Penalties: when are they awarded and when are they scored?

I asked the nice people at Infostrada Sports Group for a whole slew of data with regards to penalties and they were kind enough to provide me with it. They can be found online and on twitter.

Last time I looked at the distribution of penalties by season and found that, whilst there has been an increase in the number of penalties awarded, there hasn’t been a significant change in the percentage of penalties that result in a goal (link). But what if we look through the timeline of a typical match. When would we be most likely to see a penalty awarded? And is the conversion rate of penalties uniform throughout a match or should we expect a different result from a penalty taken at the start of the match as opposed to one at the end?

This first plot shows the distribution of penalties during a match:

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One caveat with this plot. I’ve grouped all of the penalties given in the 45th and 46th minutes of the first half, hence the spike at 45 minutes. I haven’t done this for second half injury time. If anyone wants the reasoning feel free to ask.

So what do we see? Well it’s a very noisy plot but that is because the sample size is relatively small. The points making up the red line represent an average of only 10 penalties and so are subject to a lot of random variation. The ten game moving average represents about 100 penalties and so gives a bit of a clearer picture. We can see that few penalties are given in the first few minutes of a match. In fact there has not been a single penalty given in the first minute of a match during this 4,180 game sample. There have, however, been four penalties during the first minute of the second half during this span. There’s a pretty significant rise during the first half and this continues into the second, culminating in a peak at around 75 minutes at which point the plot levels off.

So how about conversion rates? Do players begin to feel presure toward the end of a match and miss more penalties as a result?

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There are a few rises and dips in the ten minutes moving average but all within the expected random noise so, in short, there’s no difference in conversion rate. That dip at the end? Well that point represents just 26 penalties and as such is subject to a huge amount of variation due to luck.

In summary a penalty awarded in the second minute of the match is just as likely to be scored as one awarded in the 92nd minute. A penalty costs the offending team just as many goals (0.77) regardless of when it is awarded.

Next time I’m going to take a look at referees and see which ones are more likely to award a penalty. I’ll also see whether there are any with a tendency to ‘even’ the score by awarding one to the opposite team later in the match.

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