Pythagorean Expectation in the NRL
A brief look into Pythagorean Expectation in the NRL in 2024
Overview
Pythagorean expectation is a simple way to calculate an estimate for win rate (%) from only points for and points against. It does not consider any individual matches or other teams’ figures, only the total points scored and conceded for each team.
Here’s the expression to calculate it:
Note that 2 is the most commonly seen exponent due to fitting well to Baseball, the sport that the formula was first used.1
What is the ideal exponent in Rugby League?
Excellent question.
I’ve been lazy and not actually found the ideal value myself. This article by Matter of Stats, a member of the Aussie Rules modelling scene, finds an ideal exponent of 1.89 for Rugby League.
It may be worth repeating the search for optimal exponents to investigate the changes to the game since 2020, as this may have affected the ideal exponent and therefore how well this model fits.
I’ve gone and calculated the actual and expected win rates for every team since 2007 to end of round 20 in 2024, and these are shown on the visualisation below. The highlighted points represent teams from this season.
Let’s focus in on just the 2024 numbers:
The Storm are the clear standouts here. They’ve won 14 of their 17 matches this season and are 2 wins clear of 2nd place Panthers. Yet, they only have a Pythagorean expected win rate of 66.5% - for an expected 11.3 wins.
Roosters’ record this year is under what the expectation is, largely due to an absurdly high points scored value this season. They average 29.4 points per game. Only 3 teams, at the end of the regular season, have topped this.2 So, it will be interesting to whether they can maintain it for the remainder of the regular season.
Those three teams that manage to score more than the 2024 Roosters per match? They were all in the 2021 season, where rule changes brought some of the highest scores in the history of the league. It really shows how much of an outlier they are this season in that regard.
Read the Wikipedia article here if you’re interested about more on the origins of Pythagorean Expectation
(since 2007 at least, I don’t have the data prior to that)