To calculate the Targets of Interrupted matches the Duckworth Lewis Method is used. Full formulas are mentioned below.

These are not in direct proportion to the number of overs available to be faced, as with the average run rate method of correction. Instead they depend on

• No of Overs Left.
• No of Wickets Lost.

ICC has defined a combined set of Values for the no of overs left and no wickets left by coining the term Resource Percentage. For matches with less than 50-overs per innings before they start, the resource percentages available at the start of an innings will be less than 100%. But the same table and the same method of calculation are used whatever the number of overs per innings. (Table is given below as per Over wise.) This is the table of Resource Percentage Remaining- over by over.

When Team 2 (the side batting second) have less run scoring resources at their disposal than had Team 1 (the side batting first), their target is adjusted downwards using the ratio of the resources available to the two sides. But when Team 1’s innings has been interrupted, it often happens than Team 2 have more resources at their disposal than had Team 1 and it is now necessary to adjust Team 2’s target upwards. In this case the adjustment is based on the runs that would be expected to be scored on average from the extra resources at their disposal. The number of these extra runs required is calculated by applying the excess resource percentage to the average total score in a 50-over innings, referred to here as G50.

For matches involving ICC full member nations, or for matches between teams that play first class cricket, the value of G50 should be 245.And for lower levels like Under 17, Under 19, Women’s Matches and matches of the member nations the G50 would be 200.

Now few Simple things which are calculated using the above chart-

Let there be Team 1 (batting first) and Team 2 (batting 2nd) then

No of overs per innings at the start of the match — [math]N[/math]

Resource Percentage available to team 1 at start of Innings -[math] R_1[/math]

Resource Percentage when Play Stops (a overs completed and (N-a) overs left of Team 1’s innings , b wickets lost) - [math]R_2[/math] (check from the table)

When the game is stopped in between where ‘a’ overs completed and there is a got to be loss in overs.And the game has been reduced to M overs per innings.

Then Resource Percentage when Play Resumes (a overs completed and (M-a) left of Team 1’s innings, and b wickets lost) - [math]R_3[/math] (check from the table). This value is zero when the zero overs are left or Team 1’s batting is terminated.

Then Resource Percentage lost due to suspension - [math](R_2-R_3)[/math]

Resource Percentage Available to Team 1 - [math]R_c=R_1-(R_2-R_3)[/math]

And Score of Team 1 - S

Now for the Team 2 for Resources available would be 0 wickets lost and M overs left. Then their Resource Percentage would be- [math]R_d [/math](check from the table)

Now Target Calculation or DLS Par Score Calculation-

• If [math](R_d<R_c)[/math]

then Target [math]T= {S * (R_d/R_c)} + 1 ,[/math]

• If [math](R_d=R_c)[/math]

then Target [math]T= S+1 ,[/math]

• If[math] (R_d>R_c)[/math]

then Target [math]T= S+ [{(R_d - R_c) * (G50)}/100] +1[/math]

Then Scores are rounded off to the whole number when required.

Few Examples.

Example 1 (Suspension during Team 1’s innings)
In a 50 over-per-innings match, Team 1 reaches 79/3 after 20 overs and then there is a suspension in play. It is decided that 20 overs of the match should be lost, 10 of these by each team. Team 1 resumes to reach a final total of 180 in its revised allocation of 40 overs.

Number of overs per innings at the start of match, N = 50
Resource percentage available to Team 1 at start of innings = 100% (5.1)
Resource percentage remaining at suspension (30 overs left, 3 wkts lost = 61.6% Resource percentage remaining at resumption (20 overs left, 3 wkts lost) = 49.1% Resource percentage lost due to suspension = 61.6 – 49.1 = 12.5%
Resource percentage available to Team 1, R1 = 100 – 12.5 = 87.5% (5.2)
Number of overs available to Team 2 at the start of its innings = 40
Resource percentage available (40 overs left, 0 wkt lost), R2 = 89.3% (5.4)
R2 is greater than R1, i.e. Team 2 has more resource available than had Team 1, so its target should be increased. S = 180

Team 2’s revised target is

T = S + G50 x (R2 – R1)/100 + 1 = 180 + 245 x (89.3 – 87.5)/100 + 1 = 185 (rounded down).

Example 2

Team 1 scores 226/8 in 47.1 of a scheduled 50 overs. Rain then terminates Team 1’s innings and delays that of Team 2, which is given a reduced allocation of 33 overs.

Number of overs per innings at start of match, N = 50

Team 1’s innings:
|Resource percentage at start of innings is 100%
Resource percentage remaining at termination (2.5 overs left, 8 wkts lost) = 6.9% Resource percentage lost due to termination = 6.9% .
Resource percentage available, R1 = 100 – 8.1 = 93.1%

Team 2’s innings (allocated 33 overs):
Resource percentage available at start of innings (33 overs left, 0 wkts lost),

R2 = 79.8%;
R2 is less than R1;
S = 226.

Team 2’s revised target is

T = S x R2/R1 + 1 = 226 x 79.8/93.1 + 1 = 194 (rounded down).

Peace. Hope You Understand It.

Sayan.

Footnotes

This is my try to simplify the DLS method for you. Trust me, it is easy to understand.

Imagine if you have a cake,

The whole cake represents 100% of the cake. Now cut the cake into four pieces. Three pieces together will represent 75% of the cake, two pieces will show 50% while only one piece will represent 1/4 or 25%.

Now, imagine a batting side in ODI format. At the start of the innings, they have 50 overs to play and 10 wickets in hand. This 50 overs+10 wicket is 100% of the ‘resources’ they have. If they have 0 overs left to play or all their 10 wickets have been taken, then they are left with nothing. Hence, 0 overs left to play or 0 wickets in hand shows that the batting side has 0% of the resources.

Now here the main thing starts.

• How are scores adjusted according to DLS system?

Let us say there is a match between Australia and England. Australia scored 250/10 runs in 50 overs in the first innings. England were at 190/5 in 40 overs when rain interrupted the match. The rain is so much that no further play is allowed and the winner has to be decided by the DLS method.

Now according to the run rate method, it might look that Australia should win the match because they had a run rate of 5 (250/50) than 4.75 (190/40) of England but this is not the case. It is unfair because this doesn’t take into account that England still has 5 wickets left and the pace of batting won’t be the same in the last overs. This is where the DLS system helps.

DLS system uses a formula to take into account the over remaining and also the number of wickets they have in hand. This is the chart,

Now England were at 190/5 in 40 overs which means they lost 5 wickets and still have 10 overs in hand. In this table, look for 5 wickets lost and 10 overs remaining, and it will lead to the number 26.1. This means England still have 26.1% of their resource (overs+wickets) remaining.

26.1% is the resources left with them. So how much resources (overs+wickets) did they consume? It is 100–26.1=73.9. This means in reaching 190/5 in 40 overs, they consumed 73.9% of their resources (overs+wickets).

Now Australia had scored 250 in 50 overs by utilizing 100% of the overs. So now the adjusted score will be 73.9/100 multiplied by 250. This is to see how much Australia would’ve scored had they consumed the same amount of resources that England used (73.9%). So 0.739*250=184.75 which means Australia would’ve scored 185 runs with the same resources as England. England was at 190/5 so according to DLS method, England have won the match.

Had England been at 190/6, the adjusted score would’ve been 193 runs. Had England been at 190/7, the adjusted score would’ve been 205 runs. You can check this yourself from the table. As the wickets increased, the adjusted score increased and hence in rain prevailing conditions, team tend to focus more on losing minimum wickets.

Example 2

Imagine it is India VS NZ. India scored 300 runs in 50 overs but before the start of the second inning, rain starts. Due to rain, the second inning is reduced to 45 overs. What will the adjusted score be?

Now the DLS method needs to account for the reduced overs. NZ have 10 wickets but now they have only 45 overs. So search the table for 45 overs left and 0 wickets lost, it will lead you to the number 95. This means that NZ has 95% of their resource available now.

India had earlier scored 300 by using 100% of the resources. So what would India’s score be if they also had 95% of the resources like NZ? It will be 95/100 multiplied by 300. Hence 0.95*300 gives 285 runs and hence 286 runs will be the target for NZ now.

If the first innings had utilized 100% of their resources then you simply, multiply the resources used or resources available percentage of the 2nd team with the score of the first inning to get the adjusted score.

