**I asked the nice people at Infostrada Sports Group for a whole slew of data with regards to penalties taken in the Premiership and they were kind enough to provide me with it. They can be found ****online**** and on ****twitter***.*

When I asked for the data this was the only post I planned to do but it seemed a waste not to be a bit more thorough, hence the wait. First is just a little quirk I noticed when working through the data; you’re more likely to take a second penalty if your first one is missed/saved than if it is scored:

I don’t have a sensible explanation for that. The table also shows that the outcome of a players first penalty has no impact on future penalties (conversion rate is the same whether the first penalty was scored or missed).

There’s another interesting piece to pull from the second half of that table. The conversion rate of ‘subsequent penalties’ is 84%, which is well above league average. Therefore ‘first penalties’ must be scored at a level far below league average. So how large is the discrepancy?

In six posts about penalties I think this is the second time I’ve found something statistically significant. Players are much more likely to miss their first penalty than any subsequent ones they take. Nerves would be my best guess. It’s funny – whenever a penalty is saved the main reason I’ve heard commentators give is that the ‘keeper has studied where the striker had placed his previous penalties. I think this kind of makes a mockery of that assertion.

Anyway back on topic; last time I looked at teams and found that, with the possible exception of Chelsea, no team had a measurable level of skill when it came to taking or saving penalties (link). Not even the best teams. So does this translate to players? Here’s the funnel plot for penalty takers:

So to re-iterate, the bold line is equivalent to the league average penalty conversion rate and the two dotted line represent two standard errors above/below the mean. The dotted lines become closer as the sample size in creases because there is a larger sample over which the effect of random variance decreases. I’ve only added labels for players with >10 penalties. If there’s someone you want to know the specific stats on ask in the comments and I’ll get back to you.

In summary this plot is telling us that we can’t be sure there is any player is better at taking a penalty than any other. Hurray.

Say we briefly assume that the numbers here actually reflect each players true talent (they don’t) and we place hypothetical Frank Lampard (89.7% conversion) in a penalty shootout against hypothetical Alan Shearer (77.8% – basically league average). The shootout has the usual rules, five rounds followed by sudden death – how often would you expect hypothetical Lampard to win the shootout? I’ll let you take a guess and put the answer at the end of the post.

But enough with strikers. Do any keepers possess an ability to saving penalties?

Same story. In fact the grouping here is almost unnaturally tight. There’s no skill here, a ‘keeper could let in the first 13 penalties they face and we still wouldn’t be certain that they were below average.

**I’ll do a summary of this series soon but in short: With a few exceptions (home vs away, first penalty vs subsequent penalties) a penalty is a penalty is a penalty. It doesn’t matter which team it is awarded to, who takes it or who the opposition ‘keeper is, at the end of the day our best guess is that it will be scored 77% of the time.**

I think that’s it for penalties, as far as I can tell I’ve exhausted the numbers I’ve got, it’s probably time to move on anyway. That being said if anyone has any requests or ideas for anything else I could do with these numbers then let me know

**Even though he misses less than half as often as hypothetical Shearer, hypothetical Lampard would still only win 75% of the shootouts. In order to win the shootout 90% of shootouts hypothetical Lampard would have to score 96% of the penalties he takes.*

You can’t conclude that no players are better (or worse) penalty takers, only that none of the penalty takers are much better (or worse) than the other penalty takers. Presumably, the really bad penalty takers don’t get to take that many penalties…

How would you determine who is a really bad penalty taker?

That’s not really the point, the point is that your statistics don’t cover all football players. Since it is very likely that your sample mainly includes the better penalty takers among all football players, it would be more appropriate to restrict your conclusions to the penalty takers, not all football players. It’s really just a minor point, otherwise I really like your analysis.

It’s a minor point but a good one nonetheless. I would rationalise the generalisation as follows. Even those penalty takers who are assumed to be good, i.e. those who take a lot of penalties fare no better on average than the rest of the population. Whilst there may be bad penalty takers we just don’t have the proof of it here. Now it may well be possible that managers are identifying bad penalty takers (if they exist) in training or it may be that they’re just giving the responsibility to the front-line striker or, alternatively, the captain. That’s open for debate but given the group of names to the right of this plot I’d be willing to heavily bet on the latter.

