There is something profoundly uninteresting about the Duckworth – Lewis method (now Duckworth-Lewis-Stern). Despite its reputation as a mysterious statistical compendium, D-L was actually devised to require only two things: an over-by-over chart of percentages and a pocket calculator, the idea being that anyone, whether in possession of computer or not, would be able to apply it. Having spent an afternoon trying to work it, I can assure that this much, at least, is true.
The principle behind the system is a simple one. Teams are in possession of two resources: overs and wickets. As the innings progress, teams spend both of those resources, and their behavior changes accordingly. Teams with 30 overs and nine wickets in hand will score more freely than those with 30 overs and six wickets in hand.
Play starts with both teams in full possession of 100% of their resources. When play is interrupted, one or both teams lose resources: either overs played or the ability to plan the innings accordingly. Therefore, the target score must be adjusted up or down so that both teams have the same percentage of their resources available for use. Put another way, the side batting should lose something (e.g., overs) in order to compensate for the opportunity (ability to plan), of which the rain deprived their opponents – or vice versa.
Before getting into the weeds, let’s agree on the basic point that D-L is positively salvific. Without it, or some similar system, rain-interrupted games would either end unfairly or have to be abandoned altogether. Imagine a team patiently building a score of 200 for 4 off 40 overs only to be stymied by a swiftly-passing storm and with no D-L to fall back on. Enter BMac and Two-toes to polish that off in, what, 30 overs? De Villiers in 20? Even Cookie might be able to match the required run rate.
Or imagine Chris Gayle chasing down 300 with ease only for the rain to halt proceedings at 290 in the 40th over. Our natural sense of justice bridles at the thought of that being called a draw. The point being 1) that the ability to plan an innings is crucial to a batting side’s success, and 2) that we all have a pretty intuitive idea that scores can be commensurate, even if we lack the statistical nous to work out the precise figures.
But sometimes D-L departs from natural justice. As, for instance, when England lost the second Royal London ODI match against New Zealand (though, yes, some might say that this was in fact the just result. Natural justice is complicated). England were only nine runs behind on D-L with 13 balls left to bowl when the rain started. By the time the covers came off again, the DL calculation put them 34 runs behind, with a nearly impossible run rate of 16.
So what had happened? D-L thinks in percentages. When England stopped batting, it had about 15% of its resources left to use. When it resumed, it had only 6% left. The New Zealand score was therefore adjusted down by 6% from 398 to 379, which England fell to gain by 13 runs.
But what would have happened has Eoin Morgan clung to the crease? England would then have had 11.6% of their resources left to spend when play resumed, and the New Zealand total would have been adjusted down to 352, a seven run which England could have easily knocked off.
The key, of course, is that extra wicket, and the assumption made by Duckworth and Lewis that teams change attitudes and behaviors depending on how many wickets they have in hand. This flaw dovetails with another historical D-L shortcoming, which is that D-L cannot account for qualitative differences in wickets. As far as the model is concerned, the first wicket is the same quality as the 10th, which is the equivalent of assuming that Alastair Cook and Jimmy Anderson are the same caliber of batsman. True enough a year ago, a wag might say, but statisticians and wags are, well, unlikely bedfellows.
The blind spot has some obvious consequences. Top order batsmen who retire hurt have historically been emblematic of this problem, since they could score at a much faster rate late in the innings. But teams today score at a much faster rate all the way down the order, and the modern tailender is a much more useful resource than he used to be. Nor can D-L measure the quality of partnerships, nor of the bowlers, nor of the momentum of the game.
England’s case is in point: when the rain came, the crease was occupied by Adil Rashid and Liam Plunkett, both of whom handy with a bat, and averaging just over 27 and 21 respectively. Theoretically, England’s forces were spent. But in the event, England had momentum, and were scoring freely with two set batsmen. What made England’s position impossible was the restriction on play time, which had nothing to do with the D-L model, but, as it turned out, everything to do with the result.
So how to make D-L better and fairer? To some extent, this is impossible. No model will ever be able to account for all possible permutations and still be usable in real time. Models in general, and D-L in particular, rely on averages. Cricket fans are in it for the outliers. The twain cannot meet.
D-L changes all the time, with the database and calculation sheets updated to reflect growing par scores and adjusting for statistical anomalies. There are other methods, of course, of which WASP is one, but none have yet been able, so far as I know, to produce adjusted scores in quite the way D-L can.
What D-L needs, from this non-mathematical perspective, is a change in attitude towards the lower order. Rather than a sharp drop in resource percentages around the 6th wicket, the last four should be, perhaps, spread out more evenly, to reflect the added batting worth of tail-enders.
But this, too, is not without its problems, since not all tail-enders are created equal. Changing the D-L model to reflect their added batting prowess can only be done once all tailenders, or at least a mathematically meaningful amount, bat more aggressively across all formats and all countries, and do so consistently.
The short format game is in transition. D-L transitions with it. And as the great Steven Gerrard once said, we go on.
