Duckworth-Lewis-Stern in Australian Conditions
How the DLS method resets rain-affected targets, why an Australian professor now runs it, and how it is applied in the BBL and the Marsh Cup.
By CricketTaken EditorialPublished Numbers19 min read
- First international use
- 1 January 1997
- Adopted as the ICC standard
- 1999
- Renamed Duckworth-Lewis-Stern
- November 2014
- Current custodian
- Steven Stern of Bond University on the Gold Coast
- Minimum for an ODI result
- Twenty overs to the side batting second
- Minimum for a BBL or T20 result
- Five overs to the side batting second
- Resources at fifty overs and ten wickets
- 100 per cent
- Resources at twenty overs and ten wickets
- 56.6 per cent
The DLS method cricket uses to reset a rain-affected target is a resource calculation, not a run-rate one. Duckworth-Lewis-Stern treats every limited-overs innings as a stock of two things a batting side can spend, overs remaining and wickets in hand, and converts that stock into a single percentage. When rain takes overs away from one side and not the other, the target is scaled by the ratio of the two percentages. The formula is short enough to write on a beer coaster: the par score equals the first innings total multiplied by the second side's resources divided by the first side's resources.
Australia has an unusually direct stake in all of this. The rule the method replaced died in Sydney, at the 1992 World Cup semi-final, when South Africa were asked for 22 runs off one ball at the Sydney Cricket Ground. The person who now maintains the method is Australian-based: Steven Stern, Professor of Data Science at Bond University on the Gold Coast, whose 2014 revision added the third name. And the competition that tests the method hardest is the Big Bash League, where a game becomes official after five overs and the par figure sits on screen all night.
This guide works through what the resources actually are, how the numbers are produced, where the minimum-overs thresholds sit in each Australian competition, what the par score on a BBL broadcast means ball by ball, and which Australian matches have been decided, fairly or otherwise, by the calculation. It also covers what the method deliberately does not attempt to do, which is where most of the arguments start.
What the method is trying to solve
Rain in a limited-overs match creates an unfairness that has nothing to do with the weather being unlucky. If one side bats 50 overs and the other bats 30, they have not played the same game. The side with 30 overs can attack from the first ball because it has ten wickets to spend over half the deliveries. Simply prorating the target by run rate, so that a score of 250 in 50 overs becomes a chase of 150 in 30, hands the chasing team an enormous advantage, because it lets them convert wickets they never needed into runs.
Every rain rule in cricket history has been an attempt to price that advantage. Average run rate ignored wickets entirely. Most productive overs, used at the 1992 World Cup, tried to correct for it by deleting the first side's cheapest overs from the target, which produced the Sydney farce. The Duckworth-Lewis approach was the first to model both resources together, and to do it with a curve fitted to what teams actually score rather than an assumption about what they ought to score.
The key insight is that the two resources interact. Twenty overs with ten wickets in hand is worth much more than twenty overs with two wickets in hand, and the gap between those two positions is not linear. A batting side with nine wickets down cannot use its remaining overs, so those overs are worth almost nothing. The resource table encodes exactly that relationship, across every combination of balls left and wickets standing.
Sydney 1992 and the rule that died there
England made 252 for six from 45 overs in the second semi-final at the SCG on 22 March 1992. South Africa, chasing in their first World Cup after readmission, needed 47 from the last five overs, then 22 from 13 balls, when the rain that had been drifting across the ground grew heavy enough to stop play.
The most productive overs rule then did its work. Because the chasing side had lost overs, England's least productive overs were struck from the target. One of them was a maiden, worth no runs at all, so removing it took nothing off the requirement while removing six balls from the time available. The next cheapest had gone for a single. Two overs vanished, one run came off the target, and the scoreboard at the SCG displayed a revised equation of 22 runs from one delivery. The crowd, who had watched a genuine contest for three hours, booed.
