Pythagorean Wins: Who Got Lucky in 2016

Although NFL sabermetrics aren’t nearly on the same level as MLB sabermetrics, one useful metric is Pythagorean wins. Pythagorean wins are used to determine the number of games a team “should have won” based off of their points for and points against. I’m going to look at which teams won more and less than expected in an attempt to find regression candidates and evaluate what that means for fantasy purposes.

The Formula

There are a few different formulations for Pythagorean wins. Specifically, I’ll be using the Pythagenpat formula for Pythagorean expectation, which is as follows:

PythW% = (Points for^EXP)/(Points for^EXP + Points against^EXP)

where the exponent EXP is given by:

EXP = (Points for + Points against/Games Played)^0.287.

This is chosen to reduce the mean square error, and provides a better fit across the range of point outcomes than the basic Pythagorean formula, which just uses a fixed constant for the exponent.1 To get Pythagorean wins (PythW), we just multiply PythW% by the number of games.

2016 Pythagorean Wins

Here’s a table with every NFL team’s 2016 PythW%, PythW, EXP, and wins over expectation (WOE).


Here are some quick takeaways for 2017:

Fall Back Candidates

  • The Raiders are almost surely going to regress in 2017. They had a 6.67 average margin in their wins, but their losses were by 7, 8, 16, and 18 points. Every losing margin was worse than their average winning margin. However, the 18-point defeat to the Broncos can probably be forgiven, considering Matt McGloin and Connor Cook were at the helm for the Raiders. Other mitigating factors include the Raiders’ stellar offensive line and, as Josh Hermsmeyer pointed out on this week’s episode of the Numbers Game, a QB who threw right in line with expectation when adjusted for the depth of his throws. This should protect the value of the Oakland RBs. The question is, who will those RBs be?
  • The Houston Texans should be a no-brainer regression candidate. When you have a QB as bad as Brock Osweiler on depth-adjusted throws, especially downfield where his AYA was an abysmal 4.3 on passes of 15-plus yards, regression is in store. The Texans’ winning margins were that of a 6.2 win team. Expect regression next year unless there is a drastic change in QB play.
  • Jay Ajayi had three 200-plus yard games this year, and all three were in wins. However, if Miami were to regress next year, as suggested by their 2.55 WOE, that reduces the likely number of running plays Ajayi could see per game. Expect him to fall to Earth a bit, not only because three 200-yard performances will be difficult to repeat, but also because he probably won’t be in as many favorable game scripts.
  • The L.A. Rams won four games this year, congrats! Too bad that was 1.33 over expectation. I used sabermetrics as a reason to fade Todd Gurley in 2016, and crazy enough, 2017 could be even worse for the Rams. Hell, sabermetrics told us that the 49ers were lucky to finish with five wins in 2015, coming in 1.8 wins over expectation, and sure enough, they only finished with two wins this year. The 2017 Rams are this year’s 49ers and don’t even get the benefit of the easiest schedule in the NFC West thanks to the aforementioned 49ers ending up in the cellar. Instead of the Bears and Panthers who combined for 11.2 PythW, the Rams get the Vikings and Saints and their combined 17.3 PythW. Gurley could struggle again in 2017 with a full year of Jared Goff running the offense.

Improvement Candidates

  • The San Diego Chargers really had some unfortunate losses, blowing several big leads. This is part of why they ended up 2.61 wins below expected. If Keenan Allen returns healthy and the Chargers can shore up a couple holes in both their offensive line and defense, the Chargers would be playoff contenders in 2017. If Danny Woodhead departs, Melvin Gordon could have a second straight double-digit touchdown season.
  • Blake Bortles probably isn’t as good as his 2015 season, but he’s also probably not as bad as his 2016 season. If he strikes a balance somewhere in the middle and the Jaguars don’t get as unlucky as they did in 2016 per Pythagorean expectation, then there’s some hope for Bortles to return value on what should be an ADP around QB21.
  • The Cleveland Browns had only one win but did finish 1.69 wins below what is expected from their points for and against. Book ’em down for Super Bowl LII! Ah, who am I kidding. They’re the Browns.


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  1. In the NFL the fixed exponent is ~2.37.  (back)
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