How does the Duckworth-Lewis formula determine runs scored in less overs?

Answer 1

Google "Duckworth Lewis explained" & there are a host of options for you to choose from.

Answer 2

The D/L method of resetting targets in rain-affected one-day cricket matches has now been in use for well over two years and has been adopted for use in most test playing countries of the world. And it is the 'rain-rule' in use for the 1999 World Cup competition played in May and June and hosted by the England & Wales Cricket Board.

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

The method that they have invented is simple to apply provided one is prepared to take a few minutes to understand its logic. The calculations can easily be performed using nothing more than a single table of numbers and a pocket calculator although a purpose built computer program is available to undertake the calculations accurately and quickly in match situations (see further information on this below). With a little practice, however, there is no reason why anyone should not be able to calculate the revised target and in quick time. The authors firmly believe that the method is simple enough for it to be adopted for use at all levels of limited-overs cricket. This article provides a summary of the way the method works.

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.

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 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 usually result in Team 2 having more resources available and then their target is revised upwards to correct for the extra resources they have at their disposal

For more details as to how the calculation is made etc., please check the following link:

http://www.cricinfo.com/db/ABOUT_CRICKET/RAIN_RULES/DUCKWORTH_LEWIS_1999.html

Answer 3

There are only 2 people I know of who can fully explain the system - Mr Duckworth and Mr Lewis!!

The system is based on the run rate achieved by the team that batted first and the number of wickets fallen.

Try googling it ... or contact someone at the MCC to explain it for you.

Answer 4

Even the umpires & match referee had no idea in the final. What a shambles!

Answer 5

You had to ask:


Duckworth/Lewis Method of Re-calculating the Target Score in an Interrupted Match.





The Professional Edition of the Duckworth/Lewis shall be used in all matches. If any
match is suspended after it has started such that the number of overs available to be faced
by either side is reduced from that determined when the match started, the revised target
shall be computed using the latest version of CODA as distributed by ICC in accordance
with the instructions provided with that software and displayed on the screen.



Where possible, arrangements shall be made for the provision of back-up capability, in
case of computer malfunction, for the operation or continued operation of the
Professional Edition. In the event of computer non-availability or malfunction where no
such provision has been made, the Standard Edition (the method in use prior to October
2003) shall be used.



The regulations given below describe only the operation of the Standard Edition, except
that Clauses 4, 6 and 7 are also applicable to the Professional Edition.





1. Introduction




The D/L method sets revised targets in rain-interrupted limited-overs matches in
accordance with the relative run scoring resources which are at the disposal of the two
sides.



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 how many overs are
to go and how many wickets are down when the interruptions occur.

To calculate the revised targets, you need to know the resources available at the stage of
the match when suspensions and resumption of play occur. All possible values of
resources have been pre-calculated and these are listed in the accompanying table.



The table covers each individual ball in a game of up to 50-overs per side. The figures
given in the table are percentages of the resources available for a complete 50-over
innings.



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.



The single sheet over-by-over version of the table can be used for cases when play is
suspended before the start of a new 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, including Under-19 international
matches, or for matches between teams that play first class cricket, the value of G50 to
be used at present is 235. For lower levels of the game, G50 should be chosen to
represent the average score expected from the team batting first in an uninterrupted 50
overs-per-innings match. For teams between associate ICC member nations, the
recommended value of G50 is 190; for women’s ODIs, the recommended value is 175.
For U15 internationals, the recommended value is 200. For other levels of the game,
advice should be sought from the ICC.





2. Definitions




• The team batting first are referred to as ‘Team 1’ and the team batting second are
referred to as ‘Team 2’.
• In the table decimal fractions of an over are expressed in standard cricket notation;
i.e. 4.3 overs means 4 overs plus 3 balls.
• The terms ‘target’ and ‘revised target’ are reserved exclusively for the minimum
score Team 2 need to win.
• As with an uninterrupted match, if Team 2 make a score which is one run short of the
target, the match is tied.




