Penalty kick shootouts are not a goalkeeper's favorite way to settle a soccer match. Alone in the net, goalies must face off against a string of kickers and try to anticipate which way the ball will come hurtling toward the goal. Psychologists have long recognized that shots happen too fast for goalies to react after the ball leaves the kicker's foot — they just have to dive and hope for the best. But now, a new study suggests they do so in predictable ways that clever shooters could use against them.
The study, published Thursday in the journal Current Biology, looked at every shootout in every World Cup and Euro Cup tournament between 1976 and 2012. They found that goalkeepers suffered from a widespread misconception known as the "gambler's fallacy": the more often one thing happens, the more you anticipate its opposite to occur, even though the likelihood of either remains the same.
For goalkeepers in a shootout, this meant the more times kickers booted the ball to one side of the goal, the more likely keepers became to lunge in the opposite direction for the next shot.
Fortunately for goalkeepers, the authors wrote, it doesn't seem that kickers have figured this it out yet. In more than 300 kicks across 37 shootouts, no evidence suggested kickers exploited this weakness (although that may now change).
The gambler's fallacy takes its name from the fact that betting types tend to see patterns in sequences of random events, like repeatedly flipping a coin to see if it comes up heads or tails, or spinning a roulette wheel to see if it lands on red or black, odd or even.
Instead of treating each flip or spin as an independent event with a 50-50 chance of producing either outcome, they mistakenly believe the events are related — that consecutive runs of one outcome are increasingly likely to end — and place their bets accordingly.
Even if we don't gamble, we all think this way, said study leader Erman Misirlisoy, a doctoral student in neuroscience at University College London.
"It's based on a style of thinking that actually works for us in most cases," he said. For example, if we make a random choice from a box of chocolates, it directly influences our next selection because the first chocolate is now gone — we can't choose it again.
Because we rarely encounter truly unrelated events, we're not very good at assessing their odds. Misirlisoy wanted to know if even athletes at the highest level of performance fell prey to the same flawed thinking. So he looked into the data.
Together with his advisor, Patrick Haggard, Misirlisoy analyzed 361 penalty kicks from 37 shootouts that decided matches in World and Euro Cup tournaments. They reviewed statistics and watched clips of the games, noting which way the ball went and which way the goalkeeper dove. The pair rejected kicks that sent the ball into the center of the net, which only eliminated 40 shots.
Misirlisoy and Haggard found that as the number of consecutive kicks to the same side of the net grew, so did the odds that the keeper would dive in anticipation of a kick to the other side of the net.
"His job really is to get in the mind of the kicker," Misirlisoy said. "He could assume that the kickers are behaving randomly, it's just that his understanding of 'randomly' is quite similar to the rest of us."
But what is running through the minds of players as they stand on the penalty line in front of a stadium full of roaring fans, the fate of a high-stakes match at their toes?
"The pressure on the kickers is just enormous," Misirlisoy said. As the crowd knows, goalkeepers have a slim chance of saving penalty shots, but kickers are expected to score.
"They are thinking, 'I really need to get this ball in the goal,'" he said. "That's perhaps why they don't spot the predictability of the goalkeeper in that moment."
Misirlisoy's analysis showed that kickers do a surprisingly good job of acting randomly, much better than the goalkeeper's brain does. That's because each player behaves more or less independently; only the goalie keeps track of every kick, subconsciously allowing the catalog of previous shots to influence his future choices.
"The goalkeeper and kickers are in completely asymmetric situations," Misirlisoy said.
So can keepers do anything to protect themselves from their own cognitive bias?
"There is one easy way, which is a little bit boring, I suppose," Misirlisoy said. It's a technique the celebrated Danish goalkeeper, Peter Schmeichel, used throughout his career: "He always says that he decides well in advance which way he's going to dive and he never changes his mind. As long as that sequence is random, then he's got the right idea."
This tactic won't favor the keeper, but it can even the playing field.
"The equilibrium point is both being random," Misirlisoy said. "Neither of them has a disadvantage, but neither has an advantage either."