# Duckworth Lewis Calculator

This Duckworth Lewis calculator will help you decide which cricket team (but not a chirping cricket ๐) won the match, or you can use it to set a target for the second team if the game is interrupted by the rain.

This calculation is not as simple as you might think, as it's affected by human nature. We use an algorithm called the Duckworth Lewis method to take into account how aggressive the teams will play, depending on the resources available to them. We will explain **how the Duckworth Lewis method works**, based on when in play the interruption happens.

You'll find a full set of instructions and some examples of ways of how the calculator works, so there's no need to be confused by the Duckworth Lewis method anymore.

## What problem does the Duckworth Lewis method attempt to solve? DLS explained

Each team gets **50 overs each** to score as many runs as possible in regular one-day cricket while not losing more than **ten wickets**. Everything is OK, as long as the sun continues to shine. **But oh no! It's started to rain ๐ง** The players come off the field, and the covers go on. Everyone waits until it stops raining, and the ground is dry enough to play on again. But a couple of hours have gone by, and the sun is setting soon.

The organizers decide to cut the number of overs of the second innings to avoid playing in the dark. But how many runs does the chasing team now need to win the match? It's not their fault that the match was interrupted. ๐ค

๐ก *An over in cricket consists of six balls bowled to the batting side. Only legal balls are counted โ wides, no-balls, etc., don't count.*

One way to solve the problem is to cut the run target in direct proportion to the number of overs available. So if Team 1 scores 200 runs from 50 overs and Team 2 is given 25 overs, merely using the run rate per over would say that they only need 101 runs to win.

The problem with this idea is that it doesn't take into account the reaction of the players. Knowing that they only have 25 overs, they will tend to play **more aggressively** than if they had the full 50 overs to score runs. Aggressive play is riskier โ you might score more, but there is a greater chance of losing wickets. So the 101 run target will probably be too easy.

This is an excellent place to understand how the Duckworth Lewis method works. The Duckworth Lewis method attempts to calculate a **statistically fair target**, which has the same difficulty as the original target. It looks at the two resources available to both teams โ overs and wickets. The Duckworth Lewis algorithm adjusts the run target in proportion to these resources.

๐ก *A wicket is when a batter is declared out. This can happen in several ways, such as a fielder catching the ball, the ball knocking the bails off the stumps, or the batter unfairly protecting the wicket with their leg. Each team has 11 players but needs two batters on the field simultaneously, so they have 10 wickets at the start of an innings.*

You might have encountered the abbreviation **DLS** while looking for the Duckworth Lewis method. What is the DLS method? While commonly known as the Duckworth Lewis method, its official name since 2014 is the **Duckworth-Lewis-Stern method (DLS)**, as this was when Frank Duckworth and Tony Lewis retired, and Professor Steven Stern took over to look after the algorithm.

## How the Duckworth Lewis method works โ What is DLS?

Let's now look at how the Duckworth Lewis method is calculated in detail. At the start of the match, each team has **50 overs and 10 wickets**. We say that both teams have 100 percent resources to score as many runs as possible. A delay, early finish, or interruption will reduce a team's resources and mean they no longer have the same resources available.

To calculate a **fair target** for Team 2 to achieve, the Duckworth Lewis method uses the following equation:

`Teams 2's par score = Team 1's score * (Team 2's resources / Teams 1's resources)`

We round up this par score to the nearest integer to get the target `Team 2`

needs to win the match. For example, a rain delay means `Team 2`

only has 80% resources, while `Team 1`

played their innings without interruption (100% resources) and scored 231 runs. Putting these values into the equation above, we get:

`Teams 2's par score = 231 * (80% / 100%) = 184.8`

That means `Team 2`

only needs **185 runs** to win the match.

To find the total percentage of resources each team has, given the number of overs available and wickets lost, we use a lookup table for the Standard Edition of the Duckworth Lewis method:

With DLS explained, you shouldn't struggle with **setting a fair target** for the second team anymore. Remember, you can always use the Duckworth Lewis calculator that handles all the complicated computations.

