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Manchester City's sorry run of missed penalties is a once-in-a-century event

Football stats and philosophy from Kevin Pullein

Sergio Aguero's penalty for Manchester City against Leicester City on Saturday was saved
1 of 1

Manchester City scored a penalty on Wednesday in their Champions League round-of-16 first-leg win at Real Madrid. They missed their last four Premier League spot-kicks. What was the chance of missing so many? Let’s see if we can work it out, and then some other things too.

When I say a penalty was missed I mean it was not scored, so I count shots that were saved as well as shots that did not hit the target. City’s last four Premier League penalties were saved.

In the 16 Premier League seasons from 2003-04 to 2018-19 there were 334 missed penalties out of a total of 1,486. We could say the probability of an ordinary team missing a penalty would have been 334 ÷ 1,486 = 0.22. The probability of missing four penalties in a row would have been 0.22 x 0.22 x 0.22 x 0.22 = 0.0023. It was roughly a one in 400 chance.

City are not an ordinary team, though. They are much better. They should score more frequently from 12 yards. They should have better than average penalty-takers, who usually will not be kicking against better than average keepers.

Good teams do convert more penalties than bad teams, but not many more. In the last 16 Premier League seasons 22 per cent of all penalties were missed, which means 78 per cent were scored. Teams who finished in the top four scored 80 per cent of their penalties, teams who finished in the bottom four scored 76 per cent of their penalties.

City are good even by the normal standards of the top four. So let’s suppose that over time they should score 81 per cent of their penalties and miss 19 per cent. From any randomly chosen penalty there would be a 0.81 probability of scoring and a 0.19 probability of missing. This seems reasonable. And it implies that the probability of missing four penalties in a row would be 0.19 x 0.19 x 0.19 x 0.19 = 0.0013. It would be roughly a one in 750 chance.

City might average seven Premier League penalties a season, so a team like them should miss four in a row approximately once every 100 seasons. It ought to be a once a century event.

You can bet on all sorts of things related to penalties. Will there be any in a match, will one be scored, will one be missed? Will this team get any penalties, will they score, will they miss?

The figures that follow also come from the last 16 Premier League seasons.

First of all, will there be a penalty? In 21 per cent of games there was at least one penalty. In 17 per cent of games a penalty was scored and in five per cent of games a penalty was missed.

You will notice that 17 plus five adds up to 22, not 21. This is because in some games more than one penalty was taken and at least one was scored and at least one was missed.

In a randomly chosen match fair odds about a penalty being taken would have been about 15-4, fair odds about a penalty being scored would have been about 5-1 and fair odds about a penalty being missed would have been about 19-1.

What might surprise you is that the chance of a penalty being taken, scored or missed did not vary much with the type of match.

I divided games into groups according to the difference in final league positions between the teams. In that way I was able to get an impression of how things changed with the character of a fixture.

What was clear was that no matter how great the difference in ability between two teams the chance of a penalty being taken was never far from 21 per cent. In some sorts of matches it was higher and in others lower, but there was no rhyme or reason to these variations, which were mostly small anyway.

Likewise for the 17 per cent chance of a penalty being scored and the five per cent chance of a penalty being missed.

Perhaps this should not be surprising. The chance of a penalty being taken must depend heavily on how long attackers spend with the ball in the opposition penalty area. In some matches one team will spend more time than the other. In certain matches one team will spend a lot more time than the other. But a rise for one might be more or less offset by a fall for the other. Added together, the total time attackers spend with the ball in their opposition’s box might be about the same.

For a randomly chosen team in a randomly chosen match there was an 11 per cent chance of taking at least one penalty, a nine per cent chance of scoring a penalty and a three per cent chance of missing a penalty.

You will notice two things. First, those percentages for a team are slightly more than half the percentages I gave earlier for a match. This is because in some matches both teams took a penalty, scored a penalty or missed a penalty. The second thing you will notice is that nine plus three adds up to 12, not 11. A similar explanation: in some matches a team took more than one penalty, scoring at least once and missing at least once.

Fair odds for a blindly chosen team would have been about 8-1 to take a penalty, about 9-1 to score a penalty and about 33-1 to miss a penalty.

The chance of a team taking, scoring or missing a penalty did vary from match to match. The stronger they were by comparison with their opponents the more likely they were to win penalties and the less likely they were to concede penalties.

Some examples, to give you a sense of by how much. In matches featuring a home team that finished between six and ten places below the away team the chance of the home team taking a penalty was 11 per cent and the chance of the away team taking a penalty was also 11 per cent.

As home teams became progressively stronger in relation to away teams the chance of the home team taking penalties went up, and the chance of the away team taking penalties went down. And vice versa. In games featuring home teams who finished at least 16 places above the away team, the chance of the home team taking a penalty had risen to 20 per cent and the chance of the away team taking a penalty had fallen to two per cent.


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In 21 per cent of games there was at least one penalty. In 17 per cent of games a penalty was scored and in five per cent a penalty was missed
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