Duckworth/Lewis simplified

I say simplified. It may not be the case for every one.

But I have just attended a lecture by  Dr Tony Lewis or the Duckworth/Lewis Method, and through his graphs and curves, he has attempted to explain why, what, and how of the method seems to confuse players, commentators, and spectators alike.

He begins by giving a few examples, where justice had surely been thrown out of the window when rain or other factors forced shortening or abandoning of a cricket match. The most famous example being South Africa v England, semi-final 1992 World Cup, where a factor of 22 off 13 balls was reduced to 22 off 1 ball there.

Various methods have been used in the past:

– Average run rate method, where the scores are simply divided based on run rates.
– Best overs method, where the best X overs are taken when the team batting second has only X overs to play.
– Worst overs method, where the worst overs are subtracted from the total (two maidens were subtracted for those 12 balls in the Eng v SA match).
– Parabolic Method, very close to the the D/L method, but only takes averages over scoring methods but does not factor in loss of wickets.

Chasing a score, the team batting second has two things to look at: the overs/balls remaining, and the number of wickets in hand. A method was required that used both these factors, unlike the previous methods that only used the first factor.

Frank Duckworth, came up with a method that used both the factors. Sadly, the method was very complex and required at least a computer or a telephone sized directory to calculate. Being 1995, this was not the easiest way to go. However, Tony Lewis collaborated and worked with Duckworth and managed to make it much simpler.

The basic principle is that every team has a set of resources. If you have 50 overs left, and 10 wickets in hand, you have 100% of your resources left. If, however, you have only 25 overs left, but still all 10 wickets, you actually have about 66% of your resources left.

Following table and chart give an example…

imageScoring potential as a function of wickets and overs.

So for example, if you had to chase 200 in 50 overs, And were 115/5 in 25 overs. You can score 68.7%, 61.8%, and 43.4% of the remaining runs in 25 overs if you had all, 8 or 5 wickets left. Subtract that from your total at 25 overs, and if you have scored more, you win, below you lose. Based on the above numbers, you have 85 runs still to score, which is 42.5%. Which means, you just about make it to the winning side by being 0.9% or 1.8 runs above the par score. Thing to remember here is that you have to be ABOVE the par score, not equal it, as that only ties the match. (South Africa v Sri Lanka – World Cup 2003).

Interesting factors that are used in the calculation are the average ODI score over the last 4 years, which has gone from 235 to 245 in a decade.

Another interesting point was that based on numbers and stats, this rule applies perfectly to T20 cricket as well. It does not feel right, and the Eng v WI match for the T20 Championship in West Indies this year was a good example. Chasing 60 off 6 overs seems a bit too easy if you made 191 in 20. Having said that, Sir Lewis stands by his grounds, and showed graphs to prove his words.

I found the following links useful:

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

http://www.jritson.demon.co.uk/dl.htm

http://en.wikipedia.org/wiki/Duckworth%E2%80%93Lewis_method

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