๐ก *There is also a Professional Edition of the Duckworth Lewis method for international cricket matches. Unfortunately, the fine details of this version are secret and calculated by a propriety computer program. Our Duckworth Lewis calculator only supports the Standard Edition.*

## How Duckworth Lewis method is calculated? Find a team's resources

Here are some common situations and how to calculate a team's resources using the above lookup table.

- There is a delay in starting a team's innings, and 50 overs reduce to 30. Of course, the team still has 10 wickets (0 wickets lost). The table shows that the corresponding value is 75.1% of resources left.

- There is an interruption to a team's innings, and they never resume play. Say this happens with 20 overs left, and they have lost 2 wickets (so there are 8 remaining). Looking at the table, we get a figure of 52.4%, which is the amount of lost resources. So the amount of resources the team used is
`100% - 52.4% = 47.6%`

.

- This time play is interrupted, but the team resumes their innings. Play stopped with 40 overs and 2 wickets lost (8 remaining). It then resumes with 20 overs to play. Looking up 40 overs and 2 wickets lost, we see a figure of 77.8%. For 20 overs and 2 wickets lost, it is 52.4%. To find the resources used by the team, its
`100% - 77.8% + 52.4% = 74.6%`

If `Team 2's`

resources are **less than** `Team 1's`

, then we reduce the target for `Team 2`

using the equation:

`Team 2's par score = S * (R2 / R1)`

where:

`S`

โ Number of runs`Team 1`

scored;`R1`

โ Resources available to`Team 1`

; and`R2`

โ Resources available to`Team 2`

.

If both teams' resources are the **same**, then no adjustment in the run target for Team 2 is required.

If Team 2 has **more resources** than Team 1, then we increase the run target using the following formula:

`Team 2's par score = S + G50 * (R2 - R1)/100`

where:

`G50`

โ Average score expected from the team batting first.

Given the extra resources, the formula asks what additional score could we expect? The value of `G50`

will depend on the level of competition. Our DLS calculator has a default of **245 runs**, which applies to international and county cricket. Based on past results, you should update this value if you use it with your local village cricket team.

๐ก *Cricket involves a lot of running, both by batters and fielders. Why not check out our training pace calculator to ensure your team is fit enough, or the running calorie calculator to see how many calories a batter burns.*

## How to use this Duckworth Lewis calculator?

This calculator supports interruptions at the start, end, and middle of an innings. Let's go through some example situations and see how the Duckworth Lewis method is calculated to find an adjusted target for Team 2. If the match has already finished, you can enter the number of runs Team 2 scored and see if their won, lost, or drew the game, according to the DLS method.

๐ A standard game of cricket has a maximum number of 50 overs. If you are playing a game that has less than 50 overs planned, enter the number into the calculator's **Maximum overs** section.

**Team 2's innings delayed**

Rain, before play started, reduces the match to 30 overs each. `Team 1`

score 231 from their 30 overs. Due to a further delay, `Team 2's`

innings is reduced to 28 overs. Here's how to use our calculator to find the target for `Team 2`

:

- Select
`Team 2's innings delayed`

from the "Interruption" option. - Enter
`30`

into`Team 1's`

"Overs available". - Input
`231`

to tell the calculator how many runs`Team 1`

scored. - Enter
`28`

into`Team 2's`

"Overs available" variable. - The calculator shows that
, according to the DLS method.`Team 2`

needs 221 runs to win - If you enter the number of runs
`Team 2`

actually achieved, the calculator tells you how much each team won the match by or if it was a draw.

Let's see how you would calculate that result manually. Looking up 30 overs and 0 wickets left in the table, we get a resource value of 75.1%. For 28 overs and 0 wickets, it's 71.8%. Since `Team 2's`

resources are less than `Team 1's`

, we use the following equation:

`Team 2's par score = S * (R2/R1) = 231 * (71.8/75.1) = 220.85`

Rounding this up, we get a target to win for `Team 2`

of **221 runs**.

**Team 2's innings cut short**

It's mid-afternoon, and it's just started to rain. Looking at the forecast, it's not going to stop anytime soon. It seems like that's the end of any play today. So who won? No worries. The Duckworth Lewis algorithm to the rescue!

`Team 1`

scored 268 runs from 50 overs, while `Team 2`

got to 229 runs from 45 overs and lost 6 wickets. Using our Duckworth Lewis calculator, let's see if `Team 2`

won.

