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SOUTH WALES PREMIER CRICKET LEAGUE DUCKWORTH – LEWIS

WORKED EXAMPLES IN MATCH SITUATIONS

Note: Throughout the formulae given in this document, “Team A” is always the side batting first and “Team B” is always the side batting second. R1 is team A’s resources; R2 is team B’s resources.

EXAMPLE 1 – INTERUPTION IN THE SECOND INNINGS

The match is Ammanford v Cardiff

Match starts on time (12.30pm) @ 50 overs per side.

Ammanford bat (and start their innings resources set at 100. i.e. all their 50 overs and all

their wickets)

Ammanford play their innings uninterrupted and score 252-8 in 50 overs.

After tea, Cardiff come out to bat and as there have been no interruptions Cardiff also start

their innings with resources set at 100 (i.e. all their 50 overs and all their wickets).

70 minutes into Cardiff's innings with the score at 121-3 and 22 overs bowled, rain

intervenes and the players come off the field.

After 85 minutes off the field the Umpires decide that it will be possible to resume in 15

minutes.

(1) TIME & OVERS

As the interruption took place in the second innings one over is deduced from the innings of

the side batting second for each full 3½ minutes lost.

As no previous interruptions have taken place during the match then the first 60 minutes of

stoppage time is ignored. (n.b. The threshold for stoppage time can be 90 minutes if BOTH

captains agree).

By the time play resumes the players will have been off the field for 100 minutes.

(a) 100-60 = 40 nett stoppage minutes.

(b) 40÷3½ = 11.42 = 11 overs lost (always round down)

(c) Therefore Cardiff will only have 39 (50-11) overs in their innings.

(2) DUCKWORTH-LEWIS

When the players came off for rain, Cardiff's score was 121-3 after 22 overs, with still 28

(50-22) overs to bowl.

(i) Look up the Line of 28 overs in the D-L table and the column for 3 wickets

lost. This returns a resources figure for the start of the interruption of

59.5

(ii) At the restart there will only be 17 overs (39-22) remaining. Look up the

Line of 17 overs in the D-L table and the column for 3 wickets lost.

(iii) This returns a resources figure at the resumption of 44.1. So during the

stoppage D-L has computed that the resources lost for Cardiff is 15.4

(59.5-44.1).




The revised target for Cardiff now has to be calculated. As Cardiff started with their

resources set at 100, deduct 15.4 from the starting figure, to give an R2 adjustment number

to be applied to the first innings score. i.e. 100-15.4=84.6

As Cardiff with 84.6 (R2) have fewer resources than Ammanford at 100 (R1), the formula

“(First Innings Score x Team B Resources ÷ Team A Resources) + 1” is then applied to the

Ammanford score of 252 which is (252 x R2 ÷ R1)+1 calculated as follows

252 x 84.6 ÷ 100 = 213.19 = 213 (always round DOWN) + 1 = 214 to win.

(3)POINTS SCORING

a. If Cardiff score 214 they will win outright

b. If Cardiff score 213 the match will be a tie

c. If Cardiff score less that 213, but are not all out it will be a draw. (n.b. Points for the

draw will be based on proximity to 213, not 214)

d. If Ammanford bowl Cardiff out then Ammanford will be the outright winners.

e. Ammanford's batting bonus points will be based on the points awarded for a 50 over

innings. Ammanford’s bowling points will be based on a 39 overs innings. Cardiff’s

bonus points will be vice-versa.

* * * EXAMPLE 2 – DELAYED START THEN INTERUPTION IN SECOND INNINGS

The match is Newport v Sully. The match start is delayed, but gets underway at 2.20 pm

with 110 minutes lost.

In a delayed start situation overs are deducted from the innings of both sides at a rate of 1

over per side for each full 7 minutes lost. The 60 minutes allowance doesn’t apply when

calculating for a delayed start.

Therefore: - 110 ÷7 = 15.71 = 15 overs per side (always round down). The match starts at 35 overs per side.

Newport bat (and start their innings with resources set at 82.7 (as per the D-L table on the

35 line in the “0” wickets column). Note - This resources figure only becomes relevant if

there are more interruptions and there is no need to look at the tables unless and until a

further interruption occurs and a recalculation is required).

Newport bat through their innings uninterrupted and score 198-9 in 35 overs. After tea,

Sully bat (and as Newport, their starting resource figure is therefore 82.7).

