Novak Djokovic losing his cool over a line call, late in the second set, may have been a pivotal point of Andy Murray's historic Wimbledon victory yesterday. He believed a ball was out, but had run out of Hawk-Eye challenges so couldn't formally dispute the call. The BBC coverage showed Hawk-Eye's analysis of the point in question. Even if Djokovic could have challenged it, he was wrong: the ball was good.

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.

Statistics can be tricky to understand. They're necessary in a lot of science because when testing hypotheses or ideas, you usually can't test everyone and everything. You take what you hope is a representative sample, and statistics allow us to make predictions about the underlying population. They allow for chance differences between the sample and the population, so they necessarily involve some uncertainty.

All well and good, but what has this got to do with tennis? I'm sure some people will have clicked on this article purely because it'll have a tennis-related photo and headline, but that's part of the argument. The Hawk-Eye paper suggests that although stats are tricky to understand (and it should be pointed out that scientists can fall foul of misunderstanding or misinterpreting them too), it's easier to understand uncertainty when there's a burning interest in being able to do so. And who has more of a burning interest in Hawk-Eye's output than the sports fans who see it being used to determine the outcomes of major sporting events?

I know I've shouted "REF! YOU CANNOT BE SERIOUS?!" at the TV watching England play football (my team, Wycombe Wanderers, are rarely onscreen sadly). Television replays are used by umpires in rugby matches to assess on-pitch events that were obscured from or missed by them as they happened. Cricket and tennis use a different system, Hawk-Eye or similar technology, which predicts either where the ball landed, or the path a ball would have taken.

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.

In tennis, there are differences to cricket that both aid and hinder Hawk-Eye's accuracy. Line calls are often disputed by players, particularly in serves. This is good for using Hawk-Eye, as the ball has actually travelled to the position where the call needs to be made (and usually beyond), so extrapolation beyond the ball's stopping point is not needed.

But tennis balls travel extremely fast (the fastest server at Wimbledon this year was Murray's semi-final opponent Janowicz, whose serve has clocked 143 miles per hour). A faster ball travels further between each frame on a camera film, meaning more uncertainty as to its trajectory between frames.

Hawk-Eye is almost certainly going to be correct more often than a human lines-person, but it can't be perfect, and indeed the makers only claim it is accurate to 5mm (that was in 2008 – it may be more accurate now with the development of faster frame rate cameras). There have been a couple of high profile cases where Hawk-Eye appears to have got it wrong in tennis, most notably in 2007 when Nadal could identify a mark on the court where he claimed the ball landed (out) that Hawk-Eye reported was good.

If Hawk-Eye could provide a measure of uncertainty around its prediction, it wouldn't make its decision any more controversial, argues the article. The results could aid the umpire, even if the margin of error for the technology is reported and explained. They suggest the use of bails in cricket as another aid to turning the often quick and hard-to-observe live game into a binary "in" versus "out" decision. For example, a ball could roll slowly and hit the stumps, but not dislodge the bails, and this would be just "the luck of the game". A close call on Hawk-Eye, which is likely to be more accurate than a human observer but not completely infallible, is a similar enhancement to an umpire's decision making.

The paper concludes that Hawk-Eye should be used as an aid to human judgement (their italics), and that, if used with a little more nuance, it could provide added enjoyment of the games involved and public understanding of technology, its uses and its limitations. What do you think? Do you want a simple binary decision in your sports, or would you rather know the accuracy of Hawk-Eye's output?