## Relative Importance of a Players Impact on Teammate Shooting Percentage

A month and a half ago Eric T at NHLNumbers.com had a good post on quantifying the impact on teammate shooting percentage. I wanted to take a second look at the relative importance the impact on teammate shooting percentage can have because I disagreed somewhat with Eric’s conclusions.

For a very small number of elite playmakers, the ability to drive shooting percentage can be a major component of their value. For the vast majority of the league, driving possession is a more significant and more reproducible path to success.

It is my belief that it is important to consider impact on shooting percentage for more than a “very small number of elite playmakers” and I’ll attempt to show that now.

The method that Eric used to identify a players impact on shooting percentage is to compare that players line mates shooting percentages with him to their overall shooting percentage. As noted in the comments the one flaw with this is that their overall shooting percentage is impacted by the player we are trying to evaluate which will end up underestimating the impact. In the comments Eric re-did the analysis using a true “without you” shooting percentage and the impact of driving teammate shooting percentages was greater than initially expected but he concluded the conclusions didn’t chance significantly.

Overall average for the top ten is a 1.2% boost (up from 0.9% in story) and 5 goals per year (up from 4.5). I don’t think this changes the conclusions appreciably.

In the minutes that a player is on the ice with one of the very best playmakers in the league, his shooting percentage will be about 1% better. For a player who gets ~150-200 shots per year and plays ~40-60% of his ice time with that top-tier playmaker, that’s less than a one-goal boost. It’s just not that big of a factor.

He also suggested that using the “without you” shooting percentage instead of the “overall shooting percentage” would probably result in “more accurate but less precise” analysis. This is because a guy like Daniel Sedin would get very few shots when playing apart from Henrik Sedin because they rarely play apart and this small “apart” sample size might be subject to significant small sample size errors.

In this work I have taken a hybrid approach. I took 5 years of 5v5 zone start adjusted data (2007-08 through 2011-12) and estimated how many goals a players line mates would score based on their without you shooting percentage, except in instances where the player had fewer than 100 without you shots. In situations where the player had fewer than 100 shots apart the player being evaluated I used the players overall shooting percentage. Regardless of which one is used, let’s call the shooting percentage used the players expected shooting percentage. I then calculated an estimated goals scored by line mates by multiplying the expected shooting percentage by the number of shots taken when on the ice with the player being evaluated and summed up the expected goals across all line mates. This gave me an actual goals scored by a players line mates and an expected goals for by a players line mates and I also know the actual shots taken by a players line mates so I can calculate actual and expected shooting percentages. The following table shows the top 20 and bottom 20 forwards and their impact on their line mates shooting percentage (only players whose line mates had >1000 shots are considered).