30 minutes into Sully’s innings with the score at 35-1 and 9 overs bowled, rain intervenes

and the players come off the field. After 95 minutes off the field the Umpires decide that it




will be possible to resume in 20 minutes.

(1) TIME & OVERS

In the second innings one over is deduced from the innings of the side batting second for

each full 3½ minutes lost.

As no previous interruptions have taken place during the match (the delayed start doesn’t

count) then the first 60 minutes of stoppage time is ignored. (The Captains do not agree to

allow the extra 30 minutes stoppage time)




(c) Therefore Sully will now only have 20 (35-15) overs in their innings (Note - 20 overs is

the minimum allowed in the second innings and if any more time had been lost the

match would be abandoned).

(2) DUCKWORTH-LEWIS

When the players came off for rain, Sully's score was 35-1 after 9 overs, with still 26 (35-9)

overs to bowl.

(i) Look up the Line of 26 overs in the D-L table and the column for 1 wicket lost.

This returns a resources figure for the start of the interruption of 65.6

(ii) At the restart there will only be 11 overs (20-9) remaining. Look up the Line of

11 overs in the D-L table and the column for 1 wicket lost. This returns a

resources figure at the resumption of 34.2

(iii) So during the stoppage D-L has computed that the resources lost for Sully is 31.4

(65.6-34.2).

The revised target for Sully now has to be calculated. As Sully started with their resources

set at 82.7, deduct 31.4 from the starting figure, to give an R2 adjustment number to be

applied to the first innings score. i.e. 82.7-31.4=51.3

As Sully with 51.3 (R2) have fewer resources than Newport at 82.7 (R1), the formula


Newport score of 198 which is (198 x R2 ÷ R1)+1 calculated as follows:-

198 x 51.3 ÷ 82.7 = 122.82 = 122 (always round DOWN) + 1 = 123 to win.

(3)POINTS SCORING

a. If Sully score 123 they will win outright

b. If Sully score 122 the match will be a tie




c. If Sully score less that 122, but are not all out it will be a draw.

d. If Newport bowl Sully out then Newport will be the outright winners.

e. Bonus points will be awarded by reference to the relevant reduced over tables.

* * * EXAMPLE 3 – MULTIPLE INTERUPTIONS IN THE SECOND INNINGS

Usk are home to Pontarddulais on a fine sunny day. Pontarddulais win the toss and decide

to bat and are bowled out in the 50th over for 233.

It has been clouding over all afternoon and after 25 minutes of play with Usk’s score at 22-2

and 7 overs bowled the players come off the field.

One hour and ten minutes later, the match resumes and a revised target is needed (as the

captains do not agree to allow the extra thirty minutes due to the cloudy conditions)

1) TIME & OVERS

Overs are reduced in the second innings on the basis of one over being deduced for each full

3½ minutes lost.

The whole of the 60 minutes threshold is used up in the first interruption, and by the time

play resumes the players will have been off the field for 70 minutes.



(c) Therefore Usk will now only have 48 (50-2) overs in their innings.

(2) DUCKWORTH-LEWIS

At the interruption, Usk's score was 22-2 after 7 overs, with still 43 (50-7) overs remaining.

(i) Look up the Line of 43 overs in the D-L table and the column for 2 wickets lost.


(ii) At the restart there will only be 41 overs (48-7) remaining. Look up the Line of

41 overs in the D-L table and the column for 2 wickets lost. This returns a


(iii) The stoppage has resulted in D-L computing that the resources lost for Usk is 1.6

(80.3-78.7).

Usk started with resources of 100. Deduct 1.6 from the starting figure, to give an R2

adjustment number to be applied to the first innings score. i.e. 100-1.6=98.4

As Usk’s resources(R2) at 98.4 are less than Pontarddulais’ resources(R1) at 100, the formula


Pontarddulais score of 233 which is (233 x R2 ÷ R1)+1 calculated as follows:-





Then after a further 55 minutes play, when the Usk score has advanced to 83-4 after 21

overs a further shower occurs. It is 25 minutes before play can be resumed.

1) TIME & OVERS

One over is deduced for each full 3½ minutes lost. (The 60 minute threshold has been used)

(a) 25 stoppage minutes ÷3½ = 7.14 = 7 overs lost (always round down)

(b) Therefore Usk will now only have 41 (50-2-7) overs in their innings.

