24 July 2013

What is D/L Method in Cricket?

This Duckworth/Lewis Method (written as D/L Method) is considered as the most accurate method of calculating the target for team batted second, as the name indicates this Method is Invented by the two British Statisticians, Frank Duckworth and Tony Lewis in January 1997, This Method is about 16 year old but still many cricket fans dont know what this method Actually is? Today we will explain in detailed about this Method.

Match Stop due to Rain/Bad Light or Bad Weather are the top reasons, which becomes very common in todays Cricket, Due to which overs has been reduce for each team according to the amount of time, rain delayed the match, but the problem arises at this stage is that what will be the actual target for the team batted second, So the process of calculating the target Score for the team batting second in a limited overs match interrupted due to rain with some mathematical formulation is known as Duckworth / Lewis Method.

What is the Story of D/L Method?

This D/L Method is invented in 1997 but it's story Begins from 1992, When there was a clash between England and South Africa, in the 2nd Semi-Final, World Cup Match 1992, In this match overs has been reduced to 45 overs due to rain and England set a target of 252 for 6 in 45 Overs, In Reply South Africa were 231 for 6 in 42.5 Overs, but Rain stopped the play for the second time, They needed 22 runs in 13 balls which is very much possible for the Africans but according to the rule of that time "Highest Scoring Over Method", When the match started again after 12 minutes, They needed 21 Runs in 1 Ball, they hit this one ball for a single, Which becomes one of the most embarrassing moment for the Africans, They lost the match and England qualify for the final (and lost against Pakistan in the final Hurrah!!!).

How to Calculate the Target with "Highest Scoring Over Method"?

From the above story when the match interrupt for the second time then two more overs has been deducted from the South African's inning and according to the rule the target was calculated in such a way that we have to subtract the runs of those two overs in which England scored as much low runs and this two overs are the two Maiden overs bowled by South Africa, One of the Maiden over got one run extra so this one run is subtracted from the actual needed run (22-1) = 21 Runs and as we know Two overs are deducted So (45-2) = 43 overs and (43-42.5) = 1 balls left, That is how South Africa need 21 Runs in 1 balls which is totally a impossible task for them. These Rules gives Africans a shock of there life time in the world cup, 2nd Semi-final match 1992. At the end of this embarrassing match, A British Journalist and A Radio Commentator Christopher Martin said on a radio that "It's necessary that any person from any place should come in front and introduce a much better Solution for this type of match", with the thousand of people two British expert Tony Lewis and Frank Duckworth are also listening his words on the Radio.

How to Calculate the Target with "D/L Method"?

After Listening the words on the Radio two British Statisticians, Frank Duckworth and Tony Lewis come in front and invent the Mathematical function P(u,w) for calculating the target, According to them the amount of runs to be scored for each team depends on two resources, One is the amount of Overs left and Second is the amount of wickets in there hand and with the help of these two Resources they made a table for calculating the accurate target score, When the match stopped due rain then Resources has reduced from one or each team, The amount of Resources left for the team is calculated through the Table. Remember if the Target of above match is calculated through this D/L method then African's need 4 runs to tie and 5 Runs to Win in 1 balls, which is much better as compared as "highest scoring over method".
NOTE: This Method is Implemented only if the team batted for atleast 20 Overs in ODI and atleast 5 Overs in T20 Cricket.

According To The Table (Given At The Bottom):

Suppose a team Played for 20 Overs (In A 50 Overs Match) with the lost of 2 Wickets, Means they have 30 overs left and according to the table they have 68.2% Resources left, If the match reduces to 40 over due to rain, then it means 20 overs left means they have 54.0% Resources left. All it means the batting team have lost (68.2-54.0) = 14.2% it's Resources due to rain.

Example 1:

If the team batting first Score 250 runs in 50 Overs without any lost of wicket means they have 100% Resources, In Reply Team 2 were 200 for 5 in 40 Overs, When the match is Abandoned.

To calculate Result of the match through Table we should know two things one the amount of overs left and second the amount of wickets in hand, we know, 10 overs left and 5 wickets in hand, Means 27.5% Resources left at suspension of play for team 2, Then (100-27.5) = 72.5% total resources available till 40th over for Team 2, 27.5% less than Team 1 because when the match started Team 1 played 50 Overs with 100% Resources so the target must be scaled down by the ratio of resources, (72.5/100), Team 1 scored 250, so Team 2 'target' is 250 x 72.5/100 = 181.25 Runs needed, The winner is decided according to whether or not this target has been exceeded. with 200 runs on the board, They have exceeded their required target by 18.7 and declared the winners by 19 runs.

Example 2:

If the team batting first Score 200 runs in 40 Overs (10 Overs Deducted due to Rain) means they have 90.3% Resources available, In Reply Team 2 were 140 for 5 in 30 Overs with 10 over left, 5 more overs are lost due to rain from Team 2, What will be the target for Team 2?

To calculate Target for team 2 through table So we know 10 Overs Left and 5 wickets in hand Means 27.5% Resources left at the start of suspension for team 2, After Rain stopped the play 5 overs are lost, Resources left 16.4, Then (27.5-16.4)  = 11.1% Resources left for Team 2, So total resources available for team 2 is (90.3-11.1) = 79.2, 11.1% less than Team 1 because when the match started Team 1 played 40 Overs with 90.3% Resources so their target must be scaled down by the ratio of resources, 79.2/90.3, Team 1 scored 200, so Team 2's 'target' is 200*79.2/90.3 = 175.41 or 176 to win, and they require 36 runs from 5 overs with 5 wickets in hand.

Example 3:

If the team batting first Score 100 runs in 25 Overs (In a 50 Over Match) with the lost of 2 Wickets and Rain terminate the first inning, What will be the target for team 2 in 25 Overs.

To calculate Target for team 2 through table, We know 25 Overs Left and 2 wickets are lost, Means 61.8% resources left for team 1, They have had only (100-61.8) = 38.2% resources available for their innings. For Team 2 they have 25 overs and 10 wickets in hand, Means they have 68.7% resources available, which is (68.7-38.2) = 30.5% greater then team 1 because they lost 2 wickets and so they set a target which is 30.5% of 225, or 68.63, more runs than Team 1 scored. (225 is the average in 50 overs for ODIs), Team 2's target is 168.63, or 169 to win in 25 overs, and the advantage to Team 2 from knowing in advance of the reduction in their overs is neutralized.

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