Nothing about that outcome was a computational error. The rule worked exactly as written. It was simply a rule that had never been stress-tested against a close finish, and the humiliation of watching it fail on a World Cup stage in front of an Australian crowd is what created the appetite for a properly modelled replacement. Frank Duckworth and Tony Lewis, two English statisticians working outside any board, produced that replacement over the following years, and it was used in an international for the first time on 1 January 1997.
- Stop the clockUmpires suspend play and record the exact over, ball and wicket position at the moment of the interruption.
- Assess the lost timeGround staff, umpires and the match referee estimate how many overs can still be bowled inside the scheduled finish and any allowed extra time.
- Read the resourcesThe remaining overs and wickets in hand are converted into a resource percentage for each side using the professional edition software.
- Apply the ratioThe first innings total is multiplied by the second side's resources divided by the first side's, producing the par score for that moment.
- Set the targetOne run is added to the par figure to give the score the chasing side must reach, and the new target and over allocation are announced.
- Recalculate if it rains againEvery further interruption triggers a fresh calculation from the position reached, so a target can be revised several times in one match.
The sequence match officials follow in a fifty-over or Twenty20 game. Timings and who physically runs the software vary by competition, so treat this as the shape of the process rather than a fixed protocol.
Overs and wickets as resources
A side beginning a 50-over innings with ten wickets has all of its resources: 100 per cent. Every ball bowled and every wicket lost reduces that figure, and the published table gives a percentage for each combination. Thirty overs remaining with all ten wickets in hand is 75.1 per cent. Twenty overs remaining with all ten wickets is 56.6 per cent.
Look closely at those numbers and the model's logic appears. Sixty per cent of the overs have gone at the 20-over mark, but only 43.4 per cent of the resources. That is because ten wickets are still standing, and a team with a full hand of batters can score far more heavily per over than the innings average implies. Resources are not overs, and treating them as though they were is what every failed rain rule had in common.
The same principle applies in Twenty20, where the whole innings is compressed and the curve is steeper. A Big Bash side five overs into an innings has burnt a much larger share of its resources than a Marsh Cup side five overs in, because the total stock was smaller to begin with. This is the technical reason a five-over minimum produces volatile results: at that point the resource ratio is being read off the steepest part of the curve, where small differences in wickets produce large swings in the par figure.
| Overs remaining | Wickets in hand | Resources remaining |
|---|---|---|
| 50 | 10 | 100 per cent |
| 30 | 10 | 75.1 per cent |
| 20 | 10 | 56.6 per cent |
Those three published figures are enough to show the shape. The full table runs to every ball of a 50-over innings against every wicket position, which is why nobody works it by hand at senior level any more.
The formula, written out
Par score equals the first side's score multiplied by the second side's resources divided by the first side's resources. The target is the par score plus one run.
If Australia make 280 from a full 50 overs, their resources are 100 per cent. If rain then restricts the chasing side to 30 overs from the start of its innings with all ten wickets available, that side holds 75.1 per cent. The par score is 280 multiplied by 0.751, which is a little over 210, and the target is set at 211.
Run the same reduction the other way and the arithmetic changes character. If the chase is 30 overs into a 50-over innings at four wickets down when the match is called, the resources used and the resources remaining both matter, and the par figure depends on the wicket column as much as the over column. This is the part that catches casual viewers out. A wicket in the eighteenth over of a Big Bash chase can move the par line by several runs in one delivery, because it removes a slice of resource that the remaining overs cannot replace.
Standard edition and professional edition
The original published method is the standard edition. It uses fixed tables and a constant called G50, the expected first-innings score in a full 50-over match at the relevant level of cricket, to scale the calculation when the first innings total is unusual. It can be run with a printed sheet and a calculator, which is why it survives in club cricket.
The professional edition, required in international cricket since 2004, drops G50 and instead adjusts the resource curve according to the score the first side actually made. This matters enormously in modern cricket. When the first innings total is around the historical average, the two editions give similar answers. As the total rises, they diverge, and the standard edition begins to set targets that a chasing side would find implausibly easy. The professional edition is calculated with software supplied by the ICC, updated on a regular cycle, and run on a laptop by the match officials.
