Do Playmakers Drive Teammates' Shooting Percentage?
by Eric T. on Dec 9, 2011 1:58 PM EST
in Philadelphia Flyers Commentary
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PrintRecently, we had a discussion on here about how Sidney Crosby's on-ice shooting percentage is consistently above average. That made me curious: how much of that is because he personally shoots for a high percentage, how much of it is because he plays with high-percentage shooters, and how much of it is because his playmaking skills set his teammates up for easier shots?
It's the last question that I'm really looking to answer. Do individual players shoot for a higher percentage when they're on the ice with a playmaker than when they're not?
To answer this question, I pulled data from the last three years for a handful of the league's top playmakers and their teammates' shooting percentages. The data suggested an effect to me, but I wanted to test for statistical significance. Unfortunately, I wasn't sure of the best way to do that.
I consulted with a couple of stats-oriented people, some of whom got interested in the question. Hawerchuk of Arctic Ice Hockey decided to look at the question with an article comparing the Penguins' team shooting percentage with or without Mario Lemieux. Hockey Analysis then followed up on that work by doing something that I thought was almost identical to my study, even using one of the players I included (Joe Thornton). (Ed: the author has since clarified that he used on-ice shooting percentage, not individual shooting percentage, so this does not remove the influence of the playmaker's own shooting or the possible tendency of the top playmaker's line to include good shooters.)
So now I'm feeling pressured to get my data out there before this becomes old news. What follows will be somewhat qualitative, but hopefully we can find the right quantitative test soon.
If any current player's impact is going to prove to be significant, it will be Henrik Sedin. Over the last three years, here is how his teammates' shooting percentages depended on whether he was on or off the ice:
| Player | Shots with | Shots without | Sh% with | Sh% without | Sh% boost with Sedin |
| Burrows | 304 | 159 | 18.1% | 11.3% | +6.8% |
| Edler | 119 | 170 | 5.0% | 2.9% | +2.1% |
| Bieksa | 103 | 156 | 5.8% | 4.5% | +1.3% |
| Ehrhoff | 97 | 141 | 4.1% | 8.5% | -4.4% |
| Samuelsson | 91 | 253 | 15.4% | 8.3% | +7.1% |
| Salo | 56 | 97 | 7.1% | 1.0% | +6.1% |
| Mitchell | 49 | 78 | 6.1% | 5.1% | +1.0% |
| Raymond | 45 | 422 | 8.9% | 7.6% | +1.3% |
| Demitra | 39 | 114 | 15.4% | 10.5% | +4.9% |
| Ohlund | 38 | 54 | 5.3% | 1.9% | +3.4% |
| Hamhuis | 37 | 56 | 10.8% | 0.0% | +10.8% |
| DSedin | 532 | 32 | 11.5% | 15.6% | -4.2% |
A simple paired t-test says this is significant, but it gives equal weight to Hamhuis and Burrows, which can't be right given their number of shots. Moreover, the significance in that test is based largely on the number of players considered; the t-test would be less impressed by a dataset of two players who each had 1000 shots with and without Sedin, yet I would find that data more compelling. If there's a statistics expert who would be interested in showing me how to include the uncertainty on each measurement as part of the significance test, I'd love to do that, but in the meantime we'll settle for qualitative observations.
Other playmakers' effects are less clear. Here is how Martin St. Louis's teammates fared with and without him:
| Player | Shots with | Shots without | Sh% with | Sh% without | Sh% boost with St. Louis |
| Lecavalier | 236 | 294 | 8.5% | 10.2% | -1.7% |
| Stamkos | 333 | 149 | 13.5% | 14.8% | -1.3% |
| Malone | 132 | 174 | 15.9% | 9.8% | +6.1% |
| Downie | 73 | 87 | 19.2% | 10.3% | +8.8% |
| Meszaros | 69 | 99 | 1.4% | 3.0% | -1.5% |
| Prospal | 63 | 72 | 11.1% | 6.9% | +4.2% |
| Hedman | 59 | 109 | 3.4% | 4.6% | -1.2% |
| Foster | 38 | 64 | 7.9% | 3.1% | +4.8% |
| Lundin | 34 | 60 | 5.9% | 3.3% | +2.5% |
Is that a net positive? Perhaps, but not by a lot. This is where a quantitative test is really needed to know how to balance Lecavalier's large-sample -1.7% with Malone's medium-sample +6.1%. But my guess would be that this is not statistically meaningful.
