Recently, 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.