Frank Duckworth and Tony Lewis are English mathematicians who have provided the best answer so far to a problem that has bothered limited-overs cricket from the very beginning. Both are living retired lives now, after distinguished careers in academia and industry. Although they have made a number of impressive contributions to statistics and mathematics, it is their contribution to cricket that has made them famous.

The problem addressed by Duckworth and Lewis has to do with shortened limited-over matches. You know the scenario. Lets say India and Pakistan are playing each other in an ODI. India has batted first and posted 307 for 6. During the lunch break, there is a downpour and Pakistan's innings cannot start on time. By the time the skies clear and the ground staff dries the outfield, there is time for only 30 more overs. What would be a fair target for Pakistan to achieve in this shortened innings?

Prior to the Duckworth-Lewis method, a number of formulas were tried to solve this problem but none quite got it right. The calculation would end up either favouring the batting side or the bowling side, sometimes with shocking consequences. Those of you who followed the 1992 World Cup will recall how South Africa were robbed of a spot in the final when they came out after a rain interruption requiring a bizarre 21 runs off the last delivery. They had been going smoothly at 231 for 6 needing another 21 from 43 balls remaining when rain halted play. The readjustment formula used in that particular tournament was based on the most expensive overs bowled by the side batting second. As with other attempts to readjust a shortened target, it ended up in farce and created a lot of bitterness.

There can be any number of variations on the basic theme of a shortened match, but the central dilemma is common to all how should a target set by a team that has completed its innings be modified in the event that the team batting second does not have the opportunity to play all its allotted overs? The curtailment could come from bad weather, crowd disturbance, or a UFO landing in the middle of the pitch. It doesn't matter. What matters is that not enough time is available for the second team to play the same number of overs that were played by the team that batted first. Neither does it matter when the interruption happens — it could be during the innings break or in the middle of the innings itself. So long as the team batting second is forced to play a shortened innings, the Duckworth-Lewis method will be invoked.

The calculation itself cannot be conveniently reproduced in a newspaper column, because it is not straightforward and requires a computer. But if you are so inclined, then just Google Duckworth-Lewis and you will find a number of websites providing details and calculators. The set of formulas takes into account the number of wickets in hand for the side batting second, as well as the stage of the innings when the interruption occurs. This reflects the core premise of the method, which regards wickets in hand as the key asset in a run chase and also recognises that scoring rates vary over the different stages of an innings.

How this works in practice is that following an interruption in a curtailed match, the captain of the side batting second is handed a computer printout with 10 columns and 50 rows. If there is more than one interruption, then a fresh table is generated after each interruption, taking into account the stage of the innings when the interruption happened.

Each spot in the table provides the corresponding target that must be achieved by the end of a given over (anywhere from one to 50, hence the 50 rows), depending on how many wickets have been lost (which can be anywhere from zero to nine, hence the 10 columns). In fact, ICC rules stipulate that a minimum of 20 overs must be faced by the side batting second before an ODI can be considered completed, so the first 19 rows of the printout are of academic interest only.

The D/L method first received official recognition in 1997, when the England Cricket Board adopted it for use in English domestic cricket. The ICC soon followed suit, and the method made its debut in international cricket in the 1999 World Cup, becoming part of standard ICC regulations for limited-overs cricket.

In principle, the Duckworth-Lewis method can also be used for Twenty20 cricket, but the mathematical model as currently configured is based on scoring rates typical of ODI (50-over) cricket. This favours the side batting second in a Twenty20 run chase, because the formulas are projecting targets based on a 50-over innings, in which scoring rates during the initial 20-over segment are lower than in a Twenty20 innings. The effect is subtle, but it matters. During the 2010 Twenty20 world cup, England captain Paul Collingwood complained about this to anyone who would listen, after his team lost to the West Indies who were given a relatively soft Duckworth-Lewis target in a rain-shortened match. There is recognition now that the D/L formulas must be configured for Twenty20 matches incorporating the scoring patterns typically observed in Twenty20 internationals.

Despite its technicalities, the D/L method has become widely accepted and followed. It attempts to provide justice in the middle of a changed set of circumstances. This innate quality of fairness is what really makes it so much part of the ethos of cricket.