Posted April 29, 2022, reposted July 23rd 2022
As discussed from last year’s article, football is a game of inches, and by being off just one, could be the difference between a win and a loss in a league with limited games. The shape of the football itself creates it’s own sort of randomness on circumstances such as situation like field position during punts and how the ball spins during field goals. There is also a certain amount of randomness of “when” the points are scored that pertains to a team’s final win record. Let’s face it, there is a good amount of luck that happens within the football season the best teams do not always win against the worst teams. We can just go back to January 9th of this year to find an easy example of that for when the Jaguars beat the Colts.
Many of us NFL football analysts and sports bettors want to have good methods for prediction for next year’s football season in order to be more accurate. Wins and losses do not tell the whole story and they are also rarely a good indicator by itself for a team’s future success. If we find some scientific methods that will correlate well using a team’s past performances to their success in the future, it will help us become not only more knowledgeable, but it could also help us become more profitable. The method that we will be discussing today is the 2021 Pythagorean win total calculation as a method to help predict the 2022 football season results.
Is it possible for an NFL team to score more points than they give up and have a losing record? How about score less points than they allow and have a winning record? The answer to that is that it is very possible, and it happens every year. In 2019 the Houston Texas scored 378 total points, yet gave up 399 to win 10 games. In that same year, the Chargers scored 337 points while only giving up 345 (almost 50/50) and only won only 5 games.
Sometimes teams score many of their points during blowouts, and as luck will have it, those same teams might lose their close games. Due to these discrepancies, we need to formulate the data to find out what some of these teams were expected to do based on points scored compared to their actual win/loss results. Using a function that takes a look at the total points scored as a data point with the total points allowed is, at many times, a better indicator of a team’s future success compared to their actual record. This is why we can use a Pythagorean win total compilation to compare what was expected to happen based on points scored for all of the NFL teams, to what actually did happen in how these teams finished out their year. This way we can have a better idea on what to expect for next season. The 2011 edition of Football Outsiders Almanac states, “From 1988 through 2004, 11 of 16 Super Bowls were won by the team that led the NFL in Pythagorean wins, while only seven were won by the team with the most actual victories. Since then, the Pythagorean wins theorem has continued to be statistically significant.
The Pythagorean theorem is a^2+b^2=c^2. It basically figures out the distance between two points of a right triangle (c), or for what we are interested in, the expected value between the relationship of sides. Please see the figure. 
Think of points scored as (a), and points allowed as (b) where (c) is a function of the (a and b) linear equation and we just want to know what the relationship is between a^2/c^2 (c^2 is a^2 + b^2) to get a percentage of wins multiplied by the total games. Going by the diagram, if it is a tall and thin triangle, the team scored a lot more points compared to what they have given up, and if it is a short and long triangle, the team has given up many more points compared to what they actually have scored.
I know what you are thinking. Why can’t we just use the points scored over total points as a basis for predicting the expected outcomes? The answer to that simply is that the data would be wrong. For example, if a team scores 75% of the total points and only allowed 25% of the total points throughout the year, would we only expect that team to win just 75% of their games? Heck no. That is like averaging 30 points per game on offense and only allowing 10 points per game on defense. Even the 16-0 2007 patriots who scored 68.3% of the points averaging 36.8 on offense and giving up 17.1 on defense won many more than 12 games. The 2007 Patriots’ Pythagorean win total certainly didn’t equate to winning every game, but was at 13.76, which is much higher than the 12 and a much more relatable number to their fantastic season.
But wait, there is more! This Pythagorean equation does have it’s faults if adjustments are not made to it. This equation tends to bunch all of the teams more towards the middle when actual outcomes may deviate further away from the mean. Statistician Daryl Morey found this in football among other sports and was able to develop a more statically significant exponent of 2.37 (rather than 2) as a constant for better accuracy while utilizing this equation. Without getting too far into the weeds, we must make adjustments correlated to the actual variances that happened over the years pertaining to each sport, and for this column, football itself. Aaron Schatz of Football Outsiders takes this concept even farther by stating that each team’s exponent should be different as a function of their points scored. According to Schatz, the formula for each team’s exponent that works best in the NFL is 1.5 * log ((PF+PA)/G). I myself find that using the constant exponent of 2.37 doesn’t deviate significantly enough from Morey’s exponent model with respect to the actual randomness in the sport of football itself. Much of this randomness comes from inconsistent officiating, injuries, and pure luck itself.
One thing that I found that we can somewhat account for is turnovers. Every year there are teams that have something called turnover luck. Weather if the luck is good or bad, turnovers affect the scores and the results of each game. For example, some teams could have had a 3 point field goal and instead they fumble the ball away while some defenses are put on the back of their heels when teams turn the ball over in their side of the field. The Cowboys and Colts had the best turnover ratio of +14 while the Jaguars had the worst at -20. Big shocker right? Now it is well known that turnovers are worth close to about 4 points to each team respectively and the old school way of thinking is that turnovers are mostly random, but I tend to disagree with that notion. If you look at the recent histories of each team, turnovers happen to be somewhat predictable. For example, before Tom Brady became a Tampa Bay Buccaneer, Jameis Winston used to turnover the ball quite often and it would show up significantly negative year over year in Tampa Bay’s turnover margin. Jacksonville is another team that you have been able to pencil in the negatives for a while now. On the flip side of the coin, there are teams that take care of the ball more often on a consistence basis while them ore other teams might have great ball-hocking defenses that tend to force more turnovers than the others. The Green Bay Packers fit that bill and the Kansas City Chiefs have been on the high positive side for turnovers for at least the last six or seven years for the most part. Due to this, I have adjusted turnovers to be about half of what they are worth to the number from 4 to 2 points per turnover and I award or punish each team only 1 point on offense and 1 point on defense (rather than 2 and 2) with respect to their 2021 turnover ratio. Normalizing turnovers give you a better idea of what each team’s expected wins should have been based on a cleaner season. In essence, a negative turnover ratio helps those sloppier teams with better expected wins as they punish the cleaner teams that had a high positive turnover margin with lower expected wins due to the luck factor that I have applied. Even though some teams tend to take care of the ball more doesn’t mean that there isn’t some luck to the outliers and visa versa. Please see our chart below for our actual wins vs our Pythagorean expected win totals.
