Duckworth-Lewis-Stern explained: how rain rules work

A number changes on the scoreboard while the covers are still on, and the chase everybody has been watching for two hours becomes a different chase. That is the moment Duckworth-Lewis-Stern exists for, and it is also the moment most viewers give up and decide the method is arbitrary. It is not arbitrary. It follows from one observation about limited-overs cricket that, once you have it, makes the rest of the method feel almost inevitable.

The observation is this. A batting side is not spending one thing. It is spending two.

The method is named for Frank Duckworth and Tony Lewis, the statisticians who built it, and for Steven Stern, who inherited it and reworked the model when scoring patterns outgrew the original. It does not predict what would have happened. It restates one side's performance in terms of what the other side actually had to work with, which is a narrower and far more defensible claim.

The one idea underneath all of it: two resources, and they are not independent

At any instant in an innings a batting side holds two things it can convert into runs. Overs remaining, and wickets in hand. Take either to zero and the innings is over, regardless of how much of the other is left. A side with twenty overs and no wickets scores nothing. A side with ten wickets and no overs scores nothing.

That much is obvious. The part that matters is what happens in between, and it is the reason a simple rule cannot work: the two resources multiply against each other rather than adding.

Overs are only worth what the wickets in hand allow a side to do with them. Fifteen overs with nine wickets standing is a licence to attack every ball. The same fifteen overs with two wickets standing is fifteen overs of survival, and the runs that come out of them will be a fraction of the first case. Meanwhile wickets are only worth something if there are overs left to spend them in. Ten wickets in hand with three overs to go is barely different from four wickets in hand with three overs to go, because a side cannot lose more than a handful in that time and cannot use the rest.

So the value of a wicket depends on how many overs remain, and the value of an over depends on how many wickets remain. Neither can be priced on its own. Any rain rule that tries to price one while ignoring the other will be wrong, and the size of its error will depend on exactly the variable it ignored.

Everything Duckworth-Lewis-Stern does follows from taking that seriously.

• 2Resources a batting side spends
• 10Wicket states the table covers, none down through nine down
• 2Editions of the method in current use
• 1Runs added to the scaled figure to make it a target

Structural features of the method, not match figures.

Why run rate on its own cannot do the job

Start with the crudest answer, because it is the one everybody reaches for first and its failure is instructive.

A side bats its full allocation and scores at a given rate. Rain then halves the chase. Ask the chasing side for the same rate over half the overs and, on the face of it, you have been scrupulously even-handed. The same runs per over, the same ten wickets, half the time.

It is not even-handed at all, and the reason is the second resource.

A side batting a full innings has to pace it. It cannot attack from the first ball, because losing four wickets inside ten overs in a long innings leaves nobody to bat the overs that remain. So it builds, it consolidates, it accepts quiet passages, and it accelerates at the end when the wickets it has protected are finally worth spending. That shape is not timidity. It is the correct use of a resource that has to last.

Halve the innings and the shape disappears. The same side now has ten wickets to spend across half as many overs, which means it can throw them at the bowling from ball one. Wickets that would have been an insurance policy become ammunition. The run rate a side can sustain over a short innings with a full set of wickets is materially higher than the rate it can sustain over a long one, and every scoring pattern in the game confirms it. That is the same logic that produces the field restrictions and the acceleration they encourage: fewer overs and more wickets in hand always means a higher rate.

So asking for the same rate over fewer overs hands the chasing side a considerable gift. Run rate ignores wickets, and wickets are precisely the thing a shortened innings sets free.

The two methods that came before, and exactly how each one broke

Both of the serious pre-DLS answers were built by sensible people, and both failed in a way that is worth understanding, because between them they define the shape of the hole the method had to fill.

Average run rate

The first was the simplest: scale the target by the ratio of the overs. Cut the chase from fifty overs to thirty and the chasing side is asked for three fifths of the runs.

This is the run-rate error, formalised. It systematically favoured the side batting second, and it did so worst in exactly the cases that occur most often, which is a rain break during a chase that has begun well. A side cruising at two down had its target cut in proportion to overs while its wickets, the resource that actually constrains a short innings, were left untouched. The reduction it received was larger than the reduction in what it could do.

It also had a mirror-image cruelty. If the chasing side had collapsed, the proportional cut still applied, so a side eight down received the identical percentage discount as a side none down. The method could not tell the difference between those two positions because it never looked at the column where the difference lives.

