  Based on this one example, being able to drive shooting percentage resulted in more goals being scored than being able to drive shots.  If you were down by a goal in the third period, who would you rather have on the ice, Gomez and his line mates or Cammalleri and his line mates?

And the above is a perfect example of why I don’t like pure corsi/fenwick based evaluation of players.  If you just look at corsi/fenwick, Gomez looks like a very good player (see here and here), and Cammalleri does not.  But, if you look at goals, over the past 2 seasons 54.1% of all goals scored while Cammalleri was on the ice were for the Canadiens while just 47.2% of all goals scored while Gomez was on the ice were for the Canadiens.  Who is the better player, and who would I rather have on my team?  Cammalleri by a country mile.

Let’s take it one step further and how they played when they were on the ice together and when they were apart over the past 2 seasons.

Together Cammalleri Gomez
GF% 54.8% 53.9% 45.4%
Corsi% 52.3% 47.9% 51.6%

Wow, that is dramatic.  When they play together can an drive shots (corsi) and goals.  When Cammalleri is not playing without Gomez he can drive goals, but not shots (corsi) and when Gomez is playing without Cammalleri he can drive shots (corsi) but not goals.  Again, who would you rather have on your team?  For me, I’ll take the guy who can drive goals thank you very much.

And that my friends, is a perfect example of when a corsi based analysis will fail.


Dec 092011

Gabe Desjardins of Arctic Ice Hockey asks the question about whether a player can influence his teammates shooting percentage.  To answer this question he took a look at the Pittsburgh Penguins shooting percentages with and without Mario Lemieux.  The conclusion:

I’d posit that Lemieux’s playmaking contribution is about as large as we’re going to consistently find – something on the order of 7-8% – and we can use it to bound the impact that a player can truly have on the quality of his teammates’ scoring chances.

Since I have the numbers handy I figured I’d take a look at some more recent examples but instead of looking at straight shooting percentage I looked at corsi shooting percentage (since I had corsi data more available).  Corsi shooting percentage is simply goals for divided by corsi for.  I’d consider Joe Thornton one of the premiere playmaking centers in the league today so let’s take a look at how some players performed while playing with, and without, him.

CSH% With Thornton CSH% Without Boost
Marleau 4.93% 3.88% 27.02%
Setogutchi 5.09% 3.80% 33.82%
Heatley 5.59% 4.32% 29.50%

I included the past 4 years with Marleau, 3 years with Setogutchi and 2 years with Heatley.  That would indicate Thornton has an approximately 30% boost in corsi shooting percentage to his teammates.  Certainly far more than the 8% Gabe predicted as the upper bound.

Now, let’s take a look at another great player, Sidney Crosby.

CSH% With CSH% Without Boost
Malkin 7.30% 5.15% 41.89%
Dupuis 5.73% 4.06% 40.95%
Fleury 5.75% 4.22% 36.15%

All players are using 4 years of data.  I included Fleury in the list because it provides a good proxy of the Penguins shooting percentages when Crosby is on the ice vs when he is not.  This would seem to indicate that Crosby is worth a nearly 40% boost in his teams shooting percentage.  That’s significantly more than even Thornton and a massive amount more than Gabe’s estimated upper bound.  Maybe we should revise the upper bound to be 40%, not 8%.

For interest sake, here how much Crosby influenced his teammates corsi rates.

Boost in CF20
Malkin 21.15%
Dupuis 18.15%
Fleury 15.59%

While a ~20% boost is significant, it is at best only half the boost he provided to corsi shooting percentage.  Driving shooting percentage is a more significant reason why Crosby is so good offensively than driving corsi events.


Update:  Eric over at Broad St. Hockey has an interesting post looking at individual shooting percentages as opposed to on-ice shooting percentages as I did above.  Four of the players he looked at are H. Sedin, Crosby, Thornton and Datsyuk and for each he looked at a number of teammates with at least 30 shots with and without.  Taking it a step further I think it is necessary to average across players to get a better idea of what is happening.  If you do that, this is what you get:

With Without Boost
Sedin 11.19% 6.81% 64.28%
Crosby 9.14% 7.55% 21.17%
Thornton 9.69% 7.27% 33.19%
Datsyuk 9.36% 6.98% 34.09%

Wow, that might make Sedin the best playmaker in the league, by a significant margin.  Crosby doesn’t look quite as good as my “on-ice” analysis but that is because much of the reason why Crosby improves his linemates on-ice shooting percentage is because he is such a great shooter himself.

The point still stands, without considering shooting percentages we aren’t getting anywhere close to having a complete analysis of a players impact on the game.


