Intuitively, you would probably prefer Frank Lampard to be stepping up to take a kick that is vital to your side's chances, rather than Jonathon Walters. But despite their apparently polar opposite conversion rates it is still possible that Lampard is a average taker who has been lucky and Walters is equally average, but has in addition been blessed with bad luck and a lack of colleagues willing to take on the kicking duties.
The intricacies of the problem of teasing random chance from skill in infrequently repeated tasked can possibly be appreciated by using a simulation. If we allow ourselves to know the true penalty taking abilities of a group of players with absolute certainty, we can then via a spreadsheet and random number generator ask them to take as many penalties as we wish to see how the true "Franks" perform against the true "Jonathons".
These trials will inevitably still be somewhat artificial, but we will know in advance which players are really the best and by the range of their actual outcomes we may be able to see how easy or difficult it is to spot that talent differential in typically generated conversion statistics.
I've taken 5 outstanding penalty takers, whom I've given a true conversion rate of 89% and 15 lesser takers each with a rate of 75.6% to maintain the typical EPL penalty conversion rate of 79%. A rand() function complicit with their true conversion rate is then used to simulate a series of penalty kicks and the results are analyzed to see, firstly, if there is evidence for the existence of a talent differential in the group as a whole and secondly, can we spot if the five best takers are noticeably better than the rest.
Penalties, unlike other shooting opportunities are rigorous in their repeatability. The distance is always 12 yards, no defenders can intervene until the shot is taken and the keeper also has to observe the same restrictions at every kick (and sometimes they even comply with those restrictions). By comparison to open play shots, where game state, and hence defensive pressure, shot position, keeper readiness and mode of execution to name but a few, can vary greatly. We almost have a laboratory experiment.
The first trial consists of each individual player taking 6 penalties. By looking at the spread of the conversion rates of the group as a whole in comparison to that expected from a group of twenty players, each of whom was a dead eye, average penalty converter, we can give an opinion as to if there is a skill differential within the group.
In around half of the trials there was good evidence that skill exists, the spread of successful conversion rates was greater than that expected from a group of kickers whom shared the same conversion rate. Similarly, the average rate for the best five takers once an appropriate amount of mean regression had been applied was above that of the inferior takers in most cases. So the evidence for a skill differential mostly originating from the better kickers outscoring their inferior colleagues appears apparent.
Shootout Between Five 89% and Fifteen 75.6% Penalty Takers.
|Evidence of Skill Differential.||Did the Best 5 Have A Superior Conversion Rate|
|6||~50% of Trials.||Almost Always.|
|12||~80% of Trials.||Almost Always.|
|50||~90+% of Trials.||Always.|
The trend continues as we increase the number of shots taken by each player. At 12 shots by each of the 20 players, we can find evidence for players having differing conversion talent in around 80% of the trials. However, we can still in some cases, erroneously conclude that the two different groups have near identical average conversion rates because the evidence for a skill differential arises from unusual random patterns appearing within those two distinct groups.
For example, in one particular trial the top two penalty converters in that trial both came from the lesser true talent group. They were followed by two from the best group, but the elite group, over a limited test involving 12 individual kicks also saw one of their number tie for 19th spot.
It is only when we get to 50 kicks, a whole career's worth for the most frequent of takers, that evidence of a talent differential occurs in over 90% of the trials and the elite five, as a group have sufficient opportunity to always beat the rest.
In reality, a true talent differential of 89% compared to 75.6% is likely to be an unrealistically large gap and even at these levels a single less talented kicker can still out convert some of his more talented colleagues on occasion, (even if the group always wins through, overall).
If we shrink the true conversion differential between the best five and the rest down to just one percentage point, even 50 trials only identifies possible evidence for the existence of that real gap between groups around 20% of the time and the frequency with which a lesser kicker can top the twenty also greatly increases.
What penalties gain in uniformity of execution they give up due to rarity, few teams or players get to take more than a handful per season. Penalty taking ability has almost certainly a tighter range than the one used in this contrived simulation, yet it was only possible to speculate that such a talent existed around half the time with these likely inflated differences in trials with typical seasonal numbers.
Prior knowledge of the true conversion rates that had been baked into the simulation, along with which kickers had been so blessed, was also needed to simply separate the two distinct groups. Moving to an individual player level at such low sample sizes in reality and with any degree of certainty would likely prove a near impossible task.
If we want to look at possible talent displayed in conversion rates, we need to look at much more frequent, open play goal attempts, for teams and then perhaps onto individual players. But we then have to look also at the factors that make such attempts a much less structured experiment than a set piece penalty kick.
Next post, maybe.