The best way to watch a penalty shoot-out at home is with the volume turned down. It’s the only guarantee that you will not have to hear the commentator say: “And now for the lottery of the shoot-out.” The one thing I learned, above all else, from my research in writing my book Twelve Yards: The Art & Psychology of the Perfect Penalty, which is published today, is that a penalty shoot-out is not a lottery.
The penalty itself is football at its most basic: a ball, a kicker, and a goalkeeper. It’s a test of technique and of nerve and while you can never recreate the match conditions, just as you cannot with a putt to win the Ryder Cup or a second serve to win Wimbledon, purposeful practise can help prepare for the moment.
Nevertheless, there is one element of the shoot-out where luck does play a role: the coin toss which determines who chooses whether to kick first or not.
Ignacio Palacios-Huerta, Professor of Game Theory at the London School of Economics, analysed the results of 212 penalty shoot-outs, taking in 2,106 penalties, and concluded that the team kicking first win 61% of shoot-outs; compared to 39% for the team kicking second. “The coin toss to choose who goes first is not a 50-50 toss but nearer a 60-40 toss,” he said, “where the team kicking first has a 22% probability advantage over their opponents.”
To make things fairer for both teams in a shoot-out, Palacios-Huerta wants to reduce that 22% probability margin to a smaller figure, and he believes he has found a way to do it. In his paper ‘Tournaments, Fairness and the Prouhet-Thue-Morse Sequence’, he wrote: “If the order A B offers any kind of advantage to either player, then by reversing the order in the next two rounds we will tend to compensate for that advantage.”
The closest scenario to that is the tennis tie-break, where Player A serves first, then Player B serves twice, until the winner gets to seven points (and leads by two). The tennis sequence, therefore, is as follows: ABBA ABBA ABBA etc. Palacios-Huerta thinks that can be improved by reversing the original order, “to compensate for any potential advantage that might have been given to either one of the players until then.” His ideal penalty order, then, is: ABBA BAAB ABBA BAAB.
The single A and B serves/kicks at the end of each sequence of four would be too confusing to work in tennis or football, but the idea of football adopting a tie-break method would certainly make things interesting – and a little fairer.
To buy Twelve Yards: The Art & Psychology of the Perfect Penalty, by Ben Lyttleton, click here http://www.amazon.co.uk/Twelve-Yards-Ben-Lyttleton/dp/0593072685