How Duckworth-Lewis-Stern Works Guide

A one-day international gives each side fifty overs, and rain rarely splits the difference evenly. It might wash out an hour before the chase, so the second side knows from the first ball it has thirty overs. It might eat ten overs out of the middle of a chase half done. It might interrupt the first innings and never come back. In each case the two sides have been handed different jobs, and someone has to say what the second side now needs.

The naive answer is a run rate: take the first side's runs per over and ask for the same pace across whatever overs remain. That is wrong, and it is wrong in both directions depending on when the rain falls. Cut a chase from fifty overs to twenty-five and a run-rate target asks for the same scoring pace with all ten wickets still in hand, which is a gift; a side batting twenty-five overs with ten wickets can attack from the start in a way it never could over fifty. Apply the same arithmetic when eight wickets are already down and it becomes a punishment, because the runs are being demanded of batters who are not there.

The idea behind Duckworth-Lewis-Stern is that a batting innings spends two things, not one: overs remaining and wickets in hand. Together they describe how much scoring capacity the innings still has in front of it. A side ten overs in with no wickets down has a great deal left; the same side ten overs in with six down has far less, though the overs remaining are identical.

The method puts a single number on that capacity, expressed as a share of what a full, untouched innings would have had. Call it the innings' resources. Every over bowled spends some, every wicket that falls spends more. When rain removes overs, it removes a slice of the resources the side would have spent, and the size of that slice depends on both numbers at once: how many overs vanished, and how many wickets were standing when they did.

The revised target follows directly. Work out what share of a full innings each side actually got, then set the target so both are asked to do the same amount with the resources they were given. Fewer resources for the chasing side and its target comes down; more, which happens when the first innings was the one cut short, and the target goes up above the runs actually scored. Neither adjustment is a run rate. It is a comparison of two innings that were never the same length.

Take ten overs off a chase before a ball is bowled and the side loses ten of its fifty while holding every wicket. It hurts, but it is the cheap version: the side plans a forty-over innings instead, and a top order with ten wickets intact can raise its tempo to cover much of the gap.

Now take ten overs off the same side when it is two down with fifteen left. Those fifteen overs were the innings' acceleration, the part a batting side saves its wickets for, and ten have just gone. What is left is five overs and eight wickets, a stranded surplus that cannot be spent no matter how hard anyone swings. The method treats that as a far larger share of the innings' resources than the first case, and the target falls more steeply.

The same logic explains a revision supporters often read as unfair. A side that reaches the interruption with nearly all its wickets standing keeps a bigger proportion of what it had than a side that has been losing them, so the side batting well gets the steeper target and the side that has thrown wickets away gets a gentler one. That is not the method rewarding failure. It is the method refusing to hand a struggling side a discount because the weather arrived.

Interrupted matches were once settled by average run rate: the first side's scoring rate applied to the overs the second side had left. The flaw is the one above. The rule was blind to wickets entirely, so it favoured whichever side was batting second with wickets in hand, and it had no sensible answer at all when the first innings was the one cut short.

The replacement, the most productive overs rule, over-corrected. If the chasing side lost ten overs, the rule struck out the ten least productive overs of the first innings and set the target from the rest. The effect was to compare a real innings with an imaginary one: the first side was credited with its best overs and charged for none of its worst, including maidens it had been bowled by good bowling. Targets came out savage, sometimes absurd, and a short break could leave a side needing a near-impossible number off a few balls. It also punished the fielding side for bowling well, which no rule should do.

Duckworth-Lewis, devised by the English statisticians Frank Duckworth and Tony Lewis and adopted for international cricket at the end of the 1990s, was the first approach to handle both resources together and give a coherent answer to every interruption, first innings included.

The same arithmetic produces a par score for any moment of the second innings: the score the chasing side should be on, for the overs it has used and the wickets it has lost, for the match to be exactly even. It moves every ball. A boundary lifts a side above par; a wicket can drop it below without a run being scored.

So when the scoreboard says a side is fifteen ahead on DLS, it means one thing precisely: if the players walked off at that instant and never came back, and enough overs had been bowled for a result to stand, that side would win by fifteen. Level with par is a tie, behind par is a defeat. That is why the tension in a rain-threatened chase is not really about the target; it is about staying above the par line every ball, because the weather can end the match at any moment. The playing conditions also set a minimum amount of play before any result can be given, twenty overs for the side batting second in a one-day international, so a chase that has not got that far is heading for no result whoever is ahead.