Nov 222011

I hate to keep beating the “Shooting Percentage Matters” drum but it really dumbfounds me why so many people choose to ignore it, or believe it is only a small part of the game and not worth considering and instead focus their attention on corsi/fenwick, and corsi/fenwick derived stats as their primary evaluation too.

It dumbfounds me that people don’t think players have an ability to control shooting percentage yet we all seem to agree that shooting percentage is affected by game score.  Rob Vollman wrote the following in a comment thread at arctic ice hockey.

<blockqote>The score can affect the stats because teams behave differently when chasing or protecting a lead…</blockquote)

He isn’t specifically referring to shooting percentage, but shooting percentage varies based on game score and I think most people accept that.  So, while people freely accept that teams can play differently depending on score, they seemingly choose not to believe that players can play different depending on their role, or skillset.  Or rather, it isn’t that they don’t believe players can play differently (for example they realize there are defensive specialists) they just choose not to accept that a players style of play (in addition to their talents, which often dictates their style of play) will affect their stats, including shooting percentage.  An example, which I brought up at The Puck Stops Here is Marian Gaborik vs Chris Drury.  Both Gaborik and Drury played the past 2 seasons on the NY Rangers but Gaborik played an offensive role and Drury generally played a more defensive/3rd line role.  As a result, here are their offensive stats at 5v5 over the past 2 seasons.

Gaborik Drury Gaborik’s Edge
Team Fenwick For per 20min WOI 13.8 12.8 +8%
Team Sh% For WOI 10.26% 6.18% +66%
Team Goals For per 20 min WOI 1.031 .575 +79%

Shooting percentage took what was a slight edge for Gaborik in terms of offensive fenwick for and turned it into a huge advantage in goals for.  Part of that is Gaborik and his line mates better skill level and part of it is their aggressive offensive style of play, but regardless of why, we need to take shooting percentage into account or else we will undervalue Gaborik at the offensive end of the rink and over value Drury.

It isn’t just Gaborik and Drury whose offense is significantly impacted by shooting percentage.  It happens all the time.  I took a look at all players that had 2000 5v5 even strength on-ice offensive fenwick events over the past 4 seasons.  From there I calculated their expected on-ice goals scored based on their ice time using league-wide average  on-ice fenwick for per 20 minutes (FF20) and league-wide average fenwick shooting percentage (FSH%).

I next calculated an expected goals based on the league-wide FF20 and the players FSH% as well as an expected goals based on the players FF20 and the league-wide average FSH%.  When we compare these expected goals to the expected goals based solely on the league-wide average we can get an idea of whether a players on-ice goal production is driven mostly by FF20 or FSH% or some combination of the two.

The following players had their on-ice 5v5 goal production influenced the most positively or most negatively due to their on-ice 5v5 FSH%.

Player Name %Increase from FSH%
J.P. DUMONT 29.4%

And the following players had their on-ice 5v5 goal production influenced the most positively or most negatively due to their on-ice 5v5 FF20.

Player Name %Increase from FF20

Some interesting notes:

  1.  The range in the influence of FSH% is significantly larger than the range of influence of FF20 indicating that shooting percentage is more important than shot generation in terms of scoring goals.
  2. The FSH% list is not random.  The list is stratified.  Offensive players at the top, non-offensive players at the bottom (plus Scott Gomez who gets offensive minutes, but sucks).  What you see above is not luck.  There is order to the list, not randomness.
  3. Speaking of Gomez, he sucks at on-ice FSH%, but has a very good FF20, though that is partly due to offensive zone start bias.
  4. Ilya Kovalchuk is the anti-Gomez.  He has a great FSH%, but is horrible at helping his team generate shots.
  5. The standard deviation of the FSH% influence is 14.5% while it is 8.3% for FF20 influence so it seems FSH% has a much greater influence on scoring goals than FF20.  This is not inconsistent with some of my observations in the past or observations of others.

So, what does all this mean?  Shooting percentage matters, and matters a lot and thus drawing conclusions based solely on a corsi analysis is flawed.  It isn’t that generating shots and opportunities isn’t important, but that being great at it doesn’t mean you are a great player (Gomez) and being bad at it doesn’t make you a bad player (Kovalchuk).  For this reason I really cringe when I see people making conclusions about players based on a corsi analysis.  A corsi analysis will only tell you how good he is at one aspect of the game, but is not very good at telling you the players overall value to his team.  My goal is, and always will be, to try and evaluate a players overall value and this is why I really dislike corsi analysis.  It completely ignores a significant, maybe the most significant, aspect of the game.  Furthermore, I believe that offensive ability and defensive ability should be evaluated separately, which many who do corsi analysis don’t do or only partially or subjectively do.

