to take the Fifth – refuse to testify by invoking the Fifth Amendment, which states that nobody may be forced to testify as a witness against himself or herself.
Earlier there was another post here, I claimed that Rakitic taking the fifth penalty made no sense(ok I used harsher language) because there were many cases where the your fifth guy does not even get to shoot . I provided the following example
if Sevilla had 2 100% pk takers with rest at %0
Betis had only 1 100% with rest at 0%
If Sevilla saved its best penalty takers to the last 2 spots I claimed Betis would win because Sevilla would never have a chance to use its players. It has been pointed out in comments section that this was not true because with 2 more rounds and game at 1-0 match would not end. Actually Sevilla would always win this game.
I thought,ah I picked the wrong example , easy to fix. But I actually came to the conclusion that not only my example was wrong but my whole assumption as well. Mathematically, it does not matter if your fifth pk taker is your best or not as long as he is in the first 5. Actually it does not matter when anyone takes their penalties until the 6th kick. This assumes first 5 is the best 5. Here is another example:
Assume Betis has 3 players with 60% chance and rest 0%
Sevilla has 2 100% players.
Let”s assume Sevilla saves its best 2 players to last. After first 3 kicks these would be the results:
|After first 2|
So in 21.6% of cases Sevilla won’t be able to use its 2 best players and Betis wins. They do not look particularly intelligent. In 43.2% cases shootout ends in a draw. And in 35.2% cases Sevilla wins.
Now let’s assume the reverse. Sevilla uses its best players first and Betis last. After 2 kicks it is 2-0, after 5 kicks:
.6^3=21.6% Betis wins 2-3, (.6^2*.4)*3=43.2% ends in draw and so forth. Exactly same probabilities.
So what’s happening? The fact that we end the game early does not change the expected results, if Betis was up 3-0(21.6%) and if we took the remaining penalties game would have ended 3-2. That is no different from Sevilla being ahead 2-0 after first 2 kicks and Betis scoring the next 3. (21.6%) We just stop the shootout that would have ended 3-2 in the interest of time.(If I am wrong again I am converting this into a History blog!)
Now that I have proven my intuition wrong(don’t worry about me, I am used to being wrong) should Rakitic be taking the last penalty?
I still think no. Not because of math but psychology. In Soccernomics (as @SimonGleave pointed out), it is claimed that first penalty kicking team wins 60% of the games. If we assume that is correct it suggests it is harder to score when under pressure not to lose rather than shooting to go ahead. @altmandaniel suggested that we perhaps should look at not the first kicking team but first scoring team and I agree to see the advantage of going ahead early.(although 60% seems too high).
To wrap up:
1-My old post was wrong
2-Mathematically the order in which your guys take pk kicks make no difference until 6th kick.
3- Behaviorally It still seems a better idea to have your best guys kick first to put pressure on the opposing team.
And Twitter is still banned in Turkey!