A team of game theorists has devised a “Catch-Up Rule” that is designed to make sports such as volleyball, badminton, and squash more competitive—and more thrilling for spectators.

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A team of game theorists has devised a “Catch-Up Rule” that is designed to make sports such as volleyball, badminton, and squash more competitive—and more thrilling for spectators.

The rule seeks to give equally skilled players and teams the same probability of winning a game they have under under existing rules—collectively called the Standard Rule by the researchers—while keeping scores closer throughout the competition and thereby increasing the drama and tension of a close contest.

The Catch-Up Rule was devised by New York University’s Steven Brams, Maastricht University’s Mehmet Ismail, Wilfrid Laurier University’s Marc Kilgour, and Swarthmore College’s Walter Stromquist.

In general, the Catch-Up Rule gives the serve to the player who has lost the previous point—as opposed to the player who won the previous point, as is now done under the Standard Rule. This provides the loser of a previous point the opportunity to catch up, which makes the game more competitive and exciting to watch. But compared with the present Standard Rule, it neither helps nor hurts either player to win.

Their plan relies on both probability and game theory.

In the work, the researchers mathematically show that the Catch-Up Rule not only gives the same probability of winning as the Standard Rule in best-of series (for example, a best-of-15 series, wherein the first player to win 8 points is victorious), but it also ensures that the scores of the players remain close throughout the game: A win-win situation for both players and spectators.

“Unlike most service sports, table tennis and tennis have service rules that fix who serves and for how long,” the researchers say. “The tennis tiebreaker is fair in the sense of precluding a player from winning simply because he or she has had more serves than an opponent, whereas the table tennis tiebreaker favors the first server.”

In service sports such as tennis, volleyball, badminton, and squash, rules have changed over time, which suggests that the respective associations are open to innovation.

“We first discussed this with regard to our study on soccer penalty shootouts,” says Ismail, “and we realized that especially in soccer, FIFA has been traditionally conservative towards implementing more modern rules. We never even tried to contact them. But now that Marco Van Basten, who is reported to be progressive and open to innovation and new ideas, has been appointed as chief officer for technical development at FIFA, we hope the situation will change and FIFA will be more open to listening to our arguments.”