Revisiting Pythagorean Expected Points in Soccer

Jack T.
3 min readOct 24, 2022
Source: Wikipedia

Last year I wrote a post detailing how the Pythagorean Expectation theorem can be used to predict a baseball team’s expected winning percentage based on the team’s run differential throughout the course of the season. Because there are no ties in baseball, every game will end with either a winner or a loser. Soccer is obviously different — wins get teams 3 points, a draw is worth 1 point and there are 0 points for a loss. This makes it slightly more difficult to determine whether or not a club is under- or over-performing expectations based solely on goal differential. Luckily, the smart folks over at StatsBomb have come up with a pretty solid Pythagorean formula that we can use to compare last season’s over/under-performers to how teams are doing this campaign.

Using the StatsBomb formula on results from 2021/22 season shows that almost every team in League 2 over-performed their expected points. The only team to perform below expectations last year was Leyton Orient. Orient ended the 21/22 season at 58 points against a predicted point total of 62. Earning 62 points on the season would have only bumped them up by one place in the table, but the math shows a clear under-performance by Orient last season.

This season, Orient is at the top of the League 2 table through 14 matches and has been in a good run of form since the start of the season. The formula currently predicts the squad to end the season with 61 total points, which is more than their point total from the 21/22 campaign but less than what the formula had them at last season. Personally, I think it’s a bit of an under-estimate, given that every team except for Orient last season over-performed the formula’s predictions, some by 15 points.

There’s one thing I need to change in the formula for League 2’s 22/23 predicted points, though. The way it’s constructed now, the formula is predicting point totals for the whole season. But how have teams performed so far when we’re only 14 weeks into the campaign? I’ll have to account for how many matches played going into the weekend to get a true idea of club performance.

Accounting for matches played thus far in the 22/23 campaign shows that, once again, many teams are over-performing their expected points totals. This leads me to think that there’s tweaking to the formula I’ll need to make at some point in the future to get a more accurate picture of club performance. For example, Orient currently has 33 points on the season but their expected point total comes in at only 19. They’re one of only 2 teams in League 2 with a double digit goal differential, as well. It might be time to retire this StatsBomb Pythagorean points expectation and come up with a new one!

Every club in the top 5 is over-performing their expected points totals through Wk 14.

For now, I’m enjoying Orient’s stellar start to the season and look forward to seeing if they can keep it up for the duration of the campaign!

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Jack T.

Data enthusiast. Topics of interest are sports (all of them!), environment, and public policy.