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# A do it yourself tutorial on the D/L method

ANALYST
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The D/L method of resetting targets or adjudging winners in rain-affected limited overs matches is named after two statisticians Frank Duckworth and Tony Lewis. This method was officially inducted into limited-overs international cricket by the ICC in the year 1998. The impeccable method of recalculating targets is ostensibly intricate. For the fans who feel hostile to mathematics, D/L calculations seem as complex as SpaceX's Mars mission. But contrary to the belief that these calculations are laborious, they are extremely easy and anyone with a pocket calculator can perform them to figure out the new target in a rain-curtailed match.

### The concept

Unlike the 'highest scoring overs method', D/L method factors the 'resources' available to a team for scoring as many runs as possible while batting when the rain interrupted. The D/L method defines resources as a combination of the number of overs left and the number of wickets in hand. Duckworth and Lewis constructed a detailed table for figuring out the percentage resources left with the team as a factor of overs left and wickets in hand.

Have a look at the table below -

### How to read this table?

Note that 50 overs left with no wickets lost means 100% run-scoring resources of that team are left or available. Every other value in the table is relative to this value. For example, if in a 50-overs game the match was interrupted at the 30 overs mark with 5 wickets in hand then as per the table percentage resources left is 38.6%.

### How to use it?

Now that we have a fair idea of how to read the 'resources' table, let us shift our attention to the fascinating part of the tutorial which is the actual D/L calculations. Let us assume that it is a 50-over match between Team1 and Team2 and Team1 is batting first.

Following three situations may arise -

### #1 The play is interrupted during the first innings

If the play is interrupted during the first innings and it results in loss of overs, Team2 would have an advantage over the batting team which is Team1. To make sure it is fair for both the sides X runs are added to Team1's total.

Calculation of X - As in this case, Team2 has more resources than Team1. The difference in the resource percentages as a factor of 225 will give us X. Note that 225 is considered being the global average score in 50-overs cricket by ICC.

Example - In a 50-overs match between India and Australia, India is batting first and the match has been interrupted by rain. India's score when rain stopped the play was 200 - 5 in 40 overs. Due to rain 10 overs were lost and the match was reduced to 40 overs per side. What would be the revised target for Australia?

Solution -

Referring the resource percentage table for 5 wickets in hand and 10 overs left, India's unused resource percentage is 26.1%. Total resources used by India is 100-26.1 = 73.9%

As Australia on the other side will have all 10 wickets in hand and 40 overs left, the resources available to them is 89.1%.

The difference between resources available to both teams would be 89.1-73.9 = 15.2%

Thus X = 15.2% of 225 which is 34.2 ~ 34. So, the revised Indian total would be 200 + 34 = 234 and the revised target to Australia would be 235.

### #2 The play is interrupted during the second innings

If the play is interrupted during the second innings and it results in loss of overs, the target for Team2 should be brought down as it would have lesser resources than Team1. If R2 and R1 are the percentage resources available to Team2 and Team1 respectively, then R2/R1 multiplied by the original target would be the revised target.

Example - In a 50-overs match between England and South Africa, England batted first and scored 300 in their full quota of 50 overs. During South Africa's reply, rain interrupted the game. The South Africans were 150 - 4 in 25 overs at the stoppage. Due to rain 10 overs were lost and the match was reduced to 40 overs per side. What would be the revised target for South Africa?

Solution -

Resources available to England = 100%. Thus R1 = 100%

Resources left for South Africa with 6 wickets in hand and 25 overs left would be = 50%

But due to loss of 10 overs, when the game resumes South Africa will just have 15 overs left with 6 wickets in hand. This is equivalent to 37.6%. Thus South Africa is set to lose 50-37.6 = 12.4% of its run-scoring resources. Thus R2 = 100 - 12.4 = 87.6%.

Thus the revised target for South Africa would be R2/R1*300 which is (87.6/100)*300 = 262.8 ~ 263.

### #3 The match is abandoned in the middle of the second innings

If a 50-overs game is abandoned post the 20-overs mark of the second innings, the outcome of the game can still be found out using the D/L method.

Example - In a 50-overs match between Sri Lanka and Bangladesh, Sri Lanka batted first and scored 250 runs in their 50 overs. Bangladesh in reply were 140 - 5 in 30 overs when the play was interrupted. Due to excessive rain match had to be abandoned. Who was the winner?

Resources available to Sri Lanka = 100%. Thus R1 = 100%

Resources left for Bangladesh with 5 wickets in hand and 20 overs left would be = 38.6%

As the match was abandoned, Bangladesh lost its remaining 38.6% resources and thus R2 i.e the resources available to Bangladesh = 100-38.6 = 61.4%.

The par score for Bangladesh at the 30-overs mark with 5 wickets in hand would be (61.4/100)*250 = 153.5 ~ 154. Thus the outcome is Bangladesh lose by 14 runs.

### A Little modification necessary

Although the D/L method of resetting the targets is far better than its predecessor - the Highest Scoring Overs Method, the global average score of 225 for one-day internationals has to change. It would make more sense to consider average score on that particular ground rather than a global average.

ANALYST
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