NHL Elo

Predicting scores (and seasons) by Dixon-Coles is interesting, but it’s one of many ways of doing ‘game-level’ predictions. There’s a family of rating systems called Elo, which was originally developed to rank chess players. There are a number of extensions of Elo, including some modifications to parameters by the World Chess Federation (FIDE), a modification including uncertainty and ‘reliability’ called Glicko, and a more parameterized version of Glicko developed in 2012 called Stephenson. These are all implemented in the PlayerRatings package in R. There’s also an modification of Glicko developed by Microsoft called TrueSkill and this is implemented in the aptly named trueskill package. Note that TrueSkill is a closed licence product, available only for non-commercial implementations.

We’ll compare all of these methods for their historical performance in NHL, as well as (eventually) go into predicting the coming season. TrueSkill has a few oddities, so we’ll look at it later.

library(PlayerRatings)
 
nhl_all<-as.data.frame(readRDS("./_data/hockeyData.Rds"))

For the PlayerRatings package, we’ll need to add one column to our data, the ‘result’ in respect to who won the game. If the home team wins, that result value should be 1. If the away wins, the value should be 0. Logically, draws should be given a 0.5, but there’s other ways of viewing this that I’ll test (could OT wins be a win, but SO wins a draw?).

nhl_all$Result<-apply(nhl_all, 1, function(x) ifelse(x[3] > x[5], 1, ifelse(x[3]<x[5],0,0.5)))

There’s a nuance to the code as well that prefers dates input as a “numerical vector denoting the time period in which the game took place” instead of dates proper. This allows such analysis as week-by-week analysis for NFL games, or the monthly chess rankings, but doesn’t work as well for our hockey games in which a team may be a few games behind or ahead of the competition.

dates<-unique(sort(nhl_all$Date))
nhl_all$DateFactor<-apply(nhl_all, 1, function(x) which(dates == x[1]))

We’ll wrangle only the data we need:

nhl_results<-nhl_all[,c(13,2,4,12)]
nhl_results$Visitor<-as.character(nhl_results$Visitor)
nhl_results$Home<-as.character(nhl_results$Home)

The PlayerRatings code then chews on games by each day, taking an input of the prior ratings as well as the games on that day. We’ll process the whole history of the NHL for base ELO like this. Note that there are none of the common adjustors, such as regressions to the mean after each season, nor importance factors of playoff vs. regular season games, nor home ice advantage, nor adjustments for the win margin (no benefit to winning 6-1 vs. 2-1 in OT). We’ll use a k factor of 8, which splits the difference between the commonly used 20 for football, and 4 for baseball, and is a commonly accepted k for hockey.

nhlelo<-elo(nhl_results, init=1500, kfac=8, history=TRUE)
kable(nhlelo$ratings[nhlelo$ratings$Lag < 100,c(1,2)], caption="NHL Elo Ratings")

	Player	Rating
1	Pittsburgh Penguins	1605.925
2	Washington Capitals	1593.662
3	St. Louis Blues	1593.535
4	Anaheim Ducks	1585.563
5	Chicago Blackhawks	1582.401
6	Tampa Bay Lightning	1579.913
8	Dallas Stars	1574.605
9	San Jose Sharks	1571.384
10	New York Rangers	1566.841
11	Los Angeles Kings	1550.622
13	Nashville Predators	1538.125
14	New York Islanders	1537.453
15	Boston Bruins	1531.571
16	Florida Panthers	1523.907
18	Colorado Avalanche	1517.049
19	Minnesota Wild	1513.761
20	Philadelphia Flyers	1513.489
21	Montreal Canadiens	1512.463
22	Detroit Red Wings	1509.428
23	Ottawa Senators	1507.323
24	Columbus Blue Jackets	1499.695
28	Calgary Flames	1491.623
29	Winnipeg Jets	1490.907
33	New Jersey Devils	1477.679
34	Vancouver Canucks	1475.976
36	Carolina Hurricanes	1458.905
40	Arizona Coyotes	1444.929
41	Buffalo Sabres	1434.475
43	Toronto Maple Leafs	1423.959
44	Edmonton Oilers	1422.394

