drai

Zenon Ranking Plots

Uncategorized

This is a quick post visualizing my new Zenon Rankings for faceoffs. For an introduction to my Zenon Rankings and Elo-type models see this post.

The below plot shows 8 players throughout the 2015-16 season. As mentioned in the introductory post my model assumes that players start off with an initial ranking of 1500 and a deviation of 50. As players play more and more games their deviation parameters drop because we deem their rankings to be more and more reliable. Large deviations also mean that we also adjust rankings in a more extreme way in accordance with results.

Winning faceoffs particularly against tough opponents leads to ratings increases and losing lots of faceoffs especially to weak opponents causes decreases. In my other posts I focused on displaying the final Zenon Rankings or the rankings for each player after they took their last faceoff in the time-frame of the model. This only captures some of the information that an elo-type model can tell us. A well-specified elo-type model can detect improvements and declines during the season, and sometimes blending these kinds of ranking over a time-period can be more informative about actual ability than the final rankings alone.

Glicko 2015-16

Interactive Version

The bolded line represents the weighted average Zenon Ranking of 1507. Players that ended the season above the line are considered by the model above average drawmen and expected to win more than 50% of their draws against neutral competition. The opposite is true of those below the line. The numbers on the x-axis represent days during the 2015-16 season. There were 226 days in the 2015-16 season including the post-season where games were played. As you can see by looking at the Nuge or McDavid who played on teams not included in the playoffs, the post-season began on approximately day 180.

All of the players in the graph start at the same point, but they quickly diverge based on their initial results due to the deviance parameter. Although these initial divergences are drastic, they are not condemning in the sense that it is very possible to recover from a low ranking early in the season. Just look at the green line depicting Tyler Seguin for an example. On average, however, players that diverge downwards quickly, do not end up above average by the end of the season. This is part of the reason why the glicko model outperformed a standard elo-model in this application. Elo models do not have deviance parameters and so all players are adjusted equally regardless the number of faceoffs they have taken.

Looking at the purple line representing Evgeni Malkin we see that when he was hurt over two stretches that his ranking stays constant. When not playing, our model doesn’t update his ranking or deviation parameter. Second we can notice that he seemed to improve somewhat during the playoffs as represented by the uptick at the end of the season. It is too early to tell exactly how sensitive this model is to real improvements, but assuming the model is a decent measure of actual ability (it does have some levels of predictive power as outlined in the introduction post) we can say that Malkin was a better drawmen in the playoffs than the period just before he was injured. Whether this is because he was taking draws more seriously or playing injury free is another matter.

leon draisaitl

Red line represents Leon Draisaitl’s ranking after each day of the 2015-16 season including playoffs. The dark grey error bars are 95% confidence region based on Draisaitl’s deviance parameter and ranking. Here we can see that Draisaitl is approximately league average at taking faceoffs.

Here is a visualization of how the deviation parameter works. At the beginning we are assuming that Leon Draisaitl is highly likely to have a true value between 1400 and 1600. As he actually takes faceoffs his rating adjusts and his deviation shrinks. The error bars around the red line represent 95% confidence regions based on the deviance parameter. The dotted line on the graph roughly represents the beginning of playoffs. Since the Oilers didnt’t make the playoffs, Draisaitl never took any faceoffs and accordingly his ranking nor his deviation was changed. But even before the dotted line we can see that his deviance became less volatile. One feature of the glicko model that Mark Glickman originally recommended is that there is some sort of lower bound or slowing mechanism on the deviance parameter so that the model doesn’t reach a state of stasis. We can see the consequences of this model specification visually in the above graph.

All of the 2015-16 Zenon Rankings are here

For the complete rankings for 2008-2016 check here

And for a refresher on the Zenon Model check here.

If there are any specific players or teams that you would like me to take a look into, just let me know and I’ll get back to you. I’m always looking for feedback on what users find useful.

 

 

 

 

 

 

 

 

 

 

 

 

 

faceoff gordon

Zenon Rankings 2015-16

Faceoffs

These are the Zenon Faceoff Rankings for the complete 2015-16 season. For an explanation of what Zenon Rankings are see here.

For the complete rankings for 2008-2016 see here.

For some Zenon Ranking plots check here.

