by Sarthak Sethi
Let me tell you the tale of the three most hated men among the cricket fandom these days. You guessed wrong, it’s not Jadeja, Kohli and Shastri but about three gentlemen who would not have had anything to do with cricket had it not occurred to them to find an application of what they learnt in cricket. Yes, it is about Duckworth, Lewis and Stern, the likes of whom have bothered us all for a very long time and will perhaps continue to do so for some time more maybe. No achievement in all of applied mathematics could have turned so many common people to critiques of it. But why? Part of the problem is that what they did was use advanced statistics that would be out of reach for most cricket lovers. So a game that was supposed to be played in mind and on the field suddenly also required the use of pen and paper and brains and lots of it. But that’s not all. This also presented to us that the despite the valiant efforts of those gentlemen and the critiques of their research, mathematics couldn’t take into account the effect of everything that can and does take place during a cricket match.
So let’s try to simplify the overly complicated method. Whenever a match gets interrupted and it has to be curtailed, the only sure-shot way is to reduce the number of overs with the underlying assumption that the over-rate is a fixed number as laid down by the ICC laws. So for example, if a match gets interrupted after the first innings has been completed and the second innings needs to be shortened to 25 overs and the team batting first put on a score of 300/5 in their allotted 50 overs, what would be the target for the chasing team? 150 obviously, right? Wrong. To put things into perspective, let’s instead reduce the number of overs for the chasing team to 20 overs. Now going by the math applied above, the chasing team should be set a target of 120. Would you consider 300 a respectable total more often than not in an ODI or not? Now ask yourself that would you consider 120 a respectable total in a T20?
There you got it, overs are not the only “resource” a team banks on in limited overs cricket. Wickets are also fairly important in the given context. So what the DLS method does is that it considers wickets remaining and overs remaining collectively as resources and based on the resources used/available, it scales the score for the respective team. Didn’t get it, right? Let’s simplify it a bit. Now that you have the knowledge that wickets too play a significant part in determining the score, try guessing an ideal score for the chasing team in the above example with the match reduced to 20 overs. It certainly is greater than 120, probably somewhere around the 150-160 interval. Is that all? Obviously not.
It can be further broken down into cases based on when the match gets interrupted. If the match get interrupted before any team gets to bat and match thereby, gets shortened then there won’t be any readjustment of totals. That was quite straightforward. Coming to next case when it gets interrupted during the first innings, there are three subcases possible: i) Team 1 had batted aggressively that led to a huge loss of wickets in while, say the team had scored 200/6 in 20 overs. The team could not have realistically scored at the same rate had the match not been shortened significantly. In such a case the team’s actual final score would be scaled down for it used too much of its wicket side of resources (even though not using much of its overs side of resource,) ii)Team 1 had batted conservatively losing less wickets but also scoring slowly, say 70/0 in the first 20 overs. The team in highly unlikely to keep scoring at this rate for it has a huge bank of wickets for the latter part of the innings. In such a case, the team’s actual final score would most likely be scaled up as it used a fairly less amount of its resources, iii) Team 1 bats and consumes the amount of resources (wickets and overs combined) just what Team 2 would have to begin with and in such a case, their final score won’t be altered.
If match gets interrupted after the first innings got completed uninterrupted, then the target for chasing team will be adjusted as per their cumulative resources remaining as we tried to do in the example two paragraphs ago. When it gets interrupted during the second innings, it again falls into one of the three sub-cases as in the case when it got interrupted during the first innings and a chasing team will usually try to match the DLS score at every instant so that in case (due to some factors rain usually) match cannot be resumed, they are at par with the DLS.
That was all for the intuitive idea behind the DLS and how the target should be readjusted. DLS uses historic match data and a lot of statistics and mathematical modelling to compute the combined resources remaining based on the overs and wickets remaining. It also has different models for different scores making it more realistic. It gives more weightage to recent matches than to older matches for the game keeps evolving with time. So it uses data from cricket and also the application seemed fair but are its outcomes always fair? That’s what I will try to focus on from this point.