Sidney Crosby was the one who started this conversation, so let's take a look at his numbers.
| Player | Shots with | Shots without | Sh% with | Sh% without | Sh% boost with Crosby |
| Dupuis | 171 | 258 | 8.8% | 10.9% | -2.1% |
| Malkin | 139 | 304 | 12.2% | 7.6% | +4.7% |
| Letang | 135 | 248 | 4.4% | 2.4% | +2.0% |
| Kunitz | 126 | 107 | 12.7% | 13.1% | -0.4% |
| Guerin | 146 | 85 | 8.9% | 4.7% | +4.2% |
| Fedotenko | 55 | 195 | 7.3% | 9.7% | -2.5% |
| Kennedy | 47 | 469 | 6.4% | 8.1% | -1.7% |
| Orpik | 47 | 100 | 6.4% | 1.0% | +5.4% |
| Gonchar | 41 | 62 | 9.8% | 3.2% | +6.5% |
| Satan | 40 | 48 | 15.0% | 10.4% | +4.6% |
| Eaton | 37 | 43 | 8.1% | 7.0% | +1.1% |
| Talbot | 33 | 95 | 9.1% | 9.5% | -0.4% |
Again, that might be a net positive, but it's not a big one. His consistently high on-ice shooting percentage arises mostly because he shoots for a very high percentage himself, 16.9% over this period. Smaller effects arise from playing with other good shooters and perhaps elevating their shooting percentage slightly.
Next, let's look at Joe Thornton:
| Player | Shots with | Shots without | Sh% with | Sh% without | Sh% boost with Thornton |
| Marleau | 353 | 203 | 13.6% | 12.8% | +0.8% |
| Setoguchi | 285 | 192 | 10.9% | 9.9% | +1.0% |
| Boyle | 144 | 189 | 9.7% | 4.2% | +5.5% |
| Heatley | 215 | 126 | 11.6% | 7.1% | +4.5% |
| Blake | 107 | 134 | 2.8% | 3.0% | -0.2% |
| Murray | 87 | 136 | 2.3% | 1.5% | +0.8% |
| Vlasic | 71 | 144 | 4.3% | 4.2% | +0.1% |
| Clowe | 56 | 379 | 8.9% | 11.1% | -2.2% |
| Cheechoo | 46 | 75 | 8.7% | 2.7% | +6.0% |
| Ehrhoff | 40 | 72 | 2.5% | 2.8% | -0.3% |
Thornton has the second-biggest effect after Sedin. The simple paired t-test suggests this is borderline significant, but a weighting scheme which de-emphasized the guys who had only 40-50 shots with him would make this look more meaningful. Factoring in that almost any time someone is on the ice with Henrik Sedin, he is also on the ice with Daniel Sedin (who might also help create space for teammates), it may be that Thornton is the biggest individual driver of shooting percentage.
The bronze medal winner in this study is probably Pavel Datsyuk:
| Player | Shots with | Shots without | Sh% with | Sh% without | Sh% boost with Datsyuk |
| Zetterberg | 242 | 437 | 6.2% | 7.6% | -1.4% |
| Franzen | 163 | 288 | 8.6% | 10.4% | -1.8% |
| Lidstrom | 153 | 155 | 8.5% | 3.2% | +5.3% |
| Hossa | 125 | 110 | 16.8% | 8.2% | +8.6% |
| Bertuzzi | 98 | 192 | 10.2% | 9.4% | +0.8% |
| Cleary | 98 | 313 | 14.3% | 9.9% | +4.4% |
| Stuart | 92 | 187 | 2.2% | 2.1% | +0.1% |
| Rafalski | 87 | 162 | 3.4% | 4.9% | -1.5% |
| Kronwall | 48 | 153 | 8.3% | 5.2% | +3.1% |
| Holmstrom | 164 | 47 | 15.2% | 2.1% | +13.1% |
| Ericsson | 44 | 119 | 4.5% | 3.4% | +1.2% |
Finally, as a homer fan, of course I had to include Claude Giroux in the study. Unfortunately, he's been growing rapidly as a player, so there's only a small dataset for the period where he was a leading playmaker. The results from last year aren't particularly compelling, but we should revisit his play in a year or two.
| Player | Shots with | Shots without | Sh% with | Sh% without | Sh% boost with Giroux |
| Carter | 178 | 75 | 10.7% | 10.7% | 0.0% |
| Zherdev | 60 | 66 | 10.0% | 13.6% | -3.6% |
| van Riemsdyk | 47 | 103 | 14.9% | 10.7% | +4.2% |
| Coburn | 37 | 70 | 0.0% | 2.9% | -2.9% |
| Timonen | 35 | 65 | 2.9% | 3.1% | -0.2% |
| Richards | 31 | 100 | 12.9% | 11.0% | +1.9% |
The data suggests that players can influence their teammates' shooting percentages, but only the very best playmakers can do it and even then only to a modest degree. It remains safe to assume for the vast majority of players that when they post an above-average on-ice shooting percentage, it is not the result of their individual passing skills.