• If you have to judge the winner if the rain stops the match fully, then you use the resources used percentage.
• If you have to adjust the score which has to be chased now then you use the resources available percentage.

Now what if the rain had interrupted the first inning too and the first team didn’t use 100% of their resources? What if they only played for 30 overs? In that case, you simply calculate the resources utilized by Team 1 from the same table the same way you used for Team 2 earlier and then you simply use the formula,

Adjusted score= Team 1 score * Resource % with Team 2/Resource % with Team 1

Bingo!

If Resource % of Team 2 is more than Resource % of Team 1, then the fraction value will be more than 1 and the adjusted score will become greater than the first inning score and hence often you see in reality too that the adjusted score is sometimes greater than the first inning score.

This is the whole foundation of the method. Nowadays, the officials use more formulae and data which isn’t available to the public and is available only as a software but the basic logic behind the method is the same as mentioned in the answer.

Hope this answer was helpful!

:)

Intro: The Duckworth–Lewis (D/L) method is a mathematical formulation designed to calculate the target score for the team batting second in a limited overs cricket match interrupted by weather or other circumstances. It is generally accepted to be the most accurate method of setting a target score. The D/L method was devised by two English statisticians, Frank Duckworth and Tony Lewis.

After their retirements Professor Steven Stern became the custodian of the method. In November 2014, it was renamed the Duckworth–Lewis–Stern method (or DLS method).

Calculation & Theory: The essence of the D/L method is 'resources'. Each team is taken to have two 'resources' to use to score as many runs as possible: the number of overs they have to receive; and the number of wickets they have in hand. At any point in any innings, a team's ability to score more runs depends on the combination of these two resources they have left. Looking at historical scores, there is a very close correspondence between the availability of these resources and a team's final score, a correspondence which D/L exploits.

The D/L method converts all possible combinations of overs (or, more accurately, balls) and wickets left into a combined resources remaining percentage figure (with 50 overs and 10 wickets = 100%), and these are all stored in a published table or computer. The target score for the team batting second ('Team 2') can be adjusted up or down from the total the team batting first ('Team 1') achieved using these resource percentages, to reflect the loss of resources to one or both teams when a match is shortened one or more times.

In the version of D/L most commonly in use in international and first-class matches (the 'Professional Edition'), the target for Team 2 is adjusted simply in proportion to the two teams' resources, i.e.

Team 2 par score = Team 1 score *

Team 2’s resources/Team 1’s resources

Ref: Duckworth–Lewis method - Wikipedia

1. Currently used system for normalising score in Cricket Match is DLS ( Duckworth/Lewis/Stern) method.
2. The calculation involved for normalising the score by this method , involves resource percentage calculation which depends upon number of wickets lost ,number of overs or balls remaining .
3. This method is designed for different cases and different formulae are used to calculate target score everytime.
4. Now a days data analysis of runs scored by teams over the years in given set of conditions and at specific geographic locations are taken into account to determine the target score for team.
5. Latest standard edition Resource percentage calculation table available is for one day International matches. Link: International Cricket Council.
6. You can refer this table to calculate approximate score required for win.
7. I calculated target required for India in today's(7th October 2017) match against Australia but got wrong answer. If you get correct answer do let me know.

Thanks for Reading.

DLS is a very complicated method. Once Dhoni was asked if he understands it and he said “I don’t think the ICC understands it either.” :)

So we can go to DLS calculators available on the internet, but the actual method is like a secret- patented. In short, we can tell that it depends on Runs, Wickets and overs.

So in the 1st t20 on 21 Nov, AUS had scored 135 in 15 overs when it started raining with 7 wickets in hand. Later AUS batted only for 2 overs, but they lost 1 wicket. So the fact that we have 10 wickets in hand and we know that we are going to bat for 17 overs, by DLS method we were given a larger target.

Understood ?

I will try and answer that

Case 1

Suppose you and I are playing a 5 over match in your backyard.

You are batting first and we both have two wickets(since it's only the two of us playing, if you get out the first time, you will get another wicket and if you get out the second time your innings get over).

Now as it's a five over match and you're batting first, you play cautiously for the first 3 overs and make 15 runs without losing any wicket.

Now I come up to you and say that I have to go home early so let's make it a 3 over affair and let me bat if I make 16 runs in 3 overs I win.

Will you be satisfied? No. You/The person batting first would argue that had he known that it would be a 3 over match beforehand, you/he would have played more aggressively and tried to amass as many runs as possible in the third over. You played the third over defensively keeping in mind that it was a 5 over match, had you known it will convert to a 3 over match, you would have tried and hit as many runs as possible in the third over as you had 2 wickets in hand too.

So I/the person batting second agrees to adjust the score to 24 runs in three overs as to compensate for your defensive approach.

Case2

This time we are playing a 50 over match with 10 wickets, you are batting first and you make 300 runs in your 50 overs.

Now it’s my turn to bat and suddenly I request you to make it a 20 over match as I have to leave early.

Now you/the person batting first will argue that making 120 runs in 20 overs with 10 wickets in hand is way more easy than making 300 runs in 50 overs with 10 wickets.

I agree and we decide that we will have to make 160 runs in 20 overs with 10 wickets in hand.

So you see, what happened here?

We added the pressure of run rate on the team batting second to compensate for the full 10 wickets they have for a meagre 20 overs match now.

That's Duckworth Louis for you

Contrary to popular belief, Duckworth-Lewis is actually very easy to understand. It's also a highly efficient means of predicting a total after rain interruptions.

The following score-card is why Duckworth Lewis Method Exists. Previous methods would sometimes give erratic results, disastrous for teams (like South Africa in this case ).

Note: People often sight this image as an example of D/L Method's inaccuracies but it isn't, the method used in the match in question was not D/L but an older rule called the "Highest Scoring Overs Method" (1).

I'll be using notes on pen and paper to explain the rules, as I found that easier and faster to use mathematical notations (Please excuse my slightly sloppy handwriting).

--
The D/L method works using the notion that teams have two resources to make runs - these are: the number of overs left and the number of wickets they have in hand. From any stage in their innings, their further run-scoring capability depends on both these two resources in combination.

When a match is shortened after it has begun, the resources of one or both teams are depleted and the two teams usually have different amounts of resource for their innings. In this case a revised target must be set.

If stoppages cause the team batting second (Team 2) to have less resources available, then their target will be revised downwards.

If, on the other hand, when Team 1's (Batting first) innings has been interrupted, the stoppages result in Team 2 having more resources available, then their target is revised upwards to compensate for the extra resources they have at their disposal.

Calculating Resources.
We need to refer to the Table of resource percentages remaining to calculate resources remaining (2):

Link: Page on amazonaws.com

Each cell of this table represents Resources ‘left’ with team on that situation.
For example: Resources left after 42 overs and with 4 wickets remaining = 19.9% (R(8,6))

How to calculate the revised targets after 'n' rain interruptions:

If Team 2 : have less resources available than Team 1,
then, calculate the ratio of the resources available to the two teams. (R2/R1)

Team 2's revised target is obtained by scaling down Team 1's score by this ratio. (As shown in the above image)

However,
If Team 2: have more resources available than Team 1,
then, calculate the amount by which Team 2's resource percentage exceeds Team 1's.

Work out this excess as a percentage of 225 and this gives the extra runs to add on to Team 1's score to give Team 2's target.

225 is the par score for a 50 overs match.

--
1. Here's how the Highest Scoring Overs Method Worked:

Compare the maximum runs scored by team1 in any set of overs (not necessarily consecutive) equal to the number of completed overs received by team2 against the team2 in those completed overs. So if team2 received 36.3 overs their score after 36 overs is compared to the highest scoring 36 overs of team1's innings (so could be any 36 of the 50 overs).

Just goes to show how much better the D/L method is.

2. The table mentioned is for the Standard Edition (Used until 2004), For international matches a Professional Edition is used. The Professional Edition uses a computer program instead of a manual calculation. The table for that is slightly different, but isn't available for the public. However, the difference in the scores isn't very big. The Table hasn't been updated since 2002, however, Duckworth did suggest a change back in 2009, to account for newer formats.

--
Sources: Cricinfo - Duckworth-Lewis
Duckworth-Lewis Method - frequently asked questions
Duckworth–Lewis method - Wikipedia

Has anyone yet understood the Duckworth-Lewis method?

