Penalty shootout rules

The team kicking first in penalty shootout enjoys a huge advantage, winning roughly 60% of the time. A recent paper (A comparison of penalty shootout designs in soccer) discusses and compares the three rules devised to overcome the unfairness, which are:

1. Alternating (ABBA) Rule: the order of the first two penalties (AB) is the mirror image of the next two (BA), and this sequence is continued even in the possible sudden death stage of penalty shootouts (the sixth round of penalties is started by team B, the seventh by team A, and so on).
2. Catch-Up Rule: the order of the penalties in a given round (including the sudden death) is the mirror image of the previous round except if the first team failed and the second scored in the previous round when the order of the teams remains unchanged.
3. Adjusted Catch-Up Rule: the first five rounds of penalties, started by team A, are kicked according to the Catch-Up Rule, but team B is the first kicker in the sudden death (sixth round) such that the first mover is alternated in this stage.

Let's skip the mathematical computation and jump directly to the conclusion: the Catch up rule does not outperform the Alternating rule while the Adjusted Catch-up rule is fairer than both the Catch up rule and the Alternating rule.

I wrote a python program (https://github.com/sunmingtao/penalty-shootout) to simulate these rules. The assumption is the first kicker has a success rate of 3/4 while the second kicker has a success rate of 2/3. 

The result of the Alternating rule and Catch up rule is very close to that on the paper. However, my program indicates the gap of the result between the Adjusted Catch-up rule and the other two rules is not as large as the paper claims. In fact, the result seems too close to reveal any statistical significance.



In the Euro 2008 quarter final of Italy against Spain, Buffon won the coin toss and yet chose to kick second. We all know the sad outcome for Italy. I wonder if Buffon was too just proud to go first.