Who are the Best and Worst Premiership Penalty Takers?

With 56 successfully converted penalties to his name, Alan Shearer is arguably the best penalty taker of the Premiership era. Only Frank Lampard on 43 comes close. Matt le Tissier, in third, has less than half Shearer's total (25). Many, however, would insist that le Tissier was the best Premiership penalty taker by virtue of his conversion rate - he missed only one of the 26 that he took for a conversion rate of 96%. That's good, but not as good as Leighton Baines, with a 100% conversion rate. But Baines has only taken 11 penalties. Is it fair to say a record of 11/11 is better than 25/26, or for that matter 56/67?

We can choose to rank penalties taken by either total scored or by conversion percentage and evidently there will be some disagreement. In the case of Baines, a big disagreement. Can we do better? Yes, I think we can - simply by combining the two methods together.

So how to do that? First let's consider the business of penalty taking as equivalent to tossing a coin. As such it's a binomial proposition, i.e. only two possible outcomes: score or miss. Coin tossing is a 50-50 proposition. Penalty taking is not. In fact up to and including the 2014/15 season a total of 1,530 penalties have been scored from 2,004 taken. That's an average conversion rate of about 76%. So on average we can assume that Premiership penalty taking is a 76-24 proposition in favour of scoring.

If we toss a coin we expect to get about 50% heads and 50% tails. The more times we toss it the closer we should expect to be to 50-50. For example, if we saw 7 heads and 3 tails in 10 tosses we'd not think that to unusual. But if we had 70 heads and 30 tails that would be much more of a surprise. This is a consequence of the law of large numbers In fact, the probabilities of these outcomes can be calculated using the binomial distribution. 7 or more heads out of 10 coin tosses, for example, could be expected 17% of the time. 70 or more out of 100 on the other hand has a chance of just 1 in 25 thousand.

Let's apply the binomial theorem to penalty taking, and calculate the probability that a player scores at least the number of penalties he has scored out of the total number be has taken. As for coin tossing, the more penalties he's taken the less likely it is for his conversion rate to deviate significantly from the expected average of 76%. These probabilities then provide an alternative measure of the quality of a player's penalty taken record,, by considering both the number he has scored and his conversion rate. The table below show these for a number of Premiership players. Sadly, I've been unable to find a reliable source of raw data for all penalties taken and scored broken down by player so I've had to use the summary tables for some of the more significant Premiership players as made available by Premierleage.com which include data up to the middle of the 13/14 season.

Key: P = penalties taken, S = successful penalties, C = conversion rate, B = binomial percentage, R_S = ranking by successful penalties, R_C = ranking by conversion, R_B = ranking by binomial probability.

According to my Binomial ranking, Matt le Tissier is the top-ranked Premiership penalty taker. Many won't be very surprised to see that. Yet he achieved that ranking despite not actually be top-ranked on either total penalties scored or conversion rate. It just so happens that both were pretty good, and combined together his binomial probability is small. In other words, if penalty taking was simply a matter of chance (and most of it probably is) we would expect just 1% of players to score 25 (or more) out of 26 penalties.

More surprising is Alan Shearer at 8th according to the binomial ranking. Yes, he scored more penalties than anyone else, but his conversion rate was not nearly as impressive as le Tissier's. Leighton Baines with his perfect record sees the biggest improvement relative to his ranking by total scored, jumping from 23rd to 5th. The two biggest fallers are Steven Gerrard (dropping from 5th to 21st) and Teddy Sheringham (dropping from 7th to 26th).

Remember, however, this player list is not complete, there are many other players who are missing so one shouldn't read too much into the absolute rankings. Nevertheless, this binomial method is a useful way of determining who really is the best (and worst) penalty taker in the Premiership.