Player Rating Lower Bound Upper Bound Deviation Faceoff % Wins Faceoffs
1 JONATHAN.TOEWS 1570 1553 1587 8.5 58.58% 1031 1760
2 RYAN.KESLER 1563 1547 1580 8.3 58.31% 1077 1847
3 CLAUDE.GIROUX 1562 1546 1578 7.9 57.06% 1160 2033
4 PATRICE.BERGERON 1559 1543 1575 8.0 57.03% 1120 1964
5 JORDAN.STAAL 1559 1540 1578 9.4 57.78% 806 1395
6 BOYD.GORDON 1559 1536 1582 11.5 57.87% 526 909
7 MATT.DUCHENE 1558 1533 1584 12.6 57.92% 428 739
8 BRAD.MALONE 1557 1490 1624 33.4 64.52% 40 62
9 MICHAEL.CHAPUT 1556 1493 1620 31.6 65.33% 49 75
10 JAY.BEAGLE 1556 1532 1580 12.2 57.21% 464 811
11 PAUL.STASTNY 1555 1538 1572 8.7 56.70% 939 1656
12 BRIAN.FLYNN 1554 1519 1590 17.8 57.80% 200 346
13 RYAN.O’REILLY 1554 1537 1570 8.3 56.51% 1024 1812
14 PAUL.GAUSTAD 1550 1527 1572 11.5 55.96% 512 915
15 TYLER.SEGUIN 1549 1525 1573 11.9 55.61% 471 847
16 TYLER.BOZAK 1549 1527 1570 10.7 56.37% 597 1059
17 MIKKO.KOIVU 1548 1532 1564 8.0 56.19% 1089 1938
18 JARRET.STOLL 1546 1522 1569 11.7 56.26% 494 878
19 DUSTIN.JEFFREY 1545 1477 1613 33.9 60.34% 35 58
20 ANTOINE.VERMETTE 1544 1525 1563 9.5 55.81% 754 1351
21 MARTIN.HANZAL 1544 1522 1565 10.7 55.97% 586 1047
22 DOMINIC.MOORE 1541 1518 1564 11.4 55.08% 510 926
23 JIM.O’BRIEN 1541 1470 1612 35.4 59.18% 29 49
24 MATT.CULLEN 1540 1521 1558 9.2 54.77% 787 1437
25 JOE.PAVELSKI 1540 1520 1559 9.8 54.46% 690 1267
27 TOMAS.HERTL 1540 1509 1571 15.5 55.90% 270 483
28 BRAD.RICHARDSON 1539 1517 1561 11.1 54.42% 523 961
29 T.J..OSHIE 1538 1501 1575 18.3 53.89% 173 321
30 ANTON.LANDER 1537 1511 1563 13.0 54.55% 378 693
31 LUKE.GLENDENING 1537 1517 1557 9.9 54.61% 669 1225
32 TROY.BROUWER 1536 1482 1590 27.1 56.30% 67 119
33 JOHN.TAVARES 1536 1518 1553 8.8 54.44% 864 1587
34 DEREK.MACKENZIE 1536 1512 1559 11.5 54.80% 491 896
35 MATT.HENDRICKS 1535 1504 1567 15.8 55.41% 251 453
36 ANZE.KOPITAR 1534 1518 1551 8.1 53.77% 1020 1897
37 JAY.MCCLEMENT 1534 1508 1561 13.2 55.31% 375 678
38 MARK.ARCOBELLO 1534 1493 1575 20.6 54.55% 132 242
39 CHRIS.WAGNER 1533 1494 1572 19.4 54.61% 154 282
40 CHRIS.THORBURN 1532 1478 1586 26.9 55.74% 68 122
41 GABRIEL.LANDESKOG 1531 1463 1599 34.1 55.36% 31 56
42 DEREK.GRANT 1530 1475 1586 27.8 54.95% 61 111
43 DEREK.RYAN 1530 1463 1598 33.7 59.32% 35 59
44 BEN.SMITH 1530 1484 1576 22.9 54.05% 100 185
45 MIKE.FISHER 1530 1512 1548 9.0 53.05% 809 1525
46 ERIC.STAAL 1530 1507 1552 11.4 53.71% 492 916
47 PAVEL.DATSYUK 1530 1510 1550 10.0 53.28% 641 1203
48 JOE.COLBORNE 1529 1480 1579 24.6 54.84% 85 155
49 COLTON.SISSONS 1529 1492 1566 18.5 55.10% 173 314
50 JASON.SPEZZA 1528 1508 1549 10.2 53.65% 632 1178
51 JOE.THORNTON 1527 1505 1549 11.0 52.76% 525 995
52 BRANDON.DUBINSKY 1527 1509 1545 9.1 52.56% 780 1484
53 STEVE.OTT 1526 1469 1584 28.9 55.56% 55 99
55 BOONE.JENNER 1525 1487 1563 18.9 53.06% 156 294
57 JAROME.IGINLA 1523 1468 1578 27.4 53.04% 61 115
58 RYAN.JOHANSEN 1523 1504 1541 9.2 52.17% 757 1451
60 BEN.STREET 1522 1451 1594 35.8 55.32% 26 47
61 TRAVIS.ZAJAC 1522 1503 1541 9.4 51.55% 715 1387
62 RYAN.WHITE 1522 1488 1556 17.0 53.02% 202 381
63 LAURI.KORPIKOSKI 1522 1445 1598 38.4 52.94% 18 34
64 ERIK.HAULA 1521 1498 1545 11.6 52.53% 457 870
66 CHANDLER.STEPHENSON 1520 1452 1589 34.4 54.55% 30 55
67 VALTTERI.FILPPULA 1520 1502 1538 8.8 52.03% 822 1580
69 BRANDON.SAAD 1520 1443 1597 38.5 55.88% 19 34
70 ZACK.SMITH 1520 1494 1545 12.6 52.13% 380 729
71 SIDNEY.CROSBY 1520 1505 1534 7.2 51.86% 1281 2470
72 BRYAN.LITTLE 1519 1500 1539 9.6 51.29% 674 1314
75 VERNON.FIDDLER 1519 1497 1541 11.0 50.55% 501 991
76 KYLE.CHIPCHURA 1519 1471 1567 23.8 52.38% 88 168
78 RYAN.CALLAHAN 1519 1446 1591 36.2 53.33% 24 45
79 JUSTIN.WILLIAMS 1518 1464 1572 27.1 52.50% 63 120
81 SHANE.DOAN 1518 1467 1568 25.3 51.75% 74 143
82 TORREY.MITCHELL 1517 1492 1543 12.8 51.60% 370 717
83 DAVID.BACKES 1517 1499 1536 9.4 51.21% 721 1408
86 CAL.O’REILLY 1517 1461 1573 27.9 54.13% 59 109
88 KYLE.TURRIS 1516 1495 1538 10.7 51.34% 536 1044
89 JORDAN.MARTINOOK 1516 1439 1594 38.7 54.55% 18 33
90 HENRIK.ZETTERBERG 1516 1496 1537 10.3 50.27% 569 1132
92 JEAN-GABRIEL.PAGEAU 1516 1496 1536 10.1 52.17% 614 1177
93 ANDREW.AGOZZINO 1516 1444 1588 36.1 53.33% 24 45
95 SEAN.MONAHAN 1516 1499 1533 8.4 51.01% 887 1739
96 JOHAN.LARSSON 1516 1491 1540 12.4 51.12% 388 759
99 JACOB.DE LA ROSE 1515 1463 1567 26.2 51.54% 67 130
102 NICK.SHORE 1515 1490 1540 12.5 51.87% 388 748
108 TOMAS.FLEISCHMANN 1514 1441 1586 36.2 53.33% 24 45
109 MARK.LETESTU 1514 1493 1534 10.2 51.29% 596 1162
110 BRANDON.SUTTER 1513 1474 1552 19.5 52.52% 146 278
114 BO.HORVAT 1512 1494 1530 9.0 50.90% 760 1493
116 LARS.ELLER 1512 1479 1545 16.4 50.61% 207 409
117 JUSSI.JOKINEN 1512 1473 1551 19.6 50.92% 139 273
119 VICTOR.RASK 1512 1489 1534 11.3 51.23% 479 935
120 BRIAN.BOYLE 1511 1488 1534 11.5 50.33% 452 898
121 DERICK.BRASSARD 1511 1492 1529 9.2 50.35% 722 1434
122 FRANS.NIELSEN 1511 1491 1530 9.6 50.57% 663 1311
123 NICK.BJUGSTAD 1511 1488 1533 11.1 51.19% 493 963
