# Applying Elo Ratings To Football - Part One

Aug 3rd, 2012 - Posted by in Betting Theory, Football

Musings on Backing, Laying, Trading, Punting, In-Running and more on the Betting Exchanges and related items of interest in the wide world of sports investing

You may have heard of Elo Ratings. But what are they exactly? And how can we apply them to assess the performance of football teams? Today on the blog Cassini delivers part one of his series on how we can adapt Elo Ratings to football and improve our betting.

## Introduction

Often incorrectly written as ELO, Elo ratings actually take their name from the inventor, Arpad Elo, a Hungarian-born American physics professor and Chess player who invented the ratings method as a way of comparing the skill levels of players from his game. Its use has expanded, and has been adapted for several sports including American Football and basketball, but also in football, and it is their use here that is the focus for the rest of this article.

## The Basics

The essence of Elo ratings is that each team has a rating. When comparing two teams, the team with the higher rating is considered to be stronger. The ratings are constantly changing, and are calculated based upon the results of matches. The winner of a match between two teams typically gains a certain number of points in their rating while the losing team loses the same amount. The number of points in the total pool thus remains the same. The number of points won or lost in a contest depends on the difference in the ratings of the teams, so a team will gain more points by beating a higher-rated team than by beating a lower-rated team.

Raw Elo suggests that both teams ‘risk' a certain percentage of their rating in each contest, with the winner gaining the total pot, i.e. their rating increases by the losing team’s ante. In the event of a draw, the pot is shared equally.

## A Simple Example

A simple example shows how this works when two evenly matched teams meet, and both have 5% of their rating at risk. Arsenal and Chelsea both have a rating of 1000 so both teams risk 5%, i.e. 50 points, and the pot contains 100 points.

There are three possible outcomes.

1) Arsenal win, and the result of this is that Chelsea’s rating drops by 50 to 950, and Arsenal’s rating increases by 50 to 1050.

2) Chelsea win, and the result of this is that Arsenal’s rating drops by 50 to 950, and Chelsea’s rating increases by 50 to 1050.

3) The result is a draw. The pot is divided between the two teams, resulting in the ratings for both Arsenal and Chelsea remaining unchanged at 1000.

## A Second Example

A second example shows how this works when the home side is stronger. Manchester City (with a rating of 1200) plays Aston Villa (with a rating of 1000). Again both sides risk 5% (60 points and 50 points respectively), so the pot contains 110 points.

The three possible results and their effect of the ratings are:

1) Manchester City win, and the result of this is that Aston Villa’s rating drops by 50 to 950, while Manchester City’s rating increases by 50 to 1250.

2) Aston Villa win, in which case Manchester City lose their 60 points and their rating drops to 1140, while Aston Villa gain the 60 to improve their rating to 1060.

3) The result is a draw. The (60+50) 110 points in the pot are divided by two, resulting in Manchester City’s rating dropping by 5 points to 1195, and Aston Villa’s rating improving to 1005.

## A Third Example

A third example shows how this works when the away side is stronger. Wigan Athletic (with a rating of 800) plays Manchester United (with a rating of 1000). Again both sides risk 5% (40 point sand 50 points respectively), so the pot contains 90 points.

The three possible results and their effect of the ratings are:

1) Wigan win. Their rating increases by 50 to 850,while Manchester United’s rating decreases by 50 to 950.

2) Manchester United win, in which case Wigan lose their 40 points and their rating drops to 760, while Manchester United gain the 40 to improve their rating to 1040.

3) The result is a draw. The (40+50) 90points in the pot are divided by two, resulting in Manchester United’s rating dropping by 5 points to 995, and Wigan’s rating improving to 805.

The table below summarises these combinations of pre-match ratings, match results, and updated ratings

## Some Issues

All very simple, but for football, it is much too simple. Anyone with a basic understanding of football can see a number of problems with the above examples. One obvious problem is that home advantage is not taken into account, so in a match between two evenly rated teams, in the event of a draw, the away side should be rewarded, and the home side penalised. In the ‘teams evenly rated’ example above, a draw for Chelsea at Arsenal is clearly a better result for them than it is for Arsenal, and it is illogical that both teams walk away at full-time with the same rating as when the started.

In Part Two, I will look at some ways in which these problems can be remediated.