NFL predictions - Using the Pythagorean Theorem to predict regular-season win totals
Welcome to the second part of our series on predicting regular-season win totals in the NFL. In this article, we will look at how we can use the Pythagorean Theorem to evaluate a team’s performance and expected win percentage. If you haven’t read the first part of the series on using a team’s record in one-score games to predict regular-season win totals, I suggest you take a look at that before continuing.
The Pythagorean Theorem
The mathematical formula is straightforward and gives a good indication of a team’s underlying performance. Using a team’s points for (PF) and points against (PA), we can calculate an expected win number of wins using the following formula – (PF^2/(PF^2+PA^2)).
Let’s take a look at the Super Bowl champions as an example. The Kansas City Chiefs scored 451 points and allowed 308 points during the 2019 season. If we put those numbers into the formula, it tells us that they should have won 0.68 games for every one game played, multiple that by 16 games, and it gives us a full season’s predicted wins – 10.91. We can compare that with their actual wins (12) and see they over-performed by a little over one game, 1.09.
Below are the teams who were unlucky last season based on the Pythagorean Theorem. I’ve included what their 2019 record was, and what their projected number of wins should have been in parentheses.
- Detroit Lions 3-12-1 (6.30 wins)
- Cincinnati Bengals 2-14 (4.90 wins)
- LA Chargers 5-11 (7.81 wins)
- Dallas Cowboys 8-8 (10.34 wins)
- New York Giants 4-12 (5.82 wins)
The Lions come out as the unluckiest team last year with a 3.30 game difference, they still would have finished bottom of the NFC North, but their win total has come out at 6.5 for 2020.
Now let’s take a look at the teams who were lucky last season based on the Pythagorean Theorem.
- Green Bay Packers 13-3 (9.45 wins)
- Seattle Seahawks 11-5 (8.14 wins)
- New Orleans Saints 13-3 (10.29 wins)
- Houston Texans 10-6 (7.85 wins)
- San Francisco 49ers 13-3 (11.28 wins)
Green Bay was the luckiest team last year with a 3.55 game difference, they should have finished second in the NFC North with 9.45 wins behind Minnesota 10.29 wins. The Vikings are +160 favorite for the NFC North in 2020 and filled some holes on their roster with WR Justin Jefferson, CB Jeff Gladney & T Ezra Cleveland.
Full Pythagorean Theorem standings
Here’s how the full NFL standings should have looked in 2019 based on the Pythagorean Theorem (teams actual record in parenthesis).
Chiefs 10.91 wins (12-4)
Chargers 7.81 wins (5-11)
Broncos 7.09 wins (7-9)
Raiders 5.73 wins (7-9)
Patriots 12.43 wins (12-4)
Bills 9.52 wins (10-6)
Jets 5.94 wins (7-9)
Dolphins 4.44 wins (5-11)
Ravens 12.48 wins (14-2)
Steelers 7.62 wins (8-8)
Browns 6.73 wins (6-10)
Bengals 4.90 wins (2-14)
Titans 9.54 wins (9-7)
Texans 7.85 wins (10-6)
Colts 7.74 wins (7-9)
Jaguars 5.82 wins (6-10)
49ers 11.28 wins (13-3)
Rams 8.63 wins (9-7)
Seahawks 8.14 wins (11-5)
Cardinals 6.40 wins (5-10-1)
Cowboys 10.34 wins (8-8)
Eagles 8.67 wins (9-7)
Giants 5.82 wins (4-12)
Redskins 4.35 wins (3-13)
Vikings 10.29 wins (10-6)
Packers 9.45 wins (13-3)
Bears 7.50 wins (8-8)
Lions 6.30 wins (3-12-1)
Saints 10.29 wins (13-3)
Buccaneers 8.16 wins (7-9)
Falcons 7.63 wins (7-9)
Panthers 5.5 wins (5-11)
That concludes the second part of the series, in the third and final part we look at how we can use turnover margin to make this prediction even stronger.
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