The most productive overs method

The second attempt tried to fix this from the other end. Instead of scaling the target down by overs, it kept the first side's total and struck out the chasing side's lost overs from the bottom of the first innings: take five overs away from the chase, and remove the five cheapest overs the first side had scored from its total.

The logic sounds defensible for about ten seconds. It preserves what the first side actually did, and it removes overs rather than inventing them.

In practice it produced two catastrophes at once.

The first is that it punished good bowling. A side that had bowled maidens in the field had those maidens deducted from the total it was defending as zero-run overs, so the target barely moved. A side that had leaked runs evenly across the innings saw a proper deduction. The relief a chasing side received therefore depended on how tidy the opposition bowling had been, which is not a variable that has anything to do with rain.

The second is worse and is the reason the method died. Because the deduction was taken from the cheapest overs, a large interruption could remove almost nothing from the target while removing a great deal from the deliveries available to reach it. The result was targets that were not merely hard but arithmetically unreachable, requiring more runs from the remaining balls than those balls could physically produce. That is what happened in the semi-final of the 1992 World Cup at Sydney, when a short rain break left South Africa needing a figure off the final delivery that no batter could have hit, and a World Cup knockout ended on a scoreboard nobody could defend.

A method that can produce an impossible target has not made an error of degree. It has failed at the level of design.

What both failures had in common

Average run rate modelled overs and ignored wickets. Most productive overs modelled runs already scored and ignored both. Neither modelled the interaction, and the interaction is where the whole problem lives.

That is the case for a method more complicated than a reader would like. The simple answers were tried, in international cricket, in front of large crowds, and they broke in public.

What the resource table actually is

The core of Duckworth-Lewis-Stern is a table, and understanding what the table represents removes most of the mystery.

Down one axis: overs remaining. Across the other: wickets lost, from none down to nine down. In every cell: a single number, expressed as a percentage of a full uninterrupted innings, representing how much of that innings' run-scoring capacity a side in that position still holds.

At the top of a fifty-over innings, ten wickets standing, a side holds 100 per cent. It has everything. With no overs left, or all ten wickets gone, it holds zero. Every other state in the game sits somewhere between, and the table's job is to say where.

The percentages were not chosen. They were fitted, from a large body of actual limited-overs innings, to describe the average relationship between where a side stands and how many runs it goes on to make. The model behind them is a smooth mathematical function rather than a lookup of raw averages, which is why the table has no gaps, no reversals and no noise in it.

Two clarifications matter, because both are routinely misread.

The table is about capacity, not about this match. A cell does not say "this side will score this much". It says "a side in this position, on average, retains this share of a full innings' scoring capacity". Applying it to one particular game is exactly what it is for, and it is also the source of every legitimate complaint about it, which we will come to.

The table is common currency, not a chasing-side allowance. The same grid serves the side batting first and the side batting second. It is the unit in which two innings played under different conditions can be compared at all.

Why the percentages bend in both directions

The single most common misreading of the method is to assume the numbers move in straight lines. They do not, in either dimension, and both curves have a physical reason behind them.

Along the overs axis, the curve flattens. Removing ten overs from a fifty-over innings does not remove a fifth of the resource. It removes less. That is because a side facing a shorter innings redistributes its intent across the overs it has, scoring faster in each of them than it would have in a longer innings. The overs are gone; the scoring they would have produced is partly recovered elsewhere. The size of that recovery depends on where the overs are taken from and how many wickets are standing when they go.

Push this to the extreme and it becomes obvious. Take one over off a fifty-over innings and the side has lost almost nothing, because it simply attacks slightly earlier. Take forty-five overs off and it has lost a great deal, but still nowhere near ninety per cent of its capacity, because the five overs it has left will be five overs of unrestrained hitting with ten wickets behind it rather than five ordinary overs.

Along the wickets axis, the curve steepens, and sharply. The first wicket costs a side very little resource. The eighth costs an enormous amount. A side one down retains almost the capacity of a side none down, because a top order with nine wickets behind it plays much the same way as one with ten. A side eight down retains a small fraction, because it cannot use its overs at all: the two players left cannot attack, and one dismissal ends the innings regardless of how many overs are unbowled.

This is the property that generates almost every counter-intuitive DLS result, and it is why a side that loses wickets before a rain break gets so much less relief than it expected. It has already spent the resource the method cares most about.

And the two curves are not separable. The cost of an over depends on which wickets row you read it in. The cost of a wicket depends on how many overs are left when it falls. That is what it means to say the table is genuinely two-dimensional rather than two one-dimensional adjustments stapled together. A method that applied an overs discount and then a wickets discount would be a different and worse method.

