Reinventing the DLS method: Part 2

The Duckworth and Lewis method has more than its fair share of flaws. 

It is to the point where some of the targets it sets are as nonsensical as either of the two totally inadequate methods that it replaced, namely simply re-scaling the chasing team’s target to the same run rate per over off the reduced number of overs or by adding up the highest scoring same number of overs of the first team’s innings depending on the number of overs that the chasing side’s innings has been reduced to.

The reason D/L has survived virtually unthreatened for more than 20 years is because unlike both of the methods that preceded it, the very real flaws with D/L are not so obvious. They are not as plain and simple in staring me right in the face. They are more clandestine and hidden from obvious view, but they exist nonetheless.

It is far from unusual, for example, after a match has concluded in which D/L was applied for someone, whether a newsreader in the nightly or morning slot, or the man in the street to make a comment along the lines of “Does anyone actually understand how that method works?” Sometimes such a comment will be made in a “speaking the truth in jest” manner, at other times accompanied by a genuinely contemptuous rolling of the eyes.

Therein lies the rub: because the average cricket fan – and no doubt elite player – doesn’t actually know how the mechanical logic (and I use the word ‘logic’ loosely) works, it seems impossible to actually pinpoint where the flaws lie. But the average cricket fan also knows, at the same time, that the flaws are almost certainly there.

(Daniel Pockett – CA/Cricket Australia via Getty Images)

When Australia scored 4-226 off 38 overs in Sydney in January 1989, and a heavy downpour reduced the West Indies’ innings to a mere 18 overs, everyone knew it was a complete farce that they only had to score 108 off those 18 overs because they could now afford to lose a wicket across their whole shortened innings every 10.8 balls, rather than every 22.8 balls. In other words, they could now slog, taking twice as many risks, while only having to maintain the same run rate per over.

What made it even more unfair on the side that had batted first was two somewhat hidden factors. One was that with six wickets still in the shed to be utilised off their last 12 overs, the side batting first could have reasonably expected to lift their run rate per over even further by the end of their original maximum 50 overs. The other is that the chasing side’s innings had started badly, losing the prize wickets of master batsmen Gordon Greenidge and Richie Richardson, and were teetering at 2-47 when rain further interrupted their innings after 6.4 overs.

If they had been chasing a score of in the region of 310-315 off a full 50 overs, they would have still have required some 265 runs off 262 balls, only being able to afford a wicket every 33 balls, which is ten per cent higher than at the start of their innings. By ignorantly simplifying their task to a further 61 runs off the remaining 68 balls, which time permitted after the long interruption, not only was the chasing side’s Wicket Affordability Factor (WAF) now only one third of what it should have started out at, but also the huge benefit for the fielding side in taking those two aforementioned prize scalps early on was well and truly, not to mention totally unjustly, wrenched from them. It was clear that the result had been a farce and why.

Similarly, the highest scoring overs method was clearly exposed in the 1992 World Cup. What the perpetrators of this method did not realise was that eliminating the unfair advantage held by the chasing side in a reduced overs scenario and actually making it fair and just to both teams did not necessarily amount to the same thing – on 90 per cent of occasions in fact.

When England had scored 252 off the 45 overs that they received and South Africa’s innings was interrupted with 2.1 overs remaining of their own, they required a further 22 runs to win with four wickets still in hand. When playing time thereafter permitted only a further seven balls, and then only that one solitary ball to finish the over in progress by the time play did resume, the 22-run requirement did not reduce in either instance. Therefore, South Africa were punished for having bowled two maidens to greatly help restrict England to 252 in the first place. As with the fielding side in the outlined occurrence, it was crystal clear that the chasing team had been duped, and precisely how.

Compare that to an everyday D/L scenario: in a match on their 2008 tour of India, England bowled first and India’s innings was curtailed to 22 overs off which they had reached 4-166. Remaining time allowed the chasing side to also receive 22 overs and their target was set at 198. Most cricket fans, and even a large number of experienced commentators would look at this and initially think ‘how on Earth can the second team have to chase a target (off the same number of overs that the side batting first received) that is actually quite a few more runs than the first team scored?’

However, this is not actually where the flaw in this particular target set is to be found, hence the main problem in attempting to expose D/L farcical targets: your average cricket fan or commentator will usually go looking in the wrong place. I shall return to this particular example a little later when I explain the actual logical principle of the second team having to score considerably more than the first team, depending on how many wickets the first team had lost when their innings was curtailed.