Going by this diagram we can make informed judgements and educated decisions on the actual strength of these teams with respect to not only how well they can score against their opponents but also how well that they can defend. As you can see from the difference column between the actual results from the first 17 game schedule ever in the NFL with the Pythagorean (or expected) results that we can actually see how teams have either over-achieved, or under-achieved in the 2021 season. Here are the five outliers on each side:
Over-achievers:
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- Green Bay Packers: The Packers had only 9.79 expected wins compared to their 13 actual wins last year. A -3.21 difference. The Packers had good turnover luck and played in a very weak division. Their toughest games ended up being at home. Keep in mind that the Packers had two big outliers in their data. Those two data points were when they benched their players on game 17 vs the Lions, and that awful first game of the season when they were blown out by the Saints. Also, remember that garbage time, and the fact that Aaron Rogers is a clutch player probably makes some argument for higher expected wins. I personally think that around 11 expected wins is more fair for this team than 9.79.
- Las Vegas Raiders: The Raiders only had 7.34 expected wins compared to their 10 actual wins last year. A -2.66 difference. Now this number would be even bigger if the Raiders didn’t get respect for -9 turnovers. The Raiders won a lot of games that they shouldn’t have and I think it was all Derek Carr and coach Rich Bisaccia. Just amazing what they did with all of the trials and tribulations from last year, but that doesn’t make up for the fact that this really was a below .500 team.
- Pittsburgh Steelers: The Steelers had expected wins of 6.91 compared to their 9.5 adjusted actual wins last year. A -2.59 difference. The Steelers also won a lot of games that they shouldn’t have, and they got to capitalize on very injured Ravens, and Browns teams. Keep in mind that the Steeler’s 2021 schedule ended up being easier than people thought coming into the preseason.
- Atlanta Falcons: The Falcons had expected wins of 5.16 compared to their 7 actual wins last year. A -1.84 difference. The Falcons were actually +4 in turnovers believe it or not, and they had some good wins vs the Saints and Dolphins. This team had a medium schedule and I was somewhat surprised they won 7 games while only going 1-3 against the NFC East.
- Tennessee Titans: The Titans had expected wins of 10.33 compared to their 12 actual wins last year. A -1.67 difference. The Titans did hit an injury bug but it was at the right time after they somehow beat a ton of great teams the first half of the schedule and then eased into the easy part afterwards. They caught a lot of teams sleeping on them and capitalized. losing to the Jets and the Texans was somewhat telling to me that they were not the best team in the playoffs deserving of that top seed. Now I do think they were a good team, just not great.
Under-achievers:
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- New England Patriots: The Pats had expected wins of 12.12 compared to their 10 actual wins last year. A +2.12 difference. The Patriots blew out a lot of the bad teams and just couldn’t beat the very good teams minus the wind bowl in Buffalo.
- Buffalo Bills: The Bills had expected wins of 12.92 compared to their 11 actual wins last year. A +1.92 difference. Five of the Bills six losses were by seven points or less. That Jacksonville one was a pure stinker as well.
- Seattle Seahawks: The Seahawks had expected wins of 8.9 compared to their 7 actual wins last year. A +1.90 difference. Russel Wilson was injured and Geno Smith proved that he isn’t even a backup QB in the NFL. This team had a lot of injuries but really stepped it up at the end and also blew out some bad teams. Keep in mind that the data has been compromised with Russell Wilson leaving the team.
- Denver Broncos: The Broncos had expected wins of 8.84 compared to their 7 actual wins last year. A +1.84 difference. Philadelphia had lots of injury woes last year. They went 3-5-1 in games decided by a touchdown or less and the tie game with Cincinnati also hurt their total wins.
- Detroit Lions: The Lions had expected wins of 5.24 compared to 3.5 adjusted actual wins with the tie. A +1.74 difference. Detroit wasn’t quite as bad as they looked, and they played some teams very tough behind their hard nosed coach in Dan Campbell.
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In conclusion, it should now be easier to see the randomness in football were some teams will have better records than they actually deserve, while some teams will have worse records than they actually should have achieved. Remember to take this information for what it’s worth. When predicting season wins, we also must
factor in some of the less quantifiable information such as the clutch performances from quarterbacks like Tom Brady and Patrick Mahomes along with the anti-clutch performances of Matt Ryan and Kirk Cousins. Strength of schedule is another data point that is less quantifiable when it comes to actual points or season wins, but equally important when determining what these teams went through, not only in the previous season, but also in what they will be facing in the near future.
Pythagorean win totals are an important indicator of the future success of NFL teams going into their 2022 seasons and it should take some precedence over last year’s actual win results. The Pythagorean win total will remain a great method for your predictive analysis for next season and beyond. Should you have any questions or want a list that can be copied and pasted, please tweet me @OBKiev. Have a great NFL season and best of luck in your research.
Ref 1: Football Outsiders: https://www.footballoutsiders.com/dvoa-ratings/2011/week-13-dvoa-ratings
Ref 2: Wikipedia: https://en.wikipedia.org/wiki/Pythagorean_expectation#:~:text=The%20formula%20is%20used%20with,referred%20to%20as%20Pythagorean%20wins.
