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The Duckworth/Lewis system was invented by two statisticians, Frank Duckworth and Tony Lewis in an attempt to solve the perennial problem of creating a fair target for the side batting second in a limited-overs match shortened by the weather(rain,bad light,sand storm even snow storm) or problems due to artificial lights.

At its simplest, the problem is this. If the side batting first in a 50-over match makes 250 runs, the target for the side batting second is 250 to tie, 251 to win. Their average run-rate must therefore exceed 5 per over if they are to win in a full 50 overs. But if rain or bad light stops further play after only 20 overs, during which the second side score 101 runs, then comparing average run-rates would make the second side the winner. But if they had lost nine wickets in gaining those 101 runs, then few would give much for their chances in an uninterrupted 50 overs. So the old average-run rate system gave an unfair advantage to the side batting second if the number of overs was reduced. They could blaze away without worrying too much about losing wickets. Other variants were tried, such as basing the target on the best overs of the side batting first, but this was unfair to the side batting second.

Enter Messrs Duckworth and Lewis, who studied the performances in a great number of limited overs matches, and concluded that the factor to take into account was what they called the "resources" available to each side. The resources depend on the number of wickets lost and the number of balls remaining to be bowled.

But the calculations are very cumbersome,so I am giving the link to duckworth-lewis calculator.So whenever you have interrupted cricket you know where to log in.
duckworth-lewis calculator

Having said all this how often we have seen team getting duckworth-lewis wrong(for eg south africa in 2003 WC), or how often we have seen teams getting undue advantage.It's the only way to avoid bad weather is to cover the stadiums provided the floodlights are working properly,else you will require duckworth-lewis again.

Information:duckworth-lewis.com