Example 1: New Zealand vs South Africa ICC World Cup 2015 Semi Final
South Africa were playing really well with both de Villiers and du Plesis doing their job with no show of effort in their approach. Batting suddenly looked as easy as applying butter to a loaf of bread. But all was not to go that well that day as it rained just when they had started to attack New Zealand’s bowling. The match was shortened to 43 overs leaving them only with 5 overs after the interruption. South Africa had managed to score at nearly 13.85 runs an over on an average in 4 matches till that match in 2015 in the last 12 overs. This was possible because they had one or both set batsmen on almost all of those 4 occasions. Now had the match not been shortened and had they managed to score at that rate (given that both were well set and on song,) they would have scored 382 runs in 50 overs. Now even if you subtract the score that New Zealand were given to chase in 43 overs from 382, you get 83 runs in 7 overs with one set batsman and another all-rounder who had just come to the middle. Could that have been possible, we can’t comment but can at least speculate. The only loophole in the calculation is that South Africa actually scored at 13 an over in those overs and we assumed them scoring at 13.85 runs an over for 12 overs, is that a valid assumption? It does seem valid to me for they had to show urgency in their approach something that was hardly needed given the brand of cricket South Africa had been playing that season. They took far too many unnecessary risks at Anderson’s bowling which they otherwise wouldn’t and they would have had the luxury of a spinner bowling to them at least 1 over in the last 10 overs and Anderson and other part timers sharing 6 overs among themselves. So basically aggressive bowling worked in the favor of New Zealand.
Example 2: New Zealand tour of England, 2nd ODI: England v New Zealand at The Oval, Jun 12, 2015
New Zealand had set up 398 runs on board in their allotted 50 overs. England huffed and puffed in some patches and cruised in others to a stage with 54 to get from 37 balls and 3 wickets, Rashid playing on 30 from 23 and Plunkett on 38 from 26. It rained for about 3 quarters of an hour and the target was revised to 34 from 13 balls. Now DLS target was actually apt with respect to the factors that were used while modelling it because only a handful matches before that match would have seen teams with 7 wickets down chasing 54 off 37 balls. Where it failed again was to capture the fact that the batsmen were well set and the bowlers left to bowl the remaining overs had the match not been shortened. 54 off 37 seemed very competitive and to be frank, England seemed to be ahead given the match state but 34 off 13 is very difficult for even well set top order batsmen. Also had the match not been shortened, Southee and McClenaghan would have had one over left apiece. Assuming they would have gone at the rate they were, England could have scored 14 off their 13 balls leaving them with 40 runs off 24 balls McCullum(1 over remaining) going at 9.55 an over, Santner (3 overs remaining) at 10.42 an over and only part timers remaining barring them. That again could have been competitive even with a wicket falling in the meanwhile. New Zealand again got the better off DLS because of their aggressive bowling.
Example 3: Pakistan vs South Africa Champions Trophy 2017
South Africa batted first on what seemed like a good bowling wicket with the ball showing signs of reverse swing and Pakistan blazing fire all around in the bowling. They managed 219/8 in their 50 overs. Pakistan managed 119 off the 27 overs for the loss of 3 wickets. If someone was to see just the scorecard of the match, he/she would feel Pakistan would have won easily given how the game is played these days and that’s perhaps what DLS did as it weighs recent matches more than the old matches. But how often do we see such low scores these days and is the approach to chasing such totals these days the same as what was a decade ago, those questions are yet unanswered and will probably remain that way. Even I would simply, going by the brand of cricket played these days, had considered Pakistan slightly having the edge over South Africa but DLS gave them a victory margin of 19 runs which was huge. There was another reason for considering the margin to be huge that Pakistan’s batsmen had not been among runs almost throughout the Champions Trophy especially those who were batting and the ones to come except Sarfaraz’s unbeaten knock of 61 against Sri Lanka. So it had all ingredients of being a classic close encounter among the remaining Champions Trophy matches which were more or less one-sided games. But victory came easily to Pakistan courtesy of DLS.
So, as illustrated in the examples, after all the factors are taken into account the method is not all that inclusive. It obviously can never give outcomes that have rightly taken in the effect of AB’s madness, or Wood taking the match out South Africa’s esophagus in the last over. But it certainly can be improved to take into account various other factors. For eg., a match has been reduced to 35 overs before the toss itself and there is another interruption at 20 over mark and match gets reduced to 20 overs. DLS, in its current form, would consider it a case of 15 overs remaining and the actual wickets remaining like it were in a proper 50 overs match with 35 overs bowled (because it only uses the data from full 50 over matches.) Now that is obviously wrong 15 overs remaining in a 50 overs match is very different from that in a 35 over match. Other factors include the usual pitch behavior, the form of bowlers who had not been used till the interruption and of the bowlers who were supposed to bowl the remaining overs had the match not been shortened, both the teams’ performance in the recent past both with the bat and the ball, field restrictions, the way the batsmen on the crease were batting just before the interruption. There are far too many variables whose effect might not be entirely possible to model mathematically but we can hope the mathematics to keep developing incessantly so as to provide even more accurate calculations that account for as many factors as possible.