I started reading about Duckworth-Lewis method and listening carefully to my wife to understand both.

Tell you what, I have started understanding what my wife says but Duckworth-Lewis Method is still a riddle for me.

Duckworth-lewis method totally works on the table they have made after first inning;

This is the table for the match on 7th june;

By looking at table you can understand the mysterious Duckworth-lewis method;

This is the table for match on 10th june;

Source :- cricbuzz

The D/L method of resetting targets in rain-affected one-day cricket matches was trialled successfully during 1997 by the International Cricket Council (ICC), the ECB (England & Wales Cricket Board) and the Zimbabwe Cricket Union (ZCU). It has already been chosen for use in 1998 by the ECB, the ZCU and New Zealand.

The method is the invention of Frank Duckworth and Tony Lewis. Frank is a consultant statistician and editor of the Royal Statistical Society's monthly news magazine, RSS NEWS. Tony is a lecturer in mathematical subjects in the Faculty of Computer Studies and Mathematics at the University of the West of England, Bristol and chairman of the Western Branch of the Operational Research Society

Following the experience of the method's application in 1997 they have introduced a few modifications designed to make the method's use even simpler. This article provides a summary of the way the method works.

Contrary to the belief in some quarters, it does not require a degree in mathematics either to understand it or to use it! Although a purpose-written computer program is available to countries adopting the system to enable calculations to be performed speedily and accurately, this is not necessary. All calculations can easily be performed using nothing more than a single table of numbers and a pocket calculator. With a little practice there is no reason why anyone should not be able to calculate the revised targets more-or-less instantly. The authors firmly believe that the method is simple enough that it could be adopted for use at all levels of limited overs cricket

Basis of the method

The D/L method works using the notion that teams have two resources with which to make as many runs as they can - these are the number of overs they have still to receive and the number of wickets they have in hand. From any stage in their innings, their further run-scoring capability depends on both these two resources in combination. The single table gives the percentage of these combined resources that remain for any number of overs left and wickets lost. An extract of the over-by-over table is given in Table 1. (A ball-by-ball version of the table has also been produced to enable scorers to deal with instances when play is interrupted mid-over.)

When a match is shortened after it has begun, the resources of one or both teams are depleted and the two teams usually have different amounts of resource for their innings. In this case a revised target must be set. The D/L method does this in accordance with the relative run-scoring resources available to the two teams. If stoppages cause the team batting second (referred to here as Team 2) to have less resources available, as is more often than not the case, then their target will be revised downwards. If, on the other hand, as often happens when Team 1's innings has been interrupted, the stoppages result in Team 2 having more resources available, then their target is revised upwards to compensate for the extra resources they have at their disposal.

Table 1: Extract from the table of resource percentages remaining

Reading the table

The single table applies to all lengths of one-day matches from 60 overs-per-side downwards. [In 1997 there was a separate table for all lengths of matches from 60 to 10 overs per side.] Because 50 overs-per-side matches are by far the most common, the resources listed in the table are expressed as percentages of those available at the start of a 50 over innings. Thus when there are 50 overs still to be received and no wickets have been lost, the resource percentage available is 100%. 60 over innings start with a resource percentage of 107.1% compared to a 50 over innings and 40 over innings start with a resource percentage of 90.3% compared to a 50 over innings.

In order to determine the correct resource percentage the batting side has remaining at any stage of an innings, the number of overs left must be identified. This number of overs left, in conjunction with the number of wickets lost, is then used to read the resource percentage remaining from the table.

For example, suppose that after 20 out of 50 overs a team have lost 2 wickets. They have 30 overs left. From the table you will see that the resource percentage remaining is 68.2%.

Suppose now that there is an interruption in play and 10 overs are lost from the innings of the batting side. When play can resume there are only 20 overs left but there are still, of course, 2 wickets down, and the table now tells us that the resource percentage remaining is 54.0%. Thus the shortening of the innings has caused the team to lose a resource percentage of 68.2 - 54.0 = 14.2%.

Having started with a resource percentage of 100% and lost 14.2%, then if they complete their innings with no further loss of overs, they will have had a resource percentage available for their innings of 100 - 14.2 = 85.8%.

Applying the D/L method

The procedure for setting a revised target, which is the same for any number of stoppages at any stage of the match, is as follows.

1. For each team's innings
   (a) from the table note the resource percentage the team had available at the start of their innings;
   (b) using the table, calculate the resource percentage lost by each interruption;
   (c) hence calculate the resource percentage available.
2. If Team 2 have less resources available than Team 1, then calculate the ratio of the resources available to the two teams. Team 2's revised target is obtained by scaling down Team 1's score by this ratio.
3. If Team 2 have more resources available than Team 1, then calculate the amount by which Team 2's resource percentage exceeds Team 1's. Work out this excess as a percentage of 225 [the average 50 over score in ECB matches and one-day internationals (ODIs)] and this gives the extra runs to add on to Team 1's score to give Team 2's target.

Worked examples

Example 1: Premature curtailment of Team 2's innings
Team 1 have scored 250 runs from their 50 available overs and Team 2 lose 5 wickets in scoring 199 runs in 40 overs. Play is then stopped by the weather, the rain refuses to relent and the match is abandoned. A decision on the winner is required.

Team 1's innings: this was uninterrupted, so the resource percentage available is

100%.

Team 2's innings: resource % available at start of innings =

100%

After 40 overs Team 2 have 10 overs left and have lost 5 wickets.
From table, resource % left at suspension of play =

27.5%

As play is abandoned all this remaining resource is lost.
Hence resource % available for Team 2's innings = 100 - 27.5 =

72.5%

Team 2 had less resource available than Team 1 so their target must be scaled down by the ratio of resources, 72.5/100
Team 1 scored 250, so Team 2's 'target' is 250 x 72.5/100 = 181.25
As there is to be no further play, the winner is decided according to whether or not this target has been exceeded. With 199 runs on the board, they have exceeded their required target by 17.75 and so are declared the winners by 18 runs.

Note : The above result is quite fair as Team 2 were clearly in a strong position when play was stopped and would very likely have gone on to win the match if it hadn't rained. Most other methods of target revision in use would, unfairly, make Team 1 the winners. The average run rate method gives 201 to win, the Current ICC method gives 227 and the parabola method gives 226. [Setting the target by the method of Discounted Total Runs - the Australian rain-rule - requires knowledge of the runs made by Team 1 from their most productive overs but the target would almost certainly be no lower than that required under average run rate and would probably be much higher so that Team 2 would very probably lose by this method as well.]

Example 2: Interruption to Team 2's innings

In an ECB Axa Life (Sunday) League match Team 1 have scored 200 runs from their 40 available overs and Team 2 lose 5 wickets in scoring 140 runs in 30 overs. Play is then suspended and 5 overs are lost. What is Team 2's revised target?

Team 1's innings: At the start of 40 over innings resource percentage available =

90.3%

Team 2's innings: resource % available at start of 40 over innings =

90.3%

After 30 overs Team 2 have 10 overs left and have lost 5 wickets.
From table, resource % left at start of suspension =

27.5%

5 overs are lost, so when play is resumed 5 overs are left.
From table, resource % left at resumption of play =

16.4%

Hence resource % lost = 27.5 - 16.4 =

11.1%

so resource % available for Team 2's innings = 90.3 - 11.1 =

79.2%

Team 2 had less resource available than Team 1 so their target must be scaled down by the ratio of resources, 79.2/90.3
Team 1 scored 200, so Team 2's target is 200 x 79.2/90.3 =175.42, or 176 to win, and they require a further 36 runs from 5 overs with 5 wickets in hand.

Example 3: Interruption to Team 1's innings

In an ODI, Team 1 have lost 2 wickets in scoring 100 runs in 25 overs from an expected 50 when extended rain leads to Team 1's innings being terminated and Team 2's innings is also restricted to 25 overs. What is the target score for Team 2?

Because of the different stages of the teams' innings that their 25 overs are lost, they represent different losses of resource. Team 1 have lost 2 wickets and had 25 overs left when the rain arrived and so from the table you will see that the premature termination of their innings has deprived them of the 61.8% resource percentage they had remaining. Having started with 100% they have used 100 - 61.8 = 38.2%; in other words they have had only 38.2% resources available for their innings.

