When soccer games are determined by penalty kicks, it's part technical and part psychological. Players at the highest levels have good technical skills but among them, a few players on each team really stand out - and whenever possible, they are taking the kicks. But they will likely be tired and they know if they miss completely there is no chance to score regardless of what the goalie does, so they approach the shot a little more conservatively than they otherwise would, so goalies know if they can simply guess left or right they stand a decent chance of blocking the shot.

But the odds are actually with the kicker. The goal is wide and professional soccer players have practiced penalty kicks thousands of times. And kickers decide which way to kick, meaning the goalie has to guess or react. A recent paper finds kickers have one more psychological advantage, they just don't take advantage of it; goalies are prone to the gambler's fallacy.

The gambler's fallacy, also called the Monte Carlo fallacy because of a famous casino event in 1913(1), is the belief that a statistical deviation from the average will be corrected in the short term - if you flipped a coin 4 times and they all came up heads, you might quickly calculate that the chances of there being heads flipped 5 times in a row is a scant 1 in 32 and choose tails - what the victims of the gambler's fallacy neglect to realize is that the odds of rolling heads 4 times and then tails are also 1 in 32.

Four Consecutive Shots by Portuguese Kickers against the English Goalkeeper during the Euro 2004 Semifinal Penalty Shootout. The Portuguese kickers are shown in red and the English goalkeeper in blue; the green circle is the ball. All four kicks were to the left of the goal. The goalkeeper made a rightward dive following three consecutive kicks to the left. Credit: 10.1016/j.cub.2014.07.013

A paper in Current Biology studied penalty shoot-out videos from all World Cup and Euro finals tournaments between 1976 and 2012. The authors found that each team of kickers produced more or less random sequences of kicks to the left or the right of the goal. Goalkeepers’ dives to the left or the right were not related to the direction of the kick, suggesting that goalkeepers at this elite level make their decisions in advance, rather than reacting to each kick. However, goalkeepers’ decisions were non-random in one crucial respect: when the kickers repeatedly kicked in the same direction on consecutive penalties, goalkeepers became more likely to dive in the opposite direction on the next penalty.

After three consecutive shots in one direction, goalkeepers dive in the opposite direction for the next penalty around 69% of the time.

“Complete randomness is generally the best strategy in competitive games,” says lead author Erman Misirlisoy of the University College London Institute of Cognitive Neuroscience. “Because the goalkeeper displays the gambler’s fallacy, kickers could predict which way the goalkeeper is likely to dive on the next kick. That would obviously give the kicker an advantage – they would simply aim for the opposite side of the goal. Surprisingly, though, we found that kickers failed to exploit this advantage.”

“Often you can only win in elite sport by exploiting tiny weaknesses in your opponent’s strategy,” explains senior author Professor Patrick Haggard. “We can only speculate on why goalkeepers can get away with non-randomness, without the kickers exploiting it. One possibility is that penalty shoot-outs are relatively rare. But there is a more psychologically interesting possibility: shoot-outs are asymmetric, because one goalkeeper faces several different kickers, one after the other. Kickers are under enormous pressure, focused on the moment of their own kick. Each individual kicker may not pay enough attention to the sequence of preceding kicks to predict what the goalkeeper will do next.”

Misirlisoy added, “People can learn to predict: perhaps football coaches could study the gambler’s fallacy, and could train their penalty kickers in preparation for the next World Cup. At the same time, goalkeepers could also learn to be less predictable.”

How to make it work? If you know the goalie reads Science 2.0, you know he will know that if all of you kick to the left does not mean you will kick to the right, so he will go left. So you should kick to the right.

Citation: Erman Misirlisoy, Patrick Haggard, 'Asymmetric Predictability and Cognitive Competition in Football Penalty Shootouts', Current Biology DOI: 10.1016/j.cub.2014.07.013. Source: University College London

NOTE:

(1) What happened? Once black came up in roullette a few times people began to rush to bet on red - a record-setting 26 consecutive hits on black resulted in millions of dollars in profits for the casino and a story for the ages.