WATERLOO — Researchers have developed a new system for soccer penalty shootouts to negate the advantage of winning the coin toss and electing to kick first.
Under the so-called “m-n rule’’ — proposed by Marc Kilgour (Wilfrid Laurier University), Steven Brams (New York University) and Mehmet Ismail (King’s College London) — the team that opts to kick first in a shootout must score five times before the end of the round in which the team kicking second scores a fourth time.
For the team kicking second to win, it must score four penalty kicks before its opponent scores five. If both teams reach 5, 4 in the same round — when they both kick successfully at 4, 3 — then the game is decided by round-by-round sudden death, whereby the winner is the first team to score in a subsequent round when the other team does not.
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“We found some statistics that suggested that the most important thing when you’re resolving a game with penalty kicks is the coin toss, and that didn’t really seem fair, so we started to think of ways to change that,” said Kilgour, a member of Laurier’s Department of Mathematics since 1973.
“We’ve actually come up with several (proposals), but the one that’s in the (research) paper is the one that is closest to the current system, so it would be easier to implement for the referees and the officials and would be easier for the fans to follow.”
In a 2018 study, Ignacio Palacio-Huerta of the London School of Economics revealed statistics that showed the secret to winning a World Cup penalty shootout was being the first team to shoot. His research, based on 1,000 penalty kicks in World Cup and European championship competitions, showed that teams shooting first had a 20 per cent better chance of winning than the team shooting second.
At the time, Palacio-Huerta said there was an added psychological pressure of shooting second.
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Argentina won last year’s World Cup with a penalty shootout victory over France. The game ended in a 3-3 tie after extra time, and Argentina chose to shoot first in penalties after captain Lionel Messi won the coin toss. The tournament featured five penalty shootouts, and the team shooting first won three of them.
Soccer’s governing bodies, FIFA and IFAB, have acknowledged the unfairness of penalty shootouts and, in 2017, adopted the so-called ABBA rule that changed the kicking order from ABAB to ABBA. It was dropped because it was difficult to implement and was confusing to spectators.
Kilgour said there is no doubt that the new proposal is fairer than the current one.
“Yes, this is better. I certainly wouldn’t say it’s the best, but the systems that I think might be better are more complicated and therefore might be hard to do, in practice,” he said.
Kilgour, Brams and Ismail released their working paper, “Fairer Shootouts in Soccer: The M-n Rule,” last week.
“We’re hoping it gets a little bit of publicity,” said Kilgour. “Just talking about things like this can lead to rule changes.”
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