PythagoreanPAT Win Expectency

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.

Anyway, here are the results.

Some quick observations:

Chargers were the luckiest team, but they still also had the third highest expected win percent. In other words, lucky or not, they were still a top 3 team.
The team with the highest expected win percent? The Baltimore Ravens, who beat the Chargers in the playoffs. Yay Math!
Speaking of Super Bowl participants, the Saints came in as the 4th most unlucky team. They had the third best expected win percent in the NFC. Having a 10-7 team go on a Super Bowl run might have been a surprise, but not nearly as much when you see they probably should have won at least 12 games last season.
The vaunted AFC South had 3 of the 8 most lucky teams, which makes sense when you have a division that has 4 teams with a winning record.
My pick for teams that will surprise this season are the Packers and Bears. Both underperformed last season and have the building blocks for solid teams. The Lions will drop off a bit just from having an exceptional year and being slightly lucky last season. Then you add anti-media Spencer back in the mix from his cruise, look out for the NFC North to be a dog fight all year.
The Denny Green, "they are who we thought were" team? Cincinnati Bengals fished with exactly as many wins as their point differential suggests they should have had. Good job RFox!