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The Hawk-Eye, Ian Bell Controversy: an explanation of the 2.5 meter rule

March 31, 2011

Nishan de Mel in Sri Lanka

27 February 2011 saw one of the best games in the history of world cup cricket. It was the 11th game in the 2011 world cup series, pitting India against England in Kolkatta, Bengalaru, India. The toss was won by India, who chose to bat, and with a brilliant 120 by Sachin Tendulkar, went on to amass an imposing total of 338. At this time, the record for the highest successful run chase in world cup cricket was held by Sri Lanka who on February 23rd 1992 successfully chased Zimbabwe’s score of 312 to win in the second ball of the last over. Quite simply, history was on the side of India, and England’s chances seemed bleak.

The England chase began in a masterful manner. England’s captain Andrew Strauss (who went on to score 157 in 145 balls) was anchoring their innings. At the end of 24.5 overs England had scored 163 for the fall of just 2 wickets. Andrew Strauss was on 92. Ian Bell was on 17 and facing the last ball of Yuvraj Singh’s 3rd over. The ball was pitched on off stump. Ian Bell stretched out to attempt a sweep shot. He missed, and the ball struck his pads. There was a loud appeal for LBW. Umpire Billy Bowden said ‘not out’. The Indian captain called for a review of the decision by the third umpire.

The TV replays using the Hawk-Eye technology showed the ball pitching on off stump and going on to hit the middle stump. Commentators passed the verdict. Ian Bell started walking away. But the third umpire Rod Tucker did not over-rule Billy Bowden’s decision. The reason: the ball had struck the batsman’s pads more than 2.5 meters in front of the stumps.

Ex-skipper of the English team and now sports commentator Nasser Hussain roundly condemned the decision of the third umpire. “I don’t care whether it is 2.5 or 3.5 or 4.5 [meters], the ball was clearly going to hit the middle stump and he should have been given out,” said Hussain.

Ian Bell stayed on for 18 more overs, scoring 52 more runs, to reach 69 in 71 balls and leave England in a commanding position to win the game. A sudden batting collapse and a last minute recovery resulted in the match ending in a thrilling draw. But cricket fans all over the world will wonder if the decision with regard to Ian Bell was correct, and if the “not-out” decision on Ian Bell robbed India of the match.

Was it the right decision? India’s skipper M.S. Dhoni clearly thought it was not. “Adulteration of technology with human thinking is bad” he said, and insisted that if the Hawk-Eye says it’s going to hit the stumps, then there was no reason to turn down an appeal to the third umpire.

Cricketers, commentators and spectators could all benefit from a simple explanation of why a 2.5M rule might have been used to disregard the results of Hawk Eye in favour of the field umpire’s decision. This is that explanation.

Hawkeye is a technology that reconstructs the probabilistic path of the ball beyond where it stopped – in this case on Ian Bell’s pads. However, the probabilistic reconstruction of the travel path of a cricket ball is not an exact science. Because of the limitation in data that can be gathered from the camera’s any predictions always contain some margin of error. The TV replays keep it simple by not showing us the alternate paths that the ball could take with varying degrees of probabilities apart from the most probable path predicted on the basis of information gathered. The effects of the turf where the ball bounces, the short duration between bouncing and hitting the pads can further reduce the quality of information used in the predictive process.

The height of the cricket stumps is 28 inches. They are planted to span a width of 9 inches. Therefore, a ball shown as hitting middle stump (as in this case), if predicted just 4.5 inches off-course in either direction, could well be missing the stumps all-together. The figure below drawn to scale is instructive of the predictive challenge. A simple question to ask is this: from 2.5 meters away at what error margin (of the trajectory angle) would the actual point of contact vary from the predicted point by 4.5 inches. It’s a straightforward trigonometric calculation and the answer is an angle of 2.62 degrees.

Figure: Birds eye-view of the wicket drawn to scale, with stumps on the left, and the ball trajectory predicted from 2.5 meters away. The blue dotted line is the paths predicted as most probable. The red dotted lines are alternate probable paths.

The problem is the distance from the stumps being great relative to the width of the wicket. From a distance of 2.5 meters a 2.62 degree angle error can exaggerate itself to a 4.5 inch error in the position of the ball. (you can test it yourself by going to a website that will calculate for you: http://www.csgnetwork.com/righttricalc.html just remember that you need to input everything in the same units, and that 1 inch = 2.54 centimeters).

The conclusion of the matter: A predicting error of less than 3 degrees, from the point of hitting the pad 2.5 meters in front of the wicket, could change the Hawk-Eye prediction on whether or not the ball hits the stumps.

How large or small is an angle of 3 degrees? To picture it, imagine a round cake. If you can cut the cake into 120 pieces the angle of each slice at the middle is 3 degrees. It is an angle so small that it would take great skill to cut a piece of cake so thin – I’ve not seen anyone attempt 120 pieces from a round cake.

Technology is important and has been usefully engaged in sports to reduce errors caused by human fallibility. But technology is not infallible, and complex predictive mechanisms such as Hawk-Eye have significant possibility for error. Much has been written on the fallibility of Hawk-Eye’s prediction errors and perhaps most notably by Collins and Evans, 2008, in Public Understanding of Science (volume 17, no. 3), in an article titled “You Cannot Be Serious! Public understanding of technology with special reference to ‘Hawk-Eye’”. With the new decision review rules in operation being a keen spectator of cricket today requires some understanding of predictive technology and its limits

A very small error (less than 3 degrees in angle) in the Hawk-Eye mechanism could render its predictions from 2.5 meters away quite unreliable. Under the circumstances, the decision not to use Hawk-Eye to over-rule the field umpires deserves more respect than it is getting by commentators and cricketers dominating the airways.

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