(2) DUCKWORTH-LEWIS

At the interruption, Usk's score was 83.4 after 21 overs, with still 27 (48-21) overs

remaining.

(i) Looking up the line for 27 overs in the D-L table and the column for 4 wickets lost

returns a resources figure for the start of the interruption of 51.8

(ii) At the restart there will only be 20 overs (41-21) remaining; and looking up the

Line for 20 overs in the D-L table and the column for 4 wickets lost returns a


(iii) The second stoppage has resulted in D-L computing that the resources lost for

Usk is 7.2 (51.8-44.6).

In this situation, resources lost are cumulated before calculating the revised target.

Usk started with resources of 100. The first stoppage loss was computed as 1.6 and the

second of 7.2. These are added together to give a combined loss of 8.8 which is deducted

from 100 to give an updated R2 number of 91.2 (100-8.8).

R2 (91.2) is less than R1 (100) so the formula


Pontarddulais score of 233 which is (233 x R2 ÷ R1)+1 calculated as follows:-


The players have only been out on the field for another 45 minutes when there is a further

shower which clears to bright sunshine. With the scores interestingly poised on 159-6 after

32 overs the Captains decide to use the extra 30 minutes threshold time that they are

allowed.

1) TIME & OVERS

One over is deduced for each full 3½ minutes lost, but the extra 30 minute threshold has

now been invoked.

(a) 45-30 = 15 nett stoppage minutes ÷3½ = 4.28 = 4 overs lost (always round down)




(b) Therefore Usk will now only have 37 (50-2-7-4) overs in their innings.

(2) DUCKWORTH-LEWIS

At the interruption, Usk's score was 159-6 after 32 overs, with still 9 (41-32) overs

remaining.

(i) Looking up the line for 9 overs in the D-L table and the column for 6 wickets lost

returns a resources figure for the start of the interruption of 21.4




(iii) The third stoppage has resulted in D-L computing that the resources lost for Usk

is 7.1 (21.4-14.3).

Resources lost are cumulated before calculating the revised target.

Usk started with resources of 100. First Stoppage (1.6) + Second Stoppage (7.2) + Third

Stoppage (7.1) = 15.9. Therefore 100 – 15.9 = 84.1 (R2)

Once again R2 is less than R1 so the formula “(First Innings Score x Team B Resources ÷

Team A Resources) + 1” is then applied to the Pontarddulais score of 233 which is (233 x R2

÷ R1)+1 calculated as follows:-


Leaving Usk to score 37 runs in 5 overs with 4 wickets in hand.

* * * EXAMPLE 4 – RESULT IN MATCH UNABLE TO BE FINISHED

Port Talbot are home to Sully. Sully bat first and score 265-8 in 50 overs. The Port Talbot

innings is proceeding nicely when a thunderstorm strikes and makes any chance of a

resumption impossible. Port Talbot were 133-3 at the end of the 26th over when the

players fled the field.

DUCKWORTH-LEWIS

At the abandonment Port Talbot's score was 133-3 after 26 overs, with still 24 (50-23) overs

remaining.

Look up the Line of 24 overs in the D-L table and the column for 3 wickets lost.




This returns a resources figure when abandoned of 54.7 which as there will not be a restart

the figure of 54.7 becomes the resources lost number.

Port Talbot started with resources of 100. Deduct 54.7 from the starting figure, to give an

adjustment number to be applied to the first innings score. i.e. 100-54.7=45.3 (R2)

Once again R2 is less than R1 so the formula


Sully score of 265 which is (265 x R2 ÷ R1)+1 calculated as follows:-

265 x 45.3 ÷ 100 = 120.04 = 120 (always round DOWN) + 1 = 121 to win. As the target is less than the runs already scored, Port Talbot are the winners. Even though

Port Talbot were batting second the winning margin is quoted as runs, in this instance “Port

Talbot won by 13 runs (D/L method)

Note that even if Port Talbot have say lost their third wicket when the score was 125, the

bowling side still earn bonus points for the wickets they may have taken after the winning

score was (in retrospect) passed, and similarly for batting bonus points.