Similarly, we can get the Glicko and Stephenson ratings:

nhlglicko<-glicko(nhl_results, init=c(1500, 300), kfac=8, history=TRUE)
kable(nhlglicko$ratings[nhlglicko$ratings$Lag < 100,c(1,2)], caption="NHL Glicko Ratings")

Player	Rating
Pittsburgh Penguins	2056.885
San Jose Sharks	1961.899
Tampa Bay Lightning	1961.123
Washington Capitals	1919.588
Dallas Stars	1908.682
St. Louis Blues	1906.094
Nashville Predators	1879.422
Philadelphia Flyers	1875.929
Anaheim Ducks	1869.937
Chicago Blackhawks	1855.996
New York Rangers	1852.835
New York Islanders	1842.990
Florida Panthers	1841.062
Buffalo Sabres	1819.547
Ottawa Senators	1818.789
Columbus Blue Jackets	1814.828
Winnipeg Jets	1799.448
Los Angeles Kings	1797.593
Boston Bruins	1794.260
Montreal Canadiens	1791.128
Detroit Red Wings	1778.996
Minnesota Wild	1776.143
New Jersey Devils	1774.495
Calgary Flames	1764.142
Colorado Avalanche	1758.090
Arizona Coyotes	1745.809
Carolina Hurricanes	1739.298
Vancouver Canucks	1722.548
Toronto Maple Leafs	1711.570
Edmonton Oilers	1710.663

nhlsteph<-steph(nhl_results, init=c(1500, 300), kfac=8, history=TRUE)
kable(nhlsteph$ratings[nhlsteph$ratings$Lag < 100,c(1,2)], caption="NHL Stephenson Ratings")

	Player	Rating
1	Pittsburgh Penguins	1672.636
2	San Jose Sharks	1605.519
3	Tampa Bay Lightning	1604.038
4	Washington Capitals	1571.463
6	Dallas Stars	1561.292
8	St. Louis Blues	1556.631
10	Nashville Predators	1543.061
11	Philadelphia Flyers	1541.821
13	Anaheim Ducks	1529.501
14	Chicago Blackhawks	1526.866
15	New York Rangers	1525.087
17	New York Islanders	1515.128
18	Florida Panthers	1514.468
19	Buffalo Sabres	1509.621
21	Ottawa Senators	1505.674
22	Columbus Blue Jackets	1502.818
23	Winnipeg Jets	1494.553
24	Montreal Canadiens	1487.634
26	Boston Bruins	1479.551
27	Los Angeles Kings	1477.632
28	Minnesota Wild	1471.183
29	Detroit Red Wings	1467.098
30	New Jersey Devils	1466.709
31	Calgary Flames	1466.100
33	Colorado Avalanche	1451.003
35	Arizona Coyotes	1448.379
36	Carolina Hurricanes	1441.683
37	Vancouver Canucks	1435.352
39	Toronto Maple Leafs	1426.483
40	Edmonton Oilers	1424.904

Note that we’ve dropped the historic NHL teams, and this may account for some of the deviation from the average being 1500. For a better idea of the current state of teams, we’ll look at data from 1991-92 onwards, when the San Jose Sharks joined the league.

nhl_recent<-nhl_all[nhl_all$Date>as.Date("1991-07-01"),]
dates<-unique(sort(nhl_recent$Date))
nhl_recent$DateFactor<-apply(nhl_recent, 1, function(x) which(dates == x[1]))
nhl_results<-nhl_recent[,c(13,2,4,12)]
nhl_results$Visitor<-as.character(nhl_results$Visitor)
nhl_results$Home<-as.character(nhl_results$Home)
 
recent_elo<-elo(nhl_results, init=1500, kfac=8, history=TRUE)
recent_glicko<-glicko(nhl_results, init=c(1500, 300), kfac=8, history=TRUE)
recent_steph<-steph(nhl_results, init=c(1500, 300), kfac=8, history=TRUE)