124 CODY.BASS 1511 1439 1582 35.7 51.06% 24 47
125 LEO.KOMAROV 1511 1458 1563 26.4 48.82% 62 127
126 NATE.THOMPSON 1510 1481 1540 14.9 51.29% 258 503
127 VINCENT.LECAVALIER 1510 1484 1537 13.3 51.84% 338 652
129 COLTON.SCEVIOUR 1510 1439 1581 35.4 51.02% 25 49
130 NICK.SPALING 1510 1484 1535 12.8 50.49% 364 721
132 DREW.STAFFORD 1510 1452 1567 28.6 50.50% 51 101
134 RYAN.CARTER 1509 1434 1583 37.2 52.50% 21 40
135 PATRICK.MARLEAU 1509 1481 1536 13.7 50.33% 309 614
136 SHAWN.HORCOFF 1509 1482 1535 13.3 50.91% 336 660
138 TOMAS.PLEKANEC 1508 1491 1526 8.7 49.78% 804 1615
140 MIKA.ZIBANEJAD 1508 1489 1527 9.6 50.46% 659 1306
158 RADEK.FAKSA 1507 1480 1534 13.7 49.59% 302 609
161 MICHAEL.MCCARRON 1507 1459 1554 23.7 50.30% 85 169
162 ALEKSANDER.BARKOV 1507 1487 1526 9.6 49.66% 649 1307
168 MICHAEL.LATTA 1506 1461 1551 22.4 51.52% 102 198
169 ANDY.ANDREOFF 1506 1467 1545 19.7 50.55% 138 273
171 MAX.MCCORMICK 1506 1443 1569 31.3 51.32% 39 76
172 NIC.DOWD 1506 1429 1583 38.4 52.94% 18 34
176 STEVEN.STAMKOS 1505 1483 1528 11.3 49.84% 466 935
178 DAVID.KREJCI 1505 1484 1526 10.4 50.05% 553 1105
180 JORI.LEHTERA 1504 1484 1524 10.0 50.25% 610 1214
181 CORBAN.KNIGHT 1504 1448 1561 28.2 50.94% 54 106
182 BRYAN.LERG 1504 1427 1581 38.7 51.52% 17 33
183 NICKLAS.BACKSTROM 1504 1486 1522 8.8 48.42% 768 1586
184 EVANDER.KANE 1504 1451 1557 26.6 50.00% 62 124
185 RYAN.GETZLAF 1504 1485 1523 9.6 49.70% 654 1316
187 MIKE.RICHARDS 1503 1476 1531 13.8 49.17% 296 602
188 DAVID.JONES 1503 1426 1580 38.5 50.00% 17 34
189 BLAKE.COMEAU 1503 1475 1531 14.2 48.76% 276 566
190 CODY.EAKIN 1503 1484 1521 9.2 48.85% 702 1437
191 NICK.PAUL 1503 1436 1570 33.5 51.67% 31 60
194 DARREN.HELM 1502 1440 1564 31.1 50.00% 39 78
195 PATRIK.BERGLUND 1502 1468 1536 17.0 49.34% 187 379
198 CASEY.CIZIKAS 1501 1480 1522 10.4 49.37% 546 1106
204 NICK.BONINO 1501 1482 1520 9.6 49.85% 662 1328
205 NAZEM.KADRI 1501 1482 1520 9.6 49.16% 641 1304
208 KYLE.BRODZIAK 1501 1474 1527 13.4 50.08% 327 653
209 MARCUS.KRUGER 1501 1472 1529 14.2 49.13% 281 572
212 JOONAS.KEMPPAINEN 1500 1469 1532 15.6 49.46% 227 459
216 MATT.READ 1500 1431 1569 34.6 48.15% 26 54
217 VINCENT.TROCHECK 1500 1480 1520 10.1 49.06% 575 1172
224 JAMIE.BENN 1499 1469 1529 15.0 47.83% 242 506
227 KEVIN.PORTER 1499 1439 1559 30.1 50.57% 44 87
228 RILEY.NASH 1499 1465 1532 16.8 49.49% 193 390
231 ZAC.DALPE 1498 1425 1572 36.6 50.00% 21 42
232 PIERRE-EDOUARD.BELLEMARE 1498 1471 1525 13.5 47.27% 303 641
233 JOHN.MITCHELL 1498 1475 1522 11.8 48.88% 415 849
236 ALAN.QUINE 1498 1436 1560 30.9 49.37% 39 79
237 SEAN.COUTURIER 1498 1477 1519 10.4 48.56% 539 1110
238 JEFF.CARTER 1498 1478 1517 9.6 48.75% 642 1317
239 BRAD.RICHARDS 1498 1459 1536 19.4 49.29% 138 280
242 ELIAS.LINDHOLM 1497 1465 1529 16.0 49.08% 213 434
243 OSCAR.LINDBERG 1496 1457 1535 19.5 48.56% 135 278
244 CEDRIC.PAQUETTE 1496 1459 1533 18.5 48.73% 153 314
245 J.T..BROWN 1496 1426 1566 35.0 47.06% 24 51
247 NATHAN.MACKINNON 1496 1475 1517 10.7 48.42% 507 1047
248 LEON.DRAISAITL 1496 1474 1517 10.7 48.36% 502 1038
249 NICK.FOLIGNO 1496 1449 1543 23.4 47.16% 83 176
250 DAVID.DESHARNAIS 1496 1471 1520 12.1 48.69% 391 803
266 JONATHAN.MARCHESSAULT 1494 1433 1555 30.4 47.62% 40 84
280 JORDAN.WEAL 1494 1429 1558 32.4 48.53% 33 68
285 JADEN.SCHWARTZ 1493 1433 1554 30.5 48.19% 40 83
286 MIKAEL.GRANLUND 1493 1473 1514 10.5 48.46% 534 1102
316 PHILLIP.DANAULT 1493 1463 1522 14.8 47.59% 247 519
325 ANDREW.DESJARDINS 1492 1435 1550 28.7 47.00% 47 100
334 ADAM.LOWRY 1492 1468 1516 11.8 46.27% 391 845
338 BYRON.FROESE 1492 1465 1518 13.4 48.29% 310 642
343 WILLIAM.NYLANDER 1491 1453 1529 19.0 49.14% 143 291
346 DALE.WEISE 1491 1414 1567 38.3 45.71% 16 35
347 GREGORY.CAMPBELL 1490 1460 1521 15.3 47.51% 229 482
350 BRETT.CONNOLLY 1490 1411 1568 39.2 45.16% 14 31
351 JACOB.JOSEFSON 1490 1463 1516 13.2 48.43% 323 667
352 BRAYDEN.SCHENN 1490 1440 1540 25.0 45.64% 68 149
355 NICK.COUSINS 1489 1450 1529 19.5 47.81% 131 274
357 PATRICK.SHARP 1489 1416 1562 36.6 44.19% 19 43
359 ALEX.GALCHENYUK 1489 1464 1514 12.5 47.93% 359 749
361 EVGENY.KUZNETSOV 1489 1470 1508 9.6 47.98% 630 1313
362 MIKAEL.BACKLUND 1489 1468 1509 10.3 47.16% 539 1143
364 ANDRE.BURAKOVSKY 1488 1414 1562 37.0 46.34% 19 41
365 DENNIS.RASMUSSEN 1488 1451 1526 18.6 46.91% 144 307
366 TYLER.GAUDET 1488 1429 1547 29.5 46.74% 43 92
367 FREDERIK.GAUTHIER 1488 1433 1544 27.9 47.27% 52 110
368 CODY.HODGSON 1488 1430 1546 29.0 46.94% 46 98
372 MATT.STAJAN 1488 1463 1512 12.2 47.34% 373 788
374 MIKE.SANTORELLI 1488 1439 1537 24.4 47.47% 75 158
376 JOEL.WARD 1488 1460 1515 13.6 46.18% 290 628
378 CARL.SODERBERG 1487 1462 1513 12.8 47.01% 338 719
381 TYLER.JOHNSON 1487 1468 1507 9.8 47.48% 604 1272
388 DEREK.STEPAN 1486 1466 1506 10.1 46.85% 558 1191
392 ANDREW.SHAW 1486 1451 1521 17.5 47.34% 169 357
394 MIKHAIL.GRABOVSKI 1486 1455 1517 15.6 47.73% 221 463
397 MAX.TALBOT 1486 1450 1521 17.7 47.54% 164 345
