The paper is published in the Proceedings of the Royal Society.

Brief Summary of the paper

I was interested in how line-call disputes arise – are disputes largely due to gamesmanship by players or lapses by judges, or is there genuine perceptual uncertainty?

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 challenges and errors relate to the actual position of the ball reported by Hawk-Eye.

What did I do?
I usually conduct research in the lab, studying how our perceptual abilities depend on the physical information available in the image. Watching tennis it occurred to me that Hawk-Eye data allow us to look at the possible causes of line call challenges and errors, because they give a record of actual ball position to compare against player and line judge reports. What is the cause of line call disputes?

I analysed the 1473 challenges that had been made in 15 ATP tournaments during 2006 and 2007.

What did I find?
Disputes and errors were very tightly clustered around balls bouncing very close to the 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. Challenges really do reflect perceptual uncertainty. About 40% of the disputed line calls were incorrect, so judges are correct more often than players in the disputed calls, but still do make errors.

Implications
A certain number of line call errors are inevitable, simply due to limitations in our ability to judge the positions of objects in 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, 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 it moves across the field of view faster, and there is greater uncertainty along the ball’s trajectory.

What is the explanation?
Ultimately performance 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 where we need to make very fine discriminations, the noise can tip the balance between one perceptual decision and another. We know a fair amount about this kind of neural ‘noise’. I developed a simple mathematical model of line-call decisions, incorporating in a small amount of noise, and found that it predicted challenges and errors very accurately.

This kind of neural noise is not normally so strong that it is actually perceived as an external event (unless one is looking at faint stars, for example), but it still influences the hidden processes that take place during our decision making.

Line judges are more precise, or less noisy, than players, perhaps a reflection of a better vantage point and a high degree of training. Errors are more prevalent for bounces near the base and service lines.

I have created a very simple Flash demonstration of the visual task faced by line judges and players when attempting to judge bounce position.