Every senior competition in Australia, from internationals to the Marsh One-Day Cup, the Big Bash and the Women's Big Bash League, uses the professional edition.
Steven Stern and the 2014 revision
Stern's contribution, adopted in November 2014 and in place for the 2015 World Cup that Australia and New Zealand co-hosted, was a recalibration rather than a rewrite. The underlying resource concept stayed. What changed was the weighting of wickets in hand during a demanding chase.
The original curve had been fitted when a competitive one-day total was substantially lower than it is now. As scoring rates rose through the 2000s, and as Twenty20 taught batting sides to accept risk earlier, the model's assumption that a team with wickets in hand would score conservatively stopped matching behaviour. Stern's adjustment made the model reflect that a side chasing a very large total will attack from the outset regardless of wickets, and revised the resource values accordingly.
That an Australian-based academic holds the custodianship is worth noting for a local audience, because it means the model's ongoing maintenance sits inside the Australian cricket ecosystem rather than in England, where it began. Stern is at Bond University on the Gold Coast, and his work covers not only rain revisions but the broader question of how limited-overs resources should be valued as the game keeps accelerating.
Minimum overs across the Australian competitions
The threshold question, meaning how much cricket is enough cricket to declare a winner, is not answered by DLS at all. DLS will produce a par score for almost any position. The minimum is set separately in each competition's playing conditions, and it is the source of most Australian arguments about the rain rule.
| Competition | Format | Overs the chasing side must face | Method |
|---|---|---|---|
| Test match and Sheffield Shield | Multi-day | Not applicable | No DLS, time is made up or the match is drawn |
| One-day international in Australia | 50 overs | 20 | DLS professional edition |
| Marsh One-Day Cup | 50 overs | 20 | DLS professional edition |
| Big Bash League | 20 overs | 5 | DLS professional edition |
| Women's Big Bash League | 20 overs | 5 | DLS professional edition |
| Twenty20 international in Australia | 20 overs | 5 | DLS professional edition |
| Premier and grade one-day cricket | Varies | Set by the association | Usually standard edition or a local rule |
The Sheffield Shield row is the one people forget. Multi-day cricket has no rain rule in the DLS sense. Lost overs are recovered by extending the day where light and playing conditions allow, and a match that runs out of time is drawn with points shared under the competition's own system.
DLS in the Big Bash League
A Big Bash match is not a match until each side has had five overs. Before that, rain simply produces no result and the points are split. After it, the game can be awarded on the par figure at the moment of abandonment.
In practice this means the second innings of a wet Big Bash night is played against two opponents. The par line is displayed continuously, updating after every ball, and both dugouts watch it. A chasing side ahead of par will happily accept a rain delay. A side behind it will try to force the tempo before the covers come on. Captains have openly managed innings around the par figure, which is a legitimate tactic and also a slightly strange thing to watch, because the batting side's optimal behaviour is being set by a weather radar rather than by the bowling.
The five-over threshold is what makes this sharp. The BBL format already compresses everything, and five overs is a quarter of an innings. A side that loses two wickets in that window can find itself well behind a par figure that a full 20 overs would have given it every chance to overhaul.
The Sydney derby that restarted the argument
On 18 January 2020, at Sydney Showground, the Sydney Sixers were bowled out for 76 in 16 overs across an innings interrupted twice by rain. The Thunder reached two for 28 after 5.3 overs before the weather ended proceedings, and were awarded the game by four runs under DLS. It was the fifth DLS-decided match of that Big Bash season.
Thunder captain Callum Ferguson, who had just won, was the one who questioned the rule. He said he wondered whether five overs was enough time to really give a genuine result, and suggested it might need to be ten. Sixers captain Moises Henriques argued for a different fix. Rather than chasing the maximum number of overs, he said, officials should shorten both innings pre-emptively so the two teams bat in comparable conditions.
