Meet Steve Stern, Duckworth-Lewis method’s new custodian
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New Delhi: There’s a storm brewing over the ICC Cricket World Cup in Australia. No, we’re not talking about Chris Gayle.
On 23 February, while the Zimbabweans were huddled up in their locker room thinking how to chase down the 372 runs set by the West Indies, a brief spell of rain reduced the number of overs they had to 48. And the target was reset to 363.
Given that it was a group match—and not a do-or-die situation—the pressure felt by either team was nothing close to when rain spoiled South Africa’s chances during the 2003 and 1999 world cups.
If such a dampener recurs in the knockout stages of the 2015 World Cup, the dreaded English names of Duckworth and Lewis will most definitely pop up to decide the final fates of teams—as will an American’s from now onwards.
For most people, the name Steve Stern might not ring a bell. But he presently occupies the position that Frank Duckworth and Tony Lewis (both consultant statisticians for the International Cricket Council) held until they retired recently. Stern is the custodian of the newly enhanced software that sets a fair target for rain-interrupted matches: the Duckworth-Lewis-Stern (DLS) method.
Over email, Stern clarifies that this new model is “not a completely new method, but instead it is simply an adjustment and enhancement”.
The way Duckworth-Lewis method works has been a puzzle to both spectators and many cricketers themselves. It still causes outrage and anger (ask the South Africans about it) and prompts one to ask if there’s an easier way to resolve things.
Unfortunately, since we can’t just toss a coin and get moving, mathematics seems to be the only way out. Stern himself, being an American by birth, had not heard of cricket till he was studying for his doctorate at Stanford University, where he met a number of Australians and was taken in by their outlook and sense of humour.
“I was quite fortunate that just as I was finishing my degree, an Australian friend and colleague had been offered a job at a university (in Australia) and he indicated there was another position available as well. The position was only supposed to be for three years,” Stern says. Twenty years later, in 2015, Australia has become home for him. sixthMAds
To put it simply, the DLS method is a formula that says a result can be achieved if either team loses resources they were originally supposed to have—in this case, number of overs.
If an interruption happens in the form of rain, poor light, sandstorms, a swarm of bees or political protests (the last two have actually happened, according to Stern), we can still see a fair fight.
“Essentially, the core of the original method is the calculation of what, on average, each over of an innings adds to the team’s score. In other words, it is based around determining what portion of a team’s score is typically made during any given over, accounting for the number of wickets they have in hand at the time. For example, if each over added exactly the same (number of runs) as any other over, regardless of wickets down, then each over in a 50-over match would contribute 1/50th or 2% of the team’s score,” explains Stern.
Reality, however, is quite different and teams score runs unevenly, depending on the situation as the match progresses.
What the modified DLS system does is to try and capture this acceleration in the run rate and accordingly scale up or scale down targets as required, if and when overs are lost. These calculations are stored in resource tables for reference, much like logarithmic tables, which we looked up to derive answers in high school. They aren’t available for everyone to see for a simple reason: the copyright belongs to the ICC that doesn’t want to make them public.
The DL method, conceptualized in the 1990s, hasn’t been without its share of controversy and has undergone periodic revisions from time to time. It was conceived during a period when high-scoring rates were rare, says Stern, and hence as time progressed—and with the creation of Twenty20 cricket—“it didn’t quite get those all-important scoring percentages per over right for very high-scoring matches.”
“This is where DLS comes in,” Stern says.
“For matches which are not very high-scoring (say, ODIs with scores under 325 or T20s with scores less than 165), DLS and DL will give essentially identical results. But, for very high-scoring matches, it turned out that DL did not give enough scoring weight to the start and the end of the innings (and thus, by extension, gave a bit too much weight to the middle). DLS corrects this, and thus better captures the way in which very high-scoring innings progress,” he adds.
The match that really got Stern thinking was not a 50-over one, but a T20 World Cup game between West Indies and England at Providence Stadium in Guyana in 2010.
“In that match, England batted first and scored 191 in their 20 overs. The West Indies started their innings briskly (Chris Gayle doing his usual) and were 30 for zero after two overs and two balls when rain came and reduced the chase to six overs,” says Stern. While the DL method ended up giving the West Indies a target of just 59 runs, the DLS would have them given them “a higher (and probably fairer) target of 65 runs.”
“In the actual match, the West Indies won with 1 ball to spare, so had DLS been in place they would have needed a six off that last ball,” Stern says.
Back home in India, another person claims he has been trying to convince the ICC for 15 years that his own method is much better than the DLS method.
V. Jayadevan, a civil engineer from Kerala and the creator of his namesake calculation (the VJD method), says “the DLS system in fact is very, very poor, especially for ODI matches. It is so unfortunate that the ICC is using it for a major event like the World Cup”.
The chief difference between the VJD and DLS methods is that while the latter uses only one set of calculations (or resource tables), the former uses two—Jayadevan’s justification being that the tactics employed by a batting team will change before and after rain. Jayadevan says he has been regularly writing to the ICC about errors he spots in their method but has never received serious attention from the council. “If a method that sets a target of 170 runs against a score of 104 in 20 overs also sets 154 against a score of 52 (half the original target given the same resources), we can definitely say that it is mathematically wrong. And this is what the DLS does.”
Stern, when asked about the VJD method, says: “It is a clever one and certainly was worthy of consideration. I know he (Jayadevan) probably won’t agree with this (and I obviously am not a totally impartial observer here), but while his method is good, it is not as good as DL. To be honest, from a purely mathematical perspective, VJD and DL are not really all that different in philosophy, it’s just a few aspects of the implementation of that philosophy where they differ.”
There doesn’t seem to be a foreseeable end to this battle of mathematical resolutions, but Stern’s way of getting things done will sit comfortably at the top for a good time. If the game evolves, the formula will too.
How long before Stern sees his enhancement subject to a revision then?
“I’m pretty confident that DLS gets things right in all the circumstances we’re likely to see for a while now. The original version of DL, called the standard edition, was used from its inception in 1997 up until 2004, at which point Frank and Tony changed it to the professional edition, which was in use until 2014, when DLS was introduced. So, every decade or so, there seems to be a need to enhance the method to deal with changes in playing patterns. Hopefully, I’m safe until sometime in the 2020s or so,” Stern says.