Rain affected matches often rob spectators of a good ODI match. To provide some entertainment, the match is shortened so that a lesser number of overs are bowled so as to complete a match within the allotted time if the skies clear up. In some knock-out tournaments, play often continues on the next day.
After years of trial and error, two English statisticians Mess. Frank Duckworth and Tony Lewis came up with a table determining the adjusted score, if the rains or other factors interrupt an ODI match. This method, the Duckworth-Lewis Method (D/L), is named after them. This does not apply to test matches. The Duckworth-Lewis system can also be used for matches disrupted by other factors such as fog or a dust storm. In early 2004, a modified D/L system has come into play. However details about the modified version aren't well known.
When is it used?
For a match to be declared an official match with a result, both teams must have faced a minimum of 25 overs. Else it is abandoned and the outcome is a No-Result (N/R) match. However the match scores are taken into account. e.g. If a batsman got 50 runs, it is officially recorded, despite of the match being abandoned. If both teams have faced more than 25 overs, the D/L method comes into effect. However the calculations can be pretty tricky.
How it Works
The Duckworth-Lewis System makes use of "resources". Resources are
the number of balls remaining to be bowled and the number of Wickets-in-Hand
(not-out batsmen).
To under how this works is, imagine a squad of 10 planes with a collection of 50 missiles between them. For each missile fired, the less resources remaining to completely cripple the enemy, and for each plane downed, lesser the chance of the squad winning the battle.
Here the missiles fired are the overs up, and the planes are the batsmen who are not out.
Calculating the Adjusted Scores
The Duckworth-Lewis table is plotted per ball vs. wickets fallen. To make the following examples clearer, the following resource table is based on overs.
| Overs Left | 0 | 2 | 5 | 7 | 9 |
|---|---|---|---|---|---|
| 50 | 100 | 85.1 | 49 | 22 | 4.7 |
| 40 | 89.3 | 77.8 | 47.6 | 22 | 4.7 |
| 30 | 75.1 | 67.3 | 44.7 | 21.8 | 4.7 |
| 25 | 66.5 | 60.5 | 42.2 | 21.6 | 4.7 |
| 20 | 56.6 | 52.4 | 38.6 | 21.2 | 4.7 |
| 10 | 32.1 | 30.8 | 26.1 | 17.9 | 4.7 |
| 5 | 17.2 | 16.8 | 15.4 | 12.5 | 4.6 |
There are four cases when the match can be disrupted.
1) Rain delays start of play
Rain delays start of play, and a forty over-a-side match is declared. Play continues without the D/L system coming into effect if there is no further interruption to the match.
2) Team B's batting is ended prematurely
Team B is batting second and more than 25 overs of his innings are up. Team A had scored 300 runs in their 50 overs. After 40 overs, Team B has scored 250 runs and has lost 7 wickets. Rain prevents further play. After the scheduled closing time, the winner has to be declared. Who is the winner?
Team A: No disruptions, therefore 100% resource.
Team
B: Have 10 overs left and 3 wickets remaining.
From the table, Team B's resource remaining was
17.9. But because of rain, it was lost.
Now resource used: [100 × 17.9] = 82.1%.
Equivalent resource score: [300 × 82.1/100] = 246.3 – 246. (Always round down
for D/L method)
246 is the par score, or the score to tie.
Since Team B is on 250 runs (slightly ahead of the 246, they are adjudged the winner by 4
runs.
3) Rain Stops Play for a few overs
The match is reduced to a 40 over a side game. Resource remaining to both teams = 89.3%. Team A scores 217 in 40 overs. Team B, after 30 overs, scores 133/2. Rain disrupts play, and 5 overs are lost. The target has to be revised.
Overs remaining for Team B: [40 – 30] = 10%
Resources remaining:
30.8%
Resources used: 69.2%
5 overs lost due to rain, hence Resources lost: 16.8%
Resource% lost: [30.8 – 16.8] = 14%.
Resource used: [89.3 – 14] = 75.3%
Target needed: [217 × 75.3/89.3] = 182.9 ~ 182
Hence, if Team B don't lose any more wickets, the target is 183 to win.
4) Team A loses a few overs
Team A, batting first after 40 overs has had their play disrupted. Their score was 193/5. 20 overs are declared lost, 10 from each team. Since they lost resources at the end of the innings, the score the Team B has to chase has to be revised upwards. This compensates for the loss of resources of Team A, which would enable them to get a higher score.
Team A's resource remaining: 26.1%
Resource Used: 73.9%
Resource available to Team B: 40 overs, 89.3%
Difference in Resource: [89.3 – 73.9] = 15.4%
235 is the median score in Cricket.
We multiply [15.4% × 235] = 36.19
Revised score 193 + 36 = 229
Team B need 230 to win.