Chair Umpire Line Calls: What Should Roger Federer Do?

From Reports


When asked what he thought about allowing professional tennis players to challenge – via a video replay system – umpire line calls, Roger Federer, holder of a record 17 Grand Slam titles including this year’s Wimbledon, famously once said, “I have a very strong opinion. I’m absolutely against it. I’m against the challenge system.”

What would Federer – or any other professional tennis player for that matter – say if scientific analysis demonstrated that optimal decision-making in regards to replay challenges could improve a player’s chances of winning by nearly 10 percent in an otherwise even five-set Grand Slam match? Would players start spending as much time studying data-based decision-making (i.e., operational research and analytics) as they do practicing their serve? Probably not, but with the US Open upon us, the issue is certainly worth investigating, especially when, as in the case of all Grand Slams, hundreds of thousands of dollars are potentially at stake.

Using replay technology to assist officials’ decisions at sporting events is neither new nor unique. The National Football League, for example, has used video “instant replay” since 1986 to determine the outcome of certain controversial plays. Many other sports such as cricket and rugby have also resorted to videotape replays to review – and sometimes overturn – critical umpires’ decisions.

In the case of professional tennis at the Grand Slam level, players on certain monitored courts theoretically have the opportunity to challenge every point via video replay, but in order to keep the match from becoming bogged down in a series of time-consuming disputes, each player is limited to three challenges per set (unless a challenge is upheld, in which case the challenger retains his or her existing number of challenges).

Thus, the question Federer and other contestants in pro tennis face is: With a limited number of challenges, when should I challenge a line call if I want to optimize my chances of winning not just the point, but the set and ultimately the match?

College professors S.R. Clarke of the Swinburne University of Technology, Victoria, Australia, and J.M. Norman of Sheffield University Management School, Sheffield, U.K., explore the question in a research paper titled “Optimal challenges in tennis” forthcoming in the prestigious Journal of the Operational Research Society (JORS). After studying challenge outcomes from past Wimbledon tournaments and various other data sources and using dynamic programming (a computerized method of solving complex mathematical problems by breaking them down into simpler sub-problems) to analyze the results, Clarke and Norman report that an “optimal challenge strategy can increase a player’s chance of winning an otherwise even five-set match to 59 percent.”

Professional tennis players are notoriously bad in their decision-making regarding replay challenges. At this year’s Wimbledon, for example, only about 27 percent of players’ challenges were successful. The numbers are skewed because sometimes a player will make a challenge out of frustration rather than a perceived certainty that the ball is in or out, and sometimes a player has three challenges left that will likely go unused and simply wants to catch his breath while a challenge is reviewed. But clearly, “reactionary” decisions are not optimal.

So the question remains: In a tight, even match (men play best of five sets in Grand Slams, women play best of three) where every challenge is precious and perhaps critical to the outcome, what is the optimal challenge strategy? After crunching the numbers, Clarke and Norman conclude in their scientific paper that players should conserve their challenges for the “important points” that generally occur in the latter stages of games (30-30, 30-40, deuce) and sets, and when their opponent is ahead.

Federer and friends probably never heard of operational research, but they would be wise to read Clarke and Norman’s paper. It just might make the difference between winning and losing their next tough-five setter.

To read more about Roger Federer, get the book ROGER FEDERER: QUEST FOR PERFECTION at


Full details about the article

Optimal Challenges in Tennis

SR Clarke and JM Norman

Journal of the Operational Research Society advance online publication 14 March 2012; doi: 10.1057/jors.2011.147

About JORS and ORS
The Journal of the Operational Research Society (JORS) is the flagship, peer-reviewed journal of the OR Society, the world’s oldest scientific organization dedicated to the operational research profession. Founded in the United Kingdom in 1948, the OR Society includes about 2,500 members from more than 50 countries. For more information, visit 

About Palgrave Macmillan

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