Why Was It Giving Wonky Targets In Twenty20 Matches.......

[Yuva Nataratna]

[color=#333333][font=Tahoma][size=3]On May 3, 2010, there were two curious applications of the Duckworth-Lewis method in the ICC World Twenty20. [url="http://www.espncricinfo.com/world-twenty20-2010/engine/match/412685.html"]West Indies defeated England[/url] even though they only scored 60 for 2 in 6 six overs in reply to England's 191 for 5, and [url="http://www.espncricinfo.com/world-twenty20-2010/engine/match/412686.html"]Sri Lanka came perilously close to being eliminated[/url] because Zimbabwe were only required to score 44 in five overs to defeat Sri Lanka's 173 for 7.[/size][/font][/color]
[color=#333333][font=Tahoma][size=3]There was outrage at the D/L targets and also surprise. The D/L method is now proven in 50-over matches, so why was it giving wonky targets in Twenty20 matches? Clearly it was because the ICC was trying to fit a model designed for 50-over matches to 20-over games. The fit wasn't working. The trousers were too big.[/size][/font][/color]

The D/L method is well explained in the graph.When the team chasing begins its innings, it is like an ant sitting at the top left corner of the graph. There are 50 overs remaining and the "combined resource" available is the full 100%.
There are 10 curves in the graph, corresponding, to the number of wickets remaining. At the start of the innings our ant is at the topmost point of the top curve, corresponding to "10 wickets remaining". After every ball is bowled, the ant moves a step to the right along the curve. If a wicket falls, the ant drops vertically to the curve below.
Now, suppose 20 overs have been bowled and two wickets have been lost. The ant will be in line with "30 overs remaining", and on the green curve, corresponding to "8 wickets remaining". A visual guess suggests that about 65% of the combined resource is still available. If, instead, five wickets are down at this stage, the ant would be on the orange curve and the combined resource would only be 45%.
Finally, imagine that 20 overs are lost at this stage due to rain. What would our ant do? Well, it would simply trot down the green (or orange) curve and stop at the point corresponding to 10 overs remaining. The combined resource now available would be about 30% for the green line and about 25% for the orange line.
So at every stage of the match we know exactly how much of the combined resource percentage is still available. Let's call this R2. And let R1 be the combined resource that was available to the team batting first (would be 100% if the 50 overs are completed or all 10 wickets are lost). Let S be the score of the team batting first. The D/L target and the par score are then calculated by playing around with R1, R2 and S.

[img]http://www.espncricinfo.com/db/PICTURES/CMS/117200/117268.jpg[/img]

[Yuva Nataratna]