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I almost didn’t make it past the jump. Did you have to start it with Crosby?
Yes, I recognize he’s ridiculously good.
Reading about Sedin was a good way to cleanse the palate, though.
Ecstatic to be joing the Florida Panthers Organization!! Awesome day... Truly a dream come true.
- @ScottieUpshall (July 1, 2011 2:15pm EST)
Sorry this isn’t the smoothest read. I was in a rush to get it up before it became obsolete. :)
@BSH_EricT
Writer at Broad Street Hockey
I get done with your email and it’s up on the site. Impressive, sorry my help advice can’t be considered so.
being obnoxious and self righteous while ignoring the point since 9/29/11
I’m hoping that in the comments, someone will tell me how to do it — probably using words I don’t completely understand, and I’ll come back to you for help then. :)
@BSH_EricT
Writer at Broad Street Hockey
I was somewhat confused by the statement that “almost any time someone is on the ice with Henrik Sedin, he is also on the ice with Daniel Sedin” when seeing that D. Sedin’s Sh% is better without H. Sedin on the ice and nearly everyone else had a boost from playing with H. Sedin. And then I noticed the VERY LARGE discrepancy in the number of shots D. Sedin takes with and without his brother on the ice. Which is because they are almost always out there together. So then I answered my own question.
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"I think there is virtue in pissing off idiots." - Fehr and Balanced
Yeah, I think it’s pretty funny that Daniel is one of the very few players who did worse when playing with Henrik, regardless of what the reason might be (sample size, skill, I dunno, I like to imagine he secretly hates his brother).
@BSH_EricT
Writer at Broad Street Hockey
Great stuff Eric
Nice to see what I have always said be expressed in numbers. Henrik and Daniel though?
I think he makes him better too, but usually with Daniel out there with Henrik, other teams have a guy ( its probably in the pregame talk, its what you hear them all talk about in interviews as to how they are trying to play them ) looking for his brother…
What you hear about a lot from the other team’s players is that “you have to look for the other one when one has the puck”. I guess what I am trying to say is that the other team trying to take Daniel away when Henrik has the puck opens up the other shooters.
Though, sometimes its just the passes go through them both to Burrows at the end! Nice to see that expressed in numbers…as is the way he finds Salo and other defensemen at the point. Does this make him the best playmaker because only two guys have a “red” shooting % as compared to the rest?
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@Vancitydan Writer at Nucks Misconduct
Does this make him the best playmaker because only two guys have a "red" shooting % as compared to the rest?
Just counting green boxes isn’t exactly fair — it’s important to look at the number of shots taken (weight the guys at the top of a chart much more heavily than the ones at the bottom) and at how green the green box is (+6.8% obviously matters more than +0.3%).
Sedin has a pretty green table, but the big difference between him and Thornton is that his table is filled with +4’s and +6’s, even right at the top of the table.
The conjoined-twins thing complicates things, because someone playing with Henrik will also get the benefit of playing with Daniel, so Thornton-backers could make a case for him as having the strongest individual effect. But there’s no question that if you want to shoot for a high percentage, the Sedin line is the one you want to join.
@BSH_EricT
Writer at Broad Street Hockey
I’d say sample size – 32 is darn close to the minimum sample size to feel confident you’re reducing noise to an acceptable level, and without knowing the situations, we can’t be sure it’s an unbiased sample.
As far as the statistical analysis goes, the null hypothesis should be that playmakers make no difference on their teammates, and the alternative hypothesis is that playmakers do make a difference on their teammates, so you want a two-tailed test, since a negative effect on teammates from a crappy playmaker is still significant.
I think you could weight the t-test by making the sample size shots rather than players. Your null hypothesis mean would thus be the overall shooting average of each playmaker’s linemates when they’re not playing together (i.e. D Sedin’s 5 goals on 32 shots would be added to Burrows’ 18 goals on 159 shots and so on). This would reduce the impact of small sample sizes by making the overall sample larger, mitigating the noise factors.