Before looking at a cross section of both real and hypothetical but nonetheless totally realistic examples of D/L in practice it is important to note a couple of things. The first is that D/L operates on what I consider to be an unnecessary and even completely illogical double standard between situations where the chasing side knows in advance the number of reduced overs it will receive and when its innings is simply terminated at some particular point along the way without prior warning.

(Photo by Harry Trump-ICC/ICC via Getty Images)

Let’s look at a simple example: The side batting first has full access to its maximum 50 overs and scores 199 leaving the chasing side a target of 200 off its 50 overs.

In this scenario two main things can happen. The first is that the chasing side sets out in its chase and after 25 overs are bowled it rains and play does not resume and the second is that the rain occurs before the start of the run chase, which subsequently begins with the chasing side in fact knowing full well in advance that it will only receive 25 overs.

In the first case, D/L simply says how many runs the chasing side needs to have scored depending on how many wickets it has lost to this point. The ten possible winning scores are as follows: 0-66, 1-71, 2-78, 3-87, 4-99, 5-115, 6-134, 7-156, 8-175 and 9-189.

The calculations in this scenario are essentially sound and from four wickets down and onwards differ mostly only by a mere run or two from McConville-Warehouse (McWarehouse) calculations as follows: 0-80, 1-85, 2-90, 3-95, 4-100 (which is the par score), 5-117, 6-133, 7-150, 8-167 and 9-183. The starker difference in the above par required scores at zero, one, two and three wickets down is almost certainly down to one of two things: either they are based on detailed and regularly updated statistics that are impossible to keep at levels below the elite, or they are too generous and based on acceleration rates on an exceptional day, whereas McWarehouse provides for acceleration on an average day, remembering that on occasions things also go horribly wrong even from the most favourable of launching pads.

As good an example as any to highlight this is Australia batting first in the 1996 World Cup final against Sri Lanka. From 1-134 at the halfway point of the innings that Australia had reached i.e. after 25 overs, let’s imagine that rain had terminated Australia’s innings at that point. McWarehouse projects a completed 50 over total of 317, which amounts to a further 183 runs off the final 25 overs or second half of the innings, which amounts to a run rate per over of 7.32 compared with 5.36 off the initial 25 overs when wickets were kept in the shed.

Based on the above 1-71 seeing the chasing team reach the 200 run target set, D/L projects the aforementioned 1-134 off the first 25 overs to a total of 373 off the completed 50 overs, amounting to a run rate per over of 9.56 across the second half of the innings compared to 5.36 off the initial 25 overs when nine wickets were kept in the shed. While this is by no means impossible, I would have to surmise that this would amount to the top end of an exceptional day out.

McWarehouse takes the middle ground of an average day out to allow for the fact that for every such exceptional day out, there is also a corresponding occasion where the team completely loses the plot from such a seemingly impregnable launching pad, as indeed happened in that 1996 World Cup final when from the aforementioned 1-134 off 25 overs, Australia’s innings choked and spluttered and limped to a final total of only 241 having had complete access to its maximum overs of 50.

Referring back to the ten possible required scores when chasing 200 off 50 overs with the innings terminated without prior warning after 25 overs, let’s look at what D/L does in the second of the above-mentioned scenarios where the long interruption is between innings and the chasing side sets out knowing in advance that they will only receive 25 overs.

In this instance, D/L sets a blanket target score, with the chasing side’s entire batting line up of ten partnerships at its disposal, of only 133, a mere one run less than it was required to be in the first scenario if it had lost no more than six wickets to that point, with the opposition in both cases having totalled 199 batting first with full access to its maximum of 50 overs.

If the various D/L wickets in the first scenario are credible – and they mostly are – then surely I could reasonably conclude that in this second scenario that the chasing side has been gifted a very generous target, which they should be able to comfortably chase down losing no more than six wickets.

As a sub-extension, let’s now look at what D/L does when the side batting first’s innings is curtailed after 25 overs with each of those ten required scores in the first example. The key to this exercise is remembering that in the first scenario of the chasing side’s innings terminated after 25 overs, all of the scores in the left-hand column were projected to an eventual 50-over total of 200.

Remembering that all of the scores in the left-hand column were projected to the same maximum overs (50) score (of 200) in the first scenario, why firstly are they not projected to the same 50-over score (of 200) when reached at the same 25-over point batting first, and secondly, why does each lead to a different blanket target for the chasing side in the second and third scenarios?