Team 2 will also receive 25 overs. With 25 overs left and no wicket lost you will see from the table that the resource percentage which they have available (compared to a full 50 over innings) is 68.7%. Team 2 thus have 68.7 - 38.2 = 30.5% greater resource than had Team 1 and so they are set a target which is 30.5% of 225, or 68.63, more runs than Team 1 scored. [225 is the average in 50 overs for ODIs]

Team 2's revised target is therefore set at 168.63, or 169 to win in 25 overs, and the advantage to Team 2 from knowing in advance of the reduction in their overs is neutralised.

Note: Most of the other target resetting methods in use make no allowance for this interruption. They set the target of 101 to win simply because both teams are to receive the same number of overs. This is clearly an injustice to Team 1 who were pacing their innings to last 50 overs when it was curtailed, whereas Team 2 knew in advance of the reduction of their innings to 25 overs and have been handed an unfair advantage. D/L allows for this by setting Team 2 a higher target than the number of runs Team 1 actually scored, as described above.

There is only one alternative method to DLS method known as VJD method (named after an Indian engineer Jayadevan who formulated it) .Right now it is only used in the Indian domestic circuit such as Vijay Hazare,Syed Mushtaq Ali,etc.,but there plans to introduce it in IPL too though dont see it happening in the forseeable future.The calculations and methods are too complicated for the normal brain(especially me).So cant exactly differentiate between DLS and VJD.Both have a little different approach but the results have almost found to be similar,so can't argue on which is better.

The main difference I can tell you that DLS calculations are based on That the runrate increses slowly at first, but accelerates quickly during the final ten to fifteen overs .It is assumed such that the runrate is lowest in the first over and is the highest in the last over. But the VJD method takes a different approach.It assumes that the runrate is faster and accelerates till the end of the poweplay(first 20–30% of overs)due to the field restrictions.When the powerplay ends the runrate now reduces and is considered lowest during this part of innings(batsmen look to build the innings slowly and look to rotate singles rather than look for boundaries). When the death or the slog overs come they again increase rapidly.

One thing in which he has an edge over DLS method is this aspect as this is how the batting teams usually go about.

One more difference is that in DLS method always the next over is assumed to be more successful than the previous one.Example,India score 150 from 25 overs in a 50 over and it starts raining,and the match is reduced to 25 overs.DLS calculates and assumes that in the next 25 overs India in each over would have surely scored more than the previous one.But VJD takes a different approach and assumes that there's a chance India could have also scored less in that period.

In the recent match,India vs Australia T20 where Australia's score was revised to 173 from 158,it Should be noted that revised score could have been pretty Lesser considering Australia wouldn't have scored much considering Bumrah and Bhuvi had to bowl.DLS assumed probably that if it was a 20 over game and uninterrupted by rain Australia would have gone on to score around 200 but in reality we knew only around 185 would have been possible considering how well they bowled that day and they were the best at death(My opinion).This is an aspect I want DLS to improve on.

One More Main difference is that DLS emphasizes more on the wickets in hand than the VJD. It considers wickets remaining a very important aspect to the final DLS score.

But still DLS takes numerous other aspects too into the game which is why it is widely used.I can't compare the calculations and algorithms as they too complicated (they use average T20 or ODI scores,this that,blah blah blah)where in nowadays only computers are used to generate the score.I feel if you can crack the DLS and VJD methods you surely deserve a PHd. in Maths or whatever subject it is related too.I am pretty sure all the top Cricket officials wouldn't even have an ideas of whatever this is

.This match is a good comparison - Semi-Final New Zealand vs South Africa ICC Cricket World Cup

DLS Target-298

VJD Target-300

New Zealand win with 1 ball to spare.

These are the situations where even fine margins decide the game.Just imagine if VJD was used and there was a chance that South Africa would go on to win the World Cup.(Just a hypothetical case)

Check out this match also…England vs India at Bengaluru, Nov 23 2008Hope it helped to extent…Cheers…

P.S don't know why I feel Somehow South Africa has been on the wrong side of rains and revised targets.

The Duckworth–Lewis–Stern method (DLS) is a mathematical formulation designed to calculate the target score for the team batting second in a limited overs cricket match interrupted by weather or other circumstances.

The method was devised by two English statisticians, Frank Duckworth and Tony Lewis and was formerly known as the Duckworth–Lewis method (D/L). It was introduced in 1997, and adopted officially by the ICC in 1999. After the retirements of Duckworth and Lewis, Professor Steven Stern became the custodian of the method and it was renamed to its current title in November 2014.

When overs are lost, setting an adjusted target for the team batting second is not as simple as reducing the run target proportionally to the loss in overs, because a team with ten wickets in hand and 25 overs to bat can play more aggressively than if they had ten wickets and a full 50 overs, for example, and can consequently achieve a higher run rate. The DLS method is an attempt to set a statistically fair target for the second team's innings, which is the same difficulty as the original target. The basic principle is that each team in a limited-overs match has two resources available with which to score runs (overs to play and wickets remaining), and the target is adjusted proportionally to the change in the combination of these two resources.

Calculation summary:

The essence of the D/L method is 'resources'. Each team is taken to have two 'resources' to use to score as many runs as possible: the number of overs they have to receive; and the number of wickets they have in hand. At any point in any innings, a team's ability to score more runs depends on the combination of these two resources they have left. Looking at historical scores, there is a very close correspondence between the availability of these resources and a team's final score, a correspondence which D/L exploits.

In the version of D/L most commonly in use in international and first-class matches (the 'Professional Edition'), the target for Team 2 is adjusted simply in proportion to the two teams' resources, i.e.

If it is a 50-over match and Team 1 completed its innings uninterrupted, then they had 100% resource available to them, so the formula simplifies to:

The Duckworth–Lewis–Stern method is a mathematical formulation designed to calculate the target score for the team batting second in a limited overs cricket match interrupted by weather or other circumstances.

But it's not right method to describe the match.

In that just counting people not his/her value.

It is the predecessor to the current Duckworth-Lewis-Stern Method of determining the result in a shortened cricket match.

The DLS method is used when an interruption to a limited-overs cricket match causes either (a) the number of overs to be faced by each side is reduced after the match has commenced, or (b) the number of overs to be faced by the side batting second is reduced during its innings, or (c) both of these things. If weather or other environmental conditions cause a delay to the start, but the innings of both sides are reduced equally before the commencement, then DLS is not applicable.

When an interruption occurs as per (a) or (b) above, the DLS method is used to determine a table of Par Scores for every possible ending point of the innings of the side batting second. That table has for one axis the number of balls bowled in the innings, and for the other axis the number of wickets lost by the batting side. The “current” Par Score is found by cross-reference on that table.

The side batting second must exceed the Par Score to win. If its innings is interrupted (or further interrupted) and it is unable to finish the number of overs originally allocated, then the result may be determined on the basis of the score at the last moment of play - if it is greater than the Par Score for that moment, then it is good enough for a win.

The rationale of the Par Scores on the table is “resources available”. A side when it begins it innings has 100% of its resources available - all the overs and all of its batsmen. A side which has 20 overs left and only 6 batsmen available has a lesser amount of resources. The records of tens of thousands of past limited-overs matches show that with less resources, the batting side cannot score as many runs.

The DLS table is not based on any formula or equation. The resource values for each point on the table are based on past performance - the actual scores from decades of matches. Occasionally, the base table is revised. Cricket teams are scoring more these days.

To use the DLS Method requires the software. It is a proprietary application. A few simple raw numbers are entered and the Par Score table can be generated.

Suppose you get a chance to ask this question to MS Dhoni, the master minded, definitely you would have choosen Dhoni rather than me (LoL)

So let's have a look on his words on DW Lewis method

"You've been around cricket for a long time, so can I ask you a question, do you understand Duckworth-Lewis?," Dhoni was asked, according to a report

And master mind hits back as…
"I don't think even ICC understands the D/L method," replied the wicketkeeper-batsman with a smile.

Let me share you an interesting fact before going to its nature

• South Africa's first World Cup adventure ended in heartbreak due to DW LEWIS RULE.
• which changes situation where they were at 22 runs from 13 balls to win, but after DLS method, 21 runs from 1 ball.(God must be crazy)

From that possible situation to such a worse situation…that much complexity involves in that process.

Hope you don't waste your energy while searching for such solutions as it is just a program that consists of all possible considerations.

