The Effect of Home Team TSR (within a match) on the Match Result
This article first appeared as a guest post on the JamesWGrayson blog
It has been shown extensively that a team’s share of total shots, total shot ratio (TSR), is one of the most repeatable parameters in football giving only around 14% regression towards the mean from season to season.
What this means is that knowing a team’s previous TSR gives a good indication of their TSR in the near future. However, does a high TSR relate to a successful match outcome or is it simply just a repeatable statistic?
To investigate this I have taken data from the past 14 years giving over 5000 matches (or samples) to analyse. First of all I separated the data based on whether the match outcome was a Home Win, Away Win or Draw. We then calculated the TSR (from the home team’s perspective) for every game and created a histogram of TSR distribution using equi-width buckets, each with a TSR range of 0.05.
The result, shown in the figure above, shows us the % of time that a match with a certain TSR results in a Home Win, an Away Win or a Draw.
On initial inspection, the linear correlation between an increase in the home team’s TSR and the number of home wins looks promising (Home win Trendline Regression R² = 0.31). However the extremities of the TSR (towards 0 and 1) are clearly erroneous, likely due to a lack of data.
In fact, our data only shows four matches in which the Home team have registered a TSR of less than 0.1: • 25/11/2000 : Derby 0 – 3 Man United • 18/11/2006 : Middlesbrough 0 – 0 Liverpool • 23/02/2008 : Birmingham 2 – 2 Arsenal – (The game with that tackle on Eduardo) • 20/11/2010 : Birmingham 1 – 0 Chelsea
The standard error of a percentage can be estimated based upon the sample size and we have calculated this and shown it in the graph below as error bars. The majority of matches have a TSR of between 0.5 and 0.7 and so the sample size here is statistically significant.
Removing any data points with an estimated error of greater than 10% gives a much better looking graph. (Homewin Trendline Regression R² = 0.97)
There are a couple of interesting points to note from this graph. The first being that in order for the Away Team to have an equal chance of winning the match they need to have a greater share of the total shots. This could be a statistical anomaly, but I postulate that it is the mentality of the away team which causes them to take their shots from less prime positions than the home team might create for themselves.
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