These result in the following:

## 
## Elo Ratings For 30 Players Playing 29071 Games
## 
##                   Player Rating Games  Win Draw Loss Lag
## 1    Pittsburgh Penguins   1585  2156 1116  115  925   0
## 2    Washington Capitals   1573  2061 1007  122  932  21
## 3        St. Louis Blues   1573  2067 1019  139  909   7
## 4          Anaheim Ducks   1565  1879  898  107  874  34
## 5     Chicago Blackhawks   1561  2091 1001  148  942  35
## 6    Tampa Bay Lightning   1559  1938  810  112 1016   6
## 7           Dallas Stars   1554  2069 1059  141  869  20
## 8        San Jose Sharks   1550  2107  984  121 1002   0
## 9       New York Rangers   1546  2091 1021  118  952  37
## 10     Los Angeles Kings   1530  2041  916  148  977  38
## 11   Nashville Predators   1517  1430  673   60  697  19
## 12    New York Islanders   1516  1970  800  124 1046  23
## 13         Boston Bruins   1511  2077 1024  140  913  49
## 14      Florida Panthers   1503  1782  720  142  920  36
## 15    Colorado Avalanche   1496  2090 1058  136  896  49
## 16        Minnesota Wild   1493  1259  582   55  622  36
## 17   Philadelphia Flyers   1493  2106 1045  153  908  36
## 18    Montreal Canadiens   1491  2066  983  131  952  49
## 19     Detroit Red Wings   1488  2198 1266  130  802  39
## 20       Ottawa Senators   1486  1954  883  115  956  49
## 21 Columbus Blue Jackets   1479  1206  487   33  686  49
## 22        Calgary Flames   1471  1989  890  147  952  49
## 23         Winnipeg Jets   1470  1286  518   45  723  49
## 24     New Jersey Devils   1457  2121 1117  137  867  49
## 25     Vancouver Canucks   1455  2073 1008  140  925  49
## 26   Carolina Hurricanes   1438  1987  843  139 1005  49
## 27       Arizona Coyotes   1424  1978  852  138  988  49
## 28        Buffalo Sabres   1413  2042  945  135  962  49
## 29   Toronto Maple Leafs   1403  2041  936  119  986  49
## 30       Edmonton Oilers   1401  1987  796  138 1053  49

## 
## Glicko Ratings For 30 Players Playing 29071 Games
## 
##                   Player Rating Deviation Games  Win Draw Loss Lag
## 1    Pittsburgh Penguins   1890     83.81  2156 1116  115  925   0
## 2        San Jose Sharks   1795     83.56  2107  984  121 1002   0
## 3    Tampa Bay Lightning   1794     90.86  1938  810  112 1016   6
## 4    Washington Capitals   1753     91.09  2061 1007  122  932  21
## 5           Dallas Stars   1742     89.70  2069 1059  141  869  20
## 6        St. Louis Blues   1739     88.36  2067 1019  139  909   7
## 7    Nashville Predators   1712     88.47  1430  673   60  697  19
## 8    Philadelphia Flyers   1709     87.11  2106 1045  153  908  36
## 9          Anaheim Ducks   1703     87.33  1879  898  107  874  34
## 10    Chicago Blackhawks   1689     89.57  2091 1001  148  942  35
## 11      New York Rangers   1686     90.64  2091 1021  118  952  37
## 12    New York Islanders   1676     89.28  1970  800  124 1046  23
## 13      Florida Panthers   1674     88.13  1782  720  142  920  36
## 14        Buffalo Sabres   1652     89.58  2042  945  135  962  49
## 15       Ottawa Senators   1652     90.95  1954  883  115  956  49
## 16 Columbus Blue Jackets   1648     87.88  1206  487   33  686  49
## 17         Winnipeg Jets   1632     89.44  1286  518   45  723  49
## 18     Los Angeles Kings   1631     88.26  2041  916  148  977  38
## 19         Boston Bruins   1627     89.03  2077 1024  140  913  49
## 20    Montreal Canadiens   1624     90.56  2066  983  131  952  49
## 21     Detroit Red Wings   1612     87.54  2198 1266  130  802  39
## 22        Minnesota Wild   1609     91.32  1259  582   55  622  36
## 23     New Jersey Devils   1607     89.13  2121 1117  137  867  49
## 24        Calgary Flames   1597     88.55  1989  890  147  952  49
## 25    Colorado Avalanche   1591     90.13  2090 1058  136  896  49
## 26       Arizona Coyotes   1579     88.74  1978  852  138  988  49
## 27   Carolina Hurricanes   1572     89.24  1987  843  139 1005  49
## 28     Vancouver Canucks   1555     89.06  2073 1008  140  925  49
## 29   Toronto Maple Leafs   1545     87.70  2041  936  119  986  49
## 30       Edmonton Oilers   1544     93.73  1987  796  138 1053  49

