# How does Duckworth-Lewis-stern method work?

Duckworth Lewis Method: Cricket is currently among the most popular sports in the world after football and the Rugby World Cup. The enjoyment of the game is affected when rain interrupts the game. In such a condition, the Duckworth-Lewis method is used. Let’s read in detail how this method decides the winner of the match.

• The Duckworth-Lewis-Stern or DLS method has been implemented several times in cricket. The most recent instance where DLS was employed to determine a rationalized score in a major cricket game occurred during the IPL 2023 final between Chennai Super Kings and Gujarat Titans.
• Rain interrupted the match just after CSK’s chase innings, causing a delay of more than two hours. However, the DLS method was used to formulate a new score.
• GT made 214/4 in 20 overs batting first.
• CSK were given a target of 171 to chase in 15 overs. The powerplay was reduced to 4 overs and each player could bowl a maximum of 3 overs.

Inventor of the Duckworth Lewis method;

The method is the invention of statistician Frank Duckworth and Tony Lewis. Because of the name of these two guys, this method is popular as Duckworth Lewis method.

First use of the Duckworth Lewis method;

In international cricket, this method was first used in 1996-97 between a match between Zimbabwe and England. This method was approved by the ICC in 1999.

Duckworth Lewis Method: How can you use this method?

Depending on the method, there are two types of resources available with each computer.

These two resources are;

1. Remaining

2. Remaining windows

These two resources are used at every moment of the game.

Based on these two resources, Frank Duckworth and Tony Lewis have prepared a table that suggests how many resources are left with the batting side in different situations.

 lost windows Overs remaining 0 2 5 7 9 fifty 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 twenty 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

Looking at this graph, it is clear that when a team has 50 overs and 10 wickets completed before the start of the game; It can be said that the team owns 100 percent of the resources.

After this, as soon as the team uses its overs and wickets, the team’s resources decrease as the game progresses.

If a team played 20 overs and lost 2 wickets in the match, it means that the team is left with only 30 overs and 8 wickets in hand. In Duckworh-Lewis parlance, the team has just 67.3 percent of resources left.

Now suppose rain comes at this point and the match time of 10 overs disappears, it means the batting side is left with only 20 overs and has already lost two wickets; So according to the Duckworth-Lewis method, the batting team holds only 52.4% of the resources in their hands.

See the following table;

Thus, the rain took away 67.3 – 52.4 = 14.9 resources from the batting side.

As we mentioned earlier, the team (batting first) had used 100% of their resources, but the resources available to the team (batting second) are only 100 – 14.9 = 85.10 resources.

In other words, it can be said that 14.9% of the second team’s resources have vanished in the rain.

But so far this explanation seems biased because the first team has utilized 100% while the second team or second batting team only has 85.10 resources. So to ensure fair play, both teams must have equal resources. In this condition, the Duckworth Lewis method will reduce the target set by the first batting team.

The Duckworth Lewis method says that if rain affects the second team’s entry, then the goal should be modified. Hence, the objective set by the first team will be reduced.

And if the rain affects the team that bats first, then their target will increase, which means this team will have to chase more runs.

Let’s see all this through an example:

Example 1:

If rain affects the team that bats later or plays the second innings then:-

Suppose the first team scored 300 runs in 50 overs and the second team scored 250/4 in 40 overs. After this, the match could not be played and the Duckworth Lewis method will be applied to find the winner of said match.

The first team played the full 50 overs, meaning the team used 100 per cent of its resources. The second team also had 100 percent resources at the start of the inning but could not use them due to the rain. After 40 overs, the second team has 10 overs and 6 wickets in hand.

According to Duckworth Lewis’ graph, in this situation the second batting team is left with 26.1 percent resources. Now suppose that from this moment on the match is abandoned.

Now there is a difference in the resources available to both teams. As we know, the first team has used 100% of its resources, while the second team has used only 100-26.1= 73.9%.

Now the winner of the match will be decided on the basis of equal distribution of resources for both teams.

Since the second team got less resources compared to the first team, the target for the second team should be lowered.

Since the first team scored 300 runs, the target for the second team will be 300 x 73.9 / 100 = 221.7

So according to the rules, the second team needs to score 222 runs to win the match, but they already scored 250 runs.

Therefore, the second team will be declared the winner by 250 – 222 = 28 runs.

We hope that from the above discussion you have a clear idea of ​​how the Duckworth-Lewis method applied in the rain affected the match.

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Categories: Optical Illusion
Source: sef.edu.vn