No, this article isn’t an article about quarterbacks squaring off against ancient Greek mathematicians. Today, we’re going to look at quarterback win-loss records and see how they compare to their Pythagorean win-loss records.
Over 30 years ago, Bill James wrote that, on average, baseball teams’ true strengths could be measured more accurately by looking at runs scored and runs allowed than by looking at wins and losses. Since then, sports statisticians have applied the same thinking to all sports. The formula to calculate a team’s Pythagorean winning percentage is always some variation of:
(Points Scored^2) / (Points Scored ^2 + Points Allowed^2)
With the exponent changing from 2 to whatever number best fits the data for the particular sport. In football, that number is 2.53. We can look, for example, at the Pythagorean records for each team in the league last season, and line it up against their actual record:
| Year | Tm | Record | Win% | PF | PA | Pyth Wins | Diff |
|---|---|---|---|---|---|---|---|
| 2011 | KAN | 7-9 | 0.438 | 212 | 338 | 3.76 | 3.24 |
| 2011 | GNB | 15-1 | 0.938 | 560 | 359 | 12.08 | 2.92 |
| 2011 | DEN | 8-8 | 0.500 | 309 | 390 | 5.71 | 2.29 |
| 2011 | OAK | 8-8 | 0.500 | 359 | 433 | 6.14 | 1.86 |
| 2011 | NWE | 13-3 | 0.813 | 513 | 342 | 11.78 | 1.22 |
| 2011 | NYG | 9-7 | 0.563 | 394 | 400 | 7.85 | 1.15 |
| 2011 | ARI | 8-8 | 0.500 | 312 | 348 | 6.9 | 1.1 |
| 2011 | TAM | 4-12 | 0.250 | 287 | 494 | 3.23 | 0.77 |
| 2011 | TEN | 9-7 | 0.563 | 325 | 317 | 8.25 | 0.75 |
| 2011 | NOR | 13-3 | 0.813 | 547 | 339 | 12.33 | 0.67 |
| 2011 | BAL | 12-4 | 0.750 | 378 | 266 | 11.34 | 0.66 |
| 2011 | ATL | 10-6 | 0.625 | 402 | 350 | 9.39 | 0.61 |
| 2011 | SFO | 13-3 | 0.813 | 380 | 229 | 12.52 | 0.48 |
| 2011 | CIN | 9-7 | 0.563 | 344 | 323 | 8.64 | 0.36 |
| 2011 | PIT | 12-4 | 0.750 | 325 | 227 | 11.4 | 0.6 |
| 2011 | MIA | 6-10 | 0.375 | 329 | 313 | 8.5 | -2.5 |
| 2011 | MIN | 3-13 | 0.188 | 340 | 449 | 5.3 | -2.3 |
| 2011 | PHI | 8-8 | 0.500 | 396 | 328 | 9.87 | -1.87 |
| 2011 | CAR | 6-10 | 0.375 | 406 | 429 | 7.44 | -1.44 |
| 2011 | SEA | 7-9 | 0.438 | 321 | 315 | 8.19 | -1.19 |
| 2011 | IND | 2-14 | 0.125 | 243 | 430 | 3.05 | -1.05 |
| 2011 | HOU | 10-6 | 0.625 | 381 | 278 | 11.03 | -1.03 |
| 2011 | SDG | 8-8 | 0.500 | 406 | 377 | 8.75 | -0.75 |
| 2011 | CLE | 4-12 | 0.250 | 218 | 307 | 4.74 | -0.74 |
| 2011 | WAS | 5-11 | 0.313 | 288 | 367 | 5.62 | -0.62 |
| 2011 | DAL | 8-8 | 0.500 | 369 | 347 | 8.62 | -0.62 |
| 2011 | BUF | 6-10 | 0.375 | 372 | 434 | 6.46 | -0.46 |
| 2011 | NYJ | 8-8 | 0.500 | 377 | 363 | 8.38 | -0.38 |
| 2011 | CHI | 8-8 | 0.500 | 353 | 341 | 8.35 | -0.35 |
| 2011 | STL | 2-14 | 0.125 | 193 | 407 | 2.1 | -0.1 |
| 2011 | JAX | 5-11 | 0.313 | 243 | 329 | 5.08 | -0.08 |
| 2011 | DET | 10-6 | 0.625 | 474 | 387 | 10.01 | -0.01 |