Thank you.

The Duckworth–Lewis method (D/L) is a mathematical formulation designed to calculate the target score for the team batting second in a match interrupted by weather or other circumstances.

The essence of the D/L method is 'resources'. Each team is taken to have two 'resources' to use to score as many runs as possible: the number of overs they have to receive; and the number of wickets theyhave in hand. At any point , a team's ability to score more runs depends on the combination of these two resources left.

The percentage of resources left is calculated like the following model table:

In the version of D/L most commonly in use , the target for Team 2 is adjusted simply in proportion to the two teams' resources, i.e.

Team B par score= Team A's par score *(Team B's resource / Team A's resource)

If, as usually occurs, this 'par score' is a non-integer number of runs, then Team B's target to win is this number rounded up to the next integer. If Team B reaches or passes the target score, then they have won the match. If the match ends when Team B has exactly met the par score then the match is a tie. If Team B fail to reach the par score then they have lost.

Example:

Let a match is reduced to 45 overs each and Team A scored 250/6. The D/L method was applied which adjusted India's target to 268. As the number of overs was reduced during A's innings, they have only used (100–14.3{5 over left, 6 wickets lost}= )85.7 resources.

As B has 45 overs left and lost 0 wicket, they have 95 resource to use.

Team B's par score to win the match = 250*(95/85.7)= 277 in 45 overs.

Upvote if you liked !

Image & Fact Source: Google

The method is very simple as a whole but if you dive deep into the calculations you begin to face the difficulties. The method simply says, that a team’s revised target will always be depended on 2 of the resources that they have i.e. number of overs remaining and number of wickets remaining.

But as we go into the calculations, we understand that this method is not very adaption for the game if the players are not good at maths. You need to use several factors, do several calculations and then comes out the actual revised target/score. This is not really feasible if needed to be done on the field.

There have been instances where the batting team is well ahead of the D/L/S par score during the game but suddenly a wicket falls and they now lag behind the score. The batting team needs to be aware of the par score after each ball is bowled which requires some calculations being done after every ball, every wicket. This isn’t really possible if you are the batsman and on the field right now. You can’t really know about the par score until the end of the over( if umpire allows substitutes running in with the excuse of gloves or bat or simply drinks).

The simple formula of how the method works is:

Team 2’s par score = Team 1’s total x Team 2’s resources/ Team 1’s resources

So here, the final score will come out. Mind it, this is not as simple as it looks right now.

P.S. For all those nerds who want to get further deeper into the method:

Duckworth–Lewis-Stern method - Wikipedia

Cricket is one of the popular games not only in India but also in many countries of the world. The sports amateur and fan of cricket wants to enjoy without any interruption, but a rain shower sometimes causes disruption. Hence, ICC introduces a rule, i.e. Duckworth-Lewis rules that help to get results in rain-affected limited over a match i.e. 50 over match and T20. Here, we are giving the detail description of the Duckworth-Lewis rules and how it is used in rain affect limited over match result.

Principles of Duckworth-Lewis-Stern Method

It was devised by two English statisticians, Frank Duckworth and Tony Lewis. After their retirements Professor Steven Stern became the custodian of the rule. So in November 2014, it was renamed as the Duckworth–Lewis–Stern method (or D/L/S method). The principles of the Duckworth Lewis method are revolving around mathematical calculation of resources through probability, permutation and combination. Hence, we can say resources are the only thing that determines the outputs.

How Duckworth-Lewis-Stern Method use in cricket

According to the Duckworth-Lewis-Stern Rule, each team two types of resources, i.e. number of overs they have and the number of wickets in their hand. So in any situation, the team's ability can be decided on the combination of these two resources. When cricket match is started, then both the team has same resources, but over the time the resources of one or both teams are depleted and the two teams usually have different amounts of resource for their innings. Once, the match is interrupted by weather or other circumstances, and then Duckworth-Lewis-Stern Method is applied.

After analysing the above list, it is clearly shown that if team have 50 overs and 10 wickets then the probability of making run will be 100 percent, but once team uses it over and the wicket gets lost then the probability of getting run will be decreased accordingly.

In the below three examples clear the understanding of the application of the Duckworth Lewis Stern Rule:

First Instance: If rain interrupted the second inning of team and rain stop the game before maturity.

Team A Score 250 in 40 overs after losing five wicket. Team A had less resource available than Team B so their target must be scaled down by the ratio of resources, 72.5/100 Team A scored 250, so Team B's 'target' is 250 x 72.5/100 = 181.25. Hence, the winner will be decided according to the extra run or shortage of run, which mean those teams have more run than the set target as per Duckworth-Lewis-Stern Method declared as the winners by 18 runs.

Second Instance: Rain interrupted in the second inning Team’s batting

Team B had less resource available than Team A so their target must be scaled down by the ratio of resources, 79.2/90.3
Team A scored 300, so Team B's target is 300 x 79.2/90.3 =263.12, or 264 to win, and they require a further 36 runs from 5 overs with 5 wickets in hand.

Third Instance: If the rain affects the first inning

Assume that Team A score 200 runs in 40 overs after losing 7 wickets but rain interrupted the rest 10 over game. Then Team B get 40 Overs to play with new target. According to the Duckworth-Lewis-Stern method, Team A had only 17.9 % resources left. Therefore, Team A uses its resources 82.1 % of resources (100-17.9).

Team B have all the resources left but they get only 40 overs then as per D/L/S reference table and their resources will be 89.3 % which means they have 7.2 % extra resources that means they have 7.2 % more increment in their target.

As per ICC, 225 run is the average in 50 overs for ODIs then Team B have the target of 7.2 % of 200 + 235 i.e. 200 + 16.92 = 216.92 = 217 runs.

In the above description about Duckworth-Lewis-Stern method will enhance the knowledge of cricket and cricket lovers can itself analyse the term of condition when rain interrupted the cricket match in future.

How does DLS work?

The DLS (Duckworth-Lewis-Stern) method works on the principle that a batting team has two resources in hand when starting an ODI innings: 300 balls, and ten wickets. As the innings progresses, these resources keep depleting, and eventually reaches zero when a team either plays out all 300 deliveries, or loses all 10 wickets.

When, due to any reason, the batting team loses overs, they are denied the opportunity to make full use of their resources. Targets are hence revised in a way that is proportional to the amount of resources available to each team.

The rate at which these resources deplete isn't uniform across the overs, but varies depending on the scoring patterns of ODIs (calculated from studying matches over several years). At any point, the resources lost due to an interruption depends on:

- number of overs lost
- stage of an innings when the overs are lost
- wickets in hand at the time of the interruption

Losing overs in the later stages of an innings will usually impact a team more than losing the same number of overs earlier in an innings, as those overs are more productive, and teams have less opportunity to recalibrate their targets than if overs are lost early in the innings. A team which is already six down after 20 overs will have lesser to lose from a 10-over interruption, than a team which is, say, only two down at that stage. That is because in the first case, the team has already lost a huge chunk of their batting resources by the dismissals of six top-order batsmen. A team which is only two down can better capitalize on the last 30 overs than a team which is six down. However, the system doesn't take into account the specific batsmen who have been actually dismissed, or those who are still to bat.

The Duckworth Lewis is a mechanism for predicting and calculating scores in the event which stops play. Duckworth Lewis is mostly used in rain interrupted matches in limited overs where results are crucial and necessary.

What this means is that :

It is used to give value to a batsman,wicket overs remaining,run rate,etc.These parameters are then fed into some formulas and we get the result.

Suppose,England is playing India in England is the scenario.30 overs in the innings the scoreboard reads 168/4.

Suddenly dark clouds surround the skies and rain starts (typical English weather).Two hours and still there is no sign of it stopping.The extra quota of time is long exhausted.

Here,the Duckworth Lewis System DLS comes into the picture.The DLS calculates England's score keeping in mind the bo of wickets lost and their run rate at that point.Lets say they are given 285 to defend.

PS: I don't know the formulas used for the calculations.You can get them at the ICC's website.

Also VJD system has more supporters in India fue to it's supposed accuracy.

The Duckworth-Lewis method is based on the concept of batting resources, and calculates targets by taking into account the remaining resources after an interruption.

The method was first proposed in the paper 'A Fair Method for Resetting the Target in Interrupted One-Day Cricket Matches' by FC Duckworth and AJ Lewis, in the Journal of the Operational Research Society in 1998.

