21. Rain
Like all other sports, no one likes the weather gods spoiling a good day's play. So, if rain interrupts the game for a short while, the game has to be shortened so that the match gets over on time.

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 interrupt the game. This method, the Duckworth-Lewis Method (D/L), is named after them. 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, in spite of the match being abandoned. If both teams have faced more than 25 overs, the D/L method comes into effect. However the calculations are 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 example clearer, the following resource table is of selected overs. 

Wickets Lost 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 have 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 x 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 x 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 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% x 235] = 36.19 
Revised score 193 + 36 = 229
Team B need 230 to win. 
--------------------
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