- Select
`Team 2's innings cut short`

from the "Interruption" option. - Enter
`50`

overs and`268`

runs for`Team 1`

. - Enter
`45`

overs and`6`

wickets lost for`Team 2`

. - We get a target of
`230`

runs for`Team 2`

to win the match. - Entering
`Team 2's`

`229`

runs that they scored, we see that the**match is a draw**, according to the Duckworth Lewis algorithm.

Calculating this result manually using the resources table, we first lookup the resources `Team 2`

couldn't use. They had 5 overs left after losing 6 wickets, corresponding to 14.3% of resources. Therefore, `Team 2`

used `100% - 14.3% = 85.7%`

during their innings. Calculating `Team 2's`

par score:

`Team 2's par score = S * (R2/R1) = 268 * (85.7/100) = 229.68`

We round up to get the winning target of **230 runs** and round down to get the draw score, which Team 2 scored on this occasion.

**Team 2's innings interrupted**

`Team 1`

scored 273 from their uninterrupted innings. `Team 2`

got to 70 runs from 19 overs and lost 2 wickets when rain stopped play. When play resumed, `Team 2's`

total overs reduces to 36, so they had 17 overs available for the remainder of their innings. Here's how to use the Duckworth Lewis calculator to find `Team 2's`

target.

- Select
`Team 2's innings interrupted`

from the "Interruption" option. - Enter
`50`

overs and`273`

runs for`Team 1`

. - Enter
`50`

overs available for`Team 2`

. - At the start of the interruption, 19 overs had been played, leaving
`50 - 19 = 31`

overs available. - Input with the number of wickets lost,
`2`

. - Enter the number of overs remaining at the resumption of play, which is
`36 - 19 = 17`

overs. `Team 2`

need 214 runs to win. Enter the number of runs Team 2 actually got to see by how many runs they lost or won.

To calculate manually, look up resource values for 31 and 17 overs left and 2 wickets off. Then compute the resources available to `Team 2`

:

`Resources available = 100% - Resources remaining at interruption + Resources remaining at restart`

`100% - 68.6% + 46.7% = 78.1%`

We calculate `Team 2's`

par score by doing:

`Team 2's par score = S * (R2/R1) = 273 * (78.1/100) = 213.21`

Round up to `214`

to get the target for `Team 2`

to win the match.

**Team 1's innings interrupted**

This time `Team 1's`

innings is interrupted by rain. The interruption happens after 34 overs, leaving 16 overs remaining, and `Team 1`

has lost 2 wickets. At the resumption of play, `Team 1`

is given 8 overs to complete their innings. `Team 1's`

final run score is 170. `Team 1`

completed 42 overs in total, so that's how many overs Team 2 has too. Using the Duckworth Lewis algorithm in our calculator, you would do:

- Select
`Team 1's innings interrupted`

from the "Interruption" option. - Optionally adjust the average score value G50, but we will leave it at 245 for this example.
- Enter
`50`

in the "Overs available" row. - Input
`16`

in the "Overs remaining at interruption" variable. - Enter
`2`

for the number of wickets lost. - Input
`8`

as the number of overs remaining after the interruption. - Enter the number of runs
`Team 1`

scored,`170`

. - In the
`Team 2`

section, enter`42`

overs available. The calculator tells you that Team 2's target is**197 to win**. - Again, enter the number of runs
`Team 2`

actually scored to see how much they won or lost the match.

To calculate this result manually, we find the resource percentages for each team. `Team 2`

has 42 overs left and has lost no wickets, so their resources are `91.7%`

from the table. For `Team 1`

, their resources before the interruption are given by looking up 16 overs remaining and 2 wickets lost, which is `44.7%`

. At the resumption of play, they have 8 overs remaining and still have lost 2 wickets, which is `25.5%`

. `Team 1's`

resources used is, therefore:

`100% - 44.7% + 25.5% = 80.8%`

Because `Team 2`

has more resources than `Team 1`

, we need to increase the target to win to compensate, so we use the equation:

`Team 2's par score = S + G50 * (R2 - R1)/100 = 170 + 245 * (91.7 - 80.8)/100 = 196.71`