# Applying Elo Ratings To Football - Part Two

Aug 6th, 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

In part one, Cassini showed us how to apply basic Elo ratings to football. Today he takes us further, looking at how to incorporate home field advantage and the margin of victory to our football ratings.

In Part One we explained the basic premise of Elo ratings, and illustrated how they are applied. Part two will offer some suggestions on how the principles of Elo can be enhanced to make our ratings more useful. It is important to understand that these are only suggestions. There are no hard and fast rules that dictate what these parameters should be. There is no right and no wrong, only what works and what doesn’t work.

We finished Part One with an example of two evenly rated teams, risking the same percentage of their ratings, and identified one major problem which is that an away draw is better than a home draw, and it is thus illogical for both teams to end the match with the same rating as they started.

One way to handle this is by having the home team risk a slightly higher percentage of their rating than the away team. Back in the early 1980s, two authors, Tony Drapkin and Richard Forsyth wrote a book called The Punter’s Revenge: Computers In The World Of Gambling, which was targeted at computer literate punters at a time when the personal computer was just becoming popular. One of the more memorable chapters was on rating football teams, and the author’s suggestion, after running trials, was to use 7% for the home team, and 5% for the away team. I’ve found no reason to diverge too far from these numbers.

If we re-visit the earlier examples from part one, using the 7% and 5% numbers, the results become:

When the teams are identically rated going in, after a drawn match, the away team gains slightly, the home team loses slightly, something that intuitively seems right. If you’re not happy with the adjustments that 7% and 5% give you, then there’s absolutely no reason not to tweak these, but I would caution against exceeding 10% or going below3%. Changes in rating should be in modest increments, but at the same time, not too modest that it takes a season for a declining team’s rating to reflect its form.

## Result Adjustment: Incorporating Margin Of Victory

Now to address the next problem – match results. Basic Elo doesn’t quantify wins. A win is a win, whether it is by one goal or by a dozen. Most readers will agree that this is an unsatisfactory state of affairs, and will make adjustments. One method is to increase the percentages that each team risks, but to award a certain percentage of the pool to the winners / losers varying depending on the margin of victory / defeat.

For example, Arsenal and Liverpool are both rated at 1000, and Arsenal are at home. The pot (or pool) contains 120 points, 70 from Arsenal, 50 from Liverpool. If the game finishes 6-0 to Arsenal, it’s reasonable to give all the points to them. My own preference is for a four goal win or more to be sufficient to secure the entire pot. A three goal win is pretty good, and earns most of the pool, whereas a two goal win earns a little less, and a one goal win the minimum. The following table is a suggestion.

Winning is worth at least 70% of the pot, with the margin of victory becoming less significant as it grows. Winning 6-0 rather than 5-0 is neither here nor there, but winning 1-0 rather than drawing 0-0 is much more significant – even though the difference between both pairs of scores is just one goal. You may want to consider a 1-2 defeat as a better result than a 0-1 defeat, but again, decisions such as these come down to personal preference. With all the time in the world, you might analyse goal times, and conclude that a 2-0 win decided in the 30th minute is a stronger win than a 2-0 win in which the second goal was scored on a breakaway in the 93rd minute with the vanquished team pressing hard for an equalizer. A fair conclusion in my opinion, and an example of how you can modify Elo to suit your own needs, and add flexibility based on the amount of time you have available.

Maintaining accurate ratings is time consuming, and in previous years I would attempt to maintain ratings for the Premier League, Football League and Conference as well as the Scottish Leagues. These days, I restrict my tracking to the top divisions of England, France,Germany, Italy and Spain, in part because there is a wealth of data readily available to input, and on the output side, there are many liquid markets available. It is also my opinion that in the lower leagues, ratings are not so stable. A modest amount of money goes a long way, as recently seen with Crawley Town and Fleetwood Town, and ratings can soon be out of date.

In Part Three, I will look at more ideas for maintaining accurate ratings.