Saturday, March 6, 2010

DUCKWORTH - LEWIS

New Zealand 43 / 3 in 8.4 overs. The heavens open up. Mr. Duckworth and Mr. Lewis are invited to use their mathematics.

Before rain: 231 runs required from 248 balls at 5.59 runs per over.
After rain: 223 runs required from 218 balls at 6.14 runs per over.

The required run rate went up by 0.55 runs per over AND the Kiwis were denied the use of 12 Powerplay balls. Why? Just because the Aussies had managed to grab 3 wickets before the heavens opened up.

Vettori aptly said it: "There are a lot of things I don't understand about cricket, and that (D/L Method) is one of them. To lose two Powerplay overs and only have eight runs taken off, I don't know how that works. It makes things incredibly tough. It would have been better had the game gone the full 50 overs, it would have been a lot better for us."

So I decided to do a bit of research about this D/L Method. Using the official D/L Website, and the tables provided there, I found that I manually calculated the revised target at 265, which was 1 less than the actual target for the Kiwis today. So I made assumed that my calculations are sufficiently accurate, and I can proceed with my research. Here are my computations.

After 8.4 overs, having scored 43, had New Zealand lost fewer wickets, they would have had the following targets:
2 wickets down - Target 262.
1 wicket down - Target 259.
0 wickets down - Target 256.

So, here you go. Even if New Zealand had lost no wicket at the time of interruption, the target would have reduced by just 18 runs in 30 balls. The logic behind putting the 2nd Batting team in a numerically disadvantageous position is sound. In simple terms, the team batting 2nd has a target ahead and can pace the innings accordingly. The team batting 1st did not have any idea that there might be interruption in play later and therefore, their lack of such knowledge need to be compensated numerically.

However, such a reduction in target did not compensate New Zealand for their loss of 2 Powerplay overs. And that is where Daniel Vettori has a problem.

There are many issues that Duckworth Lewis method fails to consider:

1. In some cases, both the teams are aware that there might be an interruption in play later in the game, given the overhead conditions. In such a case, is there a need to compensate the team batting 1st?

There might be a case for using the weather forecasts and percentage chances of rain as numerical variables in calculations.

2. The method of dealing with the Powerplay overs also remains a concern, especially now when there is a Batting Powerplay and a Bowling Powerplay. There is also an added factor of only 2 fielders allowed outside the circle in the first 10 overs and 3 allowed in the other 2 Powerplays. As if this was not enough, we also have a rule of 2 compulsary catchers required in the first 10 overs.

If we assume that the catchers are used to take wickets (in normal cricket, they are!), then we might have to consider the number of wickets that could have gone down in the overs lost from the compulsary first 10-overs Powerplay.

There are various other factors that cannot be stated numerically, so I'll just count them: Pitch, Slower outfield after rain, Length of boundaries, Ball change after 34 overs, et cetera. You can help me with more of such shortcomings of the D/L Method.

I agree that all factors cannot be considered in setting revised targets. There will always be shortcomings, be it in the Duckworth-Lewis Method or the Jayadevan's Method (adopted by ICL in their competition). However, some of these concerns can be addressed because they can be quantified. And once we have some numbers, mathematicians simply love playing with them.

I do not have the intelligence of Mr. Frank Duckworth or Mr. Tony Lewis, both mathematicians par excellence. But I do believe that with their brains, they can address the concerns faced by a lot of cricket followers like me and indeed, captains like Dan.

1 comment:

Christopher Poshin David said...

I want to see a better method in play. But the question is what other method?

SAVE OUR TIGER!