Also, why from six wickets downwards (from Table 1 above), is the chasing side afforded more wickets when having to chase a lower score off exactly the same number of overs? When the side batting first used only seven partnerships in scoring 134 off 25 overs, the chasing side has all ten partnerships at their disposal to only have to score one run less (133). When the side batting first used only eight of its available partnership in scoring 156 off 25 overs, why does the chasing side have all ten of its partnerships available to only have to score 23 less? When the side batting first used only nine of its ten partnerships to score 175 off 25 overs, why does the chasing side get an extra partnership and only have to score 42 less? And when the side batting first used all of its partnerships to make 189 off 25 overs, why does the second side get all ten partnerships but only have to score 57 less off the same number of overs?

Given that the highest blanket target in scenario three is only 147, nine runs less than what the chasing side needed to be with seven wickets down in scenario one, then as with the blanket target in scenario two, it amounts to an overly generous blanket target, which should be comfortably achieved with no more than seven wickets down.

This might be an opportune moment to point out a very interesting statistic, which reads as follows: in ODIs where both innings run their natural course, the chasing side wins, on average, between 49 and 50 per cent of occasions. In matches where D/L is used the chasing side wins on about 63 per cent of occasions.

Given that the first of the three main scenario types outlined just now the various wickets down targets at the point of unforeseen termination appear to be sound, then this would suggest that between one quarter and one third of blanket targets set when the chasing side knows before it sets out how many overs it will receive are hopelessly lopsided in favour of the chasing side. The rather obvious question to demand an answer for is why it simply doesn’t always go on wickets lost, in any type of situation, as my own McWarehouse does.

In either of the second and third scenarios outlined previously, McWarehouse will simply say this: when a side is chasing 200 off 50 overs (whether the side batting first actually made 199 with full access to its maximum 50 overs, or was projected to do so in the event of its own innings being prematurely curtailed), and the side knows in advance that its innings will be reduced to 25 overs, a par score is set of 100 with a VBO of five.

VBO stands for Virtually Bowled Out and it works like this: losing five wickets inside 25 overs, six inside 30 overs, seven inside 35 overs, eight inside 40 overs, or nine inside 45 overs is the mathematical equivalent of losing ten inside 50 overs.

(Photo by Andy Kearns/Getty Images)

So basically, a chasing side in this situation is told this: You have to score at the same run rate per over, off the lesser number of overs your innings has been reduced to, but you can also only lose a mathematically fair proportion of your wickets. In this particular situation a team is VBO once it loses five wickets, and although its innings doesn’t end, it is required, as in D/L scenario one previously outlined, to be more and more above the par target (in this case of 4-100) for each extra wicket lost (refer to McWarehouse targets for each number of wickets in the previously outlined scenario one). The umpire calculates the par score and VBO and informs the two captains. Each captain is then free to calculate above-par and below-par targets themselves at any time during (including before) the run chase, and it is at the discretion of any particular chasing side how they actually approach their run chase or indeed what containment and/or wicket-taking tactics the fielding side approach their task with.

However, with McWarehouse, the match does not end simply upon the chasing side reaching the par, or any of the other nine moving targets sometime during the 25 overs (in this example) that they will receive. Even if the chasing side, for example, were 4-100 after 18.2 overs, they must still bat out their 25 overs, unless they are either bowled out beforehand for less than the 200 they would be chasing with full access to their maximum 50 overs (whether 199 represents what the first team actually made with full access to maximum 50 overs or were projected to do so in the event of their innings curtailed beforehand) or they actually reach 200 before the 25 overs have been bowled, irrespective of how many wickets they have lost.

I will finish by showing some other hypothetical situations that really expose the Duckworth and Lewis method when it comes to setting blanket targets for the side batting second. But firstly, I will begin by returning to an earlier example that I touched upon, namely the 2008 match where India scored 4-166 off 22 overs and that led to England being set a blanket target of 198 off the same number of overs.

Contrary to popular belief among a large percentage of cricket fans and commentators alike, the fundamental idea of a chasing side’s target being more or less than the side batting first scored off the same number of overs is actually a very sound, in fact vital principle. It is essential in order to ensure that whichever side was on top when the side batting first’s innings was prematurely curtailed is not robbed of their hard-won advantage. Consider the following two examples.

Example 1
The side batting first is 9-91 off 25 overs when it rains and their innings is terminated with eventual time remaining allowing the chasing side to also receive 25 overs.

