But how accurate is Hawk-Eye? A paper published in 2008 in a journal called Public Understanding of Science suggests that the way Hawk-Eye analyses are presented in sport may lead people to incorrectly assume that its output is definitely what happened. Hawk-Eye presents a great opportunity to discuss uncertainty, confidence intervals, and the joy of stats, so here’s a Monday morning maths class.
According to the article, Hawk-Eye works via a number of cameras that capture locations of the ball as it travels, and a model of the field of play. Cameras cannot record every moment of the ball’s flight, due to frame rate limitations, so between frames the trajectory of the ball must be estimated. With regards to cricket, where LBW calls are questioned, Hawk-Eye extrapolates beyond where the ball hits the pad, and predicts whether it would have hit the stumps or not.
A model’s ability to predict the future path of a ball depends on a number of factors. The further a ball travels before it stops, the easier it is to predict where it would have carried on to. Therefore Hawk-Eye is likely to be less accurate the further towards the batsman the ball bounces, and the further away the batsman is from his stumps. Though Hawk-Eye technology takes some uncertainties into account, its purpose is to give a binary outcome: “out” or “not-out”.
The article suggests that more information about that uncertainty should be reported to the television audience, to more honestly show the variation in the possible true paths of a ball. For example they suggest showing a ball’s predicted location, and the confidence intervals that surround it (if 95% this would mean there’s only a 5% chance the ball actually fell outside this larger area).
This would not only more accurately reflect the limitations of the technology, but it could potentially teach complex statistical concepts and principles to a huge number of people. Hawk-Eye could still provide a binary response to an umpire query, but the probability it is the true answer will also be clear to all.