## 
## Stephenson Ratings For 30 Players Playing 29071 Games
## 
##                   Player Rating Deviation Games  Win Draw Loss Lag
## 1    Pittsburgh Penguins   1686     76.78  2156 1116  115  925   0
## 2        San Jose Sharks   1619     76.62  2107  984  121 1002   0
## 3    Tampa Bay Lightning   1617     80.58  1938  810  112 1016   6
## 4    Washington Capitals   1585     80.35  2061 1007  122  932  21
## 5           Dallas Stars   1574     79.89  2069 1059  141  869  20
## 6        St. Louis Blues   1570     79.17  2067 1019  139  909   7
## 7    Nashville Predators   1556     79.11  1430  673   60  697  19
## 8    Philadelphia Flyers   1555     78.30  2106 1045  153  908  36
## 9          Anaheim Ducks   1543     78.49  1879  898  107  874  34
## 10    Chicago Blackhawks   1540     79.65  2091 1001  148  942  35
## 11      New York Rangers   1538     80.09  2091 1021  118  952  37
## 12    New York Islanders   1528     79.44  1970  800  124 1046  23
## 13      Florida Panthers   1528     78.92  1782  720  142  920  36
## 14        Buffalo Sabres   1523     79.71  2042  945  135  962  49
## 15       Ottawa Senators   1519     80.34  1954  883  115  956  49
## 16 Columbus Blue Jackets   1516     78.89  1206  487   33  686  49
## 17         Winnipeg Jets   1508     79.38  1286  518   45  723  49
## 18    Montreal Canadiens   1501     80.10  2066  983  131  952  49
## 19         Boston Bruins   1493     79.36  2077 1024  140  913  49
## 20     Los Angeles Kings   1491     78.87  2041  916  148  977  38
## 21        Minnesota Wild   1484     80.43  1259  582   55  622  36
## 22     Detroit Red Wings   1480     78.58  2198 1266  130  802  39
## 23     New Jersey Devils   1480     79.48  2121 1117  137  867  49
## 24        Calgary Flames   1479     79.04  1989  890  147  952  49
## 25    Colorado Avalanche   1464     80.03  2090 1058  136  896  49
## 26       Arizona Coyotes   1462     79.09  1978  852  138  988  49
## 27   Carolina Hurricanes   1455     79.53  1987  843  139 1005  49
## 28     Vancouver Canucks   1449     79.31  2073 1008  140  925  49
## 29   Toronto Maple Leafs   1440     78.56  2041  936  119  986  49
## 30       Edmonton Oilers   1438     81.77  1987  796  138 1053  49

It looks like both Glicko and Stephenson ratings are ‘high’ compared to the primary Elo score. Checking the average of this proves to be correct, with Glicko averaging 1661.2783659 and Stephenson averaging 1520.644328. This is not ideal, Elo should, by nature, remain centred around your starting value. Additionally, there’s no normalization at the end of every season, this is a common feature in sports team predictions (vs individual rankings in chess, as Elo was developed for). Next post we’ll build our own Elo ranking that corrects for these and more.

Written on September 23, 2016