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# Building a simple o/u betting model

Football is a complex sport with a wide variety of possible approaches to building tradable models. In this article, we shall focus on the more rudimentary approach of taking mostly market inputs and transforming them to probabilities and therefore prices to use as part of a basic approach to football betting on over/unders market.

Broadly (and somewhat simplistically) speaking, there are two things that need to be understood when modelling sports such as football which have a continuous clock and relatively simple, unconstrained scoring. These two things are:

• which distribution most accurately represents the scoring in the sport; and

• how can I work out the inputs to this distribution for a specific match.

If we focus on football, it is clear that a simple Poisson distribution describes the expected number of goals in a football match quite accurately. Compared to a normal bell-curve distribution most people will be familiar with, it is asymmetric and appears skewed towards the left-hand, ‘unders’ side of the mean expected number of goals with a long tail.

If you consider football matches, this makes complete sense as the majority of football matches result in total goals of a small range, typically 0 to 4 goals, depending on the league. Yet, there are the occasional very high scoring games. If you were to plot the historic goals scored in each game for any football league, you will see a similar shape to the above, but with slightly different mean averages. Germany, for example, is a historically high-scoring league, especially compared to France. So, while the distributions will both have similar shapes the German league will present itself further along the x axis, to the right.

This distribution can be used to estimate the probability of different numbers of goals in a game. If we assume that a football match expects 2.5 goals in a game, we can use a Poisson distribution calculator to estimate that the probability of 0 goals in game is 0.08208 (1 in 12) and a game with 5 goals or more will happen every one game in 9 times (p = 0.108).

Identifying the appropriate distribution to use when building a sports betting model is probably the simpler part of this two-part process. Deriving the inputs of the model (in this case the expected goals in a specific game) is a lot more complex and can be solved in an almost infinite number of ways. Everything from simple historical averages through to neural networking has been used to try and solve this problem. The simplest way to identify a reasonably accurate expected goals figure is to look at what the market is doing. Finding both the market’s even-money betting line and the spread bet midpoint will give you a good idea of the number of goals expected by the market for a particular game. This figure can be inserted into the Poisson distribution to get reasonably accurate over/under prices for all available betting lines so the amateur punter can identify possible betting opportunities and smart bets to place, especially with the softer domestic bookmakers.

For example, the expected goals in Wednesday’s Champions League semi-final between Lyon and Bayern Munich is approximately 3.5 as both the over and under line is currently priced at 10/11. Plugging this in to a Poisson distribution suggests the following prices and probabilities for various over/under markets in the event:

For a more advanced approach, the bivariate Poisson distribution should be used, which suggests that there is a relationship between the goals scored by team A and team B. Additionally, try deriving your own total goals inputs for the Poisson model. Once you have your model, come and bet with us on our Bookielink Pro or Bookielink Sports tools.

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