Even with the ABBA format, penalty shootouts remain a lottery

By T.A.W.

ALTHOUGH social-media sites are usually ablaze with fury after a football cup final, it is rare that supporters on both sides direct their ire at the same target. That was what happened when Arsenal beat Chelsea on August 6th to win the FA Community Shield, the annual pre-season fixture between the defending victors of English Premier League and the FA Cup, the country’s main knockout competition. The anger was caused not by the referee or the players, but by the format of the penalty shootout used to decide the contest after a 1-1 draw. Spot-kicks have always been taken alternately. Yet the Arsenal and Chelsea players lined up in a strange new sequence: ABBA (the first team kicks once, then the second team kicks twice, and then the first team kicks again) rather than the standard ABAB. That such a pattern has been used in tennis tie-breaks for decades was of little consolation. While making countless puns about Swedish pop music, fans moaned that the change was confusing, distracting and pointless. Why fix something that wasn’t broken?

In fact, however, the old shootout format was severely broken. FIFA, the sport’s international governing body, introduced it in 1970. Until then, teams that were tied after 90 minutes and extra time had been separated by a simple coin toss, as when Italy advanced ahead of the Soviet Union in the semi-finals of the 1968 European Championship. FIFA’s solution was a set of five penalties for each side followed by sudden death, with shots alternating between the two teams, as had been trialed in Spain since 1962. This format has since been used universally when knockout games are level after 30 minutes of extra time.

This system was meant to eliminate the arbitrary nature of the coin toss. However, it wound up making the call of heads or tails for the right to take the first kick the most important moment in the entire shootout, for two reasons. First, the outcome of a penalty, and indeed a series of penalties, is highly random. After analysing the 2,788 spot-kicks awarded in the English Premier League, Spains’s La Liga and Germany’s Bundesliga in the last ten seasons, we have found no statistically significant relationship between a player’s past conversion rate and his future success. This does not mean that each penalty is a total lottery. But it does suggest that any edge a skillful finisher might have is too small to be detected, given how infrequently penalty kicks occur.

If ability barely matters, then the outcomes of shootouts must be determined by extraneous factors. And it turns out that in the ABAB format, the biggest one of all is who goes first. According to a study by Ignacio Palacios-Huerta, a professor at the London School of Economics, team A has won 60% of over 1,000 such tie-breakers across various competitions between 1970 and 2013. In other words, being good at football probably won’t help a team win the World Cup after a stalemate at 120 minutes—but winning a coin toss will.

It might seem hard to believe that our data show no significant association between a penalty taker’s past career record and his subsequent performance. Take the examples of Lionel Messi and Cristiano Ronaldo, two of the greatest goal-scorers in the sport’s history. In the past ten seasons of league games, Mr Ronaldo has converted 87% of his efforts (66 of 76) and Mr Messi has succeeded with 84% (46 of 54). The overall rate for La Liga, the Spanish division in which both men ply their trade, has been 77%. Yet after the diminutive Argentine found the net 93% of the time in the first half of his sample, he prevailed just 78% of the time in the remainder. The Portuguese powerhouse suffered a similar slump: last year he endured a run of five misses out of eight attempts across all competitions.

Our sample is not comprehensive enough to prove that there is no skill involved whatsoever in an 11-metre (36-foot) strike. Data about the placement of shots are scarce, but they might be a better predictor of future outcomes. And at least a handful of players have seemed to show a knack for it: the most famous is Southampton’s Matt Le Tissier, who converted 48 of his 49 spot-kicks. Even if 1,000 league-average players were given that many opportunities, there is a 93% chance that none of them would equal his record.

Yet whatever small advantage might exist for a handful of elite shooters vanishes in a contest of ten or more players. The crapshoot-like nature of shootouts is confirmed by Mr Palacios-Huerta’s observation that the higher-ranked team is no more likely to triumph than the underdog, with no slant toward the home side either. The only predictable element is that the raffle favours the team that plucks the first ticket. This advantage appears to be mostly psychological. Team B usually needs to find the net to keep up, or to remain in the tie during sudden death. And even though footballers should in theory be trained professionals who are impervious to pressure, in practice they show a surprising tendency to choke: team B has converted just 65% of kicks when trailing in the third round or beyond. Intriguingly, this decline stems mostly from shots missing the target altogether, rather than from a spate of match-winning saves. Far from taking the power off their attempts as a form of risk aversion, stressed shooters seem to go for broke. Mr Palacios-Huerta concludes that this is “a significant and quantitatively important type of psychological effect”. Footballers seem to agree: of the 242 players and coaches interviewed for the research, not a single one preferred to go second.

Given the size of this first-taker bias, in 2014 Mr Palacios-Huerta recommended testing other formats which would split the burden of trailing on the scoreboard. The most obvious was tennis’s ABBA system. To the encouragement of sports researchers everywhere, FIFA listened: this pattern has been used in youth-team world cups and pre-season friendlies this summer, and has been adopted by the English Football League for all competitions in this coming season. The football fans that grumble about being muddled by ABBA will be irritated even more by Mr Palacios-Huerta’s next suggestion. Whereas his trials with academy teams have shown that the new method narrows the first-mover advantage to 54%, the fairest option is the Prouhet-Thue-Morse sequence (ABBABAAB), which cuts it to 51%.

There is an irony in adding so much complexity to achieve a simple 50-50 split: it might just be easier to return to the good old coin toss. Spectators, however, get greater satisfaction from seeing the unpredictability play out with a ball. The ABAB formula prevents that, whereas Mr Palacios-Huerta’s reforms ensure it. A more probing question is whether football stalemates ought to be decided by such a random process. A one-on-one dribble to the goal, as occurs in ice hockey, might favour more skilled players and be more entertaining for fans—though hockey shootouts are also something of a lucky dip.

The riposte is that underdogs, after holding back their opponents for 120 minutes, deserve an even chance at glory. Messrs Ronaldo and Messi have collected plenty of silverware. Few will complain if a gang of plucky no-hopers beats them from the spot.