I really don’t know how many different ways I can show that shooting percentage matters a lot but there are still a lot of people who believe players can’t drive or suppress shooting percentage or believe that shooting percentage is a small part of the game that is dwarfed by the randomness/luck associated with it (which is only true if sample size is not sufficiently large).  The fact is corsi analysis alone will never give you a reliable (enough to make multi-million contract offers) evaluation of a players overall ability and effectiveness.  Shooting percentage matters, and matters a lot.  Ignore at your peril.


Oct 272011

There has been a fair bit of discussion going on regarding shot quality the past few weeks among the hockey stats nuts.  It started with this article about defense independent goalie rating (DIGR) in the wall street journal and several others have chimed in on the discussion so it is my turn.

Gabe Desjardins has a post today talking about his hatred of shot quality and how it really isn’t a significant factor and is dominated by luck and randomness.  Now, generally speaking when others use the shot quality they are mostly talking about thinks like shot distance/location, shot type, whether it was on a rebound, etc.  because that is all data that is relatively easily available or easily calculated.  When I talk shot quality I mean the overall difficulty of the shot including factors that aren’t measurable such as the circumstances (i.e. 2 on 1, one timer on a cross ice pass, goalie getting screened, etc.).  Unfortunately my definition means that shot quality isn’t easily calculated but more on that later.

In Gabe’s hatred post he dismisses pretty much everything related to shot quality in one get to the point paragraph.


Alan’s initial observation – the likelihood of a shot going in vs a shooter’s distance from the net – is a good one.  As are adjustments for shot type and rebounds.  But it turned out there wasn’t much else there.  Why?  The indispensable JLikens explained why – he put an upper bound on what we could hope to learn from “shot quality” and showed that save percentage was dominated by luck.  The similarly indispensable Vic Ferrari coined the stat “PDO” – simply the sum of shooting percentage and save percentage – and showed that it was almost entirely luck.  Vic also showed that individual shooting percentage also regressed very heavily toward a player’s career averages.  An exhaustive search of players whose shooting percentage vastly exceeded their expected shooting percentage given where they shot from turned up one winner: Ilya Kovalchuk…Who proceeded to shoot horribly for the worst-shooting team in recent memory last season.

So, what Gabe is suggesting is that players have little or no ability to generate goals aside from their ability to generate shots.  Those who follow me know that I disagree.  The problem with a lot of shot quality and shooting percentage studies is that sample sizes aren’t sufficient to draw conclusions at a high confidence level.  Ilya Kovalchuk may be the only one that we can say is a better shooter than the average NHLer with a high degree of confidence, but it doesn’t mean he is the only one who is an above average shooter.  It’s just that we can’t say that about the others at a statistically significant degree of confidence.

Part of the problem is that goals are very rare events.  A 30 goal scorer is a pretty good player but 30 events is an extremely small sample size to draw any conclusions over.  Making matters worse, of the hundreds of players in the NHL only a small portion of them reach the 30 goal plateau.  The majority would be in the 10-30 goal range and I don’t care how you do your study, you won’t be able to say much of anything at a high confidence level about a 15 goal scorer.

The thing is though, just because you cannot say something at a high confidence level doesn’t mean it doesn’t exist.  What we need to do is find ways of increasing the sample size to increase our confidence levels.  One way I have done that is to use 4 years of day and instead of using individual shooting percentage I use on-ice shooting percentage (this is useful in identifying players who might be good passers and have the ability to improve their linemates shooting percentage).  Just take the list of forwards sorted by on-ice 5v5 shooting percentage over the past 4 seasons.  The top of that list is dominated by players we know to be good offensive players and the bottom of the list is dominated by third line defensive role players.  If shooting percentage were indeed random we would expect some Moen and Pahlsson types to be intermingled with the Sedin’s and Crosby’s, but generally speaking they are not.

A year ago Tom Awad did a series of posts at Hockey Prospectus on “What Makes Good Players Good.”  In the first post of that series he grouped forwards according to their even strength ice time.  Coaches are going to play the good players more than the not so good players so this seems like a pretty legitimate way of stratifying the players.  Tom came up with four tiers with the first tier of players being identified as the good players.  The first tier of players contained 83 players.  It will be much easier to draw conclusions at a high confidence level about a group of 83 players than we can about single players.  Tom’s conclusions are the following:

The unmistakable conclusions from this table? Outshooting, out-qualitying and out-finishing all contribute to why Good Players dominate their opponents. Shot Quality only represents a small fraction of this advantage; outshooting and outfinishing are the largest contributors to good players’ +/-. This means that judging players uniquely by Corsi or Delta will be flawed: some good players are good puck controllers but poor finishers (Ryan Clowe, Scott Gomez), while others are good finishers but poor puck controllers (Ilya Kovalchuk, Nathan Horton). Needless to say, some will excel at both (Alexander Ovechkin, Daniel Sedin, Corey Perry). This is not to bash Corsi and Delta: puck possession remains a fundamental skill for winning hockey games. It’s just not the only skill.

