Prof Richard Barker, of the University of Otago maths
department, talks about the Duckworth-Lewis method of
reduced over calculation. Photo by Jane Dawber.
Most cricket fans understand the Duckworth-Lewis
method about as well they understand quantum physics or
baseball's infield fly rule. Otago Daily Times cricket
writer Adrian Seconi attempts to shed some light on the formula
used when limited-overs matches are affected by weather
delays.
It certainly looks like gobbledygook when you see the
equation on a white board.
And even a wet weekend in Waitahuna would not be long enough
to come to terms with all the intricacies of the
Duckworth-Lewis method.
But the theory is not that difficult to understand at all -
simple, even.
Well, simple if you are using one of those free online
calculators where all you have to do is pop a few digits in
the right boxes and, hey presto, the magic numbers appear.
Maths aside, after several efforts to get to grips with the
system, there has been a bit of a breakthrough. All it took
was an analogy.
According to Professor Richard Barker, the head of the
department of mathematics and statistics at the University of
Otago, the Duckworth-Lewis method works like compound
interest, only in reverse.
The model is based on diminishing resources. Each team's
resources are its wickets in hand and the number of overs
available. The ability to score runs depends on the
combination of those two resources and it is that
relationship which the Duckworth-Lewis method exploits.
"It is a simple mathematical model and, like all models, it
is not reality but an abstraction of reality," Barker said.
"The question isn't whether the calculation is exactly right,
it is a question of whether it is close enough for everybody
to go away happy - most importantly, the spectators."
Therein lies the problem. The general public does not get it.
Duckworth-Lewis is often informally criticised as being too
complex.
Staring at the equation on the board once again, it is hard
to disagree. But the system Frank Duckworth and Tony Lewis
devised is streets ahead of some of the previous methods
which had been used.
Of all the various systems, it seems to deliver the fairest
result. And a fair result is one which gives both teams the
same chance of winning after the interruption as they had
before the interruption.
"One of the keys of the Duckworth-Lewis is they recognise
that the balls remaining isn't the only resource you have to
consider.
"If you scale the target back in proportion to the balls
lost, that is not going to lead to a fair outcome because
there is no adjustment made for the number of wickets lost."
It was a situation not too dissimilar which gave Duckworth
the idea in the first place. He was listening to a broadcast
of the 1992 World Cup semifinal debacle between South Africa
and England.
South Africa needed 22 runs from 13 balls when a short rain
delay left the Proteas apparently needing 22 runs from one
delivery (they actually needed 21 runs from one delivery but
a mistake was made).
He heard Christopher Martin-Jenkins saying surely someone
could come up with a better system.
It was a lightbulb moment, as they say.
The Duckworth-Lewis method made its debut in the summer of
1996-97 but was not formally adopted by the ICC until 2001.
Had it been used in the 1992 semifinal, South Africa would
have needed four runs to tie and five runs to win.
So how does it work? The system uses statistical information
and historical data, which is regularly reviewed, to give the
average amount of runs scored given the number of wickets and
number of balls remaining.
That information is tabulated and used to calculate the
percentage of resources lost when there is a stoppage in
play.
Target scores are then scaled appropriately.
If team one, for example, scored 250 runs from 50 overs and
team two was 199 for five after 40 overs when play was
abandoned, team two would win by 18 runs.
Why? Well, team two had 27.5% of its resources remaining when
the game was called off. That means team two used 72.5% of
its resources, and 72.5% of 250 is 181.25. It exceeded the
the Duckworth-Lewis adjusted target by 17.75 runs and is
declared the winner by 18 runs.
Simple, see? Of course, only God knows whether team two would
have gone on to win the game had the weather not intervened.
Perhaps the best measure of the system's fairness is the fact
the proportion of matches won by the team batting first is
about the same for uninterrupted and interrupted matches.
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