Player | Pos | LM Goals | LM Shots | LM Sh% | Exp Goals | Exp Sh% | Sh%-ExpSh% |

HENRIK SEDIN | C | 240 | 2012 | 11.928 | 177.3 | 8.811 | 3.117 |

DANIEL SEDIN | L | 174 | 1551 | 11.219 | 129.5 | 8.35 | 2.869 |

SAM GAGNER | C | 150 | 1394 | 10.76 | 115.4 | 8.281 | 2.479 |

ANDREI KOSTITSYN | L | 139 | 1390 | 10 | 105.6 | 7.598 | 2.402 |

BOBBY RYAN | R | 148 | 1439 | 10.285 | 114.4 | 7.952 | 2.333 |

MARIAN GABORIK | R | 130 | 1153 | 11.275 | 104.3 | 9.05 | 2.225 |

SIDNEY CROSBY | C | 151 | 1413 | 10.686 | 119.6 | 8.461 | 2.225 |

JASON SPEZZA | C | 178 | 1691 | 10.526 | 140.6 | 8.313 | 2.213 |

ALEX TANGUAY | L | 165 | 1500 | 11 | 132.8 | 8.852 | 2.148 |

MIKE RIBEIRO | C | 177 | 1668 | 10.612 | 143.1 | 8.579 | 2.033 |

NATHAN HORTON | R | 169 | 1562 | 10.819 | 137.5 | 8.804 | 2.015 |

J.P. DUMONT | R | 107 | 1050 | 10.19 | 85.9 | 8.179 | 2.011 |

JOE THORNTON | C | 216 | 2207 | 9.787 | 171.8 | 7.784 | 2.003 |

PAVEL DATSYUK | C | 196 | 1836 | 10.675 | 160.4 | 8.738 | 1.937 |

ALEX OVECHKIN | L | 186 | 1718 | 10.827 | 155.0 | 9.019 | 1.808 |

JOFFREY LUPUL | R | 109 | 1038 | 10.501 | 90.4 | 8.708 | 1.793 |

MARTIN HAVLAT | R | 134 | 1304 | 10.276 | 110.8 | 8.499 | 1.777 |

NICKLAS BACKSTROM | C | 211 | 1880 | 11.223 | 178.2 | 9.48 | 1.743 |

THOMAS VANEK | L | 151 | 1527 | 9.889 | 124.5 | 8.155 | 1.734 |

MARTIN ST._LOUIS | R | 218 | 1912 | 11.402 | 185.1 | 9.679 | 1.723 |

… | … | … | … | … | … | … | … |

JOE PAVELSKI | C | 126 | 1624 | 7.759 | 143.1 | 8.811 | -1.052 |

RYAN CALLAHAN | R | 96 | 1223 | 7.85 | 109.3 | 8.933 | -1.083 |

RYAN O’REILLY | C | 71 | 1004 | 7.072 | 82.0 | 8.169 | -1.097 |

DANIEL WINNIK | C | 82 | 1286 | 6.376 | 96.6 | 7.513 | -1.137 |

TOMAS HOLMSTROM | L | 111 | 1331 | 8.34 | 126.9 | 9.532 | -1.192 |

JEFF HALPERN | C | 74 | 1014 | 7.298 | 86.5 | 8.53 | -1.232 |

MARTY REASONER | C | 84 | 1217 | 6.902 | 99.3 | 8.162 | -1.26 |

RYAN KESLER | C | 133 | 1606 | 8.281 | 153.5 | 9.558 | -1.277 |

SAMUEL PAHLSSON | C | 77 | 1211 | 6.358 | 92.7 | 7.654 | -1.296 |

TROY BROUWER | R | 100 | 1203 | 8.313 | 116.4 | 9.677 | -1.364 |

MIKE GRIER | R | 64 | 1032 | 6.202 | 78.2 | 7.582 | -1.38 |

SEAN BERGENHEIM | L | 77 | 1153 | 6.678 | 93.4 | 8.097 | -1.419 |

TRAVIS MOEN | L | 77 | 1186 | 6.492 | 93.9 | 7.92 | -1.428 |

SERGEI SAMSONOV | L | 83 | 1257 | 6.603 | 101.3 | 8.062 | -1.459 |

JARRET STOLL | C | 87 | 1302 | 6.682 | 106.9 | 8.211 | -1.529 |

CHRIS KUNITZ | L | 147 | 1808 | 8.131 | 174.9 | 9.671 | -1.54 |

MICHAEL FROLIK | R | 86 | 1099 | 7.825 | 103.5 | 9.42 | -1.595 |

MAXIME TALBOT | C | 85 | 1202 | 7.072 | 104.9 | 8.724 | -1.652 |

KYLE WELLWOOD | C | 83 | 1191 | 6.969 | 104.0 | 8.729 | -1.76 |

MIKE KNUBLE | R | 109 | 1477 | 7.38 | 144.1 | 9.759 | -2.379 |

I always say that order is the enemy of randomness and the fact that the top 20 are predominantly populated by offensive oriented players, many known as playmaking centers, and the bottom 20 are significantly populated by 3rd liners and defensive players tells me that the results we are seeing aren’t due to random error or errors in the methodology.

All totaled there were 222 players in the study, 26 boosted their line mates shooting percentage by at least 1.5% and 53 players boosted their line mates shooting percentage by at least 1.0%. Only 20 players (the 20 listed above) had an observed penalty of at least 1.0% to their line mates shooting percentage and only 86 showed any negative influence whatsoever. This assymetry and bias towards having more players boost shooting percentage and by larger amounts is due to selection bias. By only considering players whose line mates take at least 1000 shots while the player is on the ice eliminates all the bad players who were so bad that they didn’t get enough ice time to have 1000 shots taken by their line mates.

