The drama of a penalty shootout may make for exciting viewing, but researchers at King’s College London have found that current rules mean one team will always have an unfair advantage. Using game theory and statistics, they suggest an update to the rules that would get rid of this advantage in a number of sports.
Dr Mehmet Ismail from the Department of Political Economy at King’s College London, along with Dr Steven Brams from New York University, propose that employing the ‘Catch-Up Rule’ during a penalty shootout would allow equally skilled players on each team roughly the same chance of winning.
Under the ‘Standard Rule,’ which is currently used in football penalty shootouts, a coin toss determines which team kicks first on all five penalties, giving a substantial advantage to the team that goes first. According to a 2010 study, the team that kicked first won the penalty shootout 60.6% of the time in major tournaments between 1970 and 2003 including World Cups and European Championships.
In contrast, after an initial coin toss, the ‘Catch-Up Rule’ gives the subsequent kick to the team who lost on the previous round – thereby giving them the opportunity to catch up.
Dr Ismail explains, “Implementing fairer rules would not only make the sport more competitive, but also more exciting, for spectators as teams’ scores would remain closer together throughout the competition.”
Using game theory and statistics, the researchers have also identified other sports with rules that are likely to give an ‘unfair’ advantage. For example, in golf the players to go last have a competitive advantage, because they know what they must score to win. Also, in most service sports including badminton, squash, and racquetball, a team that wins a point serves next, which is generally more advantageous than receiving.
However, Dr Ismail and his team point out that football is the sport that needs the most reform as the Standard Rule gives one team a significant advantage.
In 2017, the International Football Association Board (IFAB) announced that the ABBA Rule — the rule currently used in the tennis tiebreaker — will be tested in penalty shootouts during several tournaments, including the FIFA Under 20 World Cup and English Football League in 2017-18. This rule is quite different from the Catch-Up Rule, because the order of shooting is fixed and not responsive to what just happened on a round, but Dr Ismail and colleagues have shown the ABBA Rule to be fairer than the Standard Rule.
“Shootout trials, including our own, have started to try to encourage changing the Standard Rule in football. However, we need more testing of these various rules in order to reach a conclusion about which rule should be used in football games of the future.” said Dr Ismail.
Making the Rules of Sports Fairer is published in the Society for Industrial and Applied Mathematics (SIAM) Review.