# What is the Duckworth Lewis Method and how it is applied in cricket

Cricket is one of the popular games not only in India but also in many countries of the world. The sports amateur and fan of cricket wants to enjoy without any interruption, but a rain shower sometimes causes disruption. Hence, ICC introduces a rule, i.e. Duckworth-Lewis rules that help to get results in rain-affected limited over a match i.e. 50 over match and T20. Here, we are giving the detail description of the Duckworth-Lewis rules and how it is used in rain affect limited over match result.

Principles of Duckworth-Lewis-Stern Method

It was devised by two English statisticians, Frank Duckworth and Tony Lewis. After their retirements Professor Steven Stern became the custodian of the rule. So in November 2014, it was renamed as the Duckworth–Lewis–Stern method (or D/L/S method). The principles of the Duckworth Lewis method are revolving around mathematical calculation of resources through probability, permutation and combination. Hence, we can say resources are the only thing that determines the outputs.

How Duckworth-Lewis-Stern Method use in cricket

According to the Duckworth-Lewis-Stern Rule, each team two types of resources, i.e. number of overs they have and the number of wickets in their hand. So in any situation, the team's ability can be decided on the combination of these two resources. When cricket match is started, then both the team has same resources, but over the time the resources of one or both teams are depleted and the two teams usually have different amounts of resource for their innings. Once, the match is interrupted by weather or other circumstances, and then Duckworth-Lewis-Stern Method is applied.

After analysing the above list, it is clearly shown that if team have 50 overs and 10 wickets then the probability of making run will be 100 percent, but once team uses it over and the wicket gets lost then the probability of getting run will be decreased accordingly.

In the below three examples clear the understanding of the application of the Duckworth Lewis Stern Rule:

First Instance: If rain interrupted the second inning of team and rain stop the game before maturity.

Team A Score 250 in 40 overs after losing five wicket. Team A had less resource available than Team B so their target must be scaled down by the ratio of resources, 72.5/100 Team A scored 250, so Team B's 'target' is 250 x 72.5/100 = 181.25. Hence, the winner will be decided according to the extra run or shortage of run, which mean those teams have more run than the set target as per Duckworth-Lewis-Stern Method declared as the winners by 18 runs.

Second Instance: Rain interrupted in the second inning Team’s batting

 Team A's innings: At the start of 40 over innings resource percentage available 90.3% Team B's innings: resource % available at start of 40 over innings 90.3% After 30 overs Team B have 10 overs left and have lost 5 wickets.  From table, resource % left at start of suspension 27.5% 5 overs are lost, so when play is resumed 5 overs are left. From table, resource % left at resumption of play 16.4% Hence resource % lost = 27.5 - 16.4 11.1% so resource % available for Team B's innings = 90.3 - 11.1 79.2%

Team B had less resource available than Team A so their target must be scaled down by the ratio of resources, 79.2/90.3
Team A scored 300, so Team B's target is 300 x 79.2/90.3 =263.12, or 264 to win, and they require a further 36 runs from 5 overs with 5 wickets in hand.

Third Instance: If the rain affects the first inning

Assume that Team A score 200 runs in 40 overs after losing 7 wickets but rain interrupted the rest 10 over game. Then Team B get 40 Overs to play with new target. According to the Duckworth-Lewis-Stern method, Team A had only 17.9 % resources left. Therefore, Team A uses its resources 82.1 % of resources (100-17.9).

Team B have all the resources left but they get only 40 overs then as per D/L/S reference table and their resources will be 89.3 % which means they have 7.2 % extra resources that means they have 7.2 % more increment in their target.

As per ICC, 225 run is the average in 50 overs for ODIs then Team B have the target of 7.2 % of 200 + 235 i.e. 200 + 16.92 = 216.92 = 217 runs.

In the above description about Duckworth-Lewis-Stern method will enhance the knowledge of cricket and cricket lovers can itself analyse the term of condition when rain interrupted the cricket match in future.