In a paper published in the Proceedings of the Royal Society in 2008, I reported the results of some research on the psychophysics of line calls in professional tennis tournaments. I was interested in how line-call disputes arise. Are disputes largely due to gamesmanship by players, or lapses by judges, or genuine perceptual uncertainty about the location of the ball?
Line-call disputes are now resolved in many tournaments using the "Hawk-Eye" ball tracking system, which is claimed to locate the actual 3-D position of the ball to within a few millimetres. I analysed how line-call challenges and errors relate to the actual position of the ball as reported by Hawk-Eye. Psychophysical research is usually conducted in a laboratory, to investigate how our perceptual abilities depend on the physical information available in the image. Data collected by Hawk-Eye during tournaments can be viewed as psychophysical data relating the perceptual decisions of players and umpires to the physical information available in the court. This data allows us to look at the possible causes of line call challenges and errors.
The Royal Society paper analysed the 1473 challenges that had been made in 15 ATP tournaments during 2006 and 2007 (using records kindly provided by the ATP). Disputes and errors were very tightly clustered around balls bouncing very close to a court line. 95% or 19 out of every 20 challenges occurred when the ball bounced within 10 cm (4 inches) of a court line, with over half the challenges occurring for balls bouncing less that 2.25 cm (1 inch) from the line. Such a tight dependency on locations close to court lines indicates that challenges really do reflect perceptual uncertainty. About 40% of the disputed line calls were incorrect, so line judges are correct more often than players in the disputed calls, but still do make errors.
A certain number of line call errors are inevitable, simply due to limitations in our ability to judge the exact positions of the objects within our view, so it is right that players have an opportunity to challenge, and they should make careful use of these opportunities. On the other hand, line judge errors are relatively infrequent, so it seems fair to limit the number of unsuccessful challenges available. Judgements are more difficult for balls bouncing near base and service lines than for balls bouncing near side lines, probably because the ball moves across the field of view faster, and there is greater uncertainty along the ball's trajectory.
The paper concludes that ultimately the performance of players and umpires is limited by a form of noise. We are all familiar with background noise intruding on radio reception, producing hiss or crackle, and producing snow speckles on TV pictures. The brain is also an electrical system, though a hugely sophisticated one, with tiny signals travelling between masses of brain cells. A very small amount of background noise in these signals normally has no noticeable perceptual effect, but in extreme situations when we need to make very fine discriminations, the noise can tip the balance between one perceptual decision and another. A fair amount is known about this kind of neural 'noise', which is not normally so strong that it is actually perceived as an external event (unless one is looking at faint stars, for example). However neural noise still influences the hidden processes that take place during our decision making. I developed a simple mathematical model of line-call decisions, incorporating a small amount of noise, and found that it predicted challenges and errors very accurately.
Line judges are more precise, or less noisy, than players, perhaps reflecting their better vantage point and high degree of training at making these decisions. I have created a very simple demonstration of the visual task faced by line judges and players when attempting to judge bounce position. The demonstration is available in the Flash version of this page.
See:
Mather G (2008) Perceptual uncertainty and line-call challenges in professional tennis. Proceedings of the Royal Society Series B, 275, 1645-1651. PDF