Penalty Shootout Game Theory

HangTime

HangTime

HangTime

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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.
 
I would assume that there is very little to suggest that one sensible method works over another.

As you have pointed out, it doesn't matter how good your 5th penalty taker is if you don't get that far. That being said, there will be people who are mentally weak but good penalty takers who will be fine as the first 3 takers with little pressure as (in theory) they cannot lose the shootout whereas once you get to sudden death you want good penalty takers with the mental strength to not let the pressure affect them.

Its fundamentally a bit of luck in almost every shootout I have seen. In the United/Villareal one their keeper could have saved 3-4 of ours and DDG could have saved a couple of theirs if he wasn't about as useful as a chocolate teapot at penalties. Commentators talk absolute crap during penalty shootouts. I don't believe that keepers can adjust to many things. They look at the player, know which way he likes to go and how hes approaching the ball and guess. A penalty that goes in 5 foot from the post is amazing when the keeper goes the wrong way and awful when he doesn't.
 
I always thought it was the 3rd penalty taker that was more important as you are guaranteed to get to that point and its the point where the shootout can go either way, it will either keep you in for another round if the first 2 miss, or, if the opposition have missed both or either and you have scored both so far, extends your lead.

Do teams go in with mentality that they will need all 5 penalties to win? I'd much rather win the game with my 4th penalty taker.
 
HangTime said:
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.
Click to expand...

This is where things become too dependent on mentality assumptions though, if Ronaldo didn't get to take a penalty it's because they couldn't catch up, so the overall outcome wouldn't change with Ronaldo taking his earlier unless you assume that his scored penalty would then cause one of the other misses to become goals if they follow him rather than precede him.

If the actual shootout was:

Code: 
0 1 1 1 1
0 1 1 0 -
They lose 4-2

Assume Ronaldo went first and scores:

Code: 
0 1 1 1 1
1 0 1 1 0

They still lose, but only 4-3.

There is only a change if you assume that for some reason, one of those other missed penalties would have been scored due to being taken one slot later. (Or Spain missed one that they scored) Would Moutinho have scored if they were already 1 up rather than him being first? That's probably the most debatable change. Would Alves have scored if he was taking the fifth penalty to level it and stay in the game rather than the fourth penalty to stay in the game? The importance of Alves individual penalty is still effectively 'you have to score to stay in the game', so not sure that changes much.

The argument is really about how much being in front or behind actually affects any individual penalty taken and is that effect enough to worry about which order your takers line up in? I'm not convinced it actually wildly changes the pressure on any individual to score.
 
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.
 
HangTime said:
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.
Click to expand...
In your second scenario, Portugal would only get a 5th kick if Spain missed their 5th. If scoring their 5th, the last Portugal penalty would be immaterial again and so not taken.
 
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.
 
HangTime said:
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.
Click to expand...
But we had the 5th Spanish kick in the original example anyway?

If your objective is to see more penalties, then sure, front loading the goals extends the shootout for viewers.

If we're discussing theories about the best way to win, I don't see that makes a difference personally, I don't believe it changes the dynamics that much in reality.
 
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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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