If the underlying columns are unfamiliar, reading a cricket scorecard properly covers the two numbers the table is built on, and the glossary of cricket statistics defines run rate, required rate and the rest of the vocabulary that follows.

Turning a resource percentage into a revised target

Now the arithmetic, which is the easy part once the table exists.

Call the resources available to the side batting first R1, and the resources available to the side batting second R2. Both are percentages of a full innings, both come from the table, and both account for every interruption either innings suffered.

Where the chasing side has fewer resources than the first innings had:

Revised target = Team 1's score × (R2 ÷ R1), then add one run.

The extra run is there because a target is the score needed to win. Matching the scaled figure exactly is a tie, and the playing conditions are explicit about which is which.

An illustrative case, with round numbers chosen for legibility rather than taken from any match or any table. Team 1 bats its full fifty overs, so R1 is 100 per cent. Rain then washes out enough time that Team 2 will get thirty overs, and it knows this before it starts. Suppose the published table gives that position somewhere around three quarters of a full innings' resources. The target is then roughly three quarters of Team 1's score, plus one.

Notice what that is not. Thirty overs out of fifty is three fifths. The target sits well above three fifths, because Team 2 holds all ten wickets for a thirty-over innings and can use them from the first ball. The gap between three fifths and three quarters is the price of that certainty, and it is the single clearest demonstration of what the method is doing. The exact percentage in a real match comes from the published table, not from the shape of this example.

A second case, during the chase. Team 2 is fifteen overs into a fifty-over chase, four down, when the rain comes and the innings is cut. R2 is now the resource it consumed in those fifteen overs plus the resource it will hold when it resumes, added together. The scaling uses that combined figure. Because four wickets have already gone, the resource it can still deploy is lower than it would be for a side with the top order intact, and so the target falls by less. Two sides on the identical score at the identical over, one two down and one six down, will be handed noticeably different targets. That is the method working, not misfiring.

1. 1The umpires take the players offNothing is recalculated yet. Until play can restart, nobody knows how many overs will actually be lost, and a target set on a guess would only have to be set again.
2. 2Overs are cut to fit the time that remainsThe playing conditions set the required over rate and the latest permitted finish. This fixes the new innings length before any resource arithmetic begins.
3. 3Two resource figures are read offOne for the innings that batted first, taking account of any interruption it suffered. One for the chasing side's position now: overs used, wickets lost, overs it will get back.
4. 4The ratio is applied to the first innings scoreThe first side's total is multiplied by the second side's resources divided by the first side's. That is the entire calculation.
5. 5One run is addedThe scaled figure is the score that produces a tie. The target is the next run above it.
6. 6The board changesA new target and a new number of overs go up, the required rate moves with them, and the par figure the broadcast shows is recalculated from the same numbers.

The sequence match officials actually follow. Nothing in it looks at who has been batting well, only at overs and wickets.

When it is the first innings that gets cut short

The case people find hardest is the one where the interruption lands on the side batting first, and it is worth going slowly.

Team 1 is partway through its innings when rain arrives. Play resumes, both sides are cut to the same reduced number of overs, and Team 1 finishes on a score it made while planning for an innings that no longer exists. It paced for the full allocation, kept wickets back for an acceleration it never got to make, and its total reflects a strategy the weather cancelled.

Team 2 now bats the same number of overs. Same overs, ten wickets, and one enormous difference: it knows the innings length from the first delivery. It never has to hold anything back for overs that will not be bowled. In resource terms it holds more than Team 1 held, for the identical number of overs.

R2 is therefore greater than R1, and the ratio is greater than one.

The method does not simply multiply the score by it. Multiplying would assume Team 1 would have gone on scoring at its established rate through the overs it lost, and innings do not behave that way: the end of a limited-overs innings is the fastest part of it, so scaling a truncated total upwards by a flat ratio would misprice the first side's loss in both directions depending on when the rain came. Instead the excess resource is converted into runs at a rate drawn from an average innings total for that level of cricket. In the standard edition this appears as an explicit parameter, the average total for a full innings at the relevant standard, published in the playing conditions and reviewed periodically. In the professional edition the equivalent adjustment is handled inside the model.

The practical consequence is the one that generates the complaints: a chasing side can be set a target higher than the score the first side actually made.