It is imperative to consider what would most likely have happened had the side batting first’s innings run its natural course. The most likely scenario is that the last pair at the crease would not have added even another ten per cent to the team total before the tenth wicket falling, and it has become superfluous in what over their innings would most likely have been subsequently wrapped up with a minimum of fuss.

So, a logical and sound mathematical projection would likely have seen the chasing side having a target of 100 off 50 overs. Obviously, if their innings also ran its natural course, they would not labour the full 50 overs in chasing down such a small total. However, who should be awarded the match in the event that they finished on 3-81 after 25 overs, or even 5-87? In either case, who would most punters be backing to eventually win the match? Quite obviously the chasing side.

Example 2
Batting first, a side reaches 1-147 off 30 overs when it rains and their innings is prematurely terminated at this point. There might be enough time remaining for the chasing side to also receive 30 overs or perhaps only 25. Should the chasing side have reached 8-140 off 25 overs when further rain finishes the match, who should be awarded the game?

I remember an ODI in January 1988 when Australia were 1-147 off 30 overs, and batted out their 50 overs to reach 6-289. This would seem like an average acceleration through the final 40 per cent of the innings, having so many wickets up their sleeve when 60 per cent of their overs had been faced.

Therefore, when setting a fair target for the chasing team, it is imperative to greatly factor in the fact that there is a massive 44-run difference – nearly a whole run per over across the whole maximum overs – between the score they eventually reached and the score that an incorrect projection of merely the same run rate per over achieved in the first 30 overs when they had skilfully preserved 90 per cent of their wickets (245).

McWarehouse, incidentally, projects 1-147 off 30 overs to a maximum 50 overs score of 283, with the 4.9 run rate per over off the first 30 overs being bettered to 6.8 off the final 20. Further highlighting the gross inconsistencies in the D/L method across different types of scenarios, D/L says that 1-147 off 30 overs is a winning score chasing 328 (off 50 overs) if their innings is prematurely terminated at this point, while a side batting first reaching 1-147 off 30 overs and being similarly terminated is projected to a maximum 50-over score of 281.

(David Rogers/Getty Images)

So, looking at the actual 2008 match between India and England where England were set a blanket target of 198 off 22 overs after India had reached 4-166 off the same number of overs, the reason this is way too generous to the chasing side is this: they are given twice as many (or 100 per cent more) batting partnerships to utilise off the exact same number of overs (which also amounts to a WAF difference of 26.4 to 13.2 – or precisely half – between the two teams), and yet they are required to score only 20 per cent more runs. It is my firm belief that no method can possibly set an accurate blanket target for a whole batting line-up of ten wickets or partnerships in such a situation simply because wickets still standing must always be taken into account at the end of the chasing side’s innings in a reduced overs scenario – not just when their innings is prematurely terminated without prior warning. Knowing in advance the number of overs that the chasing side’s innings will be reduced to does not in any possible way alter this.

At best, D/L seems to be saying that had India known at the start of their innings that it would be a 22-over match for each side then they would have scored 197 utilising their entire line-up batting for such a maximum over innings of 22. However, there is no way known that any such credible projection could ever be made. It is as impossible as being able to accurately calculate what Don Bradman’s statistics would have been in both forms of cricket had he played in the post-1970 era. What we can do, however, is credibly project a score of 4-166 off 22 overs into a probable 50-over score based on what we know to be normal acceleration (or even deceleration) rates on an average, exceptional or diabolically poor day at the office.

McWarehouse says that at 4-166 off 22 overs, a team would be bowled out sometime between the 45th and 50th overs with their eventual total, having had full access to the maximum 50 overs, finishing at 339. Then a par target score for the chasing side off the same number of overs would be 145 with a VBO of four or simply 3-145 of the par score.

Four wickets down would require them to be 167 after 22 overs, which, quite logically, is precisely one more run than the side batting first made for the same number of wickets off the same number of overs. Above par winning scores after 22 overs would be 0-115, 1-124 and 2-134 while below par winnings scores, apart from the aforementioned 4-167, would also be 5-195 (further highlighting how ridiculously generous the blanket target on the day of 198 with a full batting line-up to do it actually was), 6-223, 7-252, 8-280 and 9-308.

Also consider these following hypothetical scenarios and ask yourself the question is it actually any sort of improvement on one or the other of the two methods that D/L replaced after they had been found perilously wanting.

