The RFL Team Rating System - By Kendall York

The TRS is based on the idea that teams are of a set skill level and that a team's skill level does not rapidly change. The math used in the system is based on the Elo rating system which was designed to measure the abilities of chess players. The Elo system has also been used in college football as a way of measuring the overall skill of teams versus other teams they may never play.

The system is based on the formula Rn = R + K(S-E). Rn will be the new rating of the team. R is the original rating of a team. K is the maximum value a team may move up or down after a single game. S is the outcome of the match. S is equal to 1 for a win, 0 for a loss and .5 for a tie or by. E is the expected odds of the team winning expressed as a decimal.

To calculate a team's odds of winning we use the formula Ea = 1 / (1+10^(Ra – Rb)/500). Ea is the is the expected odds of team A beating team B. Ra is the current rating of team A and Rb is the current rating of team B.

In the RFL all teams begin with a rating of 1500. So if team A and team B are both new and play a game which team A wins the math will look like this. The odds of team A winning is 50%. We know this because 1500 minus 1500 is 0. Take the 0 and divide it by zero and you get 0. 10 raised to the 0 is 1 (it really is try it on your calculator). So we are left with 1 over 1 plus 1 which is ½ or 50% or 1 / (1+10^(1500-1500)/500).

So now that we know team A was expected to have a 50% chance of winning the game we can calculate team A’s new rating based on their win over team B. Using Rn = R + K(S-E) we just need to plug in a few numbers. First R will be 1500, which was their rating before the game. K is set by the RFL at 25. S is 1 because team A won. E is 0.5 based on the previous calculation. So Rn = 1500 + 25(1 - 0.5). So team A’s new rating is 1512.5 or 1513 when we round.

Something interesting to note is that S is the most a team can gain or loss in a game. S is regulated by the expectancy to win. So a team will only be able to gain the maximum value if they play teams that are significantly higher rated than them and win. Also a team is only at risk of losing the maximum value if they play a team that is significantly worse than them. This means a team that is highly ranked has nothing to win and every thing to lose by playing a significantly lower ranked team. This also means that if a team wants to improve their rating they need to play teams which are significantly higher ranked then they are.

One difference in the TRS from other rating systems is that the TRS does reward frequent play. Each week a teams score is recalculated based on the games they played. If no games were played in a week by a team with a rating above 1500 than the team is given a ghost game. The ghost game counts as a tie against a team with a rating of 1500. By having these ghost games a teams must actively hold its score high. Teams which achieve a high rating and stop playing will slowly be pulled back toward the middle. This is based on the assumption that a team becomes rusty if it does not play.

The system is not intended to reward wins and losses. It is intended to statistically predict the skill of any team versus all other teams.