Tony Lewis the inventor of D/L method at the County Ground (Image Credits: Cricktracker)
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Yesterday, the cricketing world grieved the loss of Tony Lewis, the co-inventor of the Duckworth Lewis method. In his memory, we look back at the history and origin of the method that forever revolutionized cricket.
The Duckworth Lewis method is a mathematical system that helps revise targets in rain affected limited over matches. It was first used during the 2nd ODI between England and Zimbabwe in 1997.
The rule was devised by mathematicians Tony Lewis and Frank Duckworth. The England Cricket Board used the rule in 1997 which was officially adopted by the International Cricket Council (ICC) in 1999 during the World Cup.
Here’s a History to the various methods used in limited overs cricket matches
Average Rain Rule (ARR) Method
Average Rain Rule (ARR) Method was the first rule used much before Duckworth-Lewis
ARR was the first method used to revise targets. This rule focused entirely on the average run rate of the batting team and did not take into consideration the wickets lost by it.
According to the ARR, the chasing team just had to match the run rate of the team that set the target. Therefore, if Team A scores 250 runs in 50 overs and the second innings is reduced to 25 overs due to rain, Team B will have to score 125 runs to win.
In the same scenario if Team B’s score was 120-8 in 23 overs, after the application of ARR, they’ll just have to score 5 runs in 2 overs to win the match with two wickets to spare. This is clearly much easier than scoring 130 runs in 25 overs with two wickets to go.
The ARR clearly favored the team batting second. As a result, whenever there was rain forecast, the team would blindly choose to chase after winning the toss.
Most Productive Over (MPO) Rule
Duckworth-Lewis was a direct result of the 1992 World Cup semi-final when Most Productive Over (MPO) Rule was used
The ARR was replaced by the MPO rule. Australia came up with this rule ahead of 1992 Cricket World Cup.
According to this rule, Team B’s target for the reduced number of overs was decided by subtracting the runs scored in Team A’s least productive overs. So, if Team B lost 30 over due to rain, then their target was set from the 20 most productive overs of Team A’s innings.
So, consider a scenario where Team B bowls 10 maiden overs and concedes 200 runs in the first innings. If the second innings is reduced by 10 overs, Team B will still have to score 201 runs in 40 overs to win.
The defects of this rule were highlighted in the semi-finals of the 1992 Cricket World Cup. England was taking on South Africa in the semi-finals. England set a target of 252 for South Africa. Chasing the target, South Africa were 231 with six wickets down and required 22 from 12 balls before rain stopped the play for 12 minutes.
Due to the rain, two overs were lost. That meant that two lowest scoring overs were to be reduced from the equation. The two lowest scoring overs for England were a maiden and a one run over. Therefore, the equation was now revised to South Africa needing 21 runs to win from 1 ball.
As per this rule, Team B was penalized for bowling low scoring overs in the first innings. Just like ARR, MPO rule also failed to take into consideration the wickets left in play. But unlike ARR, it favored the team batting first.
Duckworth-Lewis-Stern Method
Duckworth and Tony Lewis the co-inventors of the Duckworth Lewis method
The Duckworth Lewis (D/L) method is considered to be the direct result of the 1992 World Cup semi-final. Duckworth in an interview to BBC said that he remembers hearing Christopher Jenkins on radio saying “surely someone, somewhere could come up with something better”.
According to Duckworth, this is when he realized that it was a mathematical problem that required a mathematical solution.
Both the Average Rain Rule and the Most Productive Over Rule failed to take into account the effect of wickets left. This problem was finally addressed by the D/L method.
The D/L method took into consideration 2 resources while revising a target. It looked at the number of overs left and the number of wickets currently in hand. The method was based on the belief that the team’s ability to score runs depended on these two resources.
According to D/L method, the target of the chasing team is adjusted according to the proportion of the two team’s resources at that point in their respective innings.
Later in 2015, the International Cricket Council introduced the Duckworth-Lewis-Stern (DLS) formula for the World Cup. It included the modifications of Professor Steven Stern from the department of Statistics at Queensland University of Technology.
The modification was made considering the fast paced, high scoring modern cricket. It tweaked the formula by recognizing that while chasing high targets, teams needed to start their innings with a higher scoring rate rather than keeping wickets in hand.
For their services to cricket and mathematics, Duckworth and Lewis were awarded with the Member of British Empire (MBE) in 2010. The method evolved the sport and cricket will forever be indebted to their contribution to the sport.
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