PythagoreanPAT Win Expectency

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

Now it's time to bring it back to our franchise restart. You can find a refresher on PyPAT below. For those not wanting to watch the video on opponent PyPAT, the short of it is were 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.

The below table shows PyPAT for last season (season 81), luck (difference between actual win % and PyPAT), OppPyPAT for last season (their season 81 SoS), and their season 82 SoS using PyPAT from last season of their opponents this season. (perfectly not confusing!)

Some quick observations:

Look for a huge drop from the Titans – they were very lucky last season, had one of the top 5 easiest schedules, and now have the second hardest schedule based on last season PyPat rankings.
On the other side, I see a big bounce back for Texans, Falcons, and Vikings. Vikings had the hardest schedule in the league last season based on opponent PyPat and it flips to one of the easiest this season. Falcons were both unlucky and see a drop in schedule difficulty. Lastly, Texans were one of the unluckiest teams and see an even bigger drop in schedule difficulty than the Falcons. I'd bet a Buffalo Nickel all 3 will be in the playoffs.
Colts I think will tread water. They were very unlucky last season, but also see a big jump in schedule difficulty.
Eagles were the top team in the league by PyPat and won it all – yay stats!
Lions were very good last season, but it will come even harder this season. Between the Vikings bouncing back and not being as lucky, I don’t think they’ll match last seasons win total. I expect them to be battling for a wildcard spot.

Pythagorean primer for new readers or those wanting a refresher

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.