Anyone who follows football knows how big a part of the game that parity is. One team can be good one year and bad the next and vice versa for seemingly no reason. This series, called Predicting Parity, seeks to discover why that is and figure out how to predict it. The first thing we will look at is knows as the Pythagorean Expectation.
Overview
Use of the Pythagorean Theorem in sports began with Bill James in baseball, which what he called the Pythagorean Expectation. James theorized that the amount of runs a team scored and allowed was a more accurate predictor of the quality of a team than their actual win loss record. Much like the what you’ll remember from Middle School math, the Pythagorean Expectation in baseball used the following formula.
This same method has been adapted for football, though with a different exponent.
PF^2.37
Expected record =~ -----------------
PF^2.37 + PA^2.37
Below are two charts, one sorted by Pythagorean % and one sorted by the differential of Pythagorean wins and Actual wins from the 2011 season. These charts allow us to see which teams were the best last season and which teams were actually better or worse than their record would suggest. This is important for making predictions into 2012.
Teams sorted by Pythagorean Wins
| Team | PF | PA | Pythagorean % | Pythagorean Wins | Pythagorean Losses | Actual wins | Differential |
| SF | 380 | 229 | 0.76857543 | 12.29720688 | 3.702793123 | 13 | -0.70279312 |
| NO | 547 | 339 | 0.756562223 | 12.10499557 | 3.895004431 | 13 | -0.89500443 |
| GB | 560 | 359 | 0.741491691 | 11.86386705 | 4.136132952 | 15 | -3.13613295 |
| NE | 513 | 342 | 0.723312432 | 11.57299891 | 4.427001085 | 13 | -1.42700109 |
| PIT | 325 | 227 | 0.700679179 | 11.21086686 | 4.789133141 | 12 | -0.78913314 |
| BAL | 378 | 266 | 0.696949393 | 11.15119029 | 4.848809705 | 12 | -0.84880971 |
| HOU | 381 | 278 | 0.67851866 | 10.85629856 | 5.143701439 | 10 | 0.85629856 |
| DET | 474 | 387 | 0.617888325 | 9.886213206 | 6.113786794 | 10 | -0.11378679 |
| PHI | 396 | 328 | 0.609809 | 9.756943993 | 6.243056007 | 8 | 1.75694399 |
| ATL | 402 | 350 | 0.581343219 | 9.3014915 | 6.6985085 | 10 | -0.6985085 |
| SD | 406 | 377 | 0.543796445 | 8.700743126 | 7.299256874 | 8 | 0.70074313 |
| CIN | 344 | 323 | 0.537252023 | 8.596032371 | 7.403967629 | 9 | -0.40396763 |
| DAL | 369 | 347 | 0.536357794 | 8.581724706 | 7.418275294 | 8 | 0.58172471 |
| MIA | 329 | 313 | 0.52950451 | 8.472072155 | 7.527927845 | 6 | 2.47207215 |
| NYJ | 377 | 363 | 0.522406577 | 8.358505233 | 7.641494767 | 8 | 0.35850523 |
| CHI | 353 | 341 | 0.52048049 | 8.327687845 | 7.672312155 | 8 | 0.32768785 |
| TEN | 325 | 317 | 0.514762827 | 8.236205238 | 7.763794762 | 9 | -0.76379476 |
| SEA | 321 | 315 | 0.511177714 | 8.178843429 | 7.821156571 | 7 | 1.17884343 |
| NYG | 394 | 400 | 0.491046127 | 7.856738031 | 8.143261969 | 9 | -1.14326197 |
| CAR | 406 | 429 | 0.467397347 | 7.478357548 | 8.521642452 | 6 | 1.47835755 |
| ARZ | 312 | 348 | 0.435658147 | 6.970530348 | 9.029469652 | 8 | -1.02946965 |
| BUF | 372 | 434 | 0.409668219 | 6.554691497 | 9.445308503 | 6 | 0.5546915 |
| OAK | 359 | 433 | 0.390746755 | 6.251948077 | 9.748051923 | 8 | -1.74805192 |
| DEN | 309 | 390 | 0.365458736 | 5.847339769 | 10.15266023 | 8 | -2.15266023 |
| WAS | 288 | 367 | 0.360201141 | 5.763218262 | 10.23678174 | 5 | 0.76321826 |