I should mention here that we are not taking into account quality of line mates that might impact the results. Since both the Sedin’s play together their impact on their line mates shooting percentage is really compounded (particularly for Daniel who rarely played without Henrik). There is probably a very good chance than Daniel Sedin doesn’t have that significant an impact on line mate shooting percentage, but we just can’t separate his abilities from his twin brothers abilities so they both look really good. But that said, one or some combination of both of the Sedin’s have a very significant impact on their line mates shooting percentages.

The next thing we need to do is attempt to quantify what these boosts in shooting percentages mean in terms of goals. To do this I assumed each player played 15 minutes of 5v5 ZS adjusted ice time per game over 82 games (i.e. the play a heavy ES work load over a full 82 game season). The top 25 players and bottom 25 players are listed in the table below.

Player | G/Yr | Player | G/Yr | |

HENRIK SEDIN | 15.17 | MIKE KNUBLE | -9.90 | |

DANIEL SEDIN | 11.78 | CHRIS KUNITZ | -8.13 | |

SIDNEY CROSBY | 11.11 | KYLE WELLWOOD | -7.98 | |

JOE THORNTON | 10.36 | SERGEI SAMSONOV | -7.15 | |

ANDREI KOSTITSYN | 9.95 | MAXIME TALBOT | -6.98 | |

JASON SPEZZA | 9.90 | MICHAEL FROLIK | -6.29 | |

SAM GAGNER | 9.82 | JARRET STOLL | -6.21 | |

BOBBY RYAN | 9.75 | TROY BROUWER | -5.94 | |

ALEX TANGUAY | 9.73 | TOMAS HOLMSTROM | -5.89 | |

J.P. DUMONT | 9.34 | SEAN BERGENHEIM | -5.69 | |

NATHAN HORTON | 9.25 | MIKE GRIER | -5.68 | |

PAVEL DATSYUK | 9.23 | RYAN KESLER | -5.40 | |

NICKLAS BACKSTROM | 8.54 | TRAVIS MOEN | -5.25 | |

MIKE RIBEIRO | 8.53 | MARTY REASONER | -4.96 | |

MARIAN GABORIK | 7.78 | SAMUEL PAHLSSON | -4.88 | |

MARTIN HAVLAT | 7.59 | RYAN O’REILLY | -4.79 | |

THOMAS VANEK | 7.58 | DANIEL WINNIK | -4.73 | |

JONATHAN TOEWS | 7.21 | JOE PAVELSKI | -4.73 | |

MARTIN ST._LOUIS | 7.16 | JEFF HALPERN | -4.56 | |

JOFFREY LUPUL | 7.15 | PATRICK MARLEAU | -4.40 | |

CORY STILLMAN | 7.08 | CHAD LAROSE | -4.26 | |

ALEX OVECHKIN | 6.93 | RYAN CALLAHAN | -4.07 | |

EVGENI MALKIN | 6.86 | CLARKE MACARTHUR | -3.74 | |

STEVE DOWNIE | 6.58 | JOCHEN HECHT | -3.74 | |

BRENDEN MORROW | 6.49 | SCOTTIE UPSHALL | -3.48 |

I wouldn’t necessarily consider the above numbers insignificant. All those players in the top 25 list plus 5 others boost their line mates goal scoring by 6 or more goals per season solely by boosting their line mates shooting percentages. This means there are 30 players who contribute an extra win to their team every season solely by boosting their line mates shooting percentages. The standard deviation among all 222 players is 4.18.

To put this into perspective, I compared a forwards ability to boost line mates fenwick for rate per 20 minutes of ice time (FF20). Sidney Crosby had the greatest ability to boost line mate FF20 over the past 5 seasons. His line mates FF20 when not with Crosby was 12.92 but it was 15.83 with Crosby. This equates to an extra 179 fenwick for events per season (assuming 15 minutes of ice time over 82 games) while Crosby is on the ice (note that this includes Crosby’s individual fenwick for events so it isn’t just Crosby’s ability to boost his line mates fenwick for events). Applying the league average fenwick shooting percentage of 6.29% to those 179 events we see that Crosby’s ability to boost on-ice FF20 results in an extra 11.26 goals per season. The standard deviation among all players is 3.59, or slightly less than the standard deviation for impact on goals due to influence on line mate shooting percentage. Although there is greater margin for error in the shooting percentage analysis, it is theoretically possibly that **a players ability to boost his line mates shooting percentage has a greater impact on goal scoring than the players ability to drive fenwick for events**.

