The Duckworth
Lewis rule
Let me say at the onset, there are much better and much
detailed articles on understanding the Duckworth Lewis
method. This is not an attempt to simplify the understanding
of the D/L method. I am sure if I tried, I would fail
badly. Its just another article on the web explaining
the D/L method. In the process if someone finds it comprehensible,
I would consider myself a lucky writer.
This article will not have a flow. Complicated things
cannot be explained in a flow. Hence I have broken
the whole analysis very crudely into many parts. Lets
get started.
In cricket, as you all know, the team that scores
most runs wins. Of course ODIs silly ;>).
Now to score most runs, teams have at their disposal
the number of overs to play and number of wickets
in hand. The number of overs available and the number
of wickets in hand are collectively called resources
available to a team.
Now Mr. D and Mr. L, made a table, based on the scores
of the past ODIs, which gives the percentage
of resources that are available to a team at the end
of every bowl and every wicket. Something like a log
table.
An excerpt from the table is shown below.
|
Wickets lost |
Overs left |
0 |
2 |
5 |
7 |
9 |
|
|
|
|
|
|
50 |
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 |
20 |
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 |
Please keep in mind that the official scorekeepers
and the umpires/referees have the details of these
resources for each bowl. That is there are a total
of 300 balls * 10 wickets = 3000 cells in the complete
table.
We shall consider 3 examples that cover the 3 possible
scenarios.
1st case.)
India has scored 250 runs in 50 overs. Australia
has lost 7 wickets in 40 overs scoring 180(yeah, in
my dreams). Now rain God shows mercy on Australians
and the match is not played further. Lets see who
is the winner.
Did India have any interruptions while batting? No.
So the resource at its disposal was 100%.
When Australia started batting, it had complete resources.
100%
After 40 overs and 7 wickets down, the resources
left with Australia = 20.6 %
Now since, no play is possible further, can Australia
use this remaining resource? No.
So Australia used 100 20.6 = 79.4% of its
resources.
Now lets see how much India would have scored with
79.4% resources available.
Plain and simple mathematics, isnt it?
250 * (79.4/100) = 198.50 which is rounded off to
198 and Australia needed 199 to win.
But how much did they score? 180. So India wins the
match.
Now let me state the rule corresponding to this example.
Note the resource % team had at the start of the
innings. (Here both India and Australia had 100%)
Using the table calculate the resource % lost due
to each interruption. (Australia lost 20.6 %)
Calculate the resource percentage available (Australia
had 79.4% available)
Reset the target set by the first team using the
%resource available to the second team.
With 100% resource India scored 250.
With 79.4%, it would have scored 250 *79.4 /100 =
198.50
The previous case is applicable when the team batting
first is not interrupted at all.
|
Wickets lost |
Overs left |
0 |
2 |
5 |
7 |
9 |
|
|
|
|
|
|
50 |
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 |
20 |
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 |
The table is reproduced again so that you do not
have to scroll up and down.
Case 2.)
India is playing first and the match is already made
a 40 overs match due to rains.
Lets say India scores 200 runs. (With what % of resources?
90.3%. right?)
Australia scores 150 runs in 30 overs and has lost
5 wickets. The play is interrupted again. Now only
5 overs are remaining.
Now pay attention.
After 30 overs, Australia is 150/5.
How much are the resources left? 5 wickets in hand
and 10 overs = 27.5%
Now 5 overs are lost due to rain. And only 5 overs
are remaining. So with 5 wickets in hands and 5 overs
remaining, how much Australia has? 16.4%
Clearly Australia has lost 27.5% - 16.4% = 11.1%
due to rain.
So the Resource available to Australia is 90.3% -
11.1% = 79.2%
Now reset the target set by India considering they
played with 79.2% resources.
200 * 79.2/90.3 = 175.42. So Indias score is
175 and Australia needs 26 more runs in 5 overs to
win the match
Lets formulate the rule now.
If team 2 has less resources than team 1(Australia
had 79.2% available to Indias 90.3%),
Calculate the ratio of the resources available to
the two teams. Reset the Team 1s score using
this ratio.
Simple right?
This rule is applicable when the rain has affected
the number of overs in a match before the match started.
And then again when the team batting second is batting.
Case 3)
|
Wickets lost |
Overs left |
0 |
2 |
5 |
7 |
9 |
|
|
|
|
|
|
50 |
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 |
20 |
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 |
India is batting first and the score is 200/7 at
the end of 40 overs when Rain halts the play. Now
there is sufficient rain to make the match a 40 overs
affair. Clearly Australia cant be asked to score 201
in 40 overs since that would be disadvantage to India
which went into play thinking it has to play 50 overs.
Had it known it has to play 40 overs, it would have
started hitting at the end of 33 over or so. Right?
So we need to reset the target for Australia.
India has lost 7 wickets and 10 overs. So it has
lost 20.6% of the resources due to the rains.
They started with 100% resources. But they have used
only 100% - 20.6% = 79.4%.
Now Australia will start with 90.3% since it has
lost 10 overs. The difference between the resources
available to Australia and India is
90.3% - 79.4% = 10.9%
So Australia had to be set a target of 200 + 10.9%
of 200. Right? Not quite. From the statistics gathered
over a period of time. The average score in a 50 full
overs match has been found out to be 225.
So the reset score is 200 + 10.9% of 225 = 200 +
24.53 = 224.53 or 224
So Australia would need 225 runs to win. (This 225
has nothing to do with the 225 used to calculate the
additional runs required.)
Let us set the rule for this also.
If team 2 has more resources than team 1, find out
the excess resource. (Australia had 90.3% to Indias
79.4%)
Add the excess as a % of 225(average runs scored
in 50 overs) and add those to the total of Team 1.
(10.9% of 225 is 24.53 and 24.53 + Indias score
of 200 = 224.53)
This rule is applicable when the team batting first
starts with 100% resources but the game is shortened
due to rains. And team 1 has less over than expected.
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