Duckworth-Lewis Method (part 2)

(For an introduction of Duckworth-Lewis method visit the part 1)

Below, are two examples given for the betterment in understanding the Duckworth-Lewis method used in different scenarios.A sample of reduced D/L table is given below.

	Wickets lost
Overs left	0	2	5	7	9
50	100.0	83.8	49.5	26.5	7.6
40	90.3	77.6	48.3	26.4	7.6
30	77.1	68.2	45.7	26.2	7.6
25	68.7	61.8	43.4	25.9	7.6
20	58.9	54.0	40.0	25.2	7.6
10	34.1	32.5	27.5	20.6	7.5
5	18.4	17.9	16.4	14.0	7.0

Ex. 01: Team A scored 263 runs within their allotted 50 overs and the match was interrupted when team B had scored 132 for the loss of 2 wickets in 30 overs.

Case1: If match is not resumed.

The percentage of resources lost by Team B = 54% (wickets = 2 and overs left = 20)

The percentage of resources available to Team B = 100-54 = 46%

The percentage of Team A’s resources = 100% (no interruptions occurred during 1st innings) Revised target for 30 overs = 263*46/100 = 120.98

Since Team B has scored 132, they will be declared as the winners.

Case 2: If match is reduced to a 40 overs.

The percentage of resources at the time of interruption for Team B = 54%

The percentage of resources when match resumed (10 overs left, 2 wickets down) = 32.5% Percentage loss of resources for Team B = 54-32.5 = 21.5%

The percentage of resources available to Team B=100-21.5=78.5%

Revised target in 40 overs = 263*78.5/100 = 206.45 = 207(to win)

Ex2: Team A scored 132/2 in 30 overs and the match was interrupted. The match resumed as a 30 over match.

The percentage of resources at the time of interruption for Team A = 54%

The percentage of resources used by Team A = 100-54 = 46%

The percentage of resources available for Team B = 77.1% (30 overs 10 wickets)

Since Team 2 has more resources, their “revised target” must be raised upwards. The G50 value comes into play at this moment. The additional number of runs that has to be added to the target is calculated as a percentage of G50 value with respect to the additional resource percentage available for Team B.

The additional resource percentage available for team B = 77.1-46 = 31.1%

Additional runs that should be added to the target = 225*31.1/100 = 69.975 = 70 (225 is the G50 value)
Therefore Team B should score 202 runs to win the game within 30 overs.

So this shows how simple D/L method is used during matches.The professional version of this D/L method is used in ODI's.

The Duckworth-Lewis Method (part 1)

History

Though they may not have played cricket at international or first class level, they were surely the match winners in more than 80 One Day Internationals (ODI) including a world cup final. They were neither umpires nor match referees as well. Though many won’t realize the relationship between mathematics and cricket, they both strived to describe the gentlemen’s game in a very simple yet realistic mathematical sense. Over the past few years they have become the most influential duo in limited overs cricket. They both are none other than Frank Duckworth and Tony Lewis, the statisticians who introduced the “Duckworth Lewis Method” more popularly known as The D/L method within the realm of cricket and among cricket enthusiasts.
The D/L method was successfully experimented within the year of 1997 by the International Cricket Council (ICC), the ECB (England & Wales Cricket Board) and the Zimbabwe Cricket Union (ZCU). It was first used in international cricket during the second game of the 1996/1997 Zimbabwe versus England One Day International, in which Zimbabwe won by 7 runs. Having seen its potential, the D/L method was formally adopted in 2001 by the ICC and henceforth was the standard method to calculate target scores for rain interrupted one-day matches.

Basis

Unlike previous methods used for rain affected games, The D/L method considers both the number of wickets lost and overs remaining. The said two are considered as the available resources for a particular team. A table is formulated capturing most of the variations pertaining to one-day cricket encounters based on the outcomes of a detailed analysis on hundreds of match data. Based on the depth of the mathematics used, The D/L method was split into a Professional and Standard Edition. The Standard Edition preserves the use of a single table and the adaptation of simple calculations (suitable for any one-day cricket match at any level), where else The Professional Edition utilizes a statistical modeling that is substantially sophisticated and requires the use of powerful computing. The Professional Edition had been put into use for all One Day International matches since early 2004.
This article is based on the standard edition of The D/L method. One major consideration in this Edition is the use of the G50 value which is defined as the average score obtainable in a 50 overs match. Normally, this value is taken as 225, but The D/L method states that a freedom to choose any other value is viable given that all parties involved are aware of that change from the very beginning. This greatly exemplifies the flexibility of The D/L method.

	Wickets lost
Overs left	0	2	5	7	9
50	100.0	83.8	49.5	26.5	7.6
40	90.3	77.6	48.3	26.4	7.6
30	77.1	68.2	45.7	26.2	7.6
25	68.7	61.8	43.4	25.9	7.6
20	58.9	54.0	40.0	25.2	7.6
10	34.1	32.5	27.5	20.6	7.5
5	18.4	17.9	16.4	14.0	7.0

A sample of a reduced D/L table is shown here. The resource percentage (that is, the No. of wickets and overs remaining) is indicated as shown. At the very commencement of an innings, each team has 100% of its resources available (that is, 50 overs and 10 wickets in hand). If at the end of 30 overs a team is at a loss of 5 wickets, its available resources reduces to a frail 40% percent.

Usage

The following procedure is used to recalculate a target score when an interruption occurs.
1. For the innings of each team.
(a) Note the initial resource percentage from the table (that is, at the start of an innings).
(b) Using the table, calculate the resource percentage lost due to each interruption.
(c) Henceforth determine the available resource percentage.

2. If Team 2 has fewer resources available than Team 1, the ratio of the available resources for the two teams is calculated and Team 2's “revised target” is obtained by scaling down Team 1's score by this ratio.

3. If Team 2 has more resources available than Team 1, the amount by which Team 2's resource percentage exceeds Team 1's is calculated and this excess is worked out as a percentage of The G50 value to determine the extra runs required to add on to Team 1's score to give Team 2's “revised target”.
(some examples will be calculated in the next post)