Tuesday 2 May 2017

ABBA Instead of ABAB? What’s the Fuss?

At this year’s annual International Football Association Board (IFAB) meeting, the body in charge of the Laws of the Game decided to start experimenting with an alternative sequence for taking penalties during a shootout. Instead of having both teams take turns (i.e. ABABABABAB), as they have always done in football, a sequence akin to the one of serving in a tiebreak in tennis (i.e. ABBAABBAAB) will be tried out. Could this have any impact on who is to win a shootout, really? The answer is an unequivocal ‘yes’. And science helps us understand why.

In 2010, two Basque economists, Ignacio Palacios-Huerta and José Apesteguía, showed that in actual penalty shootouts in football, the team shooting first ends up winning in approx. 60% of cases; the team going second only in about 40%. This is quite a difference with both teams winning half, which is what would have been both expected and desirable. These findings imply that the toss deciding which team could go first imparts an enormous competitive advantage.

The mechanism behind this advantage is the so-called “lagging-behind effect”. The lagging-behind effect represents the simple fact that it is more difficult to convert a given penalty if one's team is behind in the score at the point of taking the kick than when not behind, due to the enhanced pressure such a “near-to-losing” situation creates as one “has to score” to keep one's team in the game.

Source: diariosdefutbol.com

It is easy to see why such a lagging-behind effect, under the current sequence, results in an advantage for the team going first, simply by considering both teams' first kick. What is the probability that team A is lagging behind at the time of their first kick? Naturally, this is zero as all’s square at that point. Now it is up to team B to take their first kick. Their chance of lagging-behind at this point? With penalties being converted at a rate of approx. 75%, there’s about a 75% chance team A will just have scored and thus a 75% chance that team B are lagging behind when taking their own first kick. So a 0% vs. a 75% chance of lagging behind on the very same kick. Under the current ABAB-sequence, in which every time team A get to act and team B to react, this pattern will be preserved and the resulting lagging-behind effect knocked on till the end.

In case of applying an ABBA-sequence, as in a tennis tiebreak, instead, the advantage of having the opportunity to force the lagging-behind effect upon the opponent rather shifts from one team to the other: it, again, starts with team A, but then moves to team B as they get to go twice; then to team A that get to go twice, etc. The whole idea being that the influence of whoever may win the coin toss and thus be able to go first will have only minimal impact on who will win.

In addition to the abovementioned empirical research uncovering the lagging-behind effect, together with Profs. Brian McCann and Govert Vroom, we were able to prove, through theoretical (mathematical) research, soon to appear in the Journal of Sports Economics, that, in case of a lagging-behind effect, the ABBA-sequence substantially reduces the advantage of winning the toss relative to the current sequence. However, we also prove that there is yet another “natural” sequence, known as “Prouhet-Thue-Morse”, which reduces this advantage even more than the ABBA-sequence does. Perhaps something to add to next year’s IFAB meeting’s agenda J