Penalty Shootout Game Theory

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I was reading an article about Ronaldo earlier and it reminded me that when Portugal lost to Spain on pens, Ronaldo didn't even take one because he was waiting to be the 5th taker, and it didn't get that far.

My view with pens is pretty simple, just take them in order of penalty taking ability, starting with the best. Maybe you might tweak this a bit if there are players who really don't fancy it for whatever reason. To me it's illogical not to have your normal penalty taker take the first penalty, but there seems to be some school of thought around people wanting them to take the 'last' (which is a fallacy anyway as it isn't known at the start of the shootout which penalty will be the last) - I guess because that's potentially when the pressure is greatest - miss and you are out, score and you win etc. But that in itself doesn't stand up to game theory analysis, as each penalty taken is as valuable as any other, a penalty scored or missed counts the same whenever it is taken.

I think this is nonsense and you want to get ahead in the shootout as early as possible, or at least stay level. The Spain-Portugal game is a classic example of where having worse penalty takers earlier in the shootout can backfire because the competition ends before your best takers have even stepped up. Had the shootout continued longer, they might have found that e.g. their 6th or 7th takers were better than the Spanish ones. But they never got that opportunity because they didn't front-load their best takers.

Even if you subscribe to the theory that you want an experienced taker at the 'business end' of the shootout, you could make a counter argument that if you got ahead in the shootout earlier, your team would be under less pressure anyway. So you are increasing the likelihood of having to take a pressure penalty by backloading the best takers, even if they may be better equipped to deal with that pressure.
 
Yeah I know what you mean, if the previous player that missed still misses then it doesn't matter for the final result.

I know Spain missed the first pen in this specific match, but if we are talking theory, what if the shootout went like this:
Code:
1 1 1 1
0 1 1 0
They lose 4-2, all over after 4 kicks each.

Now assume Ronaldo went first and scores:
Code:
1 1 1 1
1 0 1 1
Now you are forcing it to a 5th kick. We suspect that Portugal will miss their 5th kick if it's the same player that missed the 4th one in the above scenario, but I'd still rather it went to 5 kicks.
 
Correct, but that's a completely unknown scenario, as we haven't yet seen the 5th Spanish player take a penalty yet, so unlike the 5th Portuguese (which I accept we would expect to miss if this is a 'fair' scenario) I don't think we can infer the likely outcome of the 5th Spanish kick.

The point I was making is we are forcing the 5th Spanish kick, he's not just sitting back with a Sangria like he is if Ronaldo went last.
 
Yeah but when you are picking your order pre-shootout you don't know who is going to score when, so you have to cater for all scenarios, and in my example we don't see the 5th kick from Spain. So if that was a real game we'd have no idea if the 5th pen was scored or not.

I do agree it's largely irrelevant though if you assume that the outcome of a penalty isn't impacted by the order it is taken in, i.e. moving your misses to the end rather than the beginning shouldn't impact the overall outcome.
 
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