While formulating the method, Duckworth and Lewis (hereafter DL), took into account certain stipulations that their new method must adhere to. It must be almost equally fair to both sides, furnish realistic targets that are independent of the first team's scoring pattern (as it is in normal games), and it should be easy to apply and comprehend.

The method begins by recognizing that the side batting has with it two resources that can be quantified at any point in the innings: the overs remaining, and the wickets in hand. The ability of team to score is directly dependent on these two resources.

At the point of interruption, the aim of the method is to basically reset the target score based on the change in these resources for the chasing team.

For this, DL quantify the relationship between the runs that can be scored with the set of available resources.

They begin with the expression for the runs that can be made in [math]u[/math] overs:

[math]Z(u) = Z_{0}[1 - exp(-bu)][/math]

Here, [math]Z_{0}[/math] are the hypothetical average runs a team can score given infinite overs. This factor is calculated using average ODI scoring rates. The factor [math]b[/math] is the exponential decay factor that decays the runs scored, scaling it down based on the number of overs available. So, you can see, in infinite overs a team would score [math]Z_{0}[/math] runs, but this is reduced by a difference of [math]Z_{0}exp(-bu)[/math] in the case of [math]u[/math] overs remaining.

This expression is now to be modified to include the effect of having lost some number of wickets. For this, DL simply modify the factors [math]Z_{0}[/math] and [math]b[/math] to include the effect of wickets.

We now have [math]Z_{0}(w)[/math], the runs scored in infinite overs if you have [math]w[/math] wickets down. Similarly, we have [math]b(w)[/math], the decay factor in the case of having [math]10-w[/math] wickets left. This makes sense: the number of runs you can score get affected by the wickets left. The logical assumption here is that more the number of wickets you have left, the more resources you can make, and thus, greater the runs you can make from that point on.

Bear in mind, that the two essential functions here, [math]Z_{0}(w)[/math] and [math]b(w)[/math], are empirically calculated after computing scores at different points of hundreds of ODI matches. They are then fit into analytical forms that give sensible values and smooth derivatives for all values of [math]w[/math]. The full form of both these functions is not made public, and they keep getting updated.

Here is a graph of the runs scored as a function of the two parameters from the DL paper:

The current tables and graphs might be different, as this is from a 1998 paper. You can clearly see the graphs mimicking expected behaviour. The less the wickets lost, the more the runs you are expected to score for the same number of overs remaining.

With this done, we can calculate the proportion of runs remaining to be scored when a certain number of overs remain and a certain number of wickets are down.

The expected score at the start of an innings is (N overs and 0 wickets down):

[math]Z(N,0)[/math]

After facing [math]u[/math] overs and with [math]w[/math] wickets down, this comes down to:

[math]Z(u,w)[/math]

The proportion of runs to be scored is:

[math]P(u,w) = \frac{Z(u,w)}{Z(N,0)}[/math]

This is the central number in setting revised scores, as we shall see.

Now, let us begin with the case where there is an interruption in the innings of the chasing side.

They have [math]u_{1}[/math] overs remaining and are [math]w[/math] wickets down when play is stopped. When they return, they now only have [math]u_{2}[/math] overs left. As a result of this, they have lost [math]u_{1} - u_{2}[/math] overs.

The run-scoring resources they have lost as a result are:

[math]P(u_{1},w) - P(u_{2},w)[/math]. So now, the resources they have left are:

[math]R = 1 - (P(u_{1},w) - P(u_{2},w)) [/math]

If they were chasing [math]T[/math] runs, their revised target is simply:[math]RT[/math] runs. This makes sense, because we multiply the target by the proportion of resources lost due to the interruption.

Similarly, we can also compute the par score at every point in the innings. In case the innings stops at that point, the par score monitors the target of the chasing team.

If [math]n[/math] overs have been bowled, and the team chasing is [math]w[/math] wickets down, they have used a proportion [math]R_{u} = 1 - P(N-x,w)[/math] of their resources.

Since they have used this much, the score they should have made by this point is simply their target scaled by the resources used:

[math]R_{u}T[/math].

In a different set of cases, sometimes overs are lost in the innings of the team batting first, and then the chasing team is given the same number of overs as the setting team.

In this instance, the DL method recognizes that overs lost at different points in the innings have different impacts on the scoring ability of Team 1. They factor this in, and provide a method to set revised scores for Team 2.

The method recognizes that Team 1 loses coring opportunities through unplanned interruptions, and thus it is only fair to scale the target for Team 2 to take this into account.

Suppose Team 1 stops with [math]u_{1}[/math] overs left and comes back to bat with [math]u_{2}[/math] overs left. They now have:

[math]R_{1} = 1 - (P(u_{1},w) - P(u_{2},w))[/math]

as the proportion of resources remaining.

At the beginning of their innings, with some reduced number of overs, let us say Team 2 has [math]R_{2}[/math] resources remaining.

The revised target is now set by comparing the two teams' resources available.

If the two are equal, then the target for Team 2 is simply the same as Team 1's final score. If the resources available to Team 2 are less than [math]R_{1}[/math], then a simple scaling is done by multiplying Team 1's final score with the ratio of the resources.

DL find in their paper that if the resources for Team 2 are greater than those of Team 1, the scaling method often leads to unrealistic targets. However, they agree that the target should be greater than Team 1's final score.

To resolve this with an easy-to-use method, DL multiply the difference of resources [math]R_{2} - R_{1}[/math] by the average score of all innings of [math]N[/math] overs, where [math]N[/math] is the complete number of overs of the uninterrupted match. They then add this value to the final score of Team 1.

[math] T_{Team2} = S_{Team1} + Avg(N)[R_{2} - R_{1}][/math]

Phew!

The following is an excerpt from a document by the Northwich Cricket Club, as a summarized guide for applying the DL method:

The procedure for setting a revised target, which is the same for any number of stoppages at any stage of the match, is as follows.

1. For each team's innings
   (a) from the table note the resource percentage the team had available at the start of their innings;
   (b) using the table, calculate the resource percentage lost by each interruption;
   (c) hence calculate the resource percentage available.
2. If Team 2 have less resources available than Team 1, then calculate the ratio of the resources available to the two teams. Team 2's revised target is obtained by scaling down Team 1's score by this ratio.
3. If Team 2 have more resources available than Team 1, then calculate the amount by which Team 2's resource percentage exceeds Team 1's. Work out this excess as a percentage of the average 50 over score and this gives the extra runs to add on to Team 1's score to give Team 2's target.

http://www.northwichcc.co.uk/Duckworth-Lewis

They also have worked examples for multiple cases.

For applying this method, you can find multiple online calculators, and even an Android App.

The D/L method of resetting targets in rain-affected one-day cricket matches was trialled successfully during 1997 by the International Cricket Council (ICC), the ECB (England & Wales Cricket Board) and the Zimbabwe Cricket Union (ZCU). It has already been chosen for use in 1998 by the ECB, the ZCU and New Zealand.

The method is the invention of Frank Duckworth and Tony Lewis. Frank is a consultant statistician and editor of theRoyal Statistical Society's monthly news magazine, RSS NEWS. Tony is a lecturer in mathematical subjects in theFaculty of Computer Studies and Mathematics at the University of the West of England, Bristol and chairman of the Western Branch of the Operational Research Society

Applying the D/L method
The procedure for setting a revised target, which is the same for any number of stoppages at any stage of the match, is as follows.

1. For each team's innings
   (a) from the table note the resource percentage the team had available at the start of their innings;
   (b) using the table, calculate the resource percentage lost by each interruption;
   (c) hence calculate the resource percentage available.
2. If Team 2 have less resources available than Team 1, then calculate the ratio of the resources available to the two teams. Team 2's revised target is obtained by scaling down Team 1's score by this ratio.
3. If Team 2 have more resources available than Team 1, then calculate the amount by which Team 2's resource percentage exceeds Team 1's. Work out this excess as a percentage of 225 [the average 50 over score in ECB matches and one-day internationals (ODIs)] and this gives the extra runs to add on to Team 1's score to give Team 2's target.