The following symbols are used throughout:



N is the number of overs per innings for the match as decided at the moment of
delivery of the first ball of the match.

S is Team 1’s total score.

R1 is the resource percentage (relative to a full 50-over innings) available to Team 1.

R2 is the resource percentage (relative to a full 50-over innings) available to Team 2.

T is Team 2’s target score.





3. Calculation of the Percentage Resource Lost by a Suspension in Play




To compensate for any loss of overs due to a suspension in play during either Team 1’s
or Team 2’s innings, it is necessary first to calculate the resource percentage that has
been lost on account of this suspension.



If the suspension occurs between overs, use the sheet of the table which gives the figures
for whole numbers of overs. If it occurs mid-over, use the sheets of the table which
provide the figures for each individual ball.



3.1 For the start of the suspension in play, from the table note the resource percentage that
remained for the appropriate number of overs/ball left and wickets lost.




3.2 For the resumption of play after the suspension, from the table note the resource
percentage now remaining for the revised number of overs/balls left and for the same
number of wickets lost.



3.3 Subtract the resource percentage in 3.2 from that in 3.1 to give the resource percentage
lost.



3.4 If a suspension in play causes the innings to be terminated, the resource percentage on
resumption (3.2) is zero and the percentage lost is the resource percentage which was
remaining when the suspension occurred (3.1).



3.5 If more than one suspension in play occurs, the resource percentages lost are calculated
as described in 3.1 to 3.4 and are accumulated to give updated values for the total
resource percentage lost or resource available for the innings. This is done after each
suspension as described in 5.2 and 5.5.







4. Penalties for Slow Over Rates



No overs penalties are imposed for slow over rates and hence slow over rates have no
effect on revised target calculations.



5. Calculation of Revised Targets



5.1 Note the number of overs per innings decided at the start of the game, N. From the table
note the resource percentage available to Team 1 at the start of their innings. (For N = 50
this is 100%.)

5.2 For all suspensions and any premature termination of Team 1’s innings, calculate the
total resource percentage lost using the procedure described in section 3. Subtract this
from the starting resource percentage (5.1) to give R1, the resource which was available
to Team 1 for their innings. Note Team 1’s total score, S.

5.3 There is no overs penalty for slow over rates by either side.


5.4 Note the number of overs allocated to Team 2 at the start of their innings and from the
table note the resource percentage for this number of overs remaining and 0 wicket lost.
This is R2, the resource percentage available to Team 2. If R2 differs from R1, which
will happen if Team 1’s innings was interrupted and/or Team 2’s was delayed, a revised
target must be set. Calculate this revised target, T, as described in 5.6 below.

5.5 For each suspension of play during Team 2’s innings or for premature termination of the
match, update the resource percentage available, R2, by subtracting the resource
percentage lost calculated as in section 3. Calculate the revised target, T, after each
suspension as described in 5.6 below. If the match has to be terminated, the result is
decided by comparing Team 2’s score at the time with the ‘par score’, this being the
value as calculated in the formulae for T in 5.6 below, but without the one run added. If
it is greater, Team 2 win. If it is equal, the match is tied. If it is less, Team 1 win.
5.6 If R2 is less than R1, Team 2’s revised target is obtained by reducing Team 1’s score S
in the ratio of R2 to R1, ignoring any figures after the decimal point, and adding one run
i.e. T = (S x R2/R1) + 1 (rounded down to a whole number, if necessary).





If R2 is equal to R1, no revision is needed and Team 2’s target is one more run than
Team 1’s score.

i.e. T = S + 1

If R2 is greater than R1, calculate the amount of excess resources, R2 – R1, and take this
percentage of the average 50-over total, G50, to give the extra runs needed, ignoring any
figures after the decimal point.

i.e. T = S + (R2 – R1) x G50/100 + 1 (rounded down to a whole number, if necessary)








6. Penalty Runs



6.1 During Team 1’s innings



If penalty runs are awarded to the batting side, then their score shall advance accordingly
and be taken into account when performing any future D/L calculation.



