… or is it a science? Robin van Persie’s penalty miss against West Bromwich Albion on 2 May 2015 was certainly welcome news to my ears. It eased the relegation pressures on West Brom and allowed us to advance to 40 points for the season. Relegation fears are only “mathematical” now. However, the miss also resulted in van Persie being relieved of penalty taking duties, by Manchester United manager Louis van Gaal, until further notice.

He is now at the end of the road. It is always [like that]. Wayne [Rooney] has missed also so when you miss you are at the bottom again.

The Daily Mail report linked above goes on to say that van Persie had converted his previous 6 penalties.

Van Gaal was, of course, referring to Rooney’s shot over the crossbar against West Ham in February 2013, when Rooney had himself invited then manager Sir Alex Ferguson to retire him as designated penalty taker. Rooney’s record had apparently been 9 misses from 27 penalties. I have all this from this Daily Telegraph report.

I wonder if statistics can offer any insight into soccer management?

The benchmark

It was very difficult to find, very quickly, any exhaustive statistics on penalty conversion rates on the web. However, I would like to start by establishing what constituted “good” performance for a penalty taker. As a starting point I have looked at Table 2 on this Premier League website. The data is from February 2014 and shows, at that date, data on the players with the best conversion rates in the League’s history. Players who took fewer than 10 penalties were excluded. It shows that of the ten top converting players, who must rank as the very good if not the ten best, in the aggregate they converted 155 of 166 penalties. That is a conversion rate of 93.4%. At first sight that suggests a useful baseline against which to assess any individual penalty taker.

Several questions come to mind. The aggregate statistics do not tell us how individual players have developed over time, whether improving or losing their nerve. That said, it is difficult to perform that sort of analysis on these comparatively low volumes of data when collected in this way. There is however data (Table 4) on the overall conversion rate in the Premier League since its inception.

That looks to me like a fairly stable system. That would be expected as players come and go and this is the aggregate of many effects. Perhaps there is latterly reduced season-to-season variation, which would be odd, but I am not really interested in that and have not pursued it. I am aware that during this period there has been a rule change allowing goalkeepers to move before the kick his taken but I have just spent 30 minutes on the web and failed to establish the date when that happened. The total aggregate statistics up to 2014 are 1,438 penalties converted out of 1,888. That is a conversion rate of 76.2%.

I did wonder if there was any evidence that some of the top ten players were better than others or whether the data was consistent with a common elite conversion rate of 93.4%. In that case the table positions would reflect nothing more than sampling variation. Somewhat reluctantly I calculated the chi-squared statistic for the table of successes and failures (I know! But what else to do?). The statistic came out as 2.02 which, with 9 degrees of freedom, has a p-value (I know!) of 0.8%. That is very suggestive of a genuine ranking among the elite penalty takers.

It inevitably follows that the elite are doing better than the overall success rate of 76.2%. Considering all that together I am happy to proceed with 93.4% as the sort of benchmark for a penalty taker that a team like Manchester United would aspire to.

Van Persie

This website, dated 6 Sept 2012, told me that van Persie had converted 18 penalties with a 77% success rate. That does not quite fit either 18/23 or 18/24 but let us take it at face value. If that is accurate then that is, more or less, the data on which Ferguson gave van Persie the job in February 2013. It is a surprising appointment given the Premier League average of 76.2% and the elite benchmark but perhaps it was the best that could be mustered from the squad.

Rooney’s 9 misses out of 27 yields a success rate of 67%. Not so much lower than van Persie’s historical performance but, in all the circumstances, it was not good enough.

The dismissal

What is fascinating is that, no matter what van Persie’s historical record on which he was appointed penalty taker, before his 2 May miss he had scored 6 out of 6. The miss made it 6 out of 7, 85.7%. That was his recent record of performance, even if selected to some extent to show him in a good light.

Selection of that run is a danger. It is often “convenient” to select a subset of data that favours a cherished hypothesis. Though there might be that selectivity, where was the real signal that van Persie had deteriorated or that the club would perform better were he replaced?

The process

Of course, a manager has more information than the straightforward success/ fail ratio. A coach may have observed goalkeepers increasingly guessing a penalty taker’s shot direction. There may have been many near-saves, a hesitancy on the part of the player, trepidation in training. Those are all factors that a manager must take into account. That may lead to the rotation of even the most impressive performer. Perhaps.

But that is not the process that van Gaal advocates. Keep scoring until you miss then go to the bottom of the list. The bottom! Even scorers in the elite-10 miss sometimes. Is it rational to then replace them with an alternative that will most likely be more average (i.e. worse)? And then make them wait until everyone else has missed.

With an average success rate of 76.2% it is more likely than not that van Persie’s replacement will score their first penalty. Van Gaal will be vindicated. That is the phenomenon called regression to the mean. An extreme event (a miss) is most likely followed by something more average (a goal). Economist Daniel Kahneman explores this at length in his book Thinking, Fast and Slow.

It is an odd strategy to adopt. Keep the able until they fail. Then replace them with somebody less able. But different.