How it all works

I appreciate that it’s difficult to keep up with the Pythago NRL Expanded Universe™ of metrics and ratings. Not only are they generally more complicated than standard stats, I tweak them almost every year based on what I learned during the previous season.

Here’s a short reference guide to what it all means.

Pythagorean expectation: There is a relationship between for and against and winning percentage, which is expressed by the Pythagorean expectation formula. Generally, if a team outperforms their Pythagorean expectation (that is, wins more games than predicted by the formula) they will win fewer games in the following season and vice versa. Pythagorean expectation gets increasingly accurate at estimating win percentage over a longer time period.

Elo ratings: Elo ratings were developed by Arpad Elo to rank chess players and are now used in FIFA’s official world rankings. Formerly known by the names of Greek philosophers, I’ve been using Elo ratings for four years to assess the quality of rugby league teams. I massively expanded the number of systems during the off-season to cover most major mens leagues in the world.

The variables behind each system and league are different but typically, the average rating is 1500 and a higher rating reflects a better team. We can use the difference in Elo ratings to calculate the winning probability of two teams. I maintain two systems for each league –

Form ratings are designed to reflect short term performance and move quickly to reflect recent results (I typically say about six to eight weeks). The system variables are optimised to maximise head-to-head tipping success. When two teams match up, an expected margin is estimated between the two teams based on their respective ratings. If a team beats the expected margin, and even if they lose the match, their rating goes up by exactly the same amount the other team’s rating goes down. Form ratings only track regular season performance.

Class ratings are slower moving than form ratings and take multiple seasons to change significantly. Unlike form ratings, class ratings go up only when you win. They go up more for winning finals games and more still for winning grand finals. Class ratings reflect team’s innate quality and act as a handbrake from looking too closely at the last couple of matches. For example, a team wrecked by Origin selections may have a poor form rating at the start of August but will maintain a high class rating.

  • Disappointment line: The number of wins we expect each team to gain based on their class rating compared to the system average. Failing to reach the number of wins indicates a disappointing season and the further away from the line, the more disappointing. This works surprisingly well.

Poseidon ratings: We count the number of tries scored home and away and the number of tries conceded home and away and compare that to the league average to make a basic assessment of a team’s offensive and defensive capabilities. Deeper than that, we can use this information to use Poisson distributions, as well as the binomially distributed conversion rate, to produce expected scores (expectation in the statistical sense) and put probabilities against scorelines and margins.

Taylor Player Ratings: Taylors (Ty) are the units for measuring production, the sum of valuable work done on the rugby league field, as measured by counting statistics that correlate with winning. Taylors by themselves can be misleading, so we have:

  • TPR: Taylor Player Rating. This compares the amount of production done by the player to the average player in that position, adjusting for time spent on the field. An average player has a rating of approximately .100, with fringe first graders sitting at .060 and top players nearing .180.
  • WARG: Wins Above Reserve Grade. This compares a player’s production that to a typical fringe first grader in that position to estimate the number of additional wins the player’s team gains by having him on the roster. We explored the concept in What makes a million dollar NRL player? and Rugby league’s replacement player. Jason Taumalolo is the NRL’s career leader in WARG, with 9.3 since 2013.
  • Projection: Estimating the performance of a player for the next season, measured in TPR, based on previous seasons and reversion to mean per The Art of Projection.

To qualify for TPR, a player must play at least five games in a season. A rookie is a player with no TPR in the previous three seasons, a sophomore has registered one in the previous three, a senior, two in three and a veteran has a TPR for all three of the previous seasons. Players without a TPR in 2019 are not included in roster composition considerations.

Simulations: I used to call this the Stocky but these days, with lots of different simulation variations, I refer to them as Monte Carlo simulations, which is what they are. The simulations are used to determine the probabilistic outcomes of the season. Simulations use input ratings based on Elo, Poseidon and Taylor systems to calculate winning probabilities of individual matches, a random number determines the results and we repeat ten, fifty or a hundred thousand times. The outputs are blended to give one set of predictions. The outcomes give insight in to how we expect the season to unfold, based on what we know right now.