403 LOGAN.SHAW 1485 1411 1559 37.0 41.46% 17 41
405 BROCK.NELSON 1485 1455 1515 14.9 47.32% 238 503
406 JASON.POMINVILLE 1485 1425 1544 29.8 45.56% 41 90
408 MATHIEU.PERREAULT 1484 1440 1529 22.1 46.31% 94 203
412 JOAKIM.ANDERSSON 1482 1420 1544 30.9 43.75% 35 80
418 BRENDAN.GAUNCE 1481 1425 1537 28.0 45.79% 49 107
419 CALLE.JARNKROK 1481 1457 1505 11.8 45.72% 395 864
420 BRANDON.PIRRI 1481 1430 1532 25.4 46.15% 66 143
424 HENRIK.SEDIN 1480 1461 1499 9.5 46.03% 620 1347
425 PETER.HOLLAND 1480 1449 1511 15.6 46.45% 216 465
427 LAURENT.DAUPHIN 1480 1416 1543 31.8 43.84% 32 73
428 ANDREW.COPP 1480 1449 1510 15.2 46.09% 224 486
429 BRIAN.GIONTA 1480 1426 1533 27.0 45.00% 54 120
431 LOGAN.COUTURE 1479 1456 1502 11.7 45.88% 395 861
432 GREG.MCKEGG 1479 1424 1534 27.4 44.74% 51 114
433 SAM.BENNETT 1479 1444 1514 17.7 46.11% 160 347
435 CHRIS.TIERNEY 1479 1457 1500 10.7 45.91% 488 1063
439 WILLIAM.KARLSSON 1478 1455 1500 11.4 45.66% 416 911
440 OSKAR.SUNDQVIST 1477 1427 1528 25.1 45.21% 66 146
442 ZEMGUS.GIRGENSONS 1477 1441 1513 18.0 45.67% 153 335
443 JEFF.SKINNER 1476 1405 1548 35.8 42.55% 20 47
444 RILEY.SHEAHAN 1476 1452 1500 12.1 45.83% 374 816
445 RICKARD.RAKELL 1476 1446 1506 15.1 45.20% 226 500
446 JOSH.JOORIS 1476 1436 1516 20.1 44.36% 114 257
447 CHRIS.KELLY 1476 1406 1546 35.1 42.31% 22 52
448 DAVE.BOLLAND 1476 1440 1511 17.8 45.75% 156 341
449 DAVID.LEGWAND 1476 1443 1508 16.1 45.90% 196 427
451 BENOIT.POULIOT 1475 1404 1546 35.4 40.82% 20 49
452 TANNER.KERO 1475 1422 1529 26.7 44.72% 55 123
461 VINCENT.HINOSTROZA 1473 1395 1551 39.0 40.63% 13 32
462 MARCUS.JOHANSSON 1473 1435 1511 18.8 44.19% 133 301
463 VLADISLAV.NAMESTNIKOV 1473 1443 1503 15.0 45.47% 231 508
464 ZACH.SILL 1473 1410 1535 31.3 42.86% 33 77
466 ADAM.HENRIQUE 1472 1453 1491 9.4 44.68% 617 1381
467 KYLE.OKPOSO 1472 1412 1532 30.0 42.70% 38 89
472 J.T..MILLER 1471 1423 1519 24.1 43.03% 71 165
473 SCOTT.LAUGHTON 1471 1437 1505 17.0 43.99% 172 391
474 SCOTT.GOMEZ 1471 1432 1510 19.5 45.13% 125 277
476 CHARLIE.COYLE 1470 1441 1498 14.2 45.63% 261 572
478 NIKOLAY.KULEMIN 1469 1402 1536 33.6 40.00% 24 60
482 RYAN.NUGENT-HOPKINS 1468 1444 1492 12.1 44.84% 369 823
483 ANTOINE.ROUSSEL 1468 1396 1539 35.7 37.50% 18 48
485 LINDEN.VEY 1466 1435 1498 15.8 42.98% 193 449
487 CURTIS.LAZAR 1466 1432 1500 16.9 43.75% 168 384
489 NOEL.ACCIARI 1466 1414 1518 26.0 42.86% 57 133
491 COLIN.WILSON 1465 1391 1538 36.8 38.10% 16 42
492 MARK.SCHEIFELE 1464 1444 1485 10.2 44.17% 515 1166
493 ROCCO.GRIMALDI 1464 1411 1518 26.7 42.40% 53 125
497 DYLAN.LARKIN 1463 1405 1520 28.6 41.18% 42 102
498 EVGENI.MALKIN 1462 1440 1485 11.2 43.48% 427 982
499 ARTEM.ANISIMOV 1462 1443 1482 9.9 43.86% 550 1254
500 JOSH.BAILEY 1462 1389 1536 36.8 38.10% 16 42
502 ERIC.FEHR 1462 1421 1502 20.0 44.06% 115 261
503 ALEX.WENNBERG 1461 1439 1484 11.4 43.38% 400 922
506 RYAN.STROME 1461 1405 1516 27.8 41.44% 46 111
508 MICHAEL.RAFFL 1461 1405 1517 28.0 40.37% 44 109
509 ALEX.STEEN 1460 1428 1491 15.8 41.32% 188 455
510 BRAD.MARCHAND 1460 1391 1528 34.3 37.50% 21 56
511 STEPHEN.GIONTA 1460 1433 1486 13.1 42.11% 291 691
512 TYLER.KENNEDY 1459 1392 1527 33.9 39.66% 23 58
513 TAYLOR.HALL 1459 1385 1534 37.3 35.90% 14 39
516 SCOTTIE.UPSHALL 1458 1381 1535 38.6 35.29% 12 34
517 MIKHAIL.GRIGORENKO 1458 1422 1493 17.7 42.98% 150 349
519 MARKUS.GRANLUND 1456 1425 1487 15.5 42.80% 202 472
522 TOMMY.WINGELS 1455 1397 1513 29.0 39.39% 39 99
523 ANDREAS.ATHANASIOU 1454 1401 1506 26.4 41.09% 53 129
524 JOSEPH.BLANDISI 1453 1376 1531 38.8 33.33% 11 33
526 ALEX.KILLORN 1453 1393 1513 30.1 37.93% 33 87
527 RYAN.SPOONER 1452 1426 1478 13.0 42.35% 296 699
528 SERGEY.KALININ 1452 1415 1489 18.3 41.61% 134 322
530 MAX.DOMI 1449 1381 1518 34.4 36.36% 20 55
533 TEUVO.TERAVAINEN 1447 1411 1482 17.8 39.83% 139 349
534 BROOKS.LAICH 1446 1405 1488 20.7 40.33% 98 243
536 ADAM.CRACKNELL 1446 1412 1479 16.9 39.49% 156 395
537 VIKTOR.TIKHONOV 1445 1390 1500 27.4 38.79% 45 116
538 CONNOR.MCDAVID 1444 1416 1472 14.0 41.23% 249 604
539 JIMMY.HAYES 1444 1389 1500 27.8 37.84% 42 111
541 MIKE.ANGELIDIS 1444 1366 1522 39.1 32.26% 10 31
543 TREVOR.LEWIS 1443 1404 1483 19.7 40.00% 110 275
544 THOMAS.VANEK 1443 1367 1518 37.6 31.58% 12 38
545 JACK.EICHEL 1442 1420 1464 11.1 41.02% 402 980
546 PATRICK.MAROON 1442 1372 1512 34.9 32.08% 17 53
548 ALEX.BURMISTROV 1441 1410 1471 15.0 40.04% 205 512
550 TIM.SCHALLER 1434 1379 1489 27.7 35.40% 40 113
551 SAM.GAGNER 1433 1376 1491 28.8 35.92% 37 103
552 LANDON.FERRARO 1425 1364 1486 30.4 33.72% 29 86
553 SAM.REINHART 1423 1367 1480 28.2 33.33% 36 108
554 MIKE.RIBEIRO 1421 1396 1445 12.2 37.82% 315 833
555 MATTIAS.JANMARK 1414 1375 1453 19.5 35.42% 102 288
556 KEVIN.HAYES 1413 1378 1447 17.3 35.84% 138 385
557 JARED.MCCANN 1406 1376 1437 15.1 34.67% 181 522
558 PATRICK.KANE 1400 1330 1469 34.7 21.43% 12 56
559 CRAIG.SMITH 1399 1357 1440 20.7 32.79% 81 247
136036351

