I have been following cricket passionately over many years.There have been many matches where there have been stoppages due to rain and suddenly,magically we get to know what is the new total that is to be chased by the team.Out of curiousity,I researched how this method actually works and here is the result…
The D/L method was devised by two English statisticians, Frank Duckworth and Tony Lewis. It was first used in international cricket in the second game of the 1996/7 Zimbabwe versus England One Day International series, which Zimbabwe won by 7 runs and was formally adopted by the International Cricket Council in 2001 as the standard method of calculating target scores in rain shortened one-day matches.The D/L method works using the notion that teams have two resources with which to make as many runs as they can
1. The number of overs to play
2. Number of wickets in hand.
A table, based on the scores of the past ODI’s, which gives the percentage of resources that are available to a team at the end of every bowl and every wicket has been made. Its like a log table
Case 1
India has scored 250 runs in 50 overs. Australia has lost 7 wickets in 40 overs scoring 180(yeah, in my dreams). Now rain God shows mercy on Australians and the match is not played further. Lets see who is the winner.
Did India have any interruptions while batting? No. So the resource at its disposal was 100%.
When Australia started batting, it had complete resources. 100%
After 40 overs and 7 wickets down, the resources left with Australia = 20.6 %(Acc to the Table)
Now since, no play is possible further, can Australia use this remaining resource? No.
So Australia used 100 – 20.6 = 79.4% of its resources.
Now lets see how much India would have scored with 79.4% resources available.
Plain and simple mathematics, isn’t it?
250 * (79.4/100) = 198.50 which is rounded off to 198 and Australia needed 199 to win.
But how much did they score? 180. So India wins the match.Now let me state the rule corresponding to this example.
Note the resource % team had at the start of the innings. (Here both India and Australia had 100%)
Using the table calculate the resource % lost due to each interruption. (Australia lost 20.6 %)
Calculate the resource percentage available (Australia had 79.4% available)
Reset the target set by the first team using the %resource available to the second team.
With 100% resource India scored 250.
With 79.4%, it would have scored 250 *79.4 /100 = 198.50
The previous case is applicable when the team batting first is not interrupted at all.
Case 2
India is playing first and the match is already made a 40 overs match due to rains.
Lets say India scores 200 runs. (With what % of resources? 90.3%. right?)
Australia scores 150 runs in 30 overs and has lost 5 wickets. The play is interrupted again. Now only 5 overs are remaining.
After 30 overs, Australia is 150/5.
How much are the resources left? 5 wickets in hand and 10 overs = 27.5%
Now 5 overs are lost due to rain. And only 5 overs are remaining. So with 5 wickets in hands and 5 overs remaining, how much Australia has? 16.4%
Clearly Australia has lost 27.5% - 16.4% = 11.1% due to rain.
So the Resource available to Australia is 90.3% - 11.1% = 79.2%
Now reset the target set by India considering they played with 79.2% resources.
200 * 79.2/90.3 = 175.42. So India’s score is 175 and Australia needs 26 more runs in 5 overs to win the match.Lets formulate the rule now.
If team 2 has less resources than team 1(Australia had 79.2% available to India’s 90.3%),
Calculate the ratio of the resources available to the two teams. Reset the Team 1’s score using this ratio.Simple right?
This rule is applicable when the rain has affected the number of overs in a match before the match started. And then again when the team batting second is batting.
Case 3
India is batting first and the score is 200/7 at the end of 40 overs when Rain halts the play. Now there is sufficient rain to make the match a 40 overs affair. Clearly Australia cant be asked to score 201 in 40 overs since that would be disadvantage to India which went into play thinking it has to play 50 overs. Had it known it has to play 40 overs, it would have started hitting at the end of 33 over or so. Right?
So we need to reset the target for Australia.
India has lost 7 wickets and 10 overs. So it has lost 20.6% of the resources due to the rains.They started with 100% resources. But they have used only 100% - 20.6% = 79.4%.Now Australia will start with 90.3% since it has lost 10 overs. The difference between the resources available to Australia and India is 90.3% - 79.4% = 10.9%
So Australia had to be set a target of 200 + 10.9% of 200. Right? Not quite. From the statistics gathered over a period of time. The average score in a 50 full overs match has been found out to be 225.
So the reset score is 200 + 10.9% of 225 = 200 + 24.53 = 224.53 or 224
So Australia would need 225 runs to win. (This 225 has nothing to do with the 225 used to calculate the additional runs required.)
Let us set the rule for this also.
If team 2 has more resources than team 1, find out the excess resource. (Australia had 90.3% to India’s 79.4%)
Add the excess as a % of 225(average runs scored in 50 overs) and add those to the total of Team 1.(10.9% of 225 is 24.53 and 24.53 + India’s score of 200 = 224.53)
This rule is applicable when the team batting first starts with 100% resources but the game is shortened due to rains. And team 1 has less over than expected.
(Source-Cricinfo.com,Cricbuzz.com)
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