Duckworth Lewis method

 

DUCKWORTH LEWIS METHOD- IS THE DUCK WORTH IT?!

Well, YES is the most fair answer!Why?..Go on..

Who comes to your mind when rain interrupts a cricket match? Don’t Duckworth and Lewis appear in front of your eyes! When a target is set by the D/L method, it is really difficult to comprehend and get an answer to one of the following questions that creep up in your mind:

1.Why is the target so less just because the team has wickets in hand..

2.Why has the target increased with a reduction in number of overs to play??..Crazy is it not??

3.Both teams have batted 40 overs in this match..Why does the chasing team need to chase more than the actual target because of a second rain interruption??

Conclusion that you draw:This method is just an eyewash. If it is a rain curtailed match, blame the luck. Keep your wickets intact and Duckworth and Lewis will bail you out and make you reach even an unrealistic target.

 

There was this semifinal match between India and New Zealand in the U19 world cup 2008 being played at Kuala lumpur yesterday. NZ had scored 205 in their allotted 50 overs. Before India could start their chase, the rain clouds gathered around the stadium and about 40 minutes of play was lost. So the maximum overs that could be accomodated became 43. Now comes the d/l method. India was set a revised target of 191.

The immediate question that came to my mind was “This is ridiculous.Do those two gentlemen (Duckworth and Lewis) feel that Indians would score just 14 runs in the remaining seven overs..That too slog overs???.”

 

That prompted me to go on a research into the d/l method that has been used in ODI cricket since 1997.

 

After going through articles on D/L method I find it not only a reasonable method to be adopted for rain affected games but also an interesting one for the mathematics involved in it.

With D/L method it all boils down to a single table that acts pivotal in setting revised targets – THE RESOURCE TABLE.

 

 

 

	Wickets lost
Overs left	0	1	2	3	4	5	6	7	8	9
50	100.0	92.4	83.8	73.8	62.4	49.5	37.6	26.5	16.4	7.6
40	90.3	84.5	77.6	69.4	59.8	48.3	37.3	26.4	16.4	7.6
30	77.1	73.1	68.2	62.3	54.9	45.7	36.2	26.2	16.4	7.6
20	58.9	56.7	54.0	50.6	46.1	40.0	33.2	25.2	16.3	7.6
10	34.1	33.4	32.5	31.4	29.8	27.5	24.6	20.6	14.9	7.5
0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Overs left	0	1	2	3	4	5	6	7	8	9
	Wickets los

A few sensible calculations with this table in hand gives a fair target that remains neutral from a broad view.

Each cell(corresponding to the overs left and wickets lost) in the tablerepresent the resource percentage available for the particular team and based on when rain affects the game , an algorithm is used with the resource percentage available to decide targets.

 

There can be two cases at the end of it:

1. If the resource available to the chasing team is more than that available to the team batting first, find the excess percentage. Let it be ‘x,. Now find y = x*235/100. The revised target (FOR A TIE) will be Target = Score made by Team batting first +y. To win, the chasing team must score one more run(This is because we consider the score of tema batting first in the calculation, not the actual target ).
   
2. If the resource available to the chasing team is less than that available to team batting first, make a ratio of the resource available to chasers to target setters and mutiply with actual score of team batting first. Round it off to the nearest integer to get the runs required for a tie. That plus 1 run will be the target set.

 

A few examples :

RAIN CURTAILS ONLY CHASERS PLAY:

 

1. a)Consider team1 has scored 266 in 50 overs. Now, before team 2 can start their chase, there is some rain and so the max overs is 40.What should be the revised target for team2?

 

Team 1 has played its resources fully (As they have played the full 50 0vers).

So R1 = 100.

Team 2 has only 40 overs to play. So total resources available at start = 90.3 (from table).

So R2=90.3

R2<R1. So, case 2 must be used to find target. SO, team 2 requires 90.3/100*266 = 240.
So target for team 2 is 241 runs to get in 40 overs.

 

Now, does it not appear ridiculous? But this is a fair revision because they have 10 wickets intact and have only 240 balls to face. So they can take more risk with shot making than team1 could have. They pay the price of an extra 10 20 runs in target for that!

b) Now assume that team 2 has scored 42-0 in 10 overs in the same match and rain interrupts again. Then the match officials cut it short by another 10 overs. It becomes a 30 over chase. So overs remaining now is 20.

So at the moment play was stopped, team2 had 30 overs left and 0 wickets lost..So resource % was 77.1. Now 10 overs have been eaten up. Resource available now is 58.9%. So the resource eaten up by rain is 77.1-58.9 = 18.2

So, total resource available to team 2 = 90.3 – 18.2 = 72.1 %.

Here again R2<R1.So,case 2 is used to find target. So team 2 requires 72.1/90.3*266 = 212. So target for team 2 is 213 runs to get in 30 overs.

The big pitfall here is that this method sees only the wickets left as a resource and not the runs scored when rain interrupts. So when the team has scored at a brisk rate without losing wickets it has a chance!

2. RAIN CURTAILS BOTH TEAM S PLAY:

A) Assume team1 has played 30 overs and have scored 155-3 when rain interrupts play. It is seen that the match is reduced to a 30 over game where the chasers too have only 30 overs to play. Another rain rule would have easily said 156 is the target in 30 overs for team2. But that is ridiculous again because team1 didn t know that play would get cut down to 30 overs. They would have planned for a 50 over game. Let us see what Duckworth and Lewis offer :

Initial resource available to team 1 = 100%

When rain interrupts, they have lost 3 wickets and 20 overs (equivalent toa resource percent of 50.6)which they lose. So their resource available R1 is 100-50.6=49.4 %

Team2 on the other hand knows that they have to play only 30 overs.So resource available for them is R2=77.1%

Now R1<R2. So case 1 must be used.So, y = (77.1-50.6)*235/100 = 62.27=62.

So, team 2 , for a tie, should score 155+62=217. So target for team 2 is 218 which is again reasonable, for , thewy know they have just 180 balls to face and have 10 wickets intact.

The d/l might not be the best method. But it is far better than the rain rules used in the past that have been least complex and have changed fates of certain teams!.One rain rule used in Australia meant SA had to get 22 runs off 1 ball.Before the rain interruption they had to get 23 runs off 12 balls. How insane!

 

Thank goodness.. Duckworth and Lewis have helped to a certain extent.

Anyway a full uninterrupted game is always the most pleasant thing to watch and it is always ‘Rain rain go away come again another day’ when it comes to cricket !