Introducing an Elo-type model for NHL Faceoffs (Zenon Rankings)

Faceoffs, Uncategorized

Elo Ratings

Elo ratings were created by the Hungarian-born American physicist Arpad Elo in order to compare the strengths of chess players. The idea in it’s simplest form is that Chess players should get large ratings boosts if they beat a really tough opponent, who we’d expect them to lose to, and lose rank if they lost against a relatively weak opponent.

If two roughly equally matched opponents play each other, the adjustment should be small because the initial ratings suggested that the probability of a win for either player was roughly 50%. Given those prior ratings, either result should not be a surprise to our model and we should not update our new ratings very much to reflect the fact that our model more or less expected the results that did occur.

Elo models take many different forms and can even be extended to include margin of victory. To use the last NHL season as an example, let’s say our model in the middle of the 2015-16 season had the Washington Capitals as the strongest team in the league and the Edmonton Oilers near the bottom (STRICTLY HYPOTHETICAL) . We expect Washington to win, so we should only increase their rating if they are able to outperform our models expectations. Let’s say the model predicts that Washington should win 4-2. If they win exactly 4-2, we shouldn’t change any ratings, Washington and Edmonton performed exactly like the teams we thought they were.

457690736_10_slide.jpg

You see then, it is possible in this system for a win to result in a ratings decrease and for a loss to increase a team ranking. If  Washington beats Edmonton 3-2, Edmonton outperformed their expectation, we should increase their rating to reflect the fact that they played like a slightly better team than we previously thought.

For faceoffs there are no margins of victory. The way we currently record the stat is simply win or loss and no shades of grey, so we will be sticking to a simple elo-type model without margins. That being said, the key idea in the model is still all about under/over-performing given our prior expectations and updating our rankings accordingly.

Parameters

Saying that this is an elo-type model, still doesn’t mean very much because there are many variations and a few different parameters choices which can make two elo models very different.

One of the most important choices for any elo-type ranking is the k-factor. Basically, the k-factor tells your model how big a single ratings adjustment can be. To return to the Oilers and Capitals examples, a really large k-factor would suggest that if the Oilers were able to beat the higher-rated Capitals that the Oilers should gain a bunch of points and maybe even place ahead of the Capitals in our post-game rankings. In hockey, of course, we know that single games aren’t very meaningful and that on any given night a relatively bad team can beat the best team in the league without the status of the better team being revoked. Individual hockey games are highly luck-driven and even the most hard-line, old-school fans will at a minimum agree that it makes sense to play more than 1 game in a playoff series to determine the better team. In a game where there is very little luck, we would want to have a high k-value, that way the model can adjust to real improvements or setbacks appropriately and quickly. In a game with lots of luck, we want to set a smaller k-value so the model doesn’t over-react to noisy and luck-driven results in the short-term.

My model uses a k-factor of 0.2[1], which is pretty low for these kind of models. For reference, fivethirtyeight, who is famous for adapting elo models to rank players and teams in a variety of sports, uses 4 as their k-factor for baseball[2], 20 for the NFL[3], and 20 for the NBA[4]. Chess ratings tend to use somewhere in the range of 20-32 and often have separate k-factors depending on the pre-game ratings( i.e highly ranked players have lower k-factors so that their rankings are less prone to abrupt changes.)

It makes some sense that faceoffs would have such a low k-factor – nearly every centre has a win percentage in the 45-55% range and even defensemen, who are unlikely to do any real training, win roughly 35% of the draws they take. Individual faceoffs are highly luck driven and any given result should not be weighted too heavily. Beating Patrice Bergeron in a one-off does not make you the king of face-offs, and similarly my expectations of a centremen’s ability should not drop much in the face of a single loss – even to a no-name defensemen.

Another choice to be made is the initial ranking  of a player that your model has never seen before. I chose 1500 largely in accordance with convention, but determined the starting deviation of 50 using the validation dataset.

I also ended up not using elo itself exactly, but rather Glicko which is a model inspired by the original Elo model. It is more or less the same, with an additional parameter representing deviation or how much we should trust the ratings it produces. Players who take many faceoffs will have low deviations and players who take only the occasional faceoff will have a high deviation. The idea is that those with high deviations should be adjusted slightly quicker than those with low deviations because we trust the ranking less. As players play more games the deviation falls because we become more and more confident that the ranking is an accurate reflection of the players true ability.

The deviations also translate nicely into confidence regions (well, Central Posterior Intervals if you care about that kind of thing) and in the validation stage, I found Glicko to be slightly better at making predictions on unseen data. This was largely because poor faceoffmen who tend to not take many draws were dragged far below 1500 quickly, without introducing extra volatility into the rankings of established centers. In a true elo-model the only way to get the model to adjust more quickly is to increase the k-factor, but the unintended consequence can be that the final rankings are too heavily influenced by the last few contests and not a reflection of the sample as a whole. In the case of faceoffs, the dual ability to change the rankings of new centermen quickly without weighing the recent past too heavily turns out to be a predictive advantage. If you want more math check out the orginal paper here.

In general, for a new application the only way to choose a k-factor is to test it on unseen data.I used the data from four seasons – 2008-09 through 2011-12 – as the validation data. The validation process that I used is discussed in italics below.

I used 5-fold validation whereby I shuffled the data, split it randomly into 5 groups then would train the data on four of the groups and test on the remaining one, repeating so all five folds were left out once. The test-metric was an averaged capped binomial deviance (and RMSE for further validation) to see how well the different parameters performed on the unseen data. My model isn’t amazing at making predictions. In fact, it is really only a bit more than 1.2% better than guessing 50/50 for every single faceoff. If I have time I will try and repeat the results from the Schuckers, Pasquali, and Curro paper and test my model against their logistic regression, but their results show that simple winning percentage is already a decent enough metric and substantial gains are unlikely.

My model also made a few small adjustments for the strength state (PP or SH), home ice advantage, and whether or not the opponent was a player that we wouldn’t expect to take faceoffs normally[5].

