How To Calculate Probabilities For Football Betting - Part 1

Sep 3rd, 2012 - Posted by Cassini in Betting Theory, Football

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How do we calculate the probability of outcomes for a football match? Today on the blog, Cassini adds to his series on Elo ratings for football with part 1 on how to apply a Poisson calculation to generate probabilities.

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In the conclusion of my series on Elo ratings, I mentioned how the ‘modified result’ can be used as the input to a Poisson calculation, the output from which can then in turn be used to calculate the probability of any result.

Part Four of Elo Ratings For Football explained how the modified result is generated, but the basic idea is that rather than accept the match result, I look at other statistics and modify the final score. The intent is to make the modified result more a reflection of the game than the result might be, for instance a 1-0 win by a team who were totally outplayed but got one lucky break no longer results in a 1-0 win being entered, but perhaps something like 0.82 to 1.23. As any student of mathematics, or student of football history, is aware, zero can be a problem. [In the days of goal ‘average' as opposed to goal difference, 1-0 was considered ‘infinitely’ better than10-1. Goal difference replaced goal average because the latter system encouraged defensive play.] If the intent is to calculate the goal expectancy for a team, then the zero should be considered highly improbable.

Baseline

While this number is all you need to update the ratings after a match, if you plan to use these numbers as your input to calculate odds on upcoming matches, you will need to standardise your data, and create a baseline number. Whether the team is Norwich City or Chelsea, a score of 1.82 away to Manchester United is better than the same score at Stoke City. This is where you can use the opposition’s Elo rating, with the result being a number that the team might be expected to score against an average team.

In other words our example of 1.82 might become 2.0 if it was against Manchester United or 1.5 if it was against Aston Villa. Manchester United are an above average team meaning the ‘true’ value of the 1.82 is higher, while Aston Villa are below average, and that 1.82 is truly worth less.

The baseline numbers are similarly revised depending on the strength of the next opponents. If a team is expected to score 1.5 versus an ‘average’ team, then use the Elo ratings to adjust that number for a match against Manchester City (reducing it) or Queens Park Rangers (increasing it).

Remember also that when you are attempting to estimate the goal expectancy for a team, you need to consider the number of goals that the opposition is expected to concede. For example, if the home team is expected to score 1.5 goals against an average away team, who are expected to concede 1.5 goals, then 1.5 seems reasonable enough, but if the same opposition has a stronger rated defence, then that 1.5 should be reduced.

Looking Back

How many individual matches do you factor in when calculating this number? It’s a personal choice, but my preference is to look at the last six home games, and the last six away games, assigning more weight to the most recent game, and in turn assigning more weight to the home figure for home games, and to the away figure for away games.

If you consider this to be too long a view back, I wouldn’t argue with you, except to say that your weighting system would likely mean those oldest games have little impact, but more matches helps to smooth out any blips in the data that might be caused by successive home matches versus Real Madrid, Barcelona and Manchester City!

Market Rules

How you weight the two sides is a personal choice. Some options are simply to use the (mean) average of the two numbers, weight the home team more, weigh the away team more, or weigh by Elo rating. However you arrive at it, this number is key, and if you find that your method consistently overestimates or under estimates the market or the result, then you should make adjustments.

While the idea is not to end up with prices identical to the market, in general, betting odds are excellent predictors of game outcomes and if you are consistently on the same side of the market, then your numbers are probably off.

You can of course use the markets to ‘reverse engineer' the goal expectancy numbers for both teams. Markets such as “Arsenal Clean Sheet” or “Arsenal to Score a Goal” for example, reveal the market’s implied probability that Arsenal and Manchester City will not score. The 0-0 is a useful score too, and can be found in several markets – Correct Score, Over / Under 0.5 goals, (No) Next Goal, Total Goals and First Goal Odds.

Odd Numbers

Clearly these non-integer numbers make no sense outside of the statistics world, but an accurate measure of the goal expectancy is essential for the Poisson process. In probability theory and statistics, the Poisson distribution “is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event”.

The independent nature of Poisson is problematic in football, because there is evidence that goals are not independent – the more goals that have already been scored in a match, the higher the probability of subsequent goals – but it works well enough, helped by the fact that the frequency of goals in football is low.

In the next article, I will look at the nuts and bolts, without getting too technical, of using Poisson to generate probabilities, and thus prices, for a number of markets.

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