Developing an accurate and realistic rating system is often a primary for a sports analyst. Just about every organised sport competition in the world has it’s own implicit rating system in which we expect “good” teams to be rated higher than poorer teams. In AFL footy we call this the ladder. The problem with using a team’s position on the ladder to infer how well it plays is that the ladder is sorted primarily by wins. While winning lots of games is important (#analysis), how many games a team has won previously is not always the best indicator of how many they’ll win in the future. This is especially true of a competition like the AFL which uses an uneven draw. A team towards the top of the ladder that has yet to face any other difficult teams has obviously not proven itself to be a strong side.
A “true” rating system provides us with a wonderful descriptive and predictive tool. We can compare teams over time. (Just how does this year’s Hawthorn team hold up against Brisbane of the early 2000s?). We can map changes in team rating after notable player and administrative changes. (How important will Patrick Dangerfield’s move from Adelaide to Geelong be for both sides?). And perhaps most tantalising for some, we can calculate implied probabilities for upcoming matches and even seasons and make a profit betting against inefficiencies in sports-betting odds. (What is fair price for Hawthorn to make it 4 in a row next season?)
Given this motivation, I have created a few different types of rating systems that I have been testing out over the last season. Today I’ll introduce you to simplest of these, a basic Elo model which I have donned “SimpElo”1, and show you the impressive results that can be achieved with just a few basic principles.
Elo is a rating system developed by Arpad Elo for use in determining the relative skill of players in international chess competitions. It has since found a grounding as a simple rating system in many player v player and team v team sports including football, NBA, NFL and even video gaming.2 A number of Elo-based rating systems for the AFL already exist, but as you will see, I think improvements can be made. Tony Corke at MatterOfStats uses an Elo system for his weekly ChiPS rankings and predictions, he also frequently discusses his methodology in informative posts. The Footy Maths Institute also provides season long commentary into their “modified Elo” system.
The beauty of the Elo rating system lies in it’s simplicity. At it’s heart, all the computation is done by one simple formula. All teams start the season with an initial rating (more on this later), after each match the change in team ratings is calculated as so.
Where Result is either 1, 0, or 0.5 depending on whether the team win, loses or draws. The great thing about this is that the team who won the match gain just as many points as the team who lost lose. More points are gained if you win a match in which you were given a low chance of success than are gained if you beat a team you were expected to beat. Which leads us on to how win probability is calculated. Luckily, it’s not much harder. We first calculate probability of the home team winning. The probability of the away team winning is simply 1 minus this number. (In this model a draw is not considered)
The probability of a home win is calculated as so.
Where, InitOppRat is the initial rating of the opponent, InitRat is the initial rating of the home team and HGA is the home-ground advantage that the team enjoys. This formula has the nice property that a HGA inclusive difference between team ratings of 400 equals odds of exactly 10:1.
At it’s core it’s a simple as that. After every game we add/subtract points from the winner/loser and calculate their new rating dependent only on their results and the implied difficulty of their schedule faced. Of course, there are some parameters in all this that we need to fix before we can do that.
Home-Ground Advantage is without doubt a factor. Home teams win significantly more often than would be expected if all games were played at a neutral venue. The average score for an away team is around a goal and a half lower than the average home team score. I think it’s important to understand this and account for it, which is why, even in its quest for simplicity, SimpElo recognises an HGA variable while forgoing many other game variables.