Running the model on all of the data I have from the 2008-09 season all the way through 2015-16, here are the top 30 drawmen with a minimum of 50 draws taken[6]:

Player Zenon Ranking Lower Bound Upper Bound Faceoff% Deviation Faceoffs
1 JEREMY.COLLITON 1576 1526 1626 62.99% 25.0 154
2 RADEK.BONK 1575 1550 1600 59.92% 12.7 751
3 MICHAEL.ZIGOMANIS 1575 1536 1614 61.51% 19.6 291
4 MANNY.MALHOTRA 1574 1561 1586 59.84% 6.1 6593
5 ZENON.KONOPKA 1572 1557 1587 59.81% 7.6 2884
6 ROD.BRIND’AMOUR 1570 1555 1585 59.39% 7.4 2556
7 SCOTT.NICHOL 1566 1551 1582 58.51% 7.8 2608
8 TRENT.WHITFIELD 1564 1522 1607 60.09% 21.1 233
9 DAVID.STECKEL 1564 1551 1578 58.86% 6.8 4565
10 PATRICE.BERGERON 1561 1551 1570 58.43% 4.8 13857
11 BOBBY.HOLIK 1560 1531 1590 58.54% 14.9 521
12 KRIS.DRAPER 1560 1541 1579 57.54% 9.4 1618
13 JONATHAN.TOEWS 1559 1549 1569 57.29% 4.8 13881
14 CHRIS.GRATTON 1559 1516 1601 58.52% 21.3 229
15 VLADIMIR.SOBOTKA 1556 1542 1570 56.95% 7.0 3036
16 JERRED.SMITHSON 1555 1541 1569 55.90% 7.0 3798
17 JAMIE.MCGINN 1555 1488 1622 62.50% 33.6 64
18 ADAM.HALL 1555 1539 1571 56.51% 7.9 2458
19 ANDY.MCDONALD 1555 1536 1574 56.25% 9.5 1591
20 PAUL.GAUSTAD 1555 1543 1566 57.05% 5.8 8377
21 BOYD.GORDON 1555 1543 1566 57.39% 5.7 7768
22 JAMAL.MAYERS 1553 1534 1572 55.96% 9.5 1569
23 MIKE.SILLINGER 1551 1497 1604 58.20% 26.8 122
24 JIM.SLATER 1550 1536 1564 56.58% 7.0 3694
25 BRAD.MILLS 1550 1496 1604 60.33% 27.1 121
26 RICH.PEVERLEY 1548 1535 1561 56.03% 6.4 4755
27 RYAN.KESLER 1548 1538 1557 55.49% 4.9 11968
28 ANTOINE.VERMETTE 1546 1536 1556 56.02% 5.1 11548
29 JOE.THORNTON 1546 1534 1557 55.74% 5.8 9561
30 WARREN.PETERS 1543 1517 1569 55.49% 12.9 719

How to Interpret these Results

A ranking of roughly 1500 is approximately league average, although because glicko is not exactly zero-sum like Elo (the deviation parameter changes the way rankings are updated slightly), the weighted average is closer to 1505.These rankings can be translated back into win probabilities. A 20 point gap between players is approximately 3% (but in actuality the probability calculation depends slightly on the deviation parameters as well). To take a concrete example, this model predicts that Manny Malhotra (ranking: 1574) would beat Jonathan Toews (ranking: 1559) about 52.15% of the time. Eventually I will include an adjusted faceoff percentage based off the rankings, that would be like an expected percentage against a league average player, but a few details still need to be worked out[7].

Notice also that I have included the lower and upper bounds using the final deviation parameters for each player. I think in future rankings I will list the players by lower bound in order to more explicitly account for the fact that the players who take a bunch of draws are more likely to have reliable rankings. For example, we can see that Jeremy Colliton has the highest ranking, but his lower bound is much lower than the next 5 or so guys because he took relatively few faceoffs.

The top 30 is a bit of a mixed bag. Some current allstars like Toews and Bergeron, solid two-way Olympian Rod “the bod” Brind’amour (that’s a real nickname btw), some no-namers like Jeremy Colliton and Brad Mills as well as former Oiler fourth-liners Boyd Gordon and Jerred Smithson.

The guy that popped out at me as immediately interesting was Zenon Konopka. He most recently played in Poland, bounced around with 6 NHL teams from 2003-2014, finishing the 2013-14 campaign for Buffalo with 23 games played and a single assist to his name. In the NHL the guy largely took on an enforcers role, racking up 1082 PMs in just 346 games. But in the AHL he showed that he could score some goals, putting up an impressive 11 goals and 29 points in 19 playoff games for the Portland Pirates in 2005-06. And this wasn’t a one-off, he had several AHL seasons near a point a game and finished his junior career in the OHL with an 86 point season. Not bad for a guy averaging roughly 3 PMs a game in the NHL and a goal every 30 or so.

konopk.jpg

He mentions his faceoff prowess and using faceoffs to find an edge in the bio of his personal website 3 or 4 times and seems genuinely committed to the craft. Off the ice, Zenon is the owner of several business including a wine products company and Zenon is a dedicated pet-owner to his beloved rabbit, Hoppy, who he has taken team-to-team since 2006. So in honour of Mr. Knopka –  the NHL enforcer with the silky AHL mitts – and his best bud Hoppy, I’d like to call these Zenon Rankings!

Link to the full rankings list for 2008-16 here

Link to the full 2015-16 rankings here

Link to Zenon Plots article about plots like the one feature below here

Glicko 2015-16

 

 

 



Credits, Acknowledgments

All the data for this project came from the play-by-play data on corsica.hockey. It’s a great site you should check out if you haven’t already and an excellent data source especially for those like me who are not pros at scraping their own data. If you really like it, consider contributing to the Corsica Patreon to keep it rolling. The Hockey Analytics community relies heavily on websites like Corsica and we can’t afford to lose another good one.

I used the PlayerRatings r package to implement the models. I also owe a bunch to Michael Schuckers, Tom Pasquali, and Jim Curro for their extensive work on faceoffs and the Glicko creator, Mark Glickman.



Footnotes and additional  model details (Nerds Only)

Kobe Bryant of the Los Angeles Lakers drives against the Memphis Grizzlies during their NBA game 33 at the Staples Center in Los Angeles, California on January 2, 2014.  The Grizzlies went on to win 109-106.                       AFP PHOTO/MARK RALSTONMARK RALSTON/AFP/Getty Images

Kobe Bryant Buzzer Shots

Basketball

The past 10 days or so, I participated in a data competition on Kaggle. The challenge was trying to predict how likely Kobe Bryant was to score 5000 shots, given a training set of a little over 25,000. While I was messing around with selecting features for my models, I became side-tracked with understanding how the last few seconds of a basketball quarter is different than the rest of the game and what that means for a shooter like Kobe. I thought I’d share a few visualizations from this process.

To start, the last seconds of a close basketball game can be breathtaking and the stuff of legends. Even casual fans like me know about Jordan last shot where he broke Bryon Russel’s ankles to clinch the 1998 title.