In these examples, as they are hypothetical matches rather than ones actually played, the side batting first will be referred to as Team 1 while the chasing side will be referred to as Team 2. As they are hypothetical matches, I can do the calculations myself using the downloaded mobile phone app for the original standard version of D\L.

Example 1
In a 35 maximum overs match, Team 1 has reached 7-175 off 25 overs when an interruption prematurely terminates their innings at this same point. D/L sets Team 2 a blanket target of 180 off the same number of overs, which is a mere four runs more than would have been set under the original method found to be so terribly unfair to Team 1 in the infamous Australia versus West Indies match in Sydney in January 1989.

Example 2
In a maximum of 50 overs match, Team 1 is 8-175 off 35 overs when an interruption prematurely terminates their innings at this same point. D/L sets Team 2 a blanket target of 165 off the same number of 35 overs that remaining time allows to be bowled, which is actually 11 runs less than would have been set under the original method found to be so terribly unfair to Team 1 in the infamous Australia versus West Indies match in Sydney in January 1989.

Example 3
In a maximum of 50 overs match, Team 1 is 9-175 off 35 overs when an interruption prematurely terminates their innings at this same point. D/L sets Team 2 a blanket target of 123 off the 25 overs that remaining time allows to be bowled, which is now actually three runs less than would have been set under the original method found to be so terribly unfair to Team 1 in the infamous Australia versus West Indies match in Sydney in January 1989.

Example 4
In a maximum of 50 overs match, Team 1 is 9-175 off 35 overs when an interruption prematurely terminates their innings at this same point. D/L sets Team 2 a blanket target of 152 off the same number of (35) overs that remaining time allows to be bowled, which is now 24 runs less than would have been set under the original method found to be so terribly unfair to Team 1 in the infamous Australia versus West Indies match in Sydney in January 1989.

Example 5
In a maximum of 50 overs match, Team 1 scores 6-150 off 25 overs when an interruption prematurely terminates their innings at this same point. D/L sets Team 2 a blanket target of 148 off the same number of (25) overs that remaining time allows to be bowled, which is now also three runs less than would have been set under the original method found to be so terribly unfair to Team 1 in the infamous Australia versus West Indies match in Sydney in January 1989.

At this point, I might be forgiven for thinking of the old adage ‘the more things change, the more they stay the same’, but wait until you see these next examples…

In all of the following examples, Team 1 scores 200 having had full and proper access to its maximum overs amount of 50. The following table shows the blanket target scores that D/L sets for all reduced overs amounts of 46-49 inclusive when the overs to be received by Team 2 are known in advance.

Do these above targets set by D/L when only a very small number of overs are clipped from Team 2’s innings not greatly reek of the highest scoring overs method that was found so terribly wanting at the 1992 World Cup?

In the tables on the following page, with Team 2 chasing a target of 200 off 50 overs, their innings gets reduced to 45 overs before the run chase begins. The D/L target is 190, which is precisely halfway between the original full 50-over target (of 200) and the same run rate per over (four) if applied to the reduced overs of 45 (180) to be faced by the chasing side. Is this mere coincidence or does the standard D/L calculator consider that there is some semblance of mathematical logic and cricketing justice in this?

Reduced overs amounts of 39-44 also hover at between 45 and 48 per cent of the distance between the net run rate per over and the original 50-over target, somehow going up and down, from 50 per cent for 45 overs down to 45.83 per cent for 44 overs, and then gradually rising for 43, 42, and 41 overs before falling to an even 45 per cent for 40 overs and then rising again to 45.45 per cent for 39 overs. Then it drops again slightly for 38 and 37 overs before rising once more (slightly) for 36 overs.

Only after this point does it drop continuously for each subsequent over reduced until 26 and 25 overs, between which there is no disparity whatsoever.

What about the 1997 match between England and Zimbabwe when Zimbabwe were bowled out for precisely 200 inside their maximum 50 overs that they had had complete full access to? I am not sure if D/L was actually used in that particular match, but off the 42 overs that England had available to them, D/L would have set a blanket target of 184. The 7-179 they finished with would not have been considered enough, even though seven is the par number of wickets to be down at this point (under the McWarehouse VBO principle), and they were scoring at a run rate per over of 4.26 opposed to 4.02 that would have been the requirement across the full 50 overs had they been available to them.