| MIN | 340 | 449 | 0.340954592 | 5.455273469 | 10.54472653 | 3 | 2.45527347 |
| JAC | 243 | 329 | 0.327811238 | 5.244979806 | 10.75502019 | 5 | 0.24497981 |
| CLE | 218 | 307 | 0.307597385 | 4.921558163 | 11.07844184 | 4 | 0.92155816 |
| KC | 212 | 338 | 0.248709041 | 3.979344659 | 12.02065534 | 7 | -3.02065534 |
| TB | 287 | 494 | 0.216354866 | 3.461677857 | 12.53832214 | 4 | -0.53832214 |
| IND | 243 | 430 | 0.205443127 | 3.287090036 | 12.71290996 | 2 | 1.28709004 |
| STL | 193 | 407 | 0.145752436 | 2.332038974 | 13.66796103 | 2 | 0.33203897 |
Teams sorted by differential
| Team | PF | PA | Pythagorean % | Pythagorean Wins | Pythagorean Losses | Actual wins | Differential |
| MIA | 329 | 313 | 0.52950451 | 8.472072155 | 7.527927845 | 6 | 2.47207215 |
| MIN | 340 | 449 | 0.340954592 | 5.455273469 | 10.54472653 | 3 | 2.45527347 |
| PHI | 396 | 328 | 0.609809 | 9.756943993 | 6.243056007 | 8 | 1.75694399 |
| CAR | 406 | 429 | 0.467397347 | 7.478357548 | 8.521642452 | 6 | 1.47835755 |
| IND | 243 | 430 | 0.205443127 | 3.287090036 | 12.71290996 | 2 | 1.28709004 |
| SEA | 321 | 315 | 0.511177714 | 8.178843429 | 7.821156571 | 7 | 1.17884343 |
| CLE | 218 | 307 | 0.307597385 | 4.921558163 | 11.07844184 | 4 | 0.92155816 |
| HOU | 381 | 278 | 0.67851866 | 10.85629856 | 5.143701439 | 10 | 0.85629856 |
| WAS | 288 | 367 | 0.360201141 | 5.763218262 | 10.23678174 | 5 | 0.76321826 |
| SD | 406 | 377 | 0.543796445 | 8.700743126 | 7.299256874 | 8 | 0.70074313 |
| DAL | 369 | 347 | 0.536357794 | 8.581724706 | 7.418275294 | 8 | 0.58172471 |
| BUF | 372 | 434 | 0.409668219 | 6.554691497 | 9.445308503 | 6 | 0.5546915 |
| NYJ | 377 | 363 | 0.522406577 | 8.358505233 | 7.641494767 | 8 | 0.35850523 |
| STL | 193 | 407 | 0.145752436 | 2.332038974 | 13.66796103 | 2 | 0.33203897 |
| CHI | 353 | 341 | 0.52048049 | 8.327687845 | 7.672312155 | 8 | 0.32768785 |
| JAC | 243 | 329 | 0.327811238 | 5.244979806 | 10.75502019 | 5 | 0.24497981 |
| DET | 474 | 387 | 0.617888325 | 9.886213206 | 6.113786794 | 10 | -0.11378679 |
| CIN | 344 | 323 | 0.537252023 | 8.596032371 | 7.403967629 | 9 | -0.40396763 |
| TB | 287 | 494 | 0.216354866 | 3.461677857 | 12.53832214 | 4 | -0.53832214 |
| ATL | 402 | 350 | 0.581343219 | 9.3014915 | 6.6985085 | 10 | -0.6985085 |
| SF | 380 | 229 | 0.76857543 | 12.29720688 | 3.702793123 | 13 | -0.70279312 |
| TEN | 325 | 317 | 0.514762827 | 8.236205238 | 7.763794762 | 9 | -0.76379476 |
| PIT | 325 | 227 | 0.700679179 | 11.21086686 | 4.789133141 | 12 | -0.78913314 |
| BAL | 378 | 266 | 0.696949393 | 11.15119029 | 4.848809705 | 12 | -0.84880971 |
| NO | 547 | 339 | 0.756562223 | 12.10499557 | 3.895004431 | 13 | -0.89500443 |
| ARZ | 312 | 348 | 0.435658147 | 6.970530348 | 9.029469652 | 8 | -1.02946965 |
| NYG | 394 | 400 | 0.491046127 | 7.856738031 | 8.143261969 | 9 | -1.14326197 |
| NE | 513 | 342 | 0.723312432 | 11.57299891 | 4.427001085 | 13 | -1.42700109 |
| OAK | 359 | 433 | 0.390746755 | 6.251948077 | 9.748051923 | 8 | -1.74805192 |
| DEN | 309 | 390 | 0.365458736 | 5.847339769 | 10.15266023 | 8 | -2.15266023 |
| KC | 212 | 338 | 0.248709041 | 3.979344659 | 12.02065534 | 7 | -3.02065534 |
| GB | 560 | 359 | 0.741491691 | 11.86386705 | 4.136132952 | 15 | -3.13613295 |
