Take two teams, A and B. Say that a coin selects A to kick first and B second in the first two rounds. What should the order in the next two rounds be? Well, if the order A, B offers any kind of advantage to either team, then by reversing the order in the next two rounds we would tend to compensate for that advantage. Doing so means that the resulting sequence in the first four rounds should be A,B - B,A, instead of the usual alternating order, A,B - A,B. And, of course, this reversing is innocuous if no advantage existed in the first place. There is no downside to reversing the order in the second pair of kicks, only upside.
What next? Ideally, in the next four penalties we would reverse the order of the first four again in case an advantage for either team remains. Unfortunately, reversing the order in the first two, and then in the next four, and then next eight, and so on, would result in a complicated sequence known as the Prouhet-Thue-Morse sequence. Alternatively, we could simply repeat A,B,B,A for the subsequent rounds and keep repeating A,B,B,A every four kicks, until a team wins (however winning is determined). This would result in the much simpler sequence: A,B,B,A–A,B,B,A–A,B,B,A–A,B,B,A …
This is exactly the serving order followed in tie-breaks in tennis.
I contacted members of the International Football Association Board (IFAB), which sets the universal Laws of the Game, soon after these pieces of research were published. Influenced by these findings and ideas, FIFA decided to start implementing ABBA shootouts in various youth European and world championships in 2017. The English FA followed suit in the Community Shield in 2017 and English Football League Cup and EFL Trophy competitions in the 2017-18 season. The Dutch FA followed in the 2018-19 season.
So, how has ABBA worked in these trials? For the first time, the complete dataset of the games that have used the ABBA sequence in FIFA tournaments and in England can now be revealed. (Evidence from the Netherlands outside of the Feyenoord-PSV Johan Cruyff Shield match in 2018 has not yet been obtained):
The sample indicates that ABBA works in creating a more fair and balanced outcome, bringing the frequencies with which the A and B teams win closer to 50-50 than to 60-40. In fact, in this sample they are exactly 50-50. ABBA is both theoretically and empirically fairer than ABAB, and perhaps it's just a matter of time before a league, MLS or elsewhere, has the leeway and will take a chance on implementing the progressive shootout method.
Ignacio Palacios-Huerta is a professor of managerial economics and strategy at the London School of Economics, a former head of talent ID and member of the board of directors at Athletic Bilbao and a founding partner of ASK+.
