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End of Season Review: Penalty Misses

14 May 2012

Luis Suarez misses an early-season penalty for Liverpool

One of the more noticeable early-season trends in the Premier League this year was the startling amount of missed penalties. By early October, only 11 of 22 kicks had been scored, a conversion rate so low that it led the Mail to ask why half of Premier League penalties this season have been missed.

The article suggests one or two theories – namely changes in laws for goalkeepers and more information on kickers – but provides no concrete answers. After all, twenty-two kicks is a very small sample size.

As the season’s progressed, discussion about the league’s penalty conversion rate has waned. The reason is obvious: it’s no different to what we’d expect.

The league’s penalty conversion rate has exhibited regression to the mean, “the phenomenon that after extreme events, less extreme ones are more likely [than they seem].”1 After 99 kicks in the 2011/12 season, 72 were scored at a rate of 73%, statistically no different to the league’s historical average of about 77%. The season’s kick-by-kick trend is illustrated in the chart below.

It’s a classic case of drawing conclusions too early in the season. The large random element in penalty taking means that over the course of the season we’d expect the average number of converted penalties to be roughly equal to the historical average. The season isn’t quite long enough to take us exactly to the average, but the trend is instructive.

Just as a conversion rate of 50% is unremarkable in the short run, 15 goals from 16 kicks (a 94% success rate) between 11 March and 5 May is nothing to be alarmed by either.

Regression to the mean is apparent in teams’ form, players’ goal streaks and refereeing decisions; anything that is affected by random factors. Extreme events aren’t always what they seem.

1 From ‘Alex’s Adventures in Numberland’ by Alex Bellos, which helped form this, and hopefully future posts. 

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6 Comments leave one →
  1. Mark permalink
    14 May 2012 5:59 pm

    Very good as always apart from that horror quote from Alex Bellos (what do you expect from a mathematician knowing nothing about probabilities)

    “the phenomenon that after extreme events, less extreme ones are more likely THAN THEY SEEM.”

    Extreme events are just as likely as always, it’s just that they are perceived to be more likely because of the past experience of extreme events.

  2. Raj permalink
    14 May 2012 6:26 pm

    Haha I was thinking the exact same! I’d say there’s a good case for independence between penalties, so regression to the mean is harder to put into a real life context. Remember mathematicians live in their own little world. And it isn’t this one.

    Another interesting point is the rise in the number of penalties given. In 2002-05 seasons the average was about 72 penalties per season, in the last 3, it has been 102.

  3. 21 May 2012 7:26 pm

    @Raj – Good point about the rise in number of penalty awards. Is there a correlation between increasing awards and decreasing conversions i.e. a larger sample size reduces the average conversion? Can’t imagine why there should be one, but curious nevertheless.

  4. Kurt Desender permalink
    26 May 2012 11:40 am

    Nice post!The changes in laws for goalkeepers would seem unreasonable to explain a lower success rate. And the idea that now goalkeepers havemore information on kickers is also besides the point; because the kicker also knows that the GK has more information on my kicks; so Dirk Kuyt should realise always kicking left, cannot be an optimal strategy.

    • 26 May 2012 12:34 pm

      You’re right – keepers can prepare but it’s a forever evolving cycle. Love your stuff about Palacios-Heurta’s research by the way, very interesting.

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