As you can see, Miami leads the way in differential. Though they were just a 6-10 team, they actually played as well as a 8.47 team. This was because they actually had a solid defense. As many questions as they have offensively, their strong defense should prevent them from bottoming out once again in 2012. Bad teams like Minnesota, Carolina, and Indianapolis are also high up on this list so they should be able to bounce back some in 2012, while teams with solid records like the Eagles and Seahawks should improve and possibly make the playoffs.
On the other end of the spectrum, teams like Green Bay and New England had #1 seeds last year, but they also had differentials higher than -1. That being said, that’s normally the case with really good teams like that and teams with elite quarterbacks tend to frequently exceed their Pythagorean Expectation. Peyton Manning did it over his final 9 healthy seasons in Indianapolis, while Tom Brady has done so in 8 of his 10 seasons. Aaron Rodgers is not nearly as experienced as those two, but he’s certainly just as talented. Meanwhile, Brady frequently exceeds his Pythagorean Expectation and should be able to do so again this year. The Packers and Patriots will remain among the best teams in the league this year, barring injury to Rodgers or Brady.
Meanwhile, Manning’s new team, the Denver Broncos, are near the bottom of this list, but given that he missed all of last year with injury, is joining a new and inferior supporting cast, now to has play his home games out doors, had 4 neck surgeries in less than 2 years, and turned 36 in March, I don’t know if we can still consider Manning on the same level of Brady or Rodgers or Drew Brees. Manning is certainly an upgrade at quarterback over Tim Tebow even if he’s only 70% of his old self, but he might only be barely enough of an upgrade to cancel out their differential. Anyone expecting them to make an 3 or 4 game jump to being a 11-12 team will be disappointed. 9-7 or so seems more appropriate.
Meanwhile, average teams like Kansas City and Oakland could also be much worse this year than last year, especially Oakland. Oakland has lost a lot in free agency over the past 2 offseasons, including their two starting cornerbacks from their 2010 team and their top pass rusher, Kamerion Wimbley. With minimal cap space and draft picks, they haven’t been able to make up for all of these losses and now have a pretty thin team, especially defensively.
Kansas City, on the other hand, will be getting guys back from injury, including Jamaal Charles, Eric Berry, and Tony Moeaki, and Matt Cassel. However, this says they had the talent of a mere 4 win team last year. The year before, they won 10 games, but they only went 2-5 against teams with winning percentages of .500 or better, with those two wins coming against a Jacksonville team starting its 3rd string quarterback and the early season Chargers, against whom Matt Cassel passed for just 68 yards. The Chargers avenged that loss with a 31 point win later that year. Over those 5 losses, 4 were by double digits and 3 were by 21+.
The other two teams with -1 or worse differentials were the Giants and Cardinals. The Cardinals figure to have a worse record this season and while the Giants may do the same, especially in an improved NFC East, there are some that believe they’ve turned the corner after winning the Super Bowl last year and are now an elite regular season team. I am not one of those people, but I can understand it.
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