Arguably, the game of cricket lends itself to statistical analysis more than any other sport. Hence, it is no surprise that a statistician has had a significant influence on the game as it is played today. We are talking about Frank Duckworth, who passed away last month. Duckworth, a member of the Royal Statistical Society is best known for the Duckworth-Lewis-Stern method of computing the target or a result of a truncated (mostly by rain) limited overs cricket match.
“In 1992, Duckworth presented a paper, “A fair result in foul weather” at the Royal Statistical Society. This was a response to the rather farcical ending of the 1992 South Africa vs England semi final. South Africa needed an achievable 22 from 13 balls when rain interrupted play. After the rain delay, the revised target was calculated as 22 required of one ball — an impossible task.”
The revised target was clearly based on a method which didn’t take into account the realities of the game. “Duckworth said in an interview in 2007: “[Watching the 1992 semi final] I realised that it was a mathematical problem that required a mathematical solution””
Duckworth was joined by another mathematician Tony Lewis (Stern improved upon it later) to come up with a solution. So, the best obituary is the one that helps us billions of cricket fans with little mathematical ability to understand the rule that influences our enjoyment of the game that we so much love. Here’s Indian Express:
“The DL method introduced the concept of ‘resources’ in making score estimations for truncated games. In limited-overs cricket, each team, in effect, has two ‘resources’ to score as many runs as possible — the number of overs (balls) yet to be bowled, and the number of wickets in hand. Duckworth and Lewis studied historical scores and found that there is a very close correlation between availability of these resources and a team’s final score.
In simple words, the more balls left to be bowled, the more a team can score. Similarly, the more the wickets in hand, the more it can score. As Duckworth and Lewis wrote in their 1997 paper: “Clearly, a team with 20 overs to bat with all ten wickets in hand has a greater run scoring potential than a team that has lost, say, eight wickets” (“A fair method for resetting the target in interrupted one-day cricket matches”).
The DL method converts all possible combinations of balls and wickets in hand to a combined “resources remaining” figure, which is expressed in percentage — full 50 overs, and 10 wickets in hand means 100% resources available.
Target scores for a team batting second can be adjusted (either up or down) from the total of the team batting first, simply based on the number of resources either team has lost. The following formula is used:
Team 2’s par score = Team 1’s actual score x Team 2’s resources/Team 1’s resources
The true achievement of Duckworth and Lewis was calculating the proportion between total runs that can be scored, and the resources remaining (both runs and balls). While the extremes are intuitively arrived at (100% at the beginning, 0% at the end), how each over and wicket impacts the game state was determined using a lot of number-crunching, and some statistical sorcery which is beyond the scope of this article.”
As an aside, there is apparently an Irish pop band that goes by the name The Duckworth Lewis Method.
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