In the above example bonus point are as follows:-

Sully: 5 batting and 3 bowling

Port Talbot: 3 batting and 4 bowling

In the above scenario, if Port Talbot had been 113-4 wickets then the resources lost number

would have been 49, which would have produced an R2 adjustment number of 51 (100-49)

In this case the formula would have returned

265 x 51 ÷ 100 = 135.15 = 135 (always round DOWN) + 1 = 136 to win. and as Port Talbot were not all out the match would have been a draw (within 10 runs) with

a points split of 8 to Sully and 4 to Port Talbot. Bonus points would have again have been

awarded on the basis of a normal first innings and a reduced second innings – i.e. the same

as shown above.

* * * EXAMPLE 5 – INTERUPTION IN THE FIRST INNINGS

Cardiff are playing Newport. The match starts on time with Newport batting but after 35

overs with Newport well placed on 175-2 there is a prolonged interruption of 120 minutes.

(1) TIME & OVERS

As no previous interruptions have taken place during the match then the first 60 minutes of

stoppage time is ignored. (n.b. The threshold for stoppage time can be 90 minutes if BOTH




captains agree) and as the stoppage is in the first innings, overs are reduced (for both sides)

on the basis of 1 over for each full seven minutes lost.

The players were off the field for 120 minutes.


(b) 60÷7 = 8.57 = 8 overs lost per side (always round down)

(c) Therefore both Newport and Cardiff will only have 42 (50-8) overs in their innings.

(2) DUCKWORTH-LEWIS

When the players came off for rain, Newport's score was 175-2 after 35 overs, with still 15

(50-35) overs to bowl.

(i) Look up the Line of 15 overs in the D-L table and the column for 2 wickets lost.


(ii) At the restart there will only be 7 overs (42-35) remaining for Newport to bat.

Look up the Line of 7 overs in the D-L table and the column for 2 wickets lost.

This returns a resources figure at the resumption of 22.7

(iii) So during the stoppage D-L has computed that the resources lost for Newport is

19.9 (42.6-22.7).

Therefore Newport’s resources (R1) for the innings were 80.1 (100-19.9)

Newport have obviously been disadvantaged by the stoppage coming late in their innings

when they were well placed. In the remaining 7 overs, Newport advance their score to

231-8.

As an interruption has taken place in the first innings (and there has been a reduction in

overs) a resources comparison need to take place before the second innings commences.

Cardiff will start their innings knowing that they will receive 42 (50-8) overs

The line for 42 overs is looked up on the D/L table in the column for 0 wickets (because, of

course Cardiff haven’t started their innings yet). This gives an R2 resource number of 91.7

As R2, the resources for the side batting second (Cardiff) at 91.7 are greater than R1, the

resources for the side batted first (Newport) at 80.1 - a revised target for Cardiff now has to

be calculated using the formula below applied to the Newport score of 231:-

([Team B Resources - Team A Resources] ÷ 100 x 225) + First Innings Score) + 1”.

([R2 – R1] ÷ 100 x 225) + R1 + 1 calculated as follows:-

[91.7 – 80.1] = 11.6

(11.6 ÷ 100 x 225) + 231 = 257.1 (always round DOWN) + 1 = 258 to win.




Cardiff’s target at the commencing of the 2nd Innings is 258 to win in 42 overs. This 27 more

than Newport’s score. It shows how Duckworth-Lewis is compensating Newport for losing

the last eight overs of their innings.

EXAMPLE 5A – FURTHER INTERUPTION IN SECOND INNINGS

When Cardiff have reached 120-4 after 20 overs with 22 remaining there is a shower which

causes 30 minutes of further stoppage time (and the captains do not invoke the extra

threshold time).

(1) TIME & OVERS

Second Innings stoppages reduce overs at the rate of 1 over per full 3½ minutes lost

Therefore 30 ÷ 3½ = 8.57 = 8 overs lost to Cardiff, making their innings now 34 overs (42-8).

(2) DUCKWORTH-LEWIS

It is necessary first to ensure that the resources available to Newport are still less than those

available to Cardiff to determine which formula to use when recalculating the target.

Newport’s R1 number cannot change from 80.1, whereas Cardiff’s R2 number which at the

start of the innings was 91.7 can.

(i) Looking up the line for 22 (42-20) overs in the D-L table and the column for 4

wickets lost returns a resources figure for the start of the interruption of 47.0




(iii) The stoppage has resulted in D-L computing that the resources lost for Cardiff is

11.1 (47-35.9).

