FanPost

Pythagorean Theorem for Hockey: Part D'oh

After our discussion the other day, I went back to the drawing board to come up with a Pythagorean Theorem for hockey. Beware, for below the jump, there be graphs and math!

I thought about it for a while and, while I liked my PP/PK/5v5 method, several people asked for something more akin to James' original formulation that takes Runs For and Runs Against and spits out a winning percentage. However, we all quickly realized why this doesn't work for hockey - baseball has binary results (wins or losses), but hockey doesn't.

After pondering how to square this circle for a bit, I had an epiphany: what we really want to know is point totals, not winning percentage!

Armed with this realization, the NHL.com website, Excel and some patience, I devised the following method:

  1. Figure out how many points the average team acquires in a given year (it turns out to be right around 91.3 every year since the lockout);
  2. Figure out the average goal differential (surprise, surprise. . . it's ZERO!!!);
  3. Figure out the average goal differential per point both positive and negative (it averages out to about 2.65). This was a bit of a kludge and deserves explanation because someone with an actual background in statistics could probably come up with a much better means of doing this. To get this number, I took the top and bottom team in the league by points in each year and figured out the absolute value of how far they deviated from the mean in both points and goals differential. Then I divided the goal differential number by the points number and averaged the top and bottom number. So for example, last year, SJS was the top team in the league with 117 points and a goal differential of 53, while NYI was the bottom team in the league with 61 points and a -78 differential. The average number of points in the NHL last year was 91.4. For SJS: 117-91.4=25.6 and 53 Diff/25.6=2.07 Gdiff/point. For NYI: 91.4-61=30.4 and 78 Diff/30.4=2.5658 GDiff/point;
  4. Average all the data over the four full years since the lockout and do some basic algebra and...

I came up with the following:

  • Over a full 82-game season a team's expected points PE = 91.3 + Differential/2.644
  • Mid-season, you need to modify the equation like so: PE = (91.3/82)*Games Played + Differential/2.644

Again, this only works for post-lockout rules. I'm guessing that pre-lockout data would be easy enough to collect and that would allow for a much larger sample size.

 

I'm going to post the spreadsheets below so that others can check my work and I'll apply the theorem to this year's standings in a following post:

2005 -2006
Team Points GF GA Differential
DET 124 305 209 96
OTT 113 314 211 103
DAL 112 265 218 47
CAR 112 294 260 34
BUF 110 281 239 42
NSH 106 259 227 32
CGY 103 218 200 18
NJD 101 242 229 13
PHI 101 267 259 8
NYR 100 257 215 42
SJS 99 266 242 24
ANA 98 254 229 25
COL 95 283 257 26
EDM 95 256 251 5
MTL 93 243 247 -4
TBL 92 252 260 -8
VAN 92 256 255 1
TOR 90 257 270 -13
ATL 90 281 275 6
LAK 89 249 270 -21
FLA 85 240 257 -17
MIN 84 231 215 16
PHX 81 246 271 -25
NYI 78 230 278 -48
CBJ 74 223 279 -56
BOS 74 230 266 -36
WSH 70 237 306 -69
CHI 65 211 285 -74
PIT 58 244 316 -72
STL 57 197 292 -95
91.36666667 0
Top 32.63333333 96 2.941777324
Bottom 34.36666667 95 2.764306499
2.853041911

 

2006 -2007
Team Points GF GA Differential
BUF 113 308 242 66
DET 113 254 199 55
NSH 110 272 212 60
ANA 110 258 208 50
SJS 107 258 199 59
DAL 107 226 197 29
NJD 107 216 201 15
VAN 105 222 201 21
OTT 105 288 222 66
PIT 105 277 246 31
MIN 104 235 191 44
ATL 97 246 245 1
CGY 96 258 226 32
COL 95 272 251 21
NYR 94 242 216 26
TBL 93 253 261 -8
NYI 92 248 240 8
TOR 91 258 269 -11
MTL 90 245 256 -11
CAR 88 241 253 -12
FLA 86 247 257 -10
STL 81 214 254 -40
BOS 76 219 289 -70
CBJ 73 201 249 -48
EDM 71 195 248 -53
CHI 71 201 258 -57
WSH 70 235 286 -51
LAK 68 227 283 -56
PHX 67 216 284 -68
PHI 56 214 303 -89
91.36666667 0
Top 21.63333333 66 3.050847458
Bottom 35.36666667 89 2.516493874
2.783670666

 

2007 -2008
Team Points GF GA Differential
DET 115 257 184 73
SJS 108 222 193 29
MTL 104 262 222 40
PIT 102 247 216 31
ANA 102 205 191 14
NJD 99 206 197 9
MIN 98 223 218 5
DAL 97 242 207 35
NYR 97 213 199 14
COL 95 231 219 12
PHI 95 248 233 15
WSH 94 242 231 11
OTT 94 261 247 14
CGY 94 229 227 2
BOS 94 212 222 -10
CAR 92 252 249 3
NSH 91 230 229 1
BUF 90 255 242 13
EDM 88 235 251 -16
CHI 88 239 235 4
VAN 88 213 215 -2
FLA 85 216 226 -10
PHX 83 214 231 -17
TOR 83 231 260 -29
CBJ 80 193 218 -25
NYI 79 194 243 -49
STL 79 205 237 -32
ATL 76 216 272 -56
LAK 71 231 266 -35
TBL 71 223 267 -44
91.06666667 0
Top 23.93333333 73 3.050139276
Bottom 20.06666667 44 2.19269103
2.621415153

 

 

2008 -2009
Team Points GF GA Differential
SJS 117 257 204 53
BOS 116 274 196 78
DET 112 295 244 51
WSH 108 272 245 27
NJD 106 244 209 35
CHI 104 264 216 48
VAN 100 246 220 26
PIT* 99 264 239 25
PHI* 99 264 238 26
CGY 98 254 248 6
CAR 97 239 226 13
NYR 95 210 218 -8.00
MTL 93 249 247 2
FLA 93 234 231 3
STL 92 233 233 0
CBJ 92 226 230 -4
ANA 91 245 238 7
BUF 91 250 234 16
MIN 89 219 200 19
NSH 88 213 233 -20
EDM 85 234 248 -14
DAL 83 230 257 -27
OTT 83 217 237 -20
TOR 81 250 293 -43
PHX 79 208 252 -44
LAK 79 207 234 -27
ATL 76 257 280 -23
COL 69 199 257 -58
TBL 66 210 279 -69
NYI 61 201 279 -78
91.4 0
Top 25.6 53 2.0703125
Bottom 30.4 78 2.565789474
2.318050987

Four Year Average:

               Avg. Pts      Avg. GDiff/Pt
91.3       2.644044679

If this FanPost is written by someone other than one of the blog's editors, the opinions expressed in it do not necessarily reflect those of this blog or SB Nation.

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