If penalty runs are awarded to the fielding side, then any D/L calculation in between
innings will be performed as normal, and their innings will commence with the score
equivalent to the number of penalty runs that they have been awarded.



6.2 During Team 2’s innings



If penalty runs are awarded to the batting side, then their score shall advance accordingly.
These penalty runs do not affect any subsequent D/L calculation.



If penalty runs are awarded to the fielding side, then there will be no recalculation of any
D/L target. Instead, the target score and the entire schedule of par scores will advance by
the appropriate number of penalty runs. If a loss of overs occurs after such a penalty has
been awarded, then the D/L target will be calculated based upon the original score of the
side batting first, and this target, and all par scores, will then be raised by the appropriate
number of penalty runs



7. The Result and its Description



When a revised target has been calculated and the match has been played out to its
completion, the result is described exactly as in the case of an uninterrupted match; if
Team 2 achieve their revised target they win by the number of wickets they have in hand
when they reach this score; if they fall short of their revised target by exactly one run the
result is a tie, and if they make a lower score Team 1 win by the margin of runs by which
Team 2 fall short of the score needed to achieve a tie.



When a match has to be abandoned with Team 2’s innings in progress (provided
sufficient overs have been bowled to constitute a viable match), the result is decided by
comparing Team 2’s score with the ‘par score’ as defined in 5.5 and the winning margin
is described in terms of the number of runs by which their score differs from the ‘par
score’, regardless of whether Team 1 or Team 2 are the victors.

Whenever a completed game has involved the use of the D/L method, the description
should be qualified by appending ‘(D/L method)’.




7.1 Examples of result description:




(i) Team 2 are set a revised target of 186. But they only succeed in making 180 in their
allocation of overs. They thus fall 5 runs short of the 185 runs needed to tie the
match and the result is described as ‘Team 1 win by 5 runs (D/L method)’.




(ii) Team 2 are chasing a target of 201 in a 50-over per innings match and reach 105/4
after 25 overs when rain causes the match to be abandoned. At this point the ‘par
score’ is 100. Team 2 have exceeded this by 5 runs and so the result is described as
‘Team 2 win by 5 runs (D/L method)’.



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% (3.1)

Resource percentage remaining at resumption (20 overs left, 3 wkts lost) = 49.1% (3.2)

Resource percentage lost due to suspension = 61.6 – 49.1 = 12.5% (3.3)

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 (5.6) is

T = S + G50 x (R2 – R1)/100 + 1 = 180 + 235 x (89.3 – 87.5)/100 + 1 = 185 (rounded
down).



Example 2 (delay to start of Team 2’s innings)



In an English National League match (45 overs per innings), Team 1 scores 212 in its
allocated 45 overs. Rain then causes Team 2’s response to be delayed and it is decided
that it should be shortened to 35 overs.



Number of overs at start of match, N = 45.


Resource percentage available to Team 1 at start of its innings (45 overs left, 0 wkt lost)
= 95.0% (5.1).

The innings was not interrupted, so R1 = 95.0%



Number of overs available to Team 2 at start of its innings = 35

Resource percentage available to Team 2 at start of innings (35 overs left, 0 wkt lost) R2
= 82.7% (5.4)



R2 is less than R1; S = 212

Team 2’s revised target (5.6) is

T = S x R2/R1 + 1 = 212 x 82.7/95.0 + 1 = 185 (rounded down).



Example 3 (suspension during Team 2’s innings)



In an One Day International match (50 overs per innings), Team 1 has scored 250 from
its allocation of 50 overs in an uninterrupted innings. Team 2 has received 12 overs and
has scored 40/1. Then play is suspended and 10 overs are lost.



Number of overs at start of match, N = 50.

Team 1’s innings was uninterrupted, so its resource percentage available, R1 = 100%
(5.1).



Resource percentage available to Team 2 at start of innings = 100% (5.4).

Resource percentage remaining at suspension (38 overs left, 1 wkt lost) = 82.0% (3.1).

