While wins are the ultimate goal for a team, they don't always tell a full story. In a similar way that describing an offense or defense's success on a per drive basis is more telling than evaluating on a per game level, looking at a team's expected wins can be helpful to determine which teams are driven by luck, and which teams are actually good.
The Pythagorean Win Expectation (PWE) model was developed by Football Outsiders to project a team's winning percentage based off of points scored and points allowed, and the final projection offers a little more insight into a team's stability. I have updated the exponent to 2.61 because my research shows that is a better value than the original 2.37.
For example, the 2007 Patriots went 16-0 in the regular season, which will always be a wildly impressive feat. The team posted an NFL record 315 point differential over the course of the season, but the PWE was 14.1 wins. This means that the team posted 1.9 Wins Above the Pythagorean Expectation (WAPE).
The teams with the largest WAPEs over the past decade are the 12 Colts that went 11-5 (expected 7.2 wins), the 11 Chiefs that went 7-9 (expected 3.7 wins), the 09 Colts that went 14-2 (expected 11.0 wins), the 13 Jets that went 8-8 (expected 5.1 wins), and the 11 Packers that went 15-1 (expected 12.2 wins).
Over the past decade, no team has more Wins Above the Pythagorean Expectation than the Colts, with 15.0 WAPE. The Broncos are 2nd with 9.8, the Cardinals are 3rd with 6.9, and the Panthers are 4th with 5.1, and the 49ers are 5th with 4.7. The Patriots rank 6th at 3.2.
What this could mean is that the Colts and the Broncos have been the luckiest team over the past decade, while the Patriots have been the 6th luckiest. Any team that wins far beyond their expectation has to be lucky, right?
However, I was curious to evaluate other measures to see if there was either a better way to evaluate teams and it turns out that point differential does a pretty good job on its own.
One guess to figure out the luckiest NFL team over the past decade.— Rich Hill (@PP_Rich_Hill) February 18, 2016
Fans of the least lucky team know it. pic.twitter.com/MgB0hCEogi
The expected wins from the point differential (DEW) has a marginally better correlation with winning percentage than the PWE model, although we're splitting hairs at 0.924 and 0.919, respectively, so I thought it'd be worth a look.
There's no real difference between the two models, of course, as one looks at points for and against, while the other looks at the differential. The top five luckiest teams are the same in both, with the Colts, Broncos, and Cardinals at the top, while the 49ers and Panthers flipped 4th and 5th.
What really interested me, and why I'm sharing this, is that the Patriots fell from the 6th luckiest in the PWE model to the 8th unluckiest in the DEW model. That's a drop of 19 ranks. The only other teams to move more than 5 places are the Browns (7, 24th to 31st), Saints (8, 19th to 27th), Ravens (9, 25th to 16th), and Steelers (12, 29th to 17th).
My initial reaction was to say that that the WPE model overvalues offense, as the Steelers and Ravens rose the most when looking at differential and they rank 1st and 2nd in points allowed over the past decade. The Saints rank 26th in defense. The issue is that the Patriots rank 3rd in defense over the past decade, so why would they drop?
It turns out that the WPE model forms, essentially, an "S" curve, when compared to the DEW model. This means that the WPE model values teams with large positive point differentials far less than the DEW model, while holding teams with extremely negative point differentials with greater regard.
The Patriots, more often than not, rank towards the top of the league in point differential. They have 8 of the 28 largest point differentials of the past decade (pour one out for the 2013 and 2008 teams). The DEW model expects the Patriots to win a lot, with a differential of roughly 150+ points projecting for a 12-win team.
When a team like the 2012 Patriots, with a +226 differential projecting 14.2 wins by the DEW model, "only" collects 12, that's a major disappointment. The WPE model projects just 12.7, reducing the loss.
What's a key takeaway? Well, there are flaws in each model. The DEW model doesn't create an asymptote, which is a necessary component of a game capped at 16 wins (the DEW model projects 16.6 wins for the 2007 Patriots). On the other hand, the WPE model appears to undervalue teams on the extreme ends of the points for and against spectrum. I'd agree that the WPE model is superior.
So have the Patriots been lucky over the past decade?
The WPE model would say that the Patriots were the luckiest in 2007 (agreed), 2010 (I'd disagree), 2011 (absolutely with that defense), and 2013 (no argument here), and only had really noticeably bad luck in 2009 (oh yeah, definitely).
The DEW model would argue that only the 2013 season was lucky, and that the 2009 and 2012 (losses on missed field goal and bad penalty against the Cardinals, last second pass interference leads to Ravens field goal, blown coverage by Tavon Wilson against the Seahawks, and failed comeback against the 49ers? Yeah sure.) years were unlucky.
And for the record, both models find the loss of Tom Brady (2008) and Peyton Manning (2011) to account for roughly 6 wins. Take that as you will.