This read a lot more nicely the first three times I wrote it. Damn wordpress

Maybe someone has said this already but I will say it here now:

Matt Le Tissier scored 47 out of 48 penalties in his career, that quite literally would be off the chart!

Very nice piece! A little underwhelming that there is little significance, even for Lampard who has maintained a high conversion rate over such a high number of penalties. What did the data look like? Does it allow you to investigate other relations, such as conversion rate for right-footed takers vs left-footed, left corner vs right corner, shot high vs low etc?

Thanks! Yer to be honest I expected the spread to be small going in so in a way it’s nice to se my gut instinct being proved right. Several people have asked me for the right/left foot breakdown but you’re the first to ask for the rest. Unfortunately the data is really the high level stuff, which is why I think I’ve probably exhausted it. If you have any other ideas feel free to suggest them though

Nice piece. From your funnel plots I think you are using a normal distribution or something of that ilk. That allows for conversion rates 1 and I don’t think it is the most efficient method.

I had a look into this and I can say:

1 – The penalties would be better modelled by beta distributions (parameters are scores and misses)

2 – I’m not sure there is a straightforward way to compare the different beta distributions.

3 – Whilst not completely correct we could think this: If Frank Lampard is 36-4 his beta dist is mean=0.9, sd=0.0468. If these numbers are accurate (ie no sampling error) then the probability his conversion rate on the next pen is <average (0.78(?)) is then only 1.7% (from the cdf), which looks pretty convincing to me.

This might help illustrate:

http://artint.info/demos/bayeslearn/beta.html

I'd be willing to give you a hand if you want to take this further.

Hi Martin

Yer I’m using standard error (which, as I understand it, would predict the probability of Lampard’s next penalty being scored <average about 2.2% of the time so we're not far apart here).

Thanks for the offer of help – I may come back and take you up on that. As soon as I see Bayesian I know I'm out of my depth, beta distributions aren't much easier.

I’ve only just been looking at them in the past month or so – wasn’t taught them at school. I think the most straightforward place to start would be to plot 90% confidence intervals around each penalty taker (using Beta.inv in excel).

Agreed It’s not going to make a huge diff to your results – I just still suspect Lamps may be significantly better than average!

Hi,

Nice. So was the Southampton penalty taker James Beattie? Means he missed a couple of the penalties after leaving them. 🙂

No other comments really … just one (probably slightly dumb) question …

Why do you take 2 standard deviations? Don’t really know that much about statistics etc., but why not 1 … that would mean that some players/goalies don’t fall into that “funnel”.

Oh … also, who’s the goalie that saves 60% of the penalties he faces and is above the dotted line? A young kid? If so, be interesting to see if he can keep it up and will keep an eye on him over the coming seasons … always hope that there’s one “blip” that’s the exception to the rule. 🙂 From your previous data he’ll probably face around 4 penalties (if still in the PL), which will push him over the 10 total mark … inching towards Almunia in other words. 🙂

Cheers again for the number crunching!

Hi Bart

Yep Beattie’s apparent skill didn’t translate when he moved teams.

Using two standard errors (if not three) is common practice because we can be much more certain that if a number falls outside the line then it is due to something other than luck. In this case if a player had been above/below the line then we can be ~95% sure it’s skill rather than luck, whereas one standard error would only give us ~65% certainty. The point isn’t to get more players outside the line, but get to a point where we are confident saying that they have a skill if they fall beyond the bound area.

The ‘keeper is Peter Schmeichel, I think his penalty saving days are over unfortunately!

Thanks … yeah I wasn’t sure why you took 2 and not 1 (or 3) … good to know then about the 95% assurance of skill/luck … will see how I can apply this to some of the data that I have, I’ve been putting 1stdev in little graphs I’m making and now I know that it doesn’t really give decent certainty. Cheers. 🙂

Ah ol’ Peter Schmeichel eh … if I had the energy I might backtrack through his PL career to see if he can keep up that excellent score. 🙂

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