Resource percentage remaining at resumption (28 overs left, 1 wkt lost) = 68.8% (3.2).

Resource percentage lost due to suspension = 82.0 – 68.8 = 13.2% (3.3).

Resource percentage available to Team 2, R2 = 100 – 13.2 = 86.8% (5.5).



R2 is less than R1; S = 250.

Team 2’s revised target (5.6) is

T = S x R2/R1 + 1 = 250 x 86.8/100 + 1 = 218 , and it needs a further 178 runs from 28
overs.



Example 4 (multiple suspensions and abandonment)



Suppose that in Example 3, play continues for a further 10 overs during which Team 2
takes its score on to 98/3, whereupon there is another suspension in play and 2 more
overs are lost. A further 8.2 overs are bowled and Team 2 is 154/6 when rain washes out
the match.




Team 1’s resource percentage is still R1 = 100%.



Team 2’s resource percentage has been reduced further.

Resource percentage remaining at start of second suspension (18 overs left, 3 wkts lost)
= 45.9% (3.1).

Resource percentage remaining at end of second suspension (16 overs left, 3 wkts lost) =
42.3% (3.2).

Resource percentage lost due to second suspension = 45.9 – 42.3 = 3.6% (3.3).

Resource percentage available to Team 2, R2 = 86.8 – 3.6 = 83.2% (5.5).



R2 is less than R1; S = 250.

Team 2’s revised target (5.6) is

T = S x R2/R1 + 1 = 250 x 83.2/100 + 1 = 209 and it needs a further 111 runs from 16
overs.



When the innings had to be terminated, there were 7.4 overs remaining.

Resource percentage remaining at termination of Team 2’s innings (7.4 overs left, 6 wkts
lost) = 19.4%.

This remaining resource is lost by the termination.

Resource percentage available to Team 2, R2 = 83.2 – 19.4 = 63.8% (5.5).



R2 is less than R1; S = 250.

Team 2’s par score (5.5 and 5.6) is S x R2/R1 = 250 x 63.8/100 = 159 (rounded down);
the par score at the instant of abandonment is 159 and with a score of 154 it has lost by 5
runs.

Team 1 wins by 5 runs (D/L method) (7).



Example 5 (suspension and termination of Team 1’s innings mid-over and delay to
Team 2’s innings)



This is taken form an actual ODI: India (Team 1) versus Pakistan (Team 2), Singapore,
April 1996. 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% (5.1).

Resource percentage remaining at termination (2.5 overs left, 8 wkts lost) = 6.9% (3.1).


Resource percentage lost due to termination = 6.9% (3.4).

Resource percentage available, R1 = 100 – 8.1 = 93.1% (5.2).



Team 2’s innings (allocated 33 overs):

Resource percentage available at star to f innings (33 overs left, 0 wkts lost), R2 =
79.8% (5.4).



R2 is less than R1; S = 226.

Team 2’s revised target (5.6) is

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



Example 6 (as Example 5 but with a further interruption during Team 2’s innings)



In the match of the previous example, Team 2 has scored 140 for 2 after 25 overs when a
further 5 overs are lost to the weather.



Team 1’s resource percentage is still R1 = 93.1%.



Team 2’s innings:



Resource percentage at start of innings (33 overs left, 0 wkt lost) = 79.8% (5.4).

Resource percentage remaining at suspension (8 overs left, 2 wkts lost) = 25.5% (3.1).

Resource percentage remaining at resumption (3 overs left, 2 wkts lost) = 10.4 % (3.2).

Resource percentage lost due to suspension = 25.5 – 10.4 = 15.1% (3.3).



Resource percentage available, R2 = 79.8 – 15.1 = 64.7% (5.2).



R2 is less than R1; S = 226.

Team 2’s revised target (5.6) is

T = S x R2/R1 + 1 = 226 x 64.7/93.1 + 1 = 158 (rounded down) and it needs a further 18
runs from 3 overs.