How can the “Gambler’s Fallacy” help penalty takers score?

Nooooo, Ashley Cole!

The World Cup might be over, but researchers from University College, London, are still sifting through video data in an effort to understand goalkeepers’ behavior during penalty shoot-outs.

After analysing spot kicks from World Cups and European Championships between 1976 and 2012, researchers discovered that goalkeepers were falling prey to a form of “gambler’s fallacy”–an enduring psychological mistake involoving random events that seems to have plagued human thinking for time immemorial.

The “gambler’s fallacy” is so named because it is often the staple fallback of the desperate gambler who needs to win to recoup previous losses. Imagine you’re tossing a coin five times. Assuming you’re using a fair coin, the chances of the coin landing heads or tails is even. Each coin toss is independent of the others. Of course, this doesn’t prevent, say, the first three coin tosses being all heads. The “gambler’s fallacy” however, is to then believe that because three heads have already been thrown, it is now less likely that the next toss will be a head. That’s the fallacy. The chance of heads or tails remains constant: 50/50.

The “gambler’s fallacy” is applicable in many casino games such as ones involving decks of cards, roulette wheels, dice etc. When the crucial event (dealt card, number landed on, dice number thrown) is independent of previous events, nothing concerning what went before can help you. The fallacy is actually promoted on shows like the National Lottery Live Draw, when some enthusiastic chump regales the audience with tales of the picked lottery balls previous incarnations. “And . . . number forty-five . . . we haven’t seen 45 for seven weeks after being drawn on the bounce three weeks in a row in March, so welcome back number 45!” I personally think as the lottery balls are being drawn, the commentator should give basic lessons in probability theory. Much more useful for the general public.

Anyway, how does the “gambler’s fallacy” apply to goalkeepers at penalty shoot-outs? Well, what the researchers discovered was that although most elements of player choice appeared to be random–which direction the kicker shoots, which direction the goalkeeper dives–if the goalkeeper had experienced three kicks in a row towards one side of the goal, he was more likely to dive the other way at the fourth kick. In other words, he was reacting to past events that could be shown to have no bearing on the next event. Although the kickers were discovered not to pick up on this statistical quirk, the researchers suggest that they could have exploited this pattern in the goalkeeper’s behavior to score.

As a penalty taker, I’ve always been tempted by the casual dink down the middle!

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