Simanaitis Says

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AN AMAZING thing occurred on August 18, 1913, at the Casino in Monte Carlo: At one roulette table, black came up a record 26 times in succession.

Or, then again, it’s not so amazing.

Therein lies the Gambler’s Fallacy, a practice that modern researchers have also associated with goalkeepers in international soccer matches.


The Casino, Monte Carlo, adjacent to the Monaco Grand Prix circuit,

First, let’s complete the roulette story: Beginning around the fifteenth spin of successive black wins, people rushed to the table to place bets on red. As the black run continued, betters doubled and tripled their stakes, sensing for sure that after a twentieth black, there wasn’t a chance in a million it would come up on the twenty-first.

In the end, after the twenty-sixth spin, the Casino was richer by millions of francs.


The Fallacy Files is an excellent website for analyzing such matters. See

The Gambler’s Fallacy is in failing to understand statistical independence. That is, with events that are independent, the occurrence of one has no effect upon the other. A roll of dice is an independent event; so is a toss of a coin or a spin of a roulette wheel. This assumes, of course, the dice aren’t loaded, the coin is a fair one and the roulette wheel is legit in its operation.

This may go against intuition, but consider that the dice, coin or wheel has no memory. Each outcome is unto itself.


Researchers at the Institute of Cognitive Neuroscience, University College London, found that soccer goalkeepers facing penalty shootouts fall for this same fallacy. What’s more, unlike the casinos of the world, soccer kickers seem not to have exploited things yet.

As its name suggests, a penalty shootout in soccer has a goalkeeper defending his goal without teammate assistance while an opposing series of kickers attempt to aim the ball past him into the net.


Goalkeepers often dive for their saves. Image from

Often, the kicked ball approaches too quickly for the goalkeeper to react to its direction. He must guess the likely direction and dive in anticipation.

In their paper, “Asymmetric Predictability and Cognitive Competition in Football Penalty Shootouts,” Erman Misirlisoy and Patrick Haggard examined all 361 kicks occurring in the 37 penalty shootouts of World Cup and Euro Cup matches over a 36-year period, 1976 to 2012. (See



The Gambler’s Fallacy in action: Diagramed are four consecutive shots by Portuguese kickers against an English goalkeeper during the Euro 2004 Semifinal penalty shootout. This and the following images from the Misirlisoy and Haggard paper.

Goalkeepers and gamblers have a lot in common. After defending repeated kicks in one direction, goalkeepers became increasingly likely to dive in the opposite direction on the next kick.


Statistical data of goalkeeper dives: The more consecutive kicks in one direction, the more likely the goalkeeper will dive to the opposite side.

Curiously, though, the research showed that penalty shootout kickers haven’t caught on to this as yet. The following statistical distributions show kicker behavior following sequences of kicks in the same direction.


The kickers’ choice of direction shows a different sequential pattern from that of the goalkeeper.

Overall, researchers note that kickers seem to exhibit less predictable behavior than goalkeepers. For example, following a run of three kicks in one direction, a kicker is no more likely to switch direction than would be expected by chance.

The researchers note that “The penalty shootout pits the will of one goalkeeper against the will of many kickers…. These cognitive functions have been extensively studied in individuals, but little is known about how they are coordinated across individuals in a group.”

One conclusion is that goalkeepers might be given cognitive training in random behavior. Also, kickers might improve their intercommunication. “These,” researchers note, “could help teams better prepare for nail-biting penalty shootouts in future football tournaments.” ds

© Dennis Simanaitis,, 2014

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