1. 1Rain interrupts the side batting firstIt has been pacing its innings for the full allocation, holding wickets back for an acceleration at the end.
2. 2Both innings are cut to the same lengthThe first side resumes and finishes short of where it was heading. The overs it was saving its wickets for no longer exist.
3. 3The chasing side gets the same overs, and one advantageIt knows the innings length before the first ball. It never has to hold anything back, so it can spend all ten wickets across every over it has.
4. 4The resource comparison comes out above oneThe chasing side holds more of a full innings' capacity than the first side did, for exactly the same number of overs.
5. 5The excess is converted at an average rate, not by multiplicationScaling the score up by the ratio would assume the first side kept scoring through overs it never faced. A fixed addition based on an average innings total is used instead.
6. 6The target lands above the first innings scoreThe chasing side is being charged for an advantage it genuinely holds. Leaving it uncharged would make the interruption worth having.

The direction of adjustment that produces the result viewers most often assume is a mistake.

Why a target above the score actually made is the right answer

This result feels wrong to most people the first time they see it, so here is the argument in full.

The first side's score is not a sacred quantity. It is evidence of what one team did with a particular set of resources under a particular constraint. If the second side is handed a larger set of resources, comparing it against the raw score compares two different things and calls the result fair.

Consider the alternative. Cap the target at the first innings score, and a chasing side gains something free every time the weather interrupts between the innings or during the first one. Both sides get thirty overs, one of them knew it all along and one of them did not, and the one that knew is asked for no more than the one that did not. That is not neutrality. That is a systematic advantage handed out by a cloud.

Worse, it would be an advantage that captains could see coming and play towards. Sides would have a reason to want the first innings interrupted, which is precisely the kind of incentive a rain rule exists to remove. The point of a resource method is that no side gains or loses by the timing of the rain, because the timing has been priced.

The uncomfortable feeling is real, and it comes from a scoreboard showing a target next to a smaller number and offering no explanation for the difference. The feeling is not evidence of unfairness. It is evidence that the scoreboard is showing two figures that were never denominated in the same currency.

What Steven Stern actually fixed

The original Duckworth-Lewis model was fitted to the scoring patterns of the cricket being played when it was built, and it described that cricket well. Then the game changed.

Twenty20 arrived, batting techniques built for it fed back into the fifty-over game, bats and boundaries and fielding restrictions all moved in the same direction, and first-innings totals climbed to levels the original model had rarely seen. The problem this created was specific rather than general. The model's assumption about how much a side could accelerate in a shortened innings was calibrated on ordinary totals. At the top end it under-adjusted: when the first innings total was very large, the chasing side's shortened allocation was worth more than the original model credited, because a side chasing a huge score in fewer overs attacks harder from ball one than the historical data underpinning the model suggested.

Left alone, that meant revised targets in high-scoring games came out slightly too low, and the error grew with the total. In an era where such totals stopped being freak events and became a regular feature of the fifty-over game, a small systematic bias in the most-watched matches is not a small problem.

Steven Stern's revision changed how the model treats those cases, making the conversion from resource to runs sensitive to the size of the first innings total rather than treating a big score and an ordinary one as scaled versions of each other. The method's name changed to reflect the work, and the professional edition carries the adjustment.

It is worth being precise about what this was and was not. It was not a redesign. The two-resource idea, the table, the ratio and the added run all survived unchanged. What changed was the calibration at one end of the range, which is exactly the kind of maintenance a fitted model should receive when the thing it was fitted to moves.

Standard edition, professional edition, and why one of them needs a computer

There are two implementations, and they exist for different users.

The standard edition is a published table plus a short calculation. A scorer with the table, a calculator and five minutes can produce a defensible revised target. It uses the explicit average-total parameter described above whenever the chasing side ends up with the greater resource. It is the version used in club cricket, in age-group cricket, and anywhere the officials cannot be assumed to have a licensed laptop and a trained operator. Its virtue is that anyone who wants to check it can check it, and that virtue is worth a great deal at a level of the game where trust in the number is the whole game.

The professional edition runs a licensed computer program. It applies the high-scoring adjustment continuously rather than through a fixed parameter, and it works from a finer model than a printed grid can express. It is what international and major domestic cricket uses.

Why can the professional edition not simply be printed? Because the adjustment it applies is not one correction that can be tabulated. In the standard edition, a single grid serves every match, and a single parameter handles the one case where the chase holds more resource. In the professional edition, the conversion between resource and runs depends on the first innings total itself. That means there is no one table. There is a table for every possible total, or rather a continuous function that a printed grid can only approximate, and approximating it is the thing the professional edition exists to stop doing.

