Pythagorean Win Percentage in College Football

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If you’ve listened to the Pylon U podcast this season, you’ve probably heard me reference pythagorean expectation, or pythagorean win percentage, many times. Originally designed by Bill James as a way to calculate a baseball team’s projected winning percentage based on runs scored and runs allowed, the formula has been adapted for use in other sports and is thought to more accurately represent the strength of a given team than its actual record.

The formula itself is fairly straightforward:

(Points Scored ^ 2.37)/((Points Scored ^ 2.37)+(Points Allowed ^ 2.37))

The thinking behind the calculation is that a team’s actual win-loss record treats all wins and losses the same. A 30-point victory is the same as a one-point win and the same is true for losses. Using points scored and points allowed over the course of a season makes it so not all results are equal and teams are measured more on margin of victory or loss rather than the victory or loss itself. It’s also thought to factor out luck, namely those teams that benefit greatly from pulling out a lot of close games and those that find themselves on the short end of tight ones.

While the statistical evidence that a team may be better than their actual record indicates does them no good during that particular season, a team’s pythagorean winning percentage has recently shown to have predictive utility in college football (and the NFL as well). Teams who outperform their pythagorean win percentage one year tend to regress during the next just as teams who underperform tend to improve. Looking at college football teams’ records, points scored, and points allowed from 2011-2015 provides evidence for this statement.

The below chart categorizes each year during the aforementioned five-year period by their difference between pythagorean winning percentage and actual winning percentage. Once each team was placed into a group, the average change in winning percentage the following season for each team in that group is shown:

pythagimg1Obviously using the average for a large group doesn’t highlight those teams that didn’t follow the theory being set forward. But taking a deeper dive into the numbers shows that at a certain difference between actual and pythagorean, the data is very consistent. Below is each team that had at least a 14% difference (positive or negative) from 2013-2015:


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The key for abbreviations on the following charts are as follows:

  • G: games
  • W%: Win percentage during current season
  • PW%: Pythagorean win percentage during current season
  • Diff: Difference between win percentage and Pythagorean win percentage
  • NY%: Win percentage during the following season
  • Change: Season to season change in win percentage

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Only one team in this particular group of 35 teams (Bowling Green State, 2013) didn’t follow the trend. This season, we’re seeing Michigan State and Northwestern decline, and Washington rise just as this trend predicted. While it is interesting to see how consistent the trend is, there are two other factors that need to be discussed. First, other factors are at play causing drastic improvements or declines such as coaching changes, personnel changes (through leaving for NFL or incoming recruits), and injuries. Each team’s particular situation is different and can provide context to any large difference in winning percentage. Second, those teams with high winning percentages really have no place to go but down just as teams that have low winning percentages have nowhere to go but up. It seems simple, but it’s true.

So why bring up pythagorean win percentage now, near the end, but not at the conclusion of the college football season? I believe seeing this year’s data will perhaps shine a light on some teams to watch during bowl season as they use the next month to get extra practices not just for their final game, but also to get younger players experience for next season.

Below is a chart displaying all teams during the 2016 season with at least a 10% difference between their pythagorean and actual win percentages signaling a potential rise or fall in their “luck” next season. Those teams with their winning percentage highlighted in blue are probable bowl teams this season:

pythagimg3There are a lot of intriguing names on this list. First of all, Boston College and Georgia Tech find themselves on the “Fallers” list after being the two biggest predicted “Risers” following last season and meeting in the first game of the season this year. The same can be said for Nebraska which has had some luck go its way this year. Western Michigan looks to still be good, just 10-2 or 11-2 good, not 12-0, while South Carolina could find itself out of the bowl picture next season. Playing in the SEC won’t allow the Gamecocks much room for error.

As for potential Risers, the teams to watch this bowl season include Miami, LSU, Auburn, and Michigan. Mark Richt has had a good start to his tenure in Coral Gables, but it will be interesting to see what happens if the Hurricanes need to replace quarterback Brad Kaaya. With Ed Orgeron now in place as the head coach for next season, LSU has a chance to get away from the distraction of finding a head man. The Tigers can re-focus on their bowl game, creating some momentum for next season. And it’s scary to think that two teams in the playoff picture like Auburn and Michigan could actually improve next year, but both teams are loaded regardless of departures to the NFL. Auburn specifically had the third biggest difference between pythagorean and actual win percentage in regards to underperformance.

Two teams expected to be in the playoff picture this season, but finding themselves nowhere near bowl games are Michigan State and Notre Dame. Both had horrific and maddening seasons, but the statistical evidence points to a rebound for each in 2017. The Spartans will need to replace stalwart defensive tackle Malik McDowell and the Irish may need to replace quarterback DeShone Kizer, but overall roster talent wasn’t the issue this year. For Michigan State, it was quarterback consistency and a bevy of injuries. For the Irish, it was losing four games by three points or less and three more by one possession.

Follow Jeff on Twitter @jfey5 and find his other work here.

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