Monday, March 07, 2011

Noumpere - the UDRS

MSDhoni's rant of "whether it is 2.5m or 2.4 or 2.6" had the ICC throwing the rule book at him which had the BCCI solidly defending. The media and expert commentators have done hardly anything to dispel the confusion surrounding the technology. I do wish that Cricinfo had taken the lead to explain the rule book and clauses therein. Instead we have Grey is the colour of DRS. Everyone now knows that 2.5m is a criterion but how many talk of the associated 40cm sub-clause?

Elementary, my dear captain!
Let me make a layman attempt at explaining the rationale for the having numbers like 250 and 40 ...

After pitching the ball hits the pad after 40cm. The ball has to travel a further 250cm, another 6.25 times the distance that it has already travelled (2.9m from the point the ball pitches to the stumps). Hawkeye has 40cm in which to judge the trajectory of the ball and extrapolate it to 250cm! If there is an error of 0.5cm in determining the point of impact of the ball on the pad, then the error will also get multiplied by 6.25 times (about 3+cm - which is about the radius of the ball). If Hawkeye determines that the ball will hit leg stump, a provision of 3+cm error has to be made. So in reality the ball could be missing leg ... The umpire's original decision could stand. Whereas if it hits anywhere on the middle stump, despite the 3cm error it will hit the stumps almost surely ... Thus the DRS can be used to overrule umpire's decision in this case and rightly so. With this recent change, I'm glad that ICC has acknowledged the prowess of Hawkeye through this change, while the common man sees it as an admission of the failure of technology :-).

What happens if the ball hits the pad closer to the stumps?
If the ball hits the pad 60cm after pitching and there is a further 2.3m to go (2.9m from pitch to the stumps), then the error is multiplied only about 4 times. And Hawkeye has 60cm (50% more than 40cm) of video frames in which to determine/estimate the point of impact of the ball on the pad! The error would be less (say ~0.35cm) instead of the earlier 0.5cm ... The accuracy of Hawkeye's prediction in this case would increase drastically, wouldn't it?

2.4, 2.5, 2.6 does matter, doesn't it?

The geometry of the problem!
A bit of geometry illustrates the small margin of error that Hawkeye has got to play with ...
Consider the large triangle BCE.  BC=290cm, CE=11.5cm.  At point p1 on BC (Bp1=40), there is a line parallel to CE of length 'd', which cuts BE.  What is the length of 'd'? What would be 'd' at points p2 (30cm from B), p3 (50cm).  If instead of 'd' and error of 'e' is added at p1, CE would become longer by 3.5cm.  What value of 'e' would result in 3.5cm at CE?  Would the tolerance 'e' be higher at p1 or p2?

Thoughts on the technology front
There is unlikely to be a foolproof prediction mechanism, let's make best use of what we have!  In my view the makers of Hawkeye would be glad to put the 'confidence factor' on screen along with the trajectory displayed but would the experts/cricketers/arm-chair pundits be able to digest this?


Anonymous said...

You hav any link to the 40cm clause?

rb stumped said...

@srb, I first saw the 40cm clause in the defense by ICC, a week ago. The current articles elaborate the clauses a lot more.

mcenley said...

So, does the Hawk Eye take into account the bounce of the pitch or the part where the ball lands(seam or not) ?

I am very skeptical about the Hawk Eye. It doesn't even have the best position on cricket field to judge a LBW.

rb stumped said...

@mcenley (dz) I think that it would take the bounce and deviation into account. I think that the cameras positions should be known exactly (relative to the stumps). They have at least 4 cameras to do triangulation (?).

rb stumped said...

@mcenley maybe trilateration is the right word to use instead of triangulation?