Neither idea was adopted. The five-over minimum remains, which means the situation recurs most summers somewhere in the competition. It is worth being precise about where the objection actually lands. Nobody in that debate said the arithmetic was wrong. They said five overs is not enough cricket to be worth calculating.
- England actual after 14.3 overs105
- DLS par at that moment110
England's actual score when rain ended the Twenty20 World Cup group match compared with the DLS par figure at that moment. England were five runs short, so Ireland won by five runs.
Show the numbers
| Item | Value |
|---|---|
| England actual after 14.3 overs | 105 |
| DLS par at that moment | 110 |
When rain decided a World Cup group in Melbourne
The 2022 Men's Twenty20 World Cup, played entirely in Australia, produced the clearest recent illustration of DLS shaping a tournament rather than a single game. On 26 October at the Melbourne Cricket Ground, Ireland were bowled out for 157, Andy Balbirnie top-scoring with 62 from 47 balls and Lorcan Tucker adding 34.
England reached 105 for five after 14.3 overs, Dawid Malan making 35 and Moeen Ali unbeaten on 24, when heavy rain returned and stayed. England were five runs short of the DLS par figure. Ireland won by five runs, one of the largest upsets of the tournament.
That result mattered beyond the two teams. A Melbourne spring can wash out several days in a row, and the group table was reshaped by weather across that week. The lesson for Australian scheduling is not about the method. It is about staging a global Twenty20 tournament in October, when Melbourne and the Gabba are still in a much wetter part of their calendar than the December to February window around which the Australian season is normally built.
First-innings interruptions and targets above the score
The counter-intuitive case is worth spelling out, because it produces the reaction of how can they need more runs than the other team scored.
If the side batting first has its innings cut short, it finishes with less than 100 per cent of its resources. Suppose it is 40 overs into a 50-over innings when the match is reduced, so it ends on 220 having used only part of an allocation it had been pacing for 50. The chasing side is then usually given the same 40 overs, but it starts with all ten wickets and full knowledge of exactly how many overs it has. Its resources for those 40 overs, planned from ball one, exceed the resources the first side had while batting for an innings it thought would be longer.
DLS therefore scales the target upwards. The chasing side might be set 232 from 40 overs against a score of 220. The figures are not a punishment. They are the model pricing the advantage of knowing your innings length in advance, which is a real and large advantage in one-day cricket.
What the par score is and is not
The par score displayed during a Big Bash chase is the score required at that instant, for the number of wickets already lost, to be exactly level if the match ended immediately. It is not the eventual target, and it is not a projection.
Three properties confuse people. First, it moves ball by ball rather than over by over, because the professional edition table is calculated to each delivery. Second, it jumps at a wicket, sometimes by several runs, because the wicket column of the table shifts. Third, being ahead of par with wickets in hand is worth more than the raw gap suggests, because the resources still held are large.
Broadcasters increasingly show the par figure alongside the required rate, and the two can point in different directions. A side needing eleven an over but sitting comfortably above par is one good rain shower from winning a game it would almost certainly have lost. That is not a flaw in the arithmetic. It is what a rain rule is for.
DLS and net run rate
A DLS result also has to be fed into a group table, and the interaction is not obvious. When a match is decided by DLS, the net run rate calculation uses the revised overs and the revised target rather than the original scheduled figures, so a narrow DLS win does not deliver the run-rate bonus that a comfortable full-length win would.
This has real consequences in Australia. In a rain-affected BBL season, a club that wins two matches on DLS and loses one heavily can find itself outside the finals despite an equal win-loss record, purely on run rate. Understanding that the calculation cuts both ways is part of understanding why coaches will occasionally push for extra overs even when they are already ahead of par.
Where DLS reaches in Australian club cricket
Premier cricket in the capital cities generally applies DLS in its one-day and Twenty20 formats, either through a scoring app or a printed standard-edition table, with the minimum overs written into the association's playing conditions. Below that level the picture varies enormously by state and by grade.
