Match Prediction with TSR
There has been a lot of work done in recent years with some very exotic and complex shot and goals analysis giving some very interesting performance indicators. Expected goals and Goal Impact are two of the most popular methods.
However, there is definitely still a place for parameters like Total Shots Ratio (TSR) which is very repeatable, gives a good indication of performance (correlates well with points and league table position) and maybe more importantly it is easy to calculate and to understand what it means.
TSR is best used as a long term parameter with large samples rather than something to analyse individual games. However, what I wanted to do here is to give an example of a method that can be used to predict match outcomes with TSR for both Win/Loss and also exact scores.
Average Number of Goals
The first step is to investigate the average number of goals that are scored by teams based upon their TSR. In order to take into account the strength of the opponent I decided to use the difference in TSR between the home team and the away team.
To do this I calculated the TSR for the home team and away team over the past years games (typically 38 games) and then stored the difference (∆TSR) along with the number of home goals and away goals. Each game was then placed into a bucket representing a range of ∆TSR values. The size of each bucket was adjusted in an attempt to get at least 20 games in each bucket.
For each bucket the average number of Home Goals and Away Goals was calculated and then this can be plotted against ∆TSR as in the figure below.
The figure looks as we would expect with the number of home goals increases with an increasing difference between the teams Total Shots Ratio. We can also see the home field advantage effect here as the two plots intersect at approximately -10% ∆TSR rather than 0%.
Now we can estimate the average number of goals that might be scored in a match between any two teams based upon their current TSR values (the TSR of the teams must be calculated from games within the same league).
Distribution of Scorelines
The average number of goals gives an indication of a likely outcome, however to more precisely give an estimate of various scorelines it in necessary to estimate the likely deviation of goals scored around the average.
The number of goals scored by a team in a football match tends to follow a Poisson distribution. The Poisson distribution can give the probability of an exact integer outcome (x) with the only input being the mean.
The following two figures give an example of the actual distribution of goals scored for a particular ∆TSR along with the calculated Poisson distribution based upon the average number of goals.
Prediction of Scorelines and Match Result
We have already developed a way of estimating the mean number of goals scored and so we can use the Poisson distribution method to estimate the probability of any scoreline.
As an example lets suppose there is a match between Team A with a TSR of 70.4% and Team B with a TSR of 58.8%, giving a ∆TSR between them of 11.6%. This gives average goals of 1.86 for Team A and 0.92 for Team B.
The Poisson distribution of goals scored for each tame based upon these average goals are shown in the figure below:
These two distributions can then be multiplied and summed in order to gives the probability for each goal difference outcome for the match. The negative goal differences can be summed to give a Team B win probability, the positive goal differences summed to give a Team A win and the remainder is the probability of a draw.
These figures were all based on an actual match for which the bookies were giving odds of 62% for Team A, 25% for a draw and 18% for Team B.
There is no doubt that this method has flaws, but hopefully this has shown that TSR has the capability of not only giving probabilities of season long performances but it can also give an indication of scoreline probabilities for individual games.
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