And at least anecdotally speaking, the last seconds of an NBA game seem to operate differently. For example, the flow of the game changes, as trailing teams look for quick possessions to chip away at leads and teams ahead look to manage the clock. Occasionally the final seconds produce odds-defying shots from the back court in heavy pressure that find the net to the cheers or gasps of the crowd. And with all this myth-making and hype around the final seconds there is the idea that some players perform better under this pressure than others. Some players are considered clutch and winners like Jordan, others are considered “absent from the big moments”.

So this is a post to visualize some of the ways the final seconds are different for Kobe Bryant. I am limited in my understanding of the NBA, my knowledge of advanced basketball stats, and by the Kobe Bryant specific data set the Kaggle competition happened to provide for me, so in no way will this offer hard answers to finer questions about the game of professional basketball. But what I hope to do at least, is document the ways Kobe changes his behaviour with the clock counting down and to see if there is any unexplained greatness or weakness in Kobe’s game.

This next graph I made is what motivated me to look into this closer.

new scale

Shots are binned in groups of 5 seconds. The larger the bubble, the more shots were taken in the bin. The more opaque the colour the farther away those shots were taken on average. Red represents the last 5 seconds of the quarter.

What we can see is that shots in the last 5 seconds are huge outliers. Kobe Bryant in our sample made 44.6% of the shots he took, but in the last 5 seconds of the quarter this drops to just 25.4%. Additionally, we can see from the large bubble, Kobe is much more likely to throw up a shot in the last 5 seconds than any other 5 second interval.

 Shot Selection

To establish a bit of context, the first thing I looked at was how do different shots vary in accuracy with distance. In the data set there are six basic types of shots: Bank Shots, Dunk, Hook Shot, Jump shot, Layup, and Tip Shot.

kobe type

Interactive Version of Graph 2

A few things to note from the graph. Different shots have different probabilities of going in. Dunks go in more than 90% of the time, hook shots on the other hand are pretty hit or miss. The next is that the only type of shot that has an obvious trend in distance is jump shots, which makes sense. Jump shots should get progressively more difficult as you get farther from the basket. That is probably true for layups and dunks as well, but past a certain distance we don’t see any dunk or layup attempts for obvious reasons. So as distance changes, so does shot selection. Outside of the paint, Kobe’s only reliable option is the jumpshot. And as distances gets larger, Kobe becomes a less and less reliable marksman. At around 45 feet out, the Black Mamba’s stats could be easily confused for my high school stats, zeros all around.

What I want to understand is how much of Kobe’s performance in the last 5 seconds can be attributed to the simple fact that he is likely to be shooting from farther away. Or are there factors unaccounted for like psychological pressure, or increased defensive coverage that are the culprits behind Kobe’s lackluster final moment performance?

One way to get a sense of this is to ignore shot selection for the moment and look at just Kobe’s Jump Shots to see if there is an unexplained drop in performance, and  compare apples to apples so to speak. If the only driving factor behind lower shooting percentages was simply a change in shot selection (i.e Kobe hits his shots just like normal except he is forced to take lower percentages shots like jump shots instead of dunks), we should still see Kobe hit jumpers at his normal rate. If not, there may be other factors at play.

jumper new scale.png

Interactive Version of Graph 3

So what we see is that even comparing jump shots to jump shots, Kobe is much less likely to score in the last five seconds, 21.2%, versus his normal clip of 39% during the rest of the game. Again, he also shoots many more shots in the last 5 seconds than a typical 5 second interval during the game as represented by the larger bubble.

A typical Kobe shot is taken in the 12-15 ft. range, with 13.44 ft. being the average and 15 ft. his median shot in the sample. In the last 5 seconds, these shots are taken from over 20 ft. on average. A typical jumper for Kobe is in the 17-19 ft. range, with an averate of 17.37 and a median of 18 ft. In final 5 seconds, Kobe’s averages jump shots from over 24 ft.

Let’s visualize the difference.

new range scale.png

Interactive Version of Graph 4

Only Jumpshots are included in the graph

Here we divide all of the jump shots up into categories of roughly how far away the shots were (Less than 8 ft., 8-16 ft., 16-24 ft., 24 ft. +, and back court shot), keeping the x-axis the same and colouring the last 5 seconds in red again.
Comparing the shots in each range to each other directly, the difference between the last 5 seconds and other intervals is not so large. Take the 8-16 ft. range in the above graph. When we compare how Kobe did in the last 5 seconds for shots between 8-16 ft. in the last 5 seconds to shots between 8-16 ft. in the rest of the game, it is no longer a huge outlier. It is definitely near the lower end of the expected shooting percentage range, but comparing the red dot in this panel to graph 3 above it looks more like a typical 5 second interval. This is similarly true for shots take from less than 8 ft. (Panel 1 in graph 4), shots from 16-24 ft.(Panel 3 in graph 4), and to a lesser extent 24 + ft (Panel 4 in graph 4).

Another thing that we notice in graph 4 is that many more shots were taken from 24ft. + or the back court than in the rest of the game, as seen by how the red dots are much larger in panel 4 and 5 than the black dots in the same panels. So the story that is starting to emerge is not so much that Kobe is somehow 20% worse at shooting during the last 5 seconds, but from graph 4 he seems to shoot a bit below average, but his shots are from worse distances than we typically observe during the rest of the game.

Diving deeper, I found that even within these distance ranges (each represented by a panel in graph 4), that shots in the last 5 seconds were likely to be farther away. For example, the average 24ft. + shot (panel 4, graph 4) is taken from pretty close to 24ft., but in the last 5 seconds they are taken from around 27 ft..

Even though we haven’t used any fancy regression or machine learning techniques to this point, we can reasonably believe that distance is one of the main reasons that shots in the last 5 seconds are much less likely to go in. When we compare similar shot selection at similar distances, shots in the last 5 seconds tend to look much more like typical 5 second bins in our dataset.

Let’s visualize all of the jump shots he has taken to get a better sense in how they are different in the last 5 seconds than in the rest of gameplay.

distance

Interactive Version of Graph 5

Visualation of all jump shots taken. Last 5 seconds on the right, all other jumpers on the right. Red means the basket was scored, black represents a miss.

What we see in graph 5 is that the vast majority of the shots are taken from inside the 3 point arc, and those outside the line are almost all within a couple feet of it. On the right part of the graph, the shots are much more erratic, many of which occur outside the 3 point line and on average they are far from the line. The story we see here is a Kobe that is desperately fighting the clock and throwing up whatever shots he can to hopefully score another bucket and push his team over the edge.

I used a simple logistic regression to test some of the ideas we developed with the visualizations. Once I control for distance (modeled as a 3rd degree polynomial), area on the court (as in right-side, left-side, back-court, etc), and shot selection, there is only roughly a 1.4% shooting percentage gap left to account for in the last 5 seconds of the quarter. So Kobe doesn’t shoot 20% worse in the last 5 seconds in the quarter, he mostly just shoots from crappier positions on the floor. According to this logistic model, he is also significantly less likely to take dunks and layups like we suggested earlier, and much more likely to take jump shots from beyond the 3 point arc.