In that paragraph “shot quality” and “out-qualitying” is used to reference a shot quality model that incorporates things like shot location, out-finishing is essentially shooting percentage, and outshooting is self-explanatory.  Tom’s conclusion is that the ability to generate shots from more difficult locations is a minor factor in being a better player but both being able to take more shots and being able to capitalize on those shots is of far greater importance.

In the final table in his post he identifies the variation in +/- due to the three factors.  This is a very telling table because it tells it gives us an indication of how much each factors into scoring goals.  The following is the difference in +/- between the top tier of players and the bottom tier of players:

  • +/- due to Finishing:  0.42
  • +/- due to shot quality:  0.08
  • +/- due to out shooting:  0.30

In percentages, finishing ability accounted for 52.5% of the difference, out shooting 37.5% of the difference and shot quality 10% of the difference.  Just because we can’t identify individual player shooting ability at a high confidence level doesn’t mean it doesn’t exist.

If we use the above as a guide, it is fair to suggest that scoring goals is ~40% shot generation and ~60% the ability to capitalize on those shots (either through shot location or better shooting percentages from those locations).  Shooting percentage matters and matters a lot.  It’s just a talent that is difficult to identify.

A while back I showed that goal rates are better than corsi rates in evaluating players.  In that study I showed that with just 1 season of data goal for rates will predict future goal for rates just as good as fenwick for rates can predict future goal for rates and with 2 years of data goal for rates significantly surpass fenwick for rates in terms of predictability.  I also showed that defensively, fenwick against rates are very poor predictors of future goal against rates (to the point of uselessness) while goals against rates were far better predictors of future goal against rates, even at the single season level.

The Conclusion:  There simply is no reliable way of evaluating a player statistically at even a marginally high confidence level using just a single year of data.  Our choices are either performing a Corsi analysis and doing a good job at predicting 40% of the game or performing a goal based analysis and doing a poor job at predicting 100% of the game.  Either way we end up with a fairly unreliable player evaluation.  Using more data won’t improve a corsi based analysis because sample sizes aren’t the problem, but using more data can significantly improve a goal based analysis.  This is why I cringe when I see people performing a corsi based evaluation of players.  It’s just not, and never will be, a good way of evaluating players.


Aug 212011

I have just updated my stats site (stats.hockeyanalysis.com) to include a number of new features.  The added features are:

1.  I have added a new situation – 5v5close.  5v5close is when the game is tied or within 1 goal in the first and second period or tied in the third period.  This is what I would call normal play where teams are more or less (depending on talent or game play/coaching style) equally interested in  playing offense or defense.  When teams get a larger lead or lead late in the game teams adjust their style of play to either protect that lead or go all out to score a goal to catch up.  It is probably better to use this than 5v5tied and maybe better than 5v5 (all 5v5 game score situations).

2.  I have included zone start data in the form of OZOF%, DZOF% and NZOF%.  OZOF% is the percentage of face offs taken in the offensive zone when the player is on the ice and DZOF% and NZOF% are the same for defensive zone and neutral zone faceoffs.  When we look at these by situation we can get an idea of how a players use gets changed by game score.  For example, last year Manny Malholtra had 38.8% of his 5v5 face offs in the defensive zone (29.1% offensive zone and 32.1% neutral zone) but when the Canucks were up by a goal his defensive zone faceoffs rose to 41.6% and when the Canucks were up by 2 goals they rose to 48.4%.

3.  I have once again put up with/against statistics for each player.  I had this data up a few years ago but when I re-designed my website I removed it but it is back.  Each player page (i.e. the Malhotra one linked to above) has a set of links at the top of the page to with/against statistics for each season (and multi-seasons) for 5v5 and 5v5 close situations for both goal and corsi data.  Each page shows how the player played with each teammate as well as how they played when they were not playing together as well as how the player performed against each opponent and how well the player and the opponent performed when not playing together.  These tables can give you an indication of which players are playing together and which players play well together as well as who a player plays against the most.  As an example, take a look at Manny Malhotra 5v5 goal with/against data for this past season and you will see he played the most with Raffi Torres (even more than with Roberto Luongo!) but it seems both players had better on ice results when apart.

4.  If you hadn’t noticed yet, a while back I added on ice shooting percentage (Sh%) and on ice opposition shooting percentage (OppSh%, subtract from to get on ice save %) which can be found with the goal data (but not with corsi, fenwick and shot data).

All totaled, there is well over 10 gigabytes of html, php and data base files of statistics (90% of which is in the with/against tables) so be warned, if you really wanted to you could spend days looking at it all.