Worked examples
Example 1: Premature curtailment of Team 2's innings
Team 1 have scored 250 runs from their 50 available overs and Team 2 lose 5 wickets in scoring 199 runs in 40 overs. Play is then stopped by the weather, the rain refuses to relent and the match is abandoned. A decision on the winner is required.
Team 1's innings: this was uninterrupted, so the resource percentage available is100%.Team 2's innings: resource % available at start of innings =100%After 40 overs Team 2 have 10 overs left and have lost 5 wickets.
From table, resource % left at suspension of play =27.5%As play is abandoned all this remaining resource is lost.
Hence resource % available for Team 2's innings = 100 - 27.5 =72.5%
Team 2 had less resource available than Team 1 so their target must be scaled down by the ratio of resources, 72.5/100
Team 1 scored 250, so Team 2's 'target' is 250 x 72.5/100 = 181.25
As there is to be no further play, the winner is decided according to whether or not this target has been exceeded. With 199 runs on the board, they have exceeded their required target by 17.75 and so are declared the winners by 18 runs.
Note : The above result is quite fair as Team 2 were clearly in a strong position when play was stopped and would very likely have gone on to win the match if it hadn't rained. Most other methods of target revision in use would, unfairly, make Team 1 the winners. The average run rate method gives 201 to win, the Current ICC method gives 227 and the parabola method gives 226. [Setting the target by the method of Discounted Total Runs - the Australian rain-rule - requires knowledge of the runs made by Team 1 from their most productive overs but the target would almost certainly be no lower than that required under average run rate and would probably be much higher so that Team 2 would very probably lose by this method as well.]
Example 2: Interruption to Team 2's innings
In an ECB Axa Life (Sunday) League match Team 1 have scored 200 runs from their 40 available overs and Team 2 lose 5 wickets in scoring 140 runs in 30 overs. Play is then suspended and 5 overs are lost. What is Team 2's revised target?
Team 1's innings: At the start of 40 over innings resource percentage available =90.3%Team 2's innings: resource % available at start of 40 over innings =90.3%After 30 overs Team 2 have 10 overs left and have lost 5 wickets.
From table, resource % left at start of suspension =27.5%5 overs are lost, so when play is resumed 5 overs are left.
From table, resource % left at resumption of play =16.4%Hence resource % lost = 27.5 - 16.4 =11.1%so resource % available for Team 2's innings = 90.3 - 11.1 =79.2%
Team 2 had less resource available than Team 1 so their target must be scaled down by the ratio of resources, 79.2/90.3
Team 1 scored 200, so Team 2's target is 200 x 79.2/90.3 =175.42, or 176 to win, and they require a further 36 runs from 5 overs with 5 wickets in hand.
Example 3: Interruption to Team 1's innings
In an ODI, Team 1 have lost 2 wickets in scoring 100 runs in 25 overs from an expected 50 when extended rain leads to Team 1's innings being terminated and Team 2's innings is also restricted to 25 overs. What is the target score for Team 2?
Because of the different stages of the teams' innings that their 25 overs are lost, they represent different losses of resource. Team 1 have lost 2 wickets and had 25 overs left when the rain arrived and so from the table you will see that the premature termination of their innings has deprived them of the 61.8% resource percentage they had remaining. Having started with 100% they have used 100 - 61.8 = 38.2%; in other words they have had only38.2% resources available for their innings.
Team 2 will also receive 25 overs. With 25 overs left and no wicket lost you will see from the table that the resource percentage which they have available (compared to a full 50 over innings) is 68.7%. Team 2 thus have 68.7 - 38.2 = 30.5% greater resource than had Team 1 and so they are set a target which is 30.5% of 225, or 68.63, moreruns than Team 1 scored. [225 is the average in 50 overs for ODIs]
Team 2's revised target is therefore set at 168.63, or 169 to win in 25 overs, and the advantage to Team 2 from knowing in advance of the reduction in their overs is neutralised.
Note: Most of the other target resetting methods in use make no allowance for this interruption. They set the target of 101 to win simply because both teams are to receive the same number of overs. This is clearly an injustice to Team 1 who were pacing their innings to last 50 overs when it was curtailed, whereas Team 2 knew in advance of the reduction of their innings to 25 overs and have been handed an unfair advantage. D/L allows for this by setting Team 2 a higher target than the number of runs Team 1 actually scored, as described above.

Courtesy: ESPN cricinfo

The Duckworth-Lewis method is a mathematical formula used in cricket to adjust the target score for the team batting second in a rain-affected limited-overs match. It is named after its inventors, Frank Duckworth and Tony Lewis, it was first used in 1997.

In a limited-overs match, if the match is interrupted by rain or any other unforeseen circumstances, the Duckworth-Lewis method is used to recalculate the target score for the team batting second. The method takes into account the number of overs remaining, the number of wickets lost, and the run-rate at the time of the interruption to calculate the revised target for the team batting second. The aim of the method is to provide a fair target for the team batting second, given the circumstances of the match. It is widely used in limited-overs cricket, including One Day Internationals (ODIs) and Twenty20 matches, to ensure that a result can be obtained even if the match is affected by weather or other interruptions.

Frank Duckworth (left) and Tony Lewis, the inventors of the Duckworth-Lewis method

The essence of the D/L method is 'resources'. Each team is taken to have two 'resources' to use to score as many runs as possible: the number of overs they have to receive; and the number of wickets they have in hand. At any point in any innings, a team's ability to score more runs depends on the combination of these two resources they have left. Looking at historical scores, there is a very close correspondence between the availability of these resources and a team's final score, a correspondence which D/L exploits

The D/L method converts all possible combinations of overs (or, more accurately, balls) and wickets left into a combined resources remaining percentage figure (with 50 overs and 10 wickets = 100%), and these are all stored in a published table or computer. The target score for the team batting second ('Team 2') can be adjusted up or down from the total the team batting first ('Team 1') achieved using these resource percentages, to reflect the loss of resources to one or both teams when a match is shortened one or more times.

In the version of D/L most commonly in use in international and first-class matches (the 'Professional Edition'), the target for Team 2 is adjusted simply in proportion to the two teams' resources, i.e.

Team 2 par score = Team 1 par score *(team 2 resources /team 1 resources )

If, as usually occurs, this 'par score' is a non-integernumber of runs, then Team 2's target to win is this number rounded up to the next integer, and the score to tie (also called the par score), is this number rounded down to the preceding integer. If Team 2 reaches or passes the target score, then they have won the match. If the match ends when Team 2 has exactly met (but not passed) the par score then the match is a tie. If Team 2 fail to reach the par score then they have lost.

For example, if a rain delay means that Team 2 only has 90% of resources available, and Team 1 scored 254 with 100% of resources available, then 254 × 90% / 100% = 228.6, so Team 2's target is 229, and the score to tie is 228. The actual resource values used in the Professional Edition are not publicly available,

so a computer which has this software loaded must be used.

If it is a 50-over match and Team 1 completed its innings uninterrupted, then they had 100% resource available to them, so the formula simplifies to:

Score = team 1 score * team 2 resources

The Duckworth-Lewis method is used to help decide rain-interrupted one-day and T20 cricket matches. It is named after Frank Duckworth and Tony Lewis who devised the mathematical formula. It means a result can always be reached in a reduced overs match.

For example, if the team which bats first had their innings interrupted, team two would often be set a larger run target to compensate. But should the team second at the stumps be interrupted, their run target would often be reduced. Duckworth and Lewis came up with the equation which determines how much a run target should be altered.

The D/L method of resetting targets in rain-affected one-day cricket matches was trialled successfully during 1997 by the International Cricket Council (ICC),the ECB (England & Wales Cricket Board) and the Zimbabwe Cricket Union(ZCU).

Some of the matches interrupted by D/L Method

1. Needing 22 off 13 deliveries,the D/L equation set a revised target of 22 runs from 1 delivery.

Graham Gooch consoles Brian McMillan as the players walk off the SCG

• 22 off one ball

2. A well set Malik at the crease and 21 needed off 12 deliveries, but Pakistan couldn’t get home.

• http://www.espncricinfo.com/zimbabwe-v-pakistan-2015-16/content/story/925461.html

3. Proteas, again a victim of D/L Method. WC 15

• http://www.espncricinfo.com/icc-cricket-world-cup-2015/engine/current/match/656455.html

Here’s a link to the D/L calculator: https://www.easycalculation.com/sports/duckworth-lewis-calculator.php

Finally the Culprits:)

Rain-affected targets

​

The Duckworth-Lewis method is used to help decide rain-interrupted one-day cricket matches.
It is named after Frank Duckworth and Tony Lewis who devised the mathematical formula.
It means a result can always be reached in a reduced overs match.
WHEN IS IT USED?