And this is without factoring in any sort of defensive pressure that may be put on Kobe at the end of a quarter, which is information that I do not have included in my dataset. What this suggests to me at least is that it is unlikely that the pressure of performing in the big moment is driving Kobe’s performance at the end of quarters. However, this still doesn’t tell us what Kobe’s value is in pressure moments, because his true value would be above replacement or above expectation. Should Kobe be trusted with the last shot? Does he do enough to get into good scoring position with the game on the line?

I have no idea…

The data set that I have and any models that I developed for this project are not sophisticated enough to tell us how Kobe does compared to giving the final shot to someone else, or whether or not we should have expected Kobe to get himself into better scoring position as the clock ticked down the final seconds, only that from where he was shooting he shot 1.4% worse than he did in the rest of the game.

 

 

USA_Ovie-slapshot

Shooting % Part ii

Shooter Talent, Theory

In part 1 we quickly introduced shooting percentage and examined briefly the role of luck and skill in this number. In the process we touched on regression to the mean and ‘mathematical luck’ and some of the factors, like  variables we do not control for like changing line mates or opponents and statistical noise, that lead to it.

So what is the role of skill and luck, and can we reduce the ‘luck’ that we see without compromising our data experiment?

It is important to distinguish that reducing statistical noise and reducing the other factors that look like it are not the same thing. To reduce noise, or more specifically the variance that is inherent to shooting percentage, we need to increase the number of ‘events’ or shots. If we could somehow keep everything in hockey exactly the same except everyone took two or three times as many shots, on average each players shooting percentage would be closer to his true talent level “shooting percentage”. Considering this, in small samples it is sometimes useful to think of a players talent level and his actual output as different concepts.

Shooting Percentage and Talent

Let’s imagine two twins, not named Daniel and Henrik, who have the exact same skill and talent set. Let’s say their true talent level is 20%, meaning that they should score 20% of the shots they take each. If, in practice, we made them take 5 shots each from the top of the circle would they both score exactly 1/5 shots for 20%? Of course not. In a 5 shot sample there is likely to be lots of variance, one twin might easily score 3 of his shots for 60%, while the other 0%.

Like we said earlier, we can reduce this statistical noise or variance by making them take many shots. Lets say several hundred. If each twin took 500 shots from the top of the circle, we still might not expect them to score an identical number of shots, but their percentages should be much closer. It would be highly unlikely for a 20% talented shooter to score 60% of 500 shots for 300 goals, just as it is unlikely that the other misses all 500 of his. The idea here is that as we increase the number of shots, this kind of variance should decrease and in a closed environment, like the practice rink from the top of the circle, we should see someones shooting percentage  reflect more and more closely their true talent level.

If this were the end of the story, however, what we should see is if we simply restrict our sample to players that took a lot of shots, then we shouldn’t see much luck or regression to the mean. But this is not exactly what the data tells us.

minimum shots

Original not interactive

Shooting % Part 1

Shooter Talent

This is a quick post about Shooting Percentage, meant to serve as an introduction to the topic and as a reference. If you already know a bunch about shooting percentage or fancy stats, feel free to skip to the interactive graph at the very end.

I have been working with shooter data, provided to me by the guys at fourthlineheroes, and I thought it might be useful to outline some of the basic stylized ideas about individual shooting percentage for people just trying to get into fancy stats.

First thing first, shooting percentage is number of goals that a player scores divided by the number of shots that he takes. What does it tell us though? For example, is shooting 1 for 10, any different than shooting 10 for 100? Do the best shooters have the best shooting percentages? What these questions are really asking, is how much of shooting percentage is skill and how much of it is luck?

flames

Team Puck Luck Confusion

Theory

There seems to be a great deal of confusion among fans as to what one should make of team puck luck and all this business of regressing to the mean. To be clear by Puck Luck, I am referring to the phenomenon that in small samples sizes (i.e a season worth of games or less) good portions of standings or outcomes cannot be distinguished mathematically from random distribution or luck. And by regressing to the mean, I mean the mathematical property that as sample sizes increase random distribution should decrease and the standings should more properly reflect ‘skill’ or purposeful abilities that persist in the long-run.

When fans hear that a team has been over-performing their true skill and that we should look for them to regress towards the mean, many interpret this  to be much more dramatic than it is. It does not mean that by some magical law of the universe that for every ‘lucky game’ won in the first half of a season, the gods of fairness will deduct one win in the second half, nor does it make them more likely to experience bad luck in the future. Probability, and luck for that matter, is still distributed as it was before, but we should see in the long run the percentage of games won to shift towards their true value. In other words, the distance we should expect a team to stray from their true winning percent should decrease as number of games increases.

It is possible, however, to increase the number of games in a finite season a team will win without increasing the underlying rate at which a team should win them, meaning without altering their skill level. In other words, conditional on the fact that a team has won a bunch of lucky games in the first part of the season the expected number of wins over the course of a 82 game season increases.

For example, the Calgary Flames have been extremely lucky and somehow won 27 of 50 contests for 57 points, despite being a horrendous hockey club. By many accounts, the Flames are even worse than the Oilers (more on that soon) and in an an infinitely long season their winning percentage would reflect that. This does not mean that Calgary will finish below the Oilers or even that they are likely to, the damage is at least partly done. The rate at which they win over time should slow down towards a true mean (as sample size or games played increases), but over the finite 82 game season the absolute number of wins they get this year has been permanently increased from temporary Puck Luck.

But if you ask me they picked the worst year to be lucky. There are much too bad to be in contention for the playoffs and too damn lucky for a shot at Connor McDavid. Sucks to suck.

What is the objective value of an assist?

Uncategorized

For anyone that has ever seen Gretzky thread a pass over to Jari Kurri, it is obvious that passing is vital to offensive production, but how does it compare to actually putting the puck in the net? And what about the guy that is passing to the guy making the pass, how does he fit to all of this? Surely he is important as well; he gets a whole point for his troubles.

Since the 40’s, the NHL and NHL fans have at least implicitly accepted the notion that goals are equal to first assists and they in turn are equal to second assists. But as I discussed in an earlier post, because there are 1.7 assists per goal (in today’s NHL), using points as a proxy for offensive skill suggests that more than 60% of the offense is created by the two passers, leaving only 30 some for the goal scorer. This does not pass the sniff test. How often when you watch a hockey game do you even remember what the second assist looked like? Sure, sometimes there is a really nice breakout pass from the d-man, and the odd time someone quarterbacks the puck in the offensive zone to create a good scoring chance, but in general, second assists are not noteworthy and relatively not that important.

Some fancy stats, like Goals Created or Goals Versus Threshold (Gvt), have looked at making minor modifications to the 1:1:1 weighting system, but using little more than elementary reasoning to back their findings. Goals Created arrives at the conclusion assists are worth half a goal and Gvt comes up with 66%, but once again mostly using intuition.

Following Alan Ryder’s logic, I arrived at 1 : 0.5 : 0.25 as the proper weighting, but I’d like to put it to the test.

To better attack this question, leaving rhetoric aside, I decided to construct an experiment using persistence to measure the actual value of goals and assists.