Put another way, D/L does not back the last three wickets to gather a mere 22 more runs at 2.75 per over from the remaining eight overs were they to be bowled, with a WAF (wicket affordability factor every so many balls) of only 16 compared to the 30 that each 50-over innings starts out with. And yet, had they set out chasing the original 201 off 50, and then their innings had been prematurely terminated after 42 overs, with seven wickets down, they would have only been required to be 167.

As noted at the start of this piece, a big problem in exposing large parts of the D/L method is actually identifying (firstly) and articulating (secondly) what the various flaws are. On the rare occasions any knowledgeable commentator or scribe has called a specific D/L target from an actual game into question, they have invariably been met with the seemingly standard generic PR type response of: “Yes, there is a weakness in that particular situation, but we are working on our new, updated computer program that will fix it.”

An example was when Srinivas Bhogle, Harsha’s brother, actually directly questioned the conceptors Messrs Duckworth and Lewis after a game at the 1999 World Cup involving India and Sri Lanka. With India scoring 371 at Taunton, 0-117 after 25 overs – not even one third of the way to the target with half the maximum overs bowled – would have seen them awarded the game had it been rained out on precisely that score off precisely that number of overs.

To finish off, let’s look at two real match examples that occurred in 2011 and at the 2015 World Cup respectively. The 2011 match between India and South Africa started out as a 50-over match. Two stoppages during South Africa’s innings (setting the target) saw the match reduced to 46 overs and they had reached 9-250. The adjusted blanket target set by Duckworth-Lewis was 268 off the same number of overs.

I cannot see any mathematical logic or indeed cricketing justice in this. How can a side that had their last pair at the crease after 46 overs get to defend an extra 18 runs off the same number of overs?

McConville-Warehouse urges batting sides to just bat normally, as if they are batting for the maximum overs. If they score runs, and preserve wickets, the resultant projected maximum overs total at the end of the reduced overs actually faced will take care of itself.

This applies equally for the bowling side if they take wickets and restrict runs. In this actual match, 9-250 at the end of the reduced 46 overs faced would be projected to a (innings running its natural course) total of 253. To ram home the idea of batting normally as if batting for maximum overs, 5-227 (after the reduced 46 overs) would see the same projected maximum overs total of 253. A score of 4-230 would see the projected total increase to 258. A score of 3-235 becomes 265.

(Mark Kolbe/Getty Images)

Getting back to the actual 9-250 off 46 overs being projected to 253, the resultant projected maximum overs target of 254 would require a par target of 8-233 (off the 46 overs the chasing team got to face). Nine wickets down would require the chasing team to have scored 251.

As if that 2011 match example was not bad enough, it could scarcely get more ridiculous right? Wrong! Just to take sheer stupidity even one step further, the 2015 World Cup match between Pakistan and South Africa saw Team 1 get bowled out and then the chasing side had to score ten more runs.

When Pakistan were bowled out with two balls remaining in the 47th over, the designated last of the innings, they had made 222. Then the chasing side were required to score 232 off 47 overs. Go figure.

When a side is bowled out before the end of its allotted overs (reduced overs amount from original maximum), it should be considered one and the same as having had complete and unhindered access to their full complement of overs – after all this is how it works in matches where the overs are not reduced at any point, whether before or after the start of the match.

Therefore, in this particular example, if the side batting first’s innings was reduced to 47 overs after it began, using the aforementioned McWarehouse principle of just batting normally in order to maximise a final maximum overs total projection, then the 222 all out should be considered as a maximum overs total – same as if they had been bowled out in 47 overs in an innings that wasn’t reduced.

Otherwise, where is the value in a reduced overs situation of bowling a side completely out? There is no semblance of cricketing justice or mathematical logic to justify this particular D/L calculation of increasing the chasing side’s target by ten runs. It is mind boggling.

The much more mathematically logical McWarehouse calculations would be as follows.

If it had started out as a maximum 50 overs a side match, then reduced to 47 after the first side’s innings began, then off 47 overs the chasing side would have the following targets.

The par target in runs is 209 and the VBO is nine (for a par target after 47 overs of 8-209).

The one solitary below-par target at the same end point of the innings (after the 47 overs the match was reduced to) would be 9-221. The above par targets at the same point would be 0-201, 1-202, 2-203, 3-204, 4-205, 5-206, 6-207 and 7-208.

This concludes Part 2 in this series. Part 3 will demonstrate precisely how McWarehouse works and the mathematical principles that underpin its calculations when rescaling targets.