That is a defensible engineering decision. It is also the origin of the method's largest presentational problem, which is the subject of a later section.

For an ordinary total, the two editions give answers close enough that nobody would argue about them. For a very large one they diverge, and the professional edition's answer is the better one.

• Full innings
• Minimum for a result

One-day international5020

Twenty20 international205

Per side, under the standard limited-overs playing conditions. Below the minimum, the match is a no result whatever the scoreboard says.

Show the numbers

Overs that must be bowled before a rain-hit match can have a winner

Item	Full innings	Minimum for a result
One-day international	50	20
Twenty20 international	20	5

That floor is not a formality. Until the chasing side has faced the minimum, no par score means anything, because there is no result available to be decided. A side can be a long way ahead of where par would put it and still take nothing from the match if the rain returns before the twentieth over. Treating a par score as live before the minimum has been reached is the most common way to misread an interrupted game.

Par score, and how a chasing side reads the match live

During an interrupted chase, the broadcast shows a par score. It is the same calculation, run continuously instead of once.

At any point in Team 2's innings, par is Team 1's score scaled by the resources Team 2 has used so far, relative to R1. Level with par means the match is exactly even on the method's terms. Ahead of par means the chasing side is winning, and it means it in the strongest possible sense: if the players walk off for good at that moment and the minimum overs have been bowled, the side ahead of par has won the match.

That is the difference between par and the required run rate, and it is where viewers most often go wrong. The required rate answers a question about the rest of the innings. Par answers a question about right now.

Par moves in two directions with every ball, and the second one catches people out.

Runs push a side above par. That much is intuitive.

Wickets push a side below par, often sharply. Losing a wicket does not change the runs on the board, but it reduces the resource the side still holds, which raises the score it ought to have reached by this point. A side can lose two wickets in an over without conceding a run and go from comfortably ahead of par to behind it. Nothing about the required rate will have moved much. Everything about the match will have.

This is why a side batting in a rain-threatened chase plays differently, and why watching a captain manage that situation is one of the more interesting things in limited-overs cricket. Two objectives are in tension. Getting ahead of par means scoring quickly now, which means risking wickets. Staying ahead of par after a wicket falls means having wickets to spare, which means not taking those risks. A side that has decided the rain is coming bats for par rather than for the target, which sometimes means taking risks it would never take in a dry match, and sometimes means the exact opposite: blocking out an over to protect a position that would win the game on a walk-off.

Bowling sides read the same number, and it inverts their usual priorities. A captain behind on par needs a wicket rather than a dot ball, because a wicket moves the par line and a dot ball barely does. Ring fields and containment, the default settings in a tight chase, become the wrong answer. That is a different calculation from the one that governs the field settings a T20 side uses in a dry game, and it is one of the clearest signs of a side that has understood the situation it is in.

The criticisms that are actually good ones

Plenty of complaints about Duckworth-Lewis-Stern are complaints about arithmetic that produced an unwelcome result. Three are serious.

It is opaque, and at international level it is closed

A spectator cannot check a professional edition target. Neither can a captain, a coach, or a journalist. The number arrives from a licensed program, and the only available response is to trust it.

This is a genuine cost, and a bigger one than its defenders usually concede. Cricket has spent two decades making its decision-making legible to the audience: ball-tracking is drawn on the screen, the review process is shown step by step, and edges are played back with the audio. Against that, a match-deciding number that appears with no working shown is an outlier. The standard edition is fully auditable and the professional edition is not. The reason for the gap is technical rather than sinister, but it remains true that the most consequential calculation in a rain-hit international is the one nobody in the ground can verify.

It cannot see what an innings was built for

The model knows overs and wickets. It does not know intent.

A side that has spent thirty overs constructing a platform, deliberately keeping wickets in hand for an assault in the last fifteen, has made an investment. If rain removes those last fifteen overs, the investment is written off. The method credits the wickets it still holds, but it credits them at the rate appropriate to the overs that now remain, which is a fraction of what they were being saved for. The side did exactly what the format asks of it and was charged for the discipline.

The defence is that the model has no way to distinguish a side saving wickets for an assault from one that had simply batted badly, and it should not try, because a model that inferred intent would be a model that could be gamed. That defence is correct. It does not make the outcome feel any less harsh to a team that played the situation right and lost the payoff to the weather.

The mirror case is real too, and it is rarely complained about by the side that benefits. A team that gambled early, lost wickets and was heading for a poor total can be rescued by an interruption that stops the innings before the damage compounds.