Let’s look at this in yet another way. If we take (LM Goals – ExpGoals)/LM Goals we will find the percentage of goals that the players line mates scored that were due to the players ability to boost their shooting percentages. The top and bottom 25 look like this.

Player | LM Goals | Exp Goals | %G due to Sh% Influence |

HENRIK SEDIN | 240 | 177.269 | 26.1% |

DANIEL SEDIN | 174 | 129.512 | 25.6% |

ANDREI KOSTITSYN | 139 | 105.61 | 24.0% |

SAM GAGNER | 150 | 115.439 | 23.0% |

BOBBY RYAN | 148 | 114.434 | 22.7% |

JASON SPEZZA | 178 | 140.568 | 21.0% |

SIDNEY CROSBY | 151 | 119.559 | 20.8% |

JOE THORNTON | 216 | 171.803 | 20.5% |

J.P. DUMONT | 107 | 85.878 | 19.7% |

MARIAN GABORIK | 130 | 104.341 | 19.7% |

ALEX TANGUAY | 165 | 132.78 | 19.5% |

MIKE RIBEIRO | 177 | 143.092 | 19.2% |

NATHAN HORTON | 169 | 137.52 | 18.6% |

PAVEL DATSYUK | 196 | 160.437 | 18.1% |

THOMAS VANEK | 151 | 124.534 | 17.5% |

CORY STILLMAN | 102 | 84.301 | 17.4% |

MARTIN HAVLAT | 134 | 110.829 | 17.3% |

JOFFREY LUPUL | 109 | 90.386 | 17.1% |

MIKKO KOIVU | 129 | 107.39 | 16.8% |

ALEX OVECHKIN | 186 | 154.955 | 16.7% |

FRANS NIELSEN | 97 | 81.722 | 15.8% |

NICKLAS BACKSTROM | 211 | 178.224 | 15.5% |

BRENDEN MORROW | 133 | 112.624 | 15.3% |

LOUI ERIKSSON | 170 | 143.991 | 15.3% |

MATTHEW LOMBARDI | 103 | 87.285 | 15.3% |

… | … | … | … |

CLARKE MACARTHUR | 117 | 128.858 | -10.1% |

SHAWN HORCOFF | 105 | 116.296 | -10.8% |

PATRICK MARLEAU | 151 | 168.988 | -11.9% |

SCOTTIE UPSHALL | 74 | 82.866 | -12.0% |

JOE PAVELSKI | 126 | 143.091 | -13.6% |

CHAD LAROSE | 102 | 115.857 | -13.6% |

RYAN CALLAHAN | 96 | 109.252 | -13.8% |

TOMAS HOLMSTROM | 111 | 126.873 | -14.3% |

RYAN KESLER | 133 | 153.497 | -15.4% |

RYAN O’REILLY | 71 | 82.019 | -15.5% |

TROY BROUWER | 100 | 116.417 | -16.4% |

JEFF HALPERN | 74 | 86.489 | -16.9% |

DANIEL WINNIK | 82 | 96.614 | -17.8% |

MARTY REASONER | 84 | 99.328 | -18.2% |

CHRIS KUNITZ | 147 | 174.858 | -19.0% |

SAMUEL PAHLSSON | 77 | 92.69 | -20.4% |

MICHAEL FROLIK | 86 | 103.529 | -20.4% |

SEAN BERGENHEIM | 77 | 93.363 | -21.3% |

TRAVIS MOEN | 77 | 93.927 | -22.0% |

SERGEI SAMSONOV | 83 | 101.341 | -22.1% |

MIKE GRIER | 64 | 78.245 | -22.3% |

JARRET STOLL | 87 | 106.912 | -22.9% |

MAXIME TALBOT | 85 | 104.859 | -23.4% |

KYLE WELLWOOD | 83 | 103.962 | -25.3% |

MIKE KNUBLE | 109 | 144.147 | -32.2% |

In total there were 27 players which had >15% of all their line mates goals attributed to their ability to boost their line mates shooting percentage and there were 59 players who had >10% of their line mates goals attributed to their ability to boost their line mates shooting percentage. I don’t consider this insignificant.