(iv) Deducting the resources lost (11.1) from the start resources (91.7) gives a new

R2 number of 80.6

As Cardiff’s R2 number is still greater than Newport’s R1 number of 80.1, the formula used

at the close of the Newport Innings is still appropriate, and can be recomputed as follows

80.6 - 80.1 = 0.5 (0.5 ÷ 100 x 225) + 231 = 232.12 = 232 (always round DOWN) + 1 = 233 to win.

...and then within a few minutes of the teams resuming the match there is another short

sharp shower which just takes 15 minutes out of the playing time. 4 overs were bowled in

the meantime, making 24 in all with the score at 141-5 when play was suspended.




(1) TIME & OVERS

15 minutes lost at the rate of 1 over per full 3½ minutes equates to 4 overs lost (15 ÷ 3½ =

4.29 = 4).

The Cardiff innings is now going to be only 30 (34-4) overs.

(2) DUCKWORTH-LEWIS

It is again necessary to ensure that the resources available to Newport are still less than

those available to Cardiff to determine which formula to use when recalculating the target

Newport’s (R1) was 80.1 and Cardiff’s (as at the start of their innings) was 91.7

(i) Looking up the line for 10 (34-24) overs in the D-L table and the column for 5

wickets lost returns a resources figure for the start of the interruption of 26.1

(ii) At the restart there will only be 6 overs (30-24) remaining; and looking up the Line

for 6 overs in the D-L table and the column for 5 wickets lost returns a resources

figure at the resumption of 17.8

(iii) This stoppage has resulted in D-L computing that the resources lost for Cardiff is 8.3

(26.1-17.8).

(iv) Deducting the resources lost (11.1+8.3=19.4) from the start resources (91.7) gives a

new R2 number for Cardiff of 72.3

It is plain that Cardiff’s resources (R2) at 72.3 are now less than Newport’s resources (R1)

at 80.1 and therefore the formula reverts to the one used in examples 1 to 4.

“(First Innings Score x Team B Resources ÷ Team A Resources) + 1”

i.e. (231 x R2 ÷ R1)+1 calculated as follows:-


Thus at the re-start Cardiff will require 68 runs to win in 6 overs.

* * * EXAMPLE 6 – PROLONGED STOPPAGE IN FIRST INNINGS

In this scenario Bridgend are home to Port Talbot. Bridgend have batted first and have

scored 200-6 in 44 overs when a heavy shower drives the players from the field. Tea is

taken but it is only 3 hours later that the pitch is deemed fit for play to resume.

1) TIME & OVERS

As the first innings is still in progress then 1 over is deducted from the innings of both sides

for each full seven minutes lost. As tea was taken (and the first innings will end during the

stoppage) you can allow an extra 30 minutes of threshold time. By the time play resumes

the players will have been off the field for 180 minutes.




(a) 180-(60+30) = 90 nett stoppage minutes.

(b) 90÷7 = 12.85 = 12 overs lost per side, but as Bridgend have already received 44

against a revised entitlement of 38 (50-12), the over-entitlement of 6 (44-38)

overs must be deducted from Port Talbot’s entitlement.

(c) Port Talbot will therefore receive 32 (38-6) overs.

(2) DUCKWORTH-LEWIS

When the players came off for rain, Bridgend's score was 200-6 after 44 overs, with 6 (50-

44) overs to bowl.

(i) Look up the Line of 6 (50-44) overs in the D-L table and the column for 6 wickets

lost. This returns a resources figure for the start of the interruption of 16.4

(ii) Bridgend were never able to re-start their innings, so (for reference at this stage),

the R1 resources available to them are computed as 83.6 (100-16.4).

(iii) Port Talbot now has 32 overs available to them. Thus when they start their

innings their R2 resources will be 78.3 (from the 32 overs line, 0 wickets column

on the D-L Table)

(iv) Thus Port Talbot’s R2 resources batting second are less than Bridgend’s R1

resources batting first, so the formula to be applied is

“(First Innings Score x Team B Resources ÷ Team A Resources) + 1”

i.e. (200 x R2 ÷ R1)+1 calculated as follows:-


* * * The following are examples of TIME & OVER calculations in slightly unusual situations.

