Looking at Last Season’s NHL Standings Using Pythagorean Expectation

A couple days ago, during my Sabermetrics 101 class (free online class offered by Boston University, I highly recommend), the topic was how to convert runs to wins. The team with the most runs wins a baseball game, as such, runs are the currency of baseball. While learning this, I pondered if the same statement could be applied to hockey and came to the obvious conclusion that goals (not shot attempts/Corsi events or unblocked shot attempts/Fenwick events) are the currency of hockey (with the exception of wins wrought by the shootout). Back to baseball, using runs, pioneer of sabermetrics, Bill James used the following formula, using pythagorean expectation, to predict winning percentage – W/(W+L):

What would be the results if we swapped out runs scored for goals for and runs allowed for goals against? Before I get to the results, I’ll present how the pythagorean expectation for goals (we’ll call this PEG) compares to Points % (points divided by maximum points) for each team last season:

Capture

As is illustrated here, Points % is highly correlated to PEG. Additionally, from the R-squared value, we can conclude that 93.6% of the variation in Points % can be explained by PEG. Personally, I would say that the remaining 6.4% can plausibly be explained by shootouts and luck. So with PEG, we have a number that tells us how a team should have performed. To easier illustrate non-luck-based standings, I converted PEG to Points** to see the difference between the actual points that teams had during the course of last season. I made sure to add a column that shows the change in these rankings, this shows teams that overachieved/had luck go their way in the regular season (if this number is negative) and teams that underachieved/had luck go against them in the regular season (if this number is positive). This is all presented below (sorted by PEG Points):

Rk (in actual points) Team (* means made playoffs) W L OL PTS PTS% GF GA PEG PEG Points Change (PEG Points-Actual Points)
1 New York Rangers* 53 22 7 113 0.689 252 192 0.633 113.93 0.93
5 Tampa Bay Lightning* 50 24 8 108 0.659 262 211 0.607 109.65 1.65
4 St. Louis Blues* 51 24 7 109 0.665 248 201 0.604 109.15 0.15
7 Chicago Blackhawks* 48 28 6 102 0.622 229 189 0.595 107.72 5.72
10 Washington Capitals* 45 26 11 101 0.616 242 203 0.587 106.43 5.43
2 Montreal Canadiens* 50 22 10 110 0.671 221 189 0.578 104.89 -5.11
12 Minnesota Wild* 46 28 8 100 0.61 231 201 0.569 103.50 3.50
16 Calgary Flames* 45 30 7 97 0.591 241 216 0.555 101.11 4.11
6 Nashville Predators* 47 25 10 104 0.634 232 208 0.554 101.09 -2.91
13 Ottawa Senators* 43 26 13 99 0.604 238 215 0.551 100.47 1.47
8 New York Islanders* 47 28 7 101 0.616 252 230 0.546 99.64 -1.36
14 Winnipeg Jets* 43 26 13 99 0.604 230 210 0.545 99.61 0.61
9 Vancouver Canucks* 48 29 5 101 0.616 242 222 0.543 99.22 -1.78
18 Los Angeles Kings 40 27 15 95 0.579 220 205 0.535 97.95 2.95
11 Detroit Red Wings* 43 25 14 100 0.61 235 221 0.531 97.20 -2.80
15 Pittsburgh Penguins* 43 27 12 98 0.598 221 210 0.526 96.35 -1.65
3 Anaheim Ducks* 51 24 7 109 0.665 236 226 0.522 95.72 -13.28
17 Boston Bruins 41 27 14 96 0.585 213 211 0.505 92.94 -3.06
19 Dallas Stars 41 31 10 92 0.561 261 260 0.502 92.48 0.48
23 San Jose Sharks 40 33 9 89 0.543 228 232 0.491 90.74 1.74
21 Colorado Avalanche 39 31 12 90 0.549 219 227 0.482 89.23 -0.77
22 Columbus Blue Jackets 42 35 5 89 0.543 236 250 0.471 87.45 -1.55
20 Florida Panthers 38 29 15 91 0.555 206 223 0.460 85.68 -5.32
24 Philadelphia Flyers 33 31 18 84 0.512 215 234 0.458 85.24 1.24
25 New Jersey Devils 32 36 14 78 0.476 181 216 0.413 77.82 -0.18
26 Carolina Hurricanes 30 41 11 71 0.433 188 226 0.409 77.24 6.24
27 Toronto Maple Leafs 30 44 8 68 0.415 211 262 0.393 74.69 6.69
28 Edmonton Oilers 24 44 14 62 0.378 198 283 0.329 64.06 2.06
29 Arizona Coyotes 24 50 8 56 0.341 170 272 0.281 56.24 0.24
30 Buffalo Sabres 23 51 8 54 0.329 161 274 0.257 52.26 -1.74

Adam is a student at McGill University. You can follow him on Twitter @adam_m3318.

You can follow Hit the Cut on Twitter @hitthecutblog.

**PEG was converted to points by adjusting the mean PEG to match the mean of the actual Points % (by adding a season-specific constant number to each team’s PEG – for this season it was 0.062). I then multiplied this number by 164 (the maximum amount of points possible for a team in a season).

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