One final thing to look at is how a players assist rates compare to their ability to boost line mate shooting percentages.

That is actually a fairly strong relationship between a players assist rate and the players ability to boost line mates shooting percentages. It really isn’t unexpected, but it is good to see. Playmaking is a valuable skill in generating offense.

I think this overstates things because you haven’t regressed the results to the mean at all. Over ~1000-2000 shots, simple variance will leave us with ~1-1.5% uncertainty on the shooting percentage. That variance will tend to broaden the distribution from the true talents, making the extremes look more extreme than their long-run performance will be and overstating the importance of this effect.

I will grant you that, the effects listed above quite possibly are over emphasized. But with that said, I am not sure standard methods for accounting for uncertainty necessarily apply. There is a lot more going on in hockey than goes on in ‘coin flipping’ so I am not certain uncertainty can be accounted for in the same way. For example, Mike Knuble has the largest negative impact. We also know that Knuble has one of the highest shooting percentage because he takes shots from high percentage zones (basically he stands in front of the net chipping in rebounds). So, when Knuble is on the ice he is taking away these high percentage shots away from his line mates. When his line mates are on the ice with someone other than Knuble, these high percentage shots may be available for them to take. This means some chunk of Knuble’s negative influence is systematic and not subject to uncertainty. Or, put in a different way, because of Knuble’s style of play, the mean Knuble’s line mates shooting percentages would ‘regress to’ when on the ice with him is different than another players teammates mean shooting percentage that we should ‘regress to’.

Erm, don’t get me wrong — I’m not arguing that Knuble and Crosby are equals in this regard.

Just that any finite measurement will be broadened relative to the underlying talent, and the extent of that broadening depends on the variability of the thing being measured and the sample size — and that 1000-2000 shots is a decent but not great sample size for a shooting percentage.

Phil Kessel has a 10.8% career shooting percentage after 1532 shots; would you be shocked if a magic probing device told us that his true talent is that of a 10.2% shooter (meaning he ran hot by eight goals over the course of his career to date)?

Perhaps the existence of such a device would shock you, but I don’t think its output would, because you recognize that ~1000-2000 shots gives us a good but not great sense of how good a shooter someone is. The noise on the measurement in this post is even larger, because the with-you portion of the analysis has ~1000-2000 shots and there is additional uncertainty on the without-you analysis.

You could run some split half correlations to figure out the reliability and estimate the regression to the mean to figure out whether accounting for that would reduce the measured effect by 25% or 75%, but there’s no doubt it will reduce it.

For sure and I did grant you that my numbers in the original article are most likely over emphasized. The point I was making is I am not certain using a typical coin flipping model will in any way accurately estimate this because there are so many other factors involved.

As for Phil Kessel’s shooting percentage his true-talent shooting percentage may well be 10.2%. Might be 11.2% too. Of course, if he played with Sidney Crosby it may be 11.8%, or if he learned to play more like Mike Knuble it might be 12.8% or higher. For that matter, zone starts may very well affect his shooting percentage and if he started getting more defensive and neutral zone faceoffs his expected shooting percentage may in fact rise. The point is, it is really difficult to determine how lucky, or unlucky, Phil Kessel has been because we have no clue what his expected level based on his talent level and the situations he has played in.

As for the without-you uncertainty, that may not be an issue because while any particular line mates without-you number may be full of uncertainty, across the numerous line mates any particular player has had the uncertainties are likely to start to cancel each other out and the overall uncertainty in the without-you stats probably approaches something fairly small (especially those that have changed teams and have had a lot of line mates) relative to any with-you uncertainty. The total number of shots across all of all the without-you stats I suspect would be well into the 10’s of thousands (particularly for any player who has changed teams a few times).