Bob.
Eric is testing that null hypothesis. The problem with the solution you suggest is that I would like it to be rated at that point as well (for goals versus shots) at least for regressing the data. If you are just ding a null hypothesis test, what data are you combining? You can’t combine them all or else you are left with one point each, one with, one without. I ran a couple of alternate methods for Eric with Henrik’s data, regressing it with some dummy variables as opposed to setting up a paired data set. It is significant in several different analysis, but I’ve yet to find a weighted technique that I’m truly comfortable with. I feel like it’s enough to say it’s probably significant but I’d still like a weighted paired t-test such as Donner’s, but the code that I have written doesn’t deal with paired data sets so I’m hoping someone here has something still.
being obnoxious and self righteous while ignoring the point since 9/29/11
I ran a quick and dirty look at the overall dataset – all shots by all players over the last three seasons. There were 20,530 goals on 223,622 shots, for a 9.18% mean shooting percentage. Unfortunately, this is not a standard normal distribution (0 is the minimum, and quite a few players were at or near 0), so Chebyashev’s Theorem doesn’t hold. (This is where I messed up – I was thinking of standard normal deviations, which are easier to work with). However, the standard deviation of 6.78 can still be used to determine where the player’s results wound up.
Henrik Sedin’s teammates took 1,510 shots with him and 1,732 shots without him, scoring 169 goals and 118 goals respectively, for shooting percentages of 11.19% and 6.81%. Thus, his teammates shot at -0.35 standard deviations without him, and +0.30 standard deviations with him, for a net change of +0.65 standard deviations.
Running through each player’s numbers:
H. Sedin +0.65
St. Louis +0.37
Crosby +0.24
Thornton +0.36
Datsyuk +0.35
Giroux +0.08
I’d be interested to see the raw data for some players who aren’t considered top playmakers, to see how their numbers came out. This suggests that top players can have an effect on their teammates, although the sample selected (excepting Giroux) is skewed towards players who have been considered elite playmakers for the last three years, so we should expect to see positive numbers there.
Bob.
by The Dark on Dec 12, 2011 6:36 PM EST up reply actions 1 recs
What I don’t like about this sort of composite analysis is that it’s prone to a selection bias: perhaps top playmakers just tend to play more with good shooters. (See HSedin’s with/without shot total for DSedin and Raymond, or Thornton’s total for Marleau and Clowe.)
I’m not sure it makes a significant difference, but it concerns me. Thornton’s teammates shot 9.7% with him and 7.3% without him, but if you reverse their shot totals while keeping their shooting percentages the same (e.g. counting Marleau as having shot 13.6% on 203 shots with Thornton and 12.8% on 353 shots without him), the aggregate shooting would be 8.3% with him and 7.9% without. This suggests to me that the majority of his +0.36 standard deviation difference arises from his tendency to spend more of his ice time with good shooters.
Which is not to say that I don’t think there’s an effect here — just that I think this approach overstates it.
@BSH_EricT
Writer at Broad Street Hockey
See Eric’s concern. I tend to share it in that type of analysis.
Honestly, since Eric asked me about this I’ve started to hate myself for not remembering how to do a weighted paired t-test. And the most frustrating part is everything you find online is basically a link to software or an add in that does it for you instead of giving you the equations. Argh.
being obnoxious and self righteous while ignoring the point since 9/29/11
I dont understand why the hockey analysis article compare traditional sh% with corsi sh%. I know both a sh% but they are still 2 different things and its clear looking at Erics data that corsi sh% boosts are much higher then regular sh%.
It’s worse than that — it turns out he compared on-ice shooting percentages of those players, not their individual shooting percentages.
So he’s not showing that Dupuis shoots for a higher percentage with Crosby; he’s shooting that when Dupuis and Crosby are both on the ice, the Penguins shoot for a higher percentage than when Dupuis is out there without Crosby. Which is driven to a large extent by Crosby’s own high shooting percentage.
@BSH_EricT
Writer at Broad Street Hockey
This is a little off topic but in my opinion Crosby is just one of the most accurate shooters I have seen in quite some time. If you want to see some intresting video, go on youtube and type in Crosby drills or something close to it and you will see how good he is. You don’t know how much it pains me to write this because I cannot stand his crybaby ass.
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