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The formula for winning a penalty shootout

BTo this day, this is almost 25 years ago. A Wednesday night at Wembley Stadium in London: As the semi-finals of the European Football Championship must be decided by a penalty kick, 75,900 spectators and millions of people on the screen held their breath. The top four shooters from both sides hit the goal. Then Gareth Southgate ran-and failed at the German goalkeeper. Soon after, Andy met Mueller and made football history.

Johannes Pennekamp

Editor in charge of Economic Report, responsible for “Die Lounge”.

Tomorrow, Tuesday, it may be at Wembley again. This time England and Germany met in the round of 16. If no decision is made after 90 minutes plus overtime, the penalty kick must be re-decided. Who wins the thriller first is luck and chance. At least so far, spectators, players and coaches think so. Even researchers cannot see any clear pattern in hundreds of penalty shoot-outs. For a long time, the team that was allowed to start as the first shooter had the advantage. The argument behind: Whoever hits the ball first puts extra pressure on the opponent, so that he trembles more than before—and then shoots. However, economists’ assessment refutes this argument. Therefore, the first shot has no advantage; in other sports where there are also “gun fights”, the first shot has even proved to be a disadvantage.

Courage is a good consultant

Recently, three researchers led by behavioral economist Matthias Sutter from Bonn took an important step forward. The director of the Max Planck Institute for Collective Commodities and his co-authors scrutinized nearly 100 penalty shoot-outs in world and European championships and top European competitions. Economists analyze neither the player’s shooting skills nor the player’s market value, but what happened before the first shot. The referee then tossed a coin with the captains of the two teams present. The winning captain can decide whether his team will start or let the opponent go first.

The first important finding: The victorious captain only chooses the option of the first shot every two times. Players don’t seem to believe that this is a more promising strategy. The new numbers seem to justify this: if the captain chooses to shoot for the first time, the team will win about six times in ten penalty shoot-outs.

However, after careful inspection, it is also hopeful to let the opponent go first. If the captain chooses the second shot, the probability of his team winning exceeds 60%. When the researchers evaluated only the most important games, winning a coin toss actually increased the subsequent probability of victory to two-thirds—regardless of which option the captain chose.

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