Pythagorean Expectations Using Even Strength Data

This is a method used by baseball statisticians to calculate how many games a team “should” have won in a season. I thought it would be a fun idea to apply this to the NHL this season. The formula takes the number of runs scored by the team, squares it and then divides by the sum of the squares of the runs scored and runs allowed. With that, we get a winning percentage and we multiply that by the number of games in the season and get the number of games a team “should” have won. For hockey, we used goals for and goals against for this formula. For instance, the Caps have scored 201 goals this season and have allowed 177. The formula would be 201^2/(201^2+177^2) and we get a winning percentage of .563, which equals 46 expected wins. Here’s how the league would look.

Team G GA Percentage Expected Wins Points
VAN 243 170 0.671 55 110
BOS 224 173 0.626 51 103
PHI 235 194 0.595 49 98
NYR 210 178 0.582 48 95
CHI 234 199 0.580 48 95
PIT 209 180 0.574 47 94
DET 238 209 0.565 46 93
WSH 201 177 0.563 46 92
SJS 219 194 0.560 46 92
NSH 196 175 0.556 46 91
LAK 198 179 0.550 45 90
BUF 217 209 0.519 43 85
PHX 215 208 0.517 42 85
CGY 226 219 0.516 42 85
MTL 197 193 0.510 42 84
DAL 203 204 0.498 41 82
TBL 217 222 0.489 40 80
ANA 210 215 0.488 40 80
STL 208 214 0.486 40 80
CAR 207 219 0.472 39 77
MIN 186 208 0.444 36 73
FLA 181 203 0.443 36 73
CBJ 196 223 0.436 36 71
NYI 206 236 0.432 35 71
TOR 197 227 0.430 35 70
ATL 205 239 0.424 35 70
NJD 152 187 0.398 33 65
COL 202 261 0.375 31 61
OTT 173 228 0.365 30 60
EDM 178 240 0.355 29 58

The Canucks at the top shouldn’t be a surprise, but the Eastern Conference has a few surprises with the top three teams being the Bruins, Flyers and Rangers. The Rangers near the top is interesting because they have 87 points right now with 8 shootout victories. However, the Rangers also have only 5 overtime losses, which shows that they aren’t relying a lot on charity points to get into the playoffs. Their position here indicates that they are a good team that’s somewhat underperformed this year.

The Hawks are at #2 in the West despite barely hanging onto a playoff spot right now. This could be because of their bad record in close games and bad luck in the shootout.

Let’s see how the chart looks using only even strength goals.

Team G GA Percentage Expected Wins Expected Points
BOS 182 130 0.662 54 109
VAN 174 131 0.638 52 105
PHI 190 146 0.629 52 103
NSH 159 134 0.585 48 96
NYR 162 137 0.583 48 96
PIT 163 139 0.579 47 95
PHX 171 147 0.575 47 94
WSH 160 138 0.573 47 94
CHI 174 151 0.570 47 94
SJS 155 144 0.537 44 88
LAK 152 142 0.534 44 88
DET 174 164 0.530 43 87
BUF 168 161 0.521 43 85
MTL 146 143 0.510 42 84
DAL 154 151 0.510 42 84
CGY 170 170 0.500 41 82
STL 163 165 0.494 41 81
ANA 154 163 0.472 39 77
CBJ 157 167 0.469 38 77
CAR 158 170 0.463 38 76
FLA 148 166 0.443 36 73
TOR 149 170 0.434 36 71
ATL 155 179 0.429 35 70
TBL 151 175 0.427 35 70
NYI 158 186 0.419 34 69
MIN 136 162 0.413 34 68
EDM 142 173 0.403 33 66
COL 156 194 0.393 32 64
NJD 119 150 0.386 32 63
OTT 132 184 0.340 28 56

Here we have the Bruins at the top, Nashville as the second best team in the West and the Lightning as a bottom-10 team. Huh? It’s indicating that the Lightning are 21 points better than they should be, which I’m finding hard to believe. Tampa Bay has given up a lot of goals (though it’s decreased since Dwayne Roloson joined) so they end up looking like a worse team than they actually are here. Tampa’s 6th ranked powerplay was also subtracted which also makes them look worse. Same thing happened with Chicago and their top ranked powerplay.

Then you have teams like Boston and Nashville who benefit from great goaltending and look better than they actually are here. Not that either are bad teams but I would have a hard time saying that the Preds are the 2nd best team in the West. Thus, it seems that it’s better to use this formula for overall data rather than just even strength.

This is a nice method to judge how well a team has played but goals and goals against aren’t everything when judging a team. I usually prefer adding in shot/corsi/fenwick data along with save and shooting percentages to see how lucky a team has gotten. I might try to adjust these totals in a later post by factoring in shooting percentages to see which teams have gotten lucky and which ones haven’t. Also looking at clear victories (wins decided by more than one goal) and OT/one-goal games is another idea.

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