A better class of penalty kick shootouts

There are not many times when I’m qualified to critique something. Most of my writing, while overly snarky, is equivalent to Grandpa Simpson berating the sky: I have opinions on what things suck, and I inherently think these opinions are right, but they’re often no more informed or valid than the next person’s.

Last week, however, I encountered an interesting yet incomplete news story in one of my few areas of actual expertise–penalty kick shootouts. A quick primer: The soccer shootout, initiated when two teams are tied after extra time, provides a unique tiebreaker. One team’s player shoots from twelve yards away against the opposing goalkeeper, then the other team shoots. They do this five times; if one team is ahead after five rounds, then that team wins. Otherwise, they continue into sudden-death rounds, a round at a time, until one team makes and the other misses.

The shootout, in some sense, operates in a frustrating middle ground. It removes the need for replayed matches or endless showdowns (in the 1982 NCAA Final, for example, Indiana beat Duke after a mere eight overtimes), but it generates new problems. Aesthetically, the tiebreaker only features the thinnest sliver of a soccer match (a shot on goal); more importantly, it’s unfair to the team that shoots second: Sixty percent of shootouts are won by the team that goes first. Given that the shooting order is chosen by a coin flip, the shootout suffers from a problem similar to the NFL’s overtime–that is, luck is simply too much of a factor.


Recently, UEFA (the European soccer body) announced that they’re testing a new strategy to mitigate the role that this coin flip plays. Instead of having the same team go first in every round, they’ll now alternate each round. So the team that goes first in round 1 now goes second in round 2, then first in round 3 and so on. The logic follows the findings of researchers Jose Apesteguia and Ignacios Palacios-Huerta, who documented the first-team advantage in shootouts at great length. They discovered the sixty percent statistic cited above, and they also observed that teams greatly prefer to go first upon winning the coin flip–that is, the players already inherently understand this advantage. To mitigate this advantage, Palacios-Huerta suggested an ABBA pattern for the shootout, a form of the Prouhet-Thue-Morse sequence that’s designed for equitability, much like that which UEFA has implemented. (For the record, in the two shootouts that have occurred so far under the new system, both at the ongoing European under-17 Championships, the first team to shoot has still won.)

It was on the heels of this research that Christian Britto and I wrote our thesis on the game theory of and the optimal strategies during the penalty kick shootout. Studying roughly 100 shootouts across international men’s and women’s competitions, we found–both confirming the already-existing literature and expanding upon it–that not all kicks are equal opportunities: When players have the chance to win a shootout with a successful kick, they convert at a higher than average rate. Crucially, when they need to score to continue a shootout (or prevent the opposition a chance at a winning kick), they convert at a worse clip: that is, when players have a “must-make” (or a “semi-must-make”) kick, they tend to wilt under the higher pressure. (The majority of our paper explored how different calibers of players respond to this pressure–top-tier players don’t wilt, while average and poor players do–and how coaches should organize their lineups to deploy their best players at the most important moments.)

By our classification, a player kicking in round 1 while trailing 1-0 is not in a high-stress situation, but a player kicking in round 5 while trailing 3-2 is. According to Apesteguia and Palacios-Huerta, the first-team advantage stems from the second team (potentially) trailing in perpetuity and having to handle that stress–such scenarios are identical. Yet our findings showed that worse performance occurs disproportionately in later rounds when opportunities for redemption may not exist. Teams that shoot second more frequently encounter these high-pressure situations; therefore, teams that shoot second lose more frequently.

Building on this finding, we observed that when shootouts extend into rounds 6 and beyond the first-team advantage disappears and, in fact, the second team to shoot holds a slight edge. The explanation? The first team is always in a high-pressure “semi-must-make” scenario, while the second team, should the first team miss, can encounter less pressure.

Regardless, the move to an ABBA format satisfies both us and Apesteguia and Palacios-Huerta. They like it as it evens out who shoots first; we like the format because it balances out the proportion of high-stress kicks for each team. Imagine a four-kick shootout under the old format, ABAB. The first kick for team A, then, is low-stress; even if team A misses and team B makes, team A will get a second attempt. And if the first kick is successful, as 75-80 percent of kicks are, then team B, knowing that a miss will set team A up for a clincher, is immediately in a high-pressure situation. Such a structure is inherently disadvantageous to team B.

An ABBA format complicates things. The first kick for team A is both high-stress and not. There’s a chance that a miss means team A won’t get to kick again–if both of team B’s kickers convert–but it’s a more complicated probability. It requires two things to happen that, statistically, would only coincide about fifty-five to sixty percent of the time, i.e. no longer a death sentence. And likewise, if the first kicker for team A is successful, the first kicker for team B has a backup plan: Even with an initial miss, team B would still get to kick and extend the shootout.

Said another way, the first round of kicks will feature no “semi-must-make” kicks but rather shots that are one step removed from the pressure. There’s no basis to say if such adverse performance effects will come into play in this new scenario. But it removes an obvious disadvantage to team B, and immediately, the ABBA system appears to be more equitable.


UEFA’s version, however, is insufficient. For an ABBA format to be wholly effective, the shot attempts must be deployed in pairings of two. The principle of the Prouhet-Thue-Morse sequence centers on inverting an initially unfair sequence: if AB is unfair, then it must be inverted to form an ABBA “cluster.” But UEFA’s solution retains the initial design of five shots per team, which results in an improper sequence in the fifth round. They should instead arrange the tiebreaker to initially have two (or three) “clusters” of shooters, such that the entire shootout sequence resembles ABBAABBA or ABBAABBAABBA. (Side note: Prouhet-Thue-Morse would recommend inverting rather than repeating the ABBA sequence–in the event that the ABBA pattern itself is inequitable–for an ABBABAAB pattern. However, if we believe ABBA is fair, then no further inversion is necessary.)

The current proposition of five rounds–ABBAABBAAB–is, besides being inelegant as hell to write out, incomplete and likely unfair, albeit to a much smaller degree than before. (The distribution of high-pressure kicks won’t be equal.) Moreover, the logic is flawed even by Palacios-Huerta’s logic and UEFA’s justification: A five-round shootout requires that one team kick first in at least three rounds, which would provide that team an advantage. An even number of kicks per team would allow a proper 50/50 split.

It appears that the ABBA “cluster” strategy is the cure for the inequitable shootout system. But UEFA shouldn’t neuter its solution simply because of how the traditional-yet-incredibly-flawed arrangement works today, or because five–half of the field players on a full side–is a neat, easy number to justify. UEFA can’t hope to have their cake and watch John Terry fail in excruciating fashion, too.

Similarly, should the shootout be tied after its “regulation” length (be it four or six rounds of kicks), the tiebreaker should consist of additional “clusters” until a team has won. Currently, teams go round-by-round: the sixth round would be BA, and if still tied, then AB, then BA, etc. In this sense, again, teams shooting first in each round would encounter higher pressure on average as they are immediately thrust into a high-pressure “semi-must-make” situation. Without a “clustering” of the sudden death rounds, the two teams would merely trade this pressure back and forth with the win probability undulating excessively–a scenario that savvy managers could exploit.

UEFA is on the right track, certainly. However, it’s frustrating to see professional football get so close to a satisfying answer for the penalty kick shootout and stop short. Perhaps the biggest remaining pressure to overcome, now, is the game’s conservatism toward full-throated reform.


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