EXAMPLE 7 – OVERS AND/OR TIME TRANSFERENCE

In this scenario, Sully are playing Bridgend. Sully bat first but are bowled out for 223 in the

46th over, thus leaving 4 full overs unused

In the Bridgend innings it starts to rain and it is 90 minutes before play can be resumed.

(1) TIME & OVERS



(b) 30÷3½ = 8.57 = 8 overs lost (always round down) BUT Sully failed to used 4 overs, so

this can be allowed for in the calculation of overs sue to Bridgend

(c) Therefore Bridgend will have 46 (50-8+4) overs in their innings.




(2) DUCKWORTH LEWIS

Bridgend were 36-1 after 10 overs when the stoppage started, with still 40 (50-10) overs to

bowl.

(i) Looking up the 40 overs line and the column for 1 wicket lost in the D-L

tables returns a resources figure for the start of the stoppage of 84.2

(ii) At the restart there will only be 36 overs (46-10) remaining. Looking up

the Line of 36 overs in the D-L table and the column for 1 wicket lost will

return a resources figure at the resumption of 79.7

(iii) So during the stoppage D-L has computed that the resources lost for

Bridgend is 4.5 (84.2-79.7), so they have 95.5 (R2) left

As Sully were all out they have used all their resources. The fact that they did not use all of

their overs is irrelevant. The formula “first innings score x R1 ÷ R2 is applied to the Sully

score as follows:_


Note also that sides batting first are allowed to declare and that any overs unused in the first

innings can be offset against overs lost through weather in the second innings.

* * * EXAMPLE 8 ABANDONMENT IN FIRST INNINGS

It is already only marginally playable at Mumbles when their opponents are Ynysgerwn.

A start cannot be made until 2.30 and the match is therefore reduced to 33 overs per side.

After 28 overs of the first innings at 4.25pm a heavy shower strikes. Tea is taken and

although the sun comes out afterwards, it is now 6pm with a possibility of a start in about

10 minutes.

TIME & OVERS

If play resumes at 6.10 the players will have been off the field for 105 minutes.

(a) 105-(60+20) = 25 nett stoppage minutes. (n.b. 20 minutes allowance for the tea

interval)

(b) 25÷7 = 3.57 = 3 overs lost (always round down) Therefore the match is reduced to

30 overs per side.

BUT

If the stoppage had lasted just three minutes longer the calculations would have been

(a) 108-(60+20) = 28 nett stoppage minutes. (n.b. 20 minutes allowance for the tea

interval)

(b) 28÷7 = 4 = 4 overs lost (always round down). Therefore the match having been

reduced to 29 overs per side has to be abandoned.




IF AN INTERUPTION OCCURS WHILE THE SIDE BATTING FIRST IS STILL BATTING THE

MATCH CANNOT CONTINUE UNLESS BOTH SIDES HAVE THE OPPORTUNITY TO BAT FOR

AT LEAST 30 OVERS.

* * * EXAMPLE 9 – ABANDONMENT IN SECOND INNINGS

Mumbles are home to Sully on a day that starts bright and sunny. Mumbles bat first and

their innings proceeds without any interference from the weather and after 50 overs they

post a score of 265-8. Sully start to bat as grey cloud streams in from the west. It begins

to drizzle and gets steadily heavier so that after 10 overs the Umpires take the players of the

field. On a couple of occasions the rain almost stops, but each time the players start to get

ready to resume, it starts to rain harder again.

The umpires took the players off the field at 4.40pm. It is now 7pm with a restart possible

at 7.15. Can the game proceed?

TIME & OVERS

(i) 155 gross minutes have been lost. 155-60=95 nett minutes lost

(ii) 95÷3½ = 22.85 = 27 overs

(iii) 50 overs – 27 overs = 23 overs

(iv) Since 20 overs is the minimum allowed to a side batting second then the match

can proceed

Thus there will be 13 overs still be bowled at the restart and a target recalculation to take

place.

Note that if the stoppage was just 14 minutes longer then the calculation would have been

that

(i) 169 gross minutes lost. 169-60=109 nett minutes lost

(ii) 109÷3½ = 31.14 = 31 overs

(iii) 50 overs – 31 overs = 19 overs

(iv) Since 20 overs is the minimum allowed to a side batting second then the match

has to be abandoned.

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