Very early and very deep interruptions ask the model to do something different

When a fifty-over match is reduced to twenty-five before a ball is bowled, nothing needs adjusting at all: both sides get twenty-five overs on equal terms and the method is never invoked.

The argument bites when the reduction is large and lands after one innings has started. The method will produce a number, and the number will be internally consistent, but the two innings being compared are now innings of different sports. A fifty-over innings and a fifteen-over innings are not long and short versions of one contest. They reward different skills, different bowlers, different batting orders. Reducing one to a percentage of the other is a defensible accounting exercise and a shaky claim about cricket.

The method's own answer to this is honest and worth stating in its own terms: it does not claim the shortened game is the same contest. It claims only that, given the game has been shortened, this is the fairest available restatement of what has already happened. The minimum-overs thresholds exist precisely to stop that claim being stretched past breaking point.

And the ordinary limitations, which are not really criticisms

The model does not know the pitch, and a deteriorating surface or a ball starting to move under lights changes the difficulty of batting in a way no table captures. It does not know about dew, which in many parts of the world hands the side batting second an advantage that has nothing to do with overs or wickets. It does not know whether a side has a deep batting order or a long tail, so six down means the same thing to it whether the next batter is a genuine all-rounder or a number eight who cannot bat. And it has no view on which bowlers have overs left or who is at the crease.

These are the limitations of any general model applied to a specific match. They are the price of having a rule that is identical in every ground, for every team, in every competition, and it is a price worth paying. The alternative is discretion, and discretion in a match-deciding calculation is worse than a model that is occasionally rough. The differences between the formats the method is asked to serve are set out in the comparison of Test, ODI and T20 cricket.

How other sports deal with weather, briefly

The contrast is instructive, because most sports simply refuse the question cricket has to answer.

Tennis stops and resumes. The score is preserved exactly, the players return to the same game at the same deuce, and nothing needs restating because nothing has been lost. Roofs have made this easier still at the biggest events.

Golf does the same at a finer grain. Play is suspended, players mark their positions, and the round resumes from the identical lie. Where weather makes a full tournament impossible, the competition is shortened to fewer rounds, which is a blunt reduction rather than a scaled one and is accepted because every player faces the same shortened event.

Football abandons and either replays the fixture or resumes it from the minute of the stoppage with the score intact. No restatement is required, because both sides are always playing simultaneously and neither can be part-way through an allocation the other has not had.

Baseball has the closest analogue, because it shares cricket's structure of alternating turns with a fixed allocation each. Its historical answer was blunt: once a defined number of innings had been completed the game was official and the score stood, whoever happened to be ahead. That produced its own unfairnesses, since the side batting second could be robbed of a turn it was entitled to, and the modern answer at the top level is to suspend and resume rather than to declare a winner on a partial game.

Cricket cannot borrow any of these. A limited-overs match is the one common structure where two sides consume separate, finite, non-simultaneous allocations, and where the weather can take away more of one than of the other. That is the specific problem, and a resource model is the specific solution.

Reading a revised target without the table

You will never have the table in front of you, and at international level the real numbers are not in a table anyway. Six habits get you most of the way to reading an interrupted match correctly.

Read the par score, not the required rate. Par is the number that decides the match if play stops. The required rate is a number about a future that may not arrive.

Watch the wickets column at least as hard as the runs column. Every wicket raises par. In a rain-threatened chase, wickets in hand are worth more than the scoreboard makes them look, and a side that is ahead on runs and six down is often behind on the only measure that counts.

Expect the target to fall by less than the overs do. A chase cut by forty per cent of its overs will not have its target cut by forty per cent. If you find yourself calling a revision harsh, check whether you have compared it against a proportional cut that was never the right benchmark.

Note when the interruption happened. Early stoppages move the numbers a long way, because most of the innings' resource is still unspent. Late ones barely move them, because it has already been used. Rain with three overs left will change the target far less than the drama around it suggests.

Check the minimum overs before you take a par score seriously. Below the floor there is no result to be had, and the par figure on screen is decoration.

Do not treat the first innings score as a ceiling. If the chasing side holds more resource, it will be asked for more runs, and that is the method working correctly rather than a fault in it.

The method's reputation for impenetrability comes almost entirely from the table being invisible. The idea underneath the table is not hard, and it fits in a sentence: count what a batting side has left, count it in two dimensions instead of one, and compare like with like.

More on the rules, the numbers and the arguments they cause is collected in the cricket archive.