PythagoreanPAT Win Expectancy Season 86

A few season ago I introduced PythagoreanPAT (PyPAT for short) to the league and why it's an improvement over determining team strength from Won/Loss records or even Pythagorean win expectancy. Later I published a video where I described and went through strength of schedule based on opponents PythagoreanPAT. (check it out here: https://youtu.be/SweB-Tg7uUI)

Pythagorean primer for new readers or those wanting a refresher

If you’ve heard my shtick before, feel free to move on down to the good stuff.

You may have heard this before, but point differential is a better indicator of future success than won-loss record. In other words, when trying to determine if a team will win or lose a set of games, looking at their point differential in past games only, will be more accurate to predict their success than actual wins and losses. This has been demonstrated with lots of research over many years. You can use this knowledge to see which teams were lucky and unlucky to win as many games as they did and try to predict who will outperform or underperform general public expectations in the future.

Long-time readers may be aware of Pythagorean Win Expectancy. This was first developed for baseball but has since between adapted to the NFL. It's named after the famous Pythagorean theorem because it kind of looks like the formula you learned in junior high:

win expectancy = [points scored^2.37 / (points scored^2.37 + points scored^2.37)]

It turns out there is an even better way to calculate a team's win expectancy that does not use a hardcoded constant. (2.37 above) This is beneficial because a) scoring in the NFL and RedZone is not constant from year to year and b) high scoring teams and low scoring teams should not be using the same constant to determine their win expectancy. Think about it, a 10-point loss in a 48-38 game is not the same as losing 20-10.

So, this is where PythagoreanPAT comes in. It is the same formula as above, but instead of 2.37 for the exponent, you calculate the exponent for each team individually. The formula for the exponent is:

exponent = [ (points scored + points allowed) / number of games] ^ 0.251

I know, using an exponent constant to calculate an exponent constant is odd. The original modification for this was log10 of the formula above minus the exponent, but that proved to be less accurate than using a constant based on historical data. I actually used both methods to see how Red Zone compared to real-life, and sure enough PythagoreanPAT was more accurate than the original Pythagorean win expectancy formula and the formula based on log10 (this is called PythagoreanPORT, if you're wondering). So, we will go with that.

Opponent PyPAT SoS

Now that you have had a refresher on PyPAT, here is the Cliff Notes for Opponent PyPAT (the video above goes into much greater detail). We are going to take PyPAT a step further and use PyPAT to calculate each team’s strength of schedule. We do this by calculating PyPAT for every opponent of a specific team. And to make it so that opponent PyPAT isn’t skewed by the team we’re trying to determine SoS for, we take out games involving that team.

Season 85 PyPAT

The below table shows PyPAT for last season (season 85), Win Diff (difference between actual wins and PyPAT calculated wins -- or luck), OppPyPAT for last season (their season 85 SoS), and their season 86 SoS using PyPAT from last season of their opponents this season. (perfectly not confusing!)

New York Jets were by far the luckiest team in the league last season, playing more like a 9-8 team than a 12-win team. They had a pretty hard schedule last season, but it didn’t ease up in season 86. So don’t expect that same success we saw in season 85.
Vikings and Buccaneers show up on the lucky teams list because any time a team avoids slipping up even just once, it’s incredibly lucky. But we wouldn’t consider them lucky in the traditional sense when discussing team success.
Eagles had an easy schedule and overperformed their PyPAT win expectancy. This is typically a recipe for regression. BP has made several aggressive moves in season 86 to get into the contender conversation. In the end, I think he’s lucky to match the 10 wins from last season, even factoring in his fast start.
None of us are surprised by the Bears SoS in season 85 because Astin told us every day how hard the schedule was. Not only that, the Bears underperformed PyPAT win expectancy. I expect the Bears to push for the top seed in the NFC this season with a much easier schedule, an improved team, and a little bit of luck.
I’m not sure what to make of the Panthers. They were somewhat unlucky last season with their win total, but also faced a much easier schedule than what they have coming in season 86. I don’t think they get to 14 wins, but I do expect them to comfortably make the playoffs. But this one could go either direction and I wouldn’t be too surprised.

Season 86 (early) PyPAT

First thing we notice is that no one has as hard of a schedule this season as the Bears did in season 85. That’s good news for the Steelers, Titans, Commanders, and Browns who face the hardest schedules in season 86.
Now that most teams have played 6 games, we can take a look at some early lucky/unlucky teams and predict if it will continue. Giants, Pats, Vikings, and Titans all have a game under their belt that they wouldn’t otherwise have if PyPAT had resulted in the expected number of wins for each. Given the Pats are the only one of the bunch playing like a sub-.500 team, I think they fall off and the rest ride their early success to the playoffs.
On the flip side, poor Ravens and Cards can’t catch a break. Both are playing better than their record but are in deep holes at this point. Even with better luck going forward, I don’t think they’ll be able to rebound to make a playoff push.
According to PyPAT, the two best teams in the league are in an NFC North battle, with the Vikings and Bears sitting at the top. With schedule difficulty almost identical between them, I’ll give the slight edge to the Vikings who beat the Bears by one score in week 1. For my money, week 14 will determine the top seed in the NFC when these two teams face off again.