How good is Patrik Laine’s shot?

Patrik Laine is playing his first season in the NHL and currently leads the league in scoring with 12 goals. With 51 shots on goal, his shooting percentage is 23.5 %. How does this number compare to great goal scores over the years? I downloaded NHL player statistics for each season from 1967–1968 onwards, which was the first year the number of shots was recorded. I then calculated career summaries for each player. But if we simply look for players with the highest shooting percentages, the first 12 all scored one goal with just one shot. Obviously these are not the best shooters, just some random flukes. In its official leaderboard for all-time career shooting percentage (S%), the NHL only counts players with at least 800 shots. This is what the top 10 looks like:

Name Pos GP G A PTS S S%
1 Craig Simpson LW 634 247 250 497 1,044 23.7
2 Charlie Simmer LW 712 342 369 711 1,531 22.3
3 Paul MacLean RW 719 324 349 673 1,513 21.4
4 Mike Bossy RW 752 573 553 1,126 2,705 21.2
5 Yvon Lambert LW 683 206 273 479 1,038 19.8
6 Rick Middleton RW 1,005 448 540 988 2,275 19.7
7 Blaine Stoughton RW 526 258 191 449 1,322 19.5
8 Darryl Sutter LW 406 161 118 279 829 19.4
9 Rob Brown RW 543 190 248 438 979 19.4
10 Mike Ridley C 866 292 466 758 1,513 19.3

Requiring a minimum number of shots (or goals) does get rid of the flukes, but how can you compare a rookie player? What kind of method could be used to take the scarcity of evidence into account, until the player catches up with the threshold? David Robinson has written a terrific series of articles for situations like this, using baseball statistics as an example. I’ll follow one of his tutorials and use empirical Bayes estimation to obtain a more reliable picture. In short, we’ll first use all players’ data to obtain an estimate for a beta prior, and then use each player’s own data to update the prior based on individual evidence. Put another way, we start by assuming everyone is average, and if and only if they show more and more evidence to the contrary, we start to gradually consider them as special. For a more much better description, please see the original blog post. All R code is also adapted from that post.

Before we get to estimation of the beta prior, let’s first check if we should use all of the available data or only a subset. Since in this case we are estimating only one prior, we would like all players to come from a single distribution. As the gameplay has surely changed a bit over the years, let’s look at the overall shooting percentages over the 49 seasons. Also, since defensemen normally play futher away from the opponent’s net than forwards, player position is likely to have an effect as well. Let’s look at shooting percentages separately for each position (excluding players with less than ten goals).

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As we can see, shooting percentages used to be much higher around the 1980s. For this simple analysis, I’ll only include data from season 1996–1997 onwards. I’ll also leave out the defensemen, as they tend to have lower shooting percentages. (I hope to write follow-ups posts later with all of the data included and handled properly, either using some of the other approaches David has described for empirical Bayes, with a standard Bayesian analysis, or maybe even both.)

Overall, the average shooting percentage for all forwards over the last 20 seasons is 11.0 %. Next, let’s estimate a beta prior from the data and see how it fits:

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Shooting percentages can now be adjusted using this prior. This will shrink individual players’ estimates towards the horizontal dashed line. The more evidence there is for an individual (the brighter the blue dot), the more we trust it. The darker dots show a lot of shrinkage, whereas the light ones are much closer to the diagonal red line, which marks the case of no shrinkage at all.

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Finally, let’s look at the ranking (from season 1996–1997 onwards) for shooting percentage estimated with empirical Bayes (EB). Patrik Laine currently sits at number 40, and only time will tell where he moves on that list. But what we do know today, is that he is one of only four 18-year-olds to score two hat tricks in the NHL (others being Jack Hamilton, Dale Hawerchuk, and Trevor Linden), and he still has the rest of the regular season to hunt for a third one before his 19th birthday on April 19th, 2017.

Name Pos GP G A PTS S S% EB
1 Alex Tanguay LW 1,088 283 580 863 1,525 18.6 17.9
2 Andrew Brunette LW 1,099 265 462 727 1,500 17.7 17.1
3 Steven Stamkos C 586 321 261 582 1,876 17.1 16.7
4 Mark Parrish RW 722 216 171 387 1,247 17.3 16.7
5 Dmitri Khristich C 420 111 171 282 633 17.5 16.3
6 Mike Ridley C 75 20 32 52 79 25.3 16.1
7 Tomas Holmstrom LW 1,026 243 287 530 1,489 16.3 15.9
8 Gary Roberts LW 639 181 224 405 1,120 16.2 15.6
9 Brenden Morrow LW 991 265 310 575 1,670 15.9 15.5
10 Jan Hrdina C 513 101 196 297 619 16.3 15.3
11 Jason Allison C 519 152 326 478 962 15.8 15.2
12 Ziggy Palffy RW 565 276 333 609 1,799 15.3 15.0
13 John LeClair LW 624 281 274 555 1,833 15.3 15.0
14 Alexander Mogilny RW 530 207 274 481 1,341 15.4 15.0
15 Pierre Turgeon C 622 197 351 548 1,285 15.3 14.9
16 Tyler Bozak C 451 112 169 281 717 15.6 14.8
17 Sergei Kostitsyn LW 353 67 109 176 414 16.2 14.8
18 Joe Nieuwendyk C 628 236 242 478 1,555 15.2 14.8
19 Anson Carter RW 674 202 219 421 1,331 15.2 14.8
20 Tony Hrkac C 425 70 105 175 438 16.0 14.7
21 Mark Messier C 555 155 264 419 1,015 15.3 14.7
22 Yanic Perreault C 742 217 237 454 1,436 15.1 14.7
23 Adam Deadmarsh RW 441 154 154 308 1,010 15.2 14.7
24 Adam Henrique C 364 101 109 210 650 15.5 14.7
25 Teemu Selanne RW 1,192 521 594 1,115 3,528 14.8 14.6
26 Jonathan Toews C 662 255 321 576 1,710 14.9 14.6
27 Jiri Hudler C 680 161 256 417 1,068 15.1 14.6
28 Paul Byron C 217 34 43 77 198 17.2 14.5
29 Brad Marchand C 470 158 147 305 1,057 14.9 14.5
30 Sidney Crosby C 716 348 603 951 2,376 14.6 14.4
31 Mike Sillinger C 831 210 234 444 1,420 14.8 14.4
32 Keith Tkachuk LW 893 394 382 776 2,713 14.5 14.3
33 Peter Forsberg C 579 204 515 719 1,390 14.7 14.3
34 Milan Lucic LW 664 164 242 406 1,111 14.8 14.3
35 Dany Heatley RW 869 372 419 791 2,565 14.5 14.3
36 David Desharnais C 420 78 168 246 511 15.3 14.3
37 Martin Straka LW 714 206 370 576 1,408 14.6 14.3
38 Thomas Vanek LW 824 320 337 657 2,213 14.5 14.2
39 Stephane Matteau LW 471 75 88 163 493 15.2 14.2
40 Patrik Laine RW 18 12 5 17 51 23.5 14.2
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