Technologies: Duck Worth & Lewis

Duck Worth & Lewis

Frank Duckworth and Tony Lewis

The D/L method was created by two British statisticians, Frank Duckworth and Tony Lewis. It was first used in international cricket in the second game of the 1996/7 Zimbabwe versus England One Day International series, which Zimbabwe won by 7 runs,[5] and was formally adopted by the International Cricket Council in 2001 as the standard method of calculating target scores in rain shortened one-day matches.

Variouss different methods had been previously used to achieve the same task, including run-rate ratios, the score that the first team had achieved at the same point in their innings, and targets derived by totaling the best scoring overs in the initial innings. All of these methods have flaws that are easily exploitable. For example, run-rate ratios do not account for how many wickets the team batting second have lost, but simply reflect how quickly they were scoring at the point the match was interrupted; thus, if a team felt a rain stoppage was likely, they could attempt to force the scoring rate without regard for the corresponding highly likely loss of wickets, skewing the comparison with the first team. Notoriously, the “best-scoring overs” method, used in the 1992 Cricket World Cup, left the South African cricket team requiring 21 runs from one ball (when the maximum score from any one ball is generally six runs). Prior to a brief rain interruption, South Africa was chasing a target of 22 runs from 13 balls – which was difficult but at least attainable – but the possibility of an exciting conclusion to the game was destroyed when the team’s target was reduced by only one run, to be scored off 12 fewer balls.[6] The D/L method removes – or at least normalises – this flaw: in this match, the revised D/L target would have been four runs to tie or five to win from the final ball.

The Professional Edition of the Duckworth-Lewis method 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 the ‘ICC Duckworth/Lewis Calculator’ as distributed by ICC in accordance with the instructions provided with that software.

The regulations given below describe only the operation of the Standard 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.

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, or for matches between teams that play first class cricket, the value of G50 should be 245.
For lower levels of the game:
• under 19 international matches
• under 15 international matches
• women’s international matches
• matches between associate ICC member nations
the value of G50 should be 200.

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 P ercentage R esource Lost by a Suspension in P lay

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/balls 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 S low O ver R ates
No overs penalties are imposed for slow over rates and hence slow over rates
have no effect on revised target calculations.

5 Calculation of R evised T argets
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 R 2/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 – R 1) x G50/100 + 1 (rounded down to a whole number,
if necessary)

6 Penalty R uns
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 R esult and its D escription
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)’.