The method was built from how real limited-overs innings had actually been scored, and real innings changed. Totals rose, especially at the top end and especially in the last ten overs, as bats improved, fielding restrictions shifted and sides grew willing to attack from the first ball. A picture of scoring capacity drawn from an era of 230-run totals began to misprice innings in an era where 320 was routine, and the gap showed most where it mattered most: very high first-innings scores, and heavily shortened chases.

In the mid-2010s the method was updated for modern scoring and renamed Duckworth-Lewis-Stern, after Steven Stern, the Australian statistician who had taken over as its custodian. The principle did not change; the picture of what a given combination of overs and wickets is worth did. International cricket uses a computerised version that handles the top end properly, rather than the simplified paper tables used in club cricket.

Most arguments about a revised target are really arguments about something the method never claimed to see. DLS knows two things: overs remaining and wickets in hand. That is all.

It does not know the pitch, and a target that is fair on a flat surface is a different proposition on one turning square. It does not know which bowlers are left: a captain still holding overs from his two best is far better placed than the resource numbers suggest. It does not know who is batting, so ten wickets in hand counts the same whether two set batters are at the crease or the best player in the side has just been dismissed. And it does not know the conditions, the obvious case being a day-night match, where batting under lights against a wet ball on a dewy outfield is a different game from batting in the afternoon. A side whose innings is shifted into the hardest part of the evening gets no credit for it.

None of that makes the method wrong. It makes it what it is: a fair, consistent and predictable way of comparing two unequal innings, not a judgement about who was going to win.

CricArcade's ODI archive holds 4,981 matches. Of those, 259 have a result line naming the Duckworth-Lewis or DLS method, which is 5.2% of the archive, and 255 of them produced a winner. A further 172 matches, 3.5%, ended with no result at all: rain that leaves too little play for a revised target to mean anything simply takes the match away. The share moves a great deal by decade.

Read that table carefully, because it is not a rainfall chart. The earliest result line in the archive naming the method is dated 1998-10-30, and the 1970s and 1980s rows show none at all, which plainly does not mean it never rained on a one-day international in those years. Older result lines often record the margin without recording how the target was reached, so the early figures are a floor rather than a total: they count the matches that said so, not the matches that were affected. The archive does not store how many overs each innings was allotted either, so the missing cases cannot be recovered from the scorecards.

With that caveat, the broad shape still tells you something. The method spread into routine use across the 2000s, reached its highest recorded share in the 2010s at 9.9% of 1,287 matches, and sits lower again in the 2020s at 3.8%. How much of that recent fall is fewer interruptions, how much is scheduling and drainage, and how much is a different mix of venues and seasons, the scorecards cannot say.

There is a deeper limit on reading weather out of scorecards, and it applies even to the decades that are well recorded. A match can be shortened by rain and still finish without leaving any trace in its result line. Suppose the covers come on before the start, both sides agree to forty overs, and the chase is completed inside them with wickets to spare. No revised target was ever applied, so no method is named, and the result reads as an ordinary win by six wickets. In the archive it is indistinguishable from a dry day.

The same goes for a first innings interrupted and resumed with the overs reduced, where the second side is simply set the runs actually scored across the same reduced allocation. The weather changed the match completely and the scorecard records none of it. The numbers above therefore count one specific thing, matches whose stated result depended on the method, and are not a measure of how often rain has had a hand in a one-day international.

The quickest way to feel why wickets in hand matter as much as overs remaining is to bat through a tight target and watch your options narrow every time one falls. Take a nation through a tournament in The Chase, CricArcade's one-day game, or read how to chase a big ODI total for the tactics that decide a full fifty-over pursuit, rain or no rain.

• MCC Laws of Cricket
• ICC playing conditions for one-day internationals: interruptions and revised targets
• CricArcade ODI archive
• Figures computed with scripts/build-guide-facts.ts over the archive's scorecards

• How to Read a Cricket Scorecard: A plain-English guide to the batting card, bowling figures, extras, fall of wickets and the result line, with what every abbreviation actually means.
• How DRS Works: Who can review, what ball-tracking actually shows, and why umpire's call is not a bug: the Decision Review System explained, with what the archive says it changed.
• Fielding Positions Explained: The map of a cricket field, from slip to deep backward square leg, and the modifier system that lets you decode a position you have never heard named.
• Economy, Strike Rate and Average: Reading Bowling Figures: The four numbers on a bowling line, the three rates built from them, and the scorecard notation that catches everyone out: 51.2 overs is not 51 and a fifth.
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