Many suburban and country competitions use simpler rules: a straight comparison of run rates, a fixed number of overs before a result stands, or an automatic tie. The reason is logistical rather than philosophical. The professional edition needs software and someone trained to operate it, and a Saturday afternoon fourth-grade fixture has neither. Anyone officiating at that level should read the by-laws before the season rather than during a downpour, and the same advice applies to anyone working through the umpiring pathway or coaching a side through their first wet summer after finishing an accreditation course.
- 20Overs a chasing side needs for an ODI result
- 5Overs a chasing side needs for a BBL result
- 75Resource percentage at 30 overs and 10 wickets
- 2014Year the method was renamed with Stern
Fixed structural values rather than measurements. The resource percentage shown is a published table value for a fifty-over innings with all ten wickets standing, rounded to a whole number.
The criticisms that have substance
Three objections come up repeatedly, and only some of them are about the mathematics.
The first is the five-over Twenty20 minimum, discussed above. This is a playing-conditions choice, not a modelling flaw, and it could be changed tomorrow without touching a single resource value.
The second is that the model was fitted to historical scoring patterns and therefore always lags the game. Stern's 2014 revision addressed a real drift, and the method is periodically recalibrated for exactly this reason, but any statistical model built on past matches will be slightly behind a sport whose scoring rates keep climbing.
The third is transparency. The professional edition's resource values are not published in the way the standard tables are, which means a spectator cannot check the par figure independently. For a rule that decides matches on television, that is a reasonable complaint, even if the reason, which is preventing teams from gaming the exact curve, is defensible.
What DLS does not attempt
It does not account for the conditions. A drop-in pitch at Optus Stadium under lights after rain is a different surface from the one used in the first innings, and DLS knows nothing about that. It does not account for a wet ball, a slow outfield, or the dew that changes a Brisbane evening. It does not account for which bowlers a side has already used, or for the fact that a chasing team's two best batters are unavailable.
It also does not account for who is at the crease. A resource percentage is identical whether the two batters are Travis Head and Glenn Maxwell or the numbers ten and eleven. Six wickets down is six wickets down.
These are deliberate omissions. Any model that tried to price them would require judgement calls that no board would let an umpire make in the middle of a storm, and the resulting figure would be arguable in a way that a table lookup is not. DLS trades accuracy in edge cases for the ability to produce an answer in ninety seconds that both captains agreed in advance to accept.
How to follow the calculation as a viewer
Three habits make a rain-affected match far easier to read.
Watch the wicket column, not just the over count. If the chasing side is above par by fifteen with two wickets down, that is a strong position. Above par by fifteen with seven down is precarious, because the next wicket will move the line.
Watch the reduced-overs announcement rather than the run chase. The moment officials confirm a shorter match, the target changes, and a side that looked out of it can be back in within a single message from the middle.
And watch the clock at the end. Every competition has a latest possible finish time built into its conditions, and once the arithmetic says a five-over chase cannot be completed inside that window, the game is over regardless of what the radar shows. That is why matches at the Adelaide Oval and the MCG are sometimes abandoned while the sun is out.
Why the method has survived
Three decades after Sydney, DLS remains in place because it does the only thing a rain rule must do. It produces a defensible number, quickly, that both sides accepted before the toss. It is not perfect, it is not fully transparent, and it produces results that look silly at the extremes of a five-over Twenty20 chase.
It has also never produced anything as absurd as 22 from one ball. That is the standard against which it should be judged, and by that standard it has done its job. The remaining arguments in Australian cricket are about thresholds, scheduling and how much cricket ought to constitute a game, which are questions for the people who write playing conditions rather than for the statistician on the Gold Coast who maintains the tables.
For more on how the Australian season is put together and where the rain risk sits, see the cricket in Australia hub, the Australia guides index, and the practical how to watch page. The wider cricket section and the players index cover the people involved.