Teams start a match with the same resources - the number of overs they receive and number of wickets in hand.
If a match is shortened once it is started, so the resources are reduced.
For example, if the team which bats first had their innings interrupted, team two would often be set a larger run target to compensate.
But should the team second at the stumps be interrupted, their run target would often be reduced.
Duckworth and Lewis came up with the equation which determines how much a run target should be altered.
HOW DOES IT WORK?

For example: a team have lost five wickets after receiving 25 of their 50 overs when rain stops play.
At this point, using the table produced by the Duckworth-Lewis method, the team's remaining resources are valued at 42.2%.
If 15 overs are then lost because of the weather, the innings will be completed after only 10 more overs.
The D/L method says that, with 10 overs left and five wickets lost, the team has 26.1% of their resources left.
To compensate for the lost overs, we must calculate the resource % lost.

​

This works out to 42.2 - 26.1 = 16.1.
If the team had been chasing a total of 250 runs, their new target is calculated in the following way.
Resources available at the start = 100%
Resources lost = 16.1
Resources available after rain interruption = 83.9%
Then reduce team one's score in the following way. Multiply team one's runs scored by the recalculated resources divided by the resources available at the start.
That is: 250 x 83.9/100 = 209.75.
The target is then rounded to the nearest whole number, so the team batting second would be set a target of 210 to win.
Simple!

In the version of D/L most commonly in use in international and first-class matches (the 'Professional Edition'), the target for the team batting second ('Team 2') is adjusted up or down from the total the team batting first ('Team 1') scored, in proportion to the two teams' resources (combination of overs and wickets available), i.e.

[math]{\displaystyle {\text{Team 2's par score }}={\text{ Team 1's score}}\times {\frac {\text{Team 2's resources}}{\text{Team 1's resources}}}.}[/math]

If, as usually occurs, this 'par score' is a non-integer number of runs, then Team 2's target to win is this number rounded up to the next integer, and the score to tie (also called the par score), is this number rounded down to the preceding integer. For example, if a rain delay means that Team 2 only has 90% of the resources that were available to Team 1, and Team 1 scored 254, then 254 × 90% = 228.6, so Team 2's target is 229, and the score to tie is 228. The actual resource values used in the Professional Edition are not publicly available,

[11]

so a computer which has this software loaded must be used.

If it's a 50-over match and Team 1 completed its innings uninterrupted, then they had 100% resource available to them, so the formula simplifies to:

[math]{\displaystyle {\text{Team 2's par score }}={\text{ Team 1's score}}\times {\text{Team 2's resources}}.}[/math]

Summary of impact on Team 2's targetEdit

• If there is a delay before the first innings starts, so that the numbers of overs in the two innings are reduced (but still the same as each other), then D/L will make no change to the target score. This is because both sides will be in the same position of having the same number of overs and 10 wickets available, and they will know this throughout their innings, thus having the same amount of resource available.
• Team 2's target score is first calculated once Team 1's innings has finished.
• If there were interruption(s) during Team 1's innings, or Team 1's innings was cut short, so the numbers of overs in the two innings are reduced (but still the same as each other), then D/L will adjust Team 2's target score as described above. The adjustment to Team 2's target after interruptions in Team 1's innings is often an increase, implying that Team 2 has more resource available than Team 1 had. Although both teams have 10 wickets and the same (reduced) number of overs available, an increase is fair as, for some of their innings, Team 1 thought they would have more overs available than they actually ended up having. If Team 1 had known that their innings was going to be shorter, they would have batted less conservatively, and scored more runs (at the expense of more wickets). They saved some wicket resource to use up in the overs that ended up being cancelled, which Team 2 doesn't need to do, therefore Team 2 doeshave more resource to use in the same number of overs. Therefore, increasing Team 2's target score compensates Team 1 for the denial of some of the overs they thought they would get to bat. The increased target is what D/L thinks Team 1 would have scored in the overs it ended up having, if it had known throughout that the innings would be only as long as it was.

For example, if Team 1 batted for 20 overs before rain came, thinking they would have 50 overs in total, but at the re-start there was only time for Team 2 to bat for 20 overs, it would clearly be unfair to give Team 2 the target that Team 1 achieved, as Team 1 would have batted less conservatively and scored more runs, if they'd known they would only have the 20 overs.

• If there are interruption(s) to Team 2's innings, either before it starts, during, or it's cut short, then D/L will reduce Team 2's target score from the initial target set at the end of Team 1's innings, in proportion to the reduction in Team 2's resources. If there are multiple interruptions in the second innings, the target will be adjusted downwards each time.
• If there are interruptions which both increase and decrease the target score, then the net effect on the target could be either an increase or decrease, depending on which interruptions were bigger.

The Duckworth–Lewis (D/L) method is a mathematical formulation designed to calculate the target score for the team batting second in a limited overs cricket match interrupted by weather or other circumstances. It is generally accepted to be the most accurate method of setting a target score. The D/L method was devised by two English statisticians, Frank Duckworth and Tony Lewis.

After their retirements Professor Steven Stern became the custodian of the method. In November 2014, it was renamed the Duckworth–Lewis–Stern method (or D/L/S method).

Calculation

In the version of D/L most commonly in use in international and first-class matches (the 'Professional Edition'), the target for the team batting second ('Team 2') is adjusted up or down from the total the team batting first ('Team 1') scored, in proportion to the two teams' resources (combination of overs and wickets available), i.e.

If, as usually occurs, this 'par score' is a non-integer number of runs, then Team 2's target to win is this number rounded up to the next integer, and the score to tie (also called the par score), is this number rounded down to the preceding integer. For example, if a rain delay means that Team 2 only has 90% of the resources that were available to Team 1, and Team 1 scored 254, then 254 × 90% = 228.6, so Team 2's target is 229, and the score to tie is 228. The actual resource values used in the Professional Edition are not publicly available,

so a computer which has this software loaded must be used.

If it's a 50-over match and Team 1 completed its innings uninterrupted, then they had 100% resource available to them, so the formula simplifies to:

Summary of impact on Team 2's target

• If there is a delay before the first innings starts, so that the numbers of overs in the two innings are reduced (but still the same as each other), then D/L will make no change to the target score. This is because both sides will be in the same position of having the same number of overs and 10 wickets available, and they will know this throughout their innings, thus having the same amount of resource available.
• Team 2's target score is first calculated once Team 1's innings has finished.
• If there were interruption(s) during Team 1's innings, or Team 1's innings was cut short, so the numbers of overs in the two innings are reduced (but still the same as each other), then D/L will adjust Team 2's target score as described above. The adjustment to Team 2's target after interruptions in Team 1's innings is often an increase, implying that Team 2 has more resource available than Team 1 had. Although both teams have 10 wickets and the same (reduced) number of overs available, an increase is fair as, for some of their innings, Team 1 thought they would have more overs available than they actually ended up having. If Team 1 had known that their innings was going to be shorter, they would have batted less conservatively, and scored more runs (at the expense of more wickets). They saved some wicket resource to use up in the overs that ended up being cancelled, which Team 2 doesn't need to do, therefore Team 2 does have more resource to use in the same number of overs. Therefore, increasing Team 2's target score compensates Team 1 for the denial of some of the overs they thought they would get to bat. The increased target is what D/L thinks Team 1 would have scored in the overs it ended up having, if it had known throughout that the innings would be only as long as it was.

For example, if Team 1 batted for 20 overs before rain came, thinking they would have 50 overs in total, but at the re-start there was only time for Team 2 to bat for 20 overs, it would clearly be unfair to give Team 2 the target that Team 1 achieved, as Team 1 would have batted less conservatively and scored more runs, if they'd known they would only have the 20 overs.

• If there are interruption(s) to Team 2's innings, either before it starts, during, or it's cut short, then D/L will reduce Team 2's target score from the initial target set at the end of Team 1's innings, in proportion to the reduction in Team 2's resources. If there are multiple interruptions in the second innings, the target will be adjusted downwards each time.
• If there are interruptions which both increase and decrease the target score, then the net effect on the target could be either an increase or decrease, depending on which interruptions were bigger.