ICC's inflexible attitude towards VJD is most disappointing

If Virender Sehwag had batted for seven more deliveries in the 2003 World Cup final and managed another 10 runs from them with Rahul Dravid to take the score to 157 for three, and if rain had indeed pelted down as had seemed very likely, Messrs Duckworth and Lewis would have ruled in India’s favour. After scoring 359 for two batting first, Australia would have lost that World Cup to a thoroughly undeserving team. That would have been a sad day for cricket and possibly the end of the Duckworth-Lewis Method. © Getty Images

ICC has once again rejected the claims of V Jayadevan (VJD) and stuck to the Duckworth-Lewis system of target revision.  


Arunabha Sengupta looks at the two methods and explains why VJD would have been a better bet at least in T20.



“The elements are cricket’s presiding geniuses,” wrote the inimitable Neville Cardus.


But, gone are the days when we could let our thoughts wander as clouds passed by, pouring their contents on the greens. In the shorter versions of the game, when Cardus’ geniuses intervene, it is a signal for scientific geniuses to peer into the future and come up with results and revised targets. And sometimes these gods of mathematical figures do give a glimpse of their feet of clay.


Yet, gods imply devotion. As things stand, the International Cricket Council (ICC) has refused to withdraw their zealous support for the Duckworth Lewis (D/L) method, much to the chagrin of V. Jayadevan, the creator of VJD, and many cricketing and statistical experts.


Rain and pain from the past


On March 23, 2003, India had surprisingly put Australia into bat in the World Cup final. The happy Aussies had got off to a flier and had kept soaring all the way, to end with 359 for two.


As India had tripped and faltered in reply, some desperate fans armed with D/L sheets had kept praying for the distant skies to open up at a calculated moment. Ultimately Virender Sehwag was run out for a fighting 82 as India slipped into the gloom of 147 for four in 23.5 overs in overcast conditions. The rains did not come and finally the much better side was the winner. But if Sehwag had stayed for the next seven deliveries, and he and Dravid had managed another 10 runs from them to take the score to 157 for three, and if rain had indeed pelted down as had seemed very likely, Messrs Duckworth and Lewis would have ruled in favour of India. A thoroughly undeserving team would have won the World Cup – and it would have been a sad day for cricket.


Rain, which stayed away to dash the wafer thin Indian hopes, also managed to take D/L home and dry. However, a major relook at the algorithm was initiated.


If India had won a truncated match that day, it would have been curtains for the method – just as the infamous Most Productive Over rule had been whisked away from sight after it had forced South Africa to go back into the field and conjure up a way of scoring 21 runs off one ball.


This 1992 farce has become a sort of benchmark for target revision methods. England had made 252 in 45 overs. The South Africans had replied with 231 for six in 42.5. Two overs had been lost due to rain. Even considering the continuation of brain freeze making two additional overs impossible under glaring lights, if the same situation was revisited today, how much would South Africa have to make in the last ball?


D/L would bring it down from 21 to a much more manageable and perhaps fair three.


Interestingly, the VJD method also returns a revised target of three.


As in this case, the two techniques give very similar results to a variety of match situations. Yet, according to many, VJD is more suited to the modern game than D/L.


Let us briefly look at how the two methods work.


The Theoretical Mathematicians and the Engineer


Frank Duckworth was born in 1939 and Tony Lewis (no relation to the former English captain of the same name) in 1942. Their solution for the long standing cricket problem is nothing short of beautiful application of Mathematics.


D/L considers the remaining number of overs and wickets as resources. Based on 300 rows, one for every ball bowled, and 10 columns, for 0,1, …,9 wickets,  percentage remaining resources are tabulated for each scenario.


To do this, D/L uses an exponential decay function, which very loosely means that the percentage resource available decreases rather sharply with wickets lost rather than being a linear function. Based on this remaining resource percentage, D/L computes the revised target based on elegant mathematical equations derived from the ODI scoring patterns.



  Wickets Left
Overs remaining 0 1 2 3 4 5 6 7 8 9
50 100 93.4 85.1 74.9 62.7 49 34.9 22 11.9 4.7
49 99.1 92.6 84.5 74.4 62.5 48.9 34.9 22 11.9 4.7
48 98.1 91.7 83.8 74 62.2 48.8 34.9 22 11.9 4.7
47 97.1 90.9 83.2 73.5 61.9 48.6 34.9 22 11.9 4.7

D/L percentage Resource table extract


Jayadevan, a civil engineer from Kerala, also uses a table for remaining resources. However, his approach is that of regression. The VJD system, released in 1998 and fine-tuned to a competitive state by 2001, was published in the Current Science journal. After a careful study of closely fought matches, Jayadevan framed a curve representing the normal development of an innings (normal curve). Next, a Target curve was derived by considering the highest scores off overs in descending order – a clever caveat of the Most Productive Overs.

ICC's inflexible attitude towards VJD is most disappointing

VJD Curve

The VJD Curves


Both these curves follow cubic functions (of the form Runs = ax +bx2+cx3+d where x is the number of overs and a, b, c, d variable coefficients). Finally, the pattern of fall of wickets with required number of runs scored were also derived based on observation of these games. The target table was derived from these percentages – an extract of which is given below.


VJD table Target Runs
Normal runs percentages for diff % Wicket falling
Percentage Overs 0 10 20 30 40 50 60 70 80 90
1 1.7 0.8 10 20 35 50 60 70 79 87 95
2 3.3 1.6 10 20 35 50 60 70 79 87 95
3 4.9 2.6 10 20 35 50 60 70 79 87 95
20 29.8 16.9 20.8 22.5 35 50 60 70 79 87 95


Revised targets can be computed from the Target percentage column; and to decide the winner of a curtailed match, the percentage runs corresponding to percentage overs completed and percentage wickets lost need to be identified. The method is simple, and workable.


Jayadevan’s approach did not use complex mathematics. It was more of designing a system to do the job and refining it, quite the engineering approach.


The D/L did enjoy better results during the first few years, as a scrupulous mathematical model is expected to, but down the years, the practical flexibility of the Jayadevan seemed to gain a distinct advantage.


Pros and Cons


Able and respected in their fields, Duckworth and Lewis have designed the very first scientific technique for computing revised targets, and, indeed, the method works exceptionally well– successfully implemented for almost a decade and a half with just a few matches creating controversies.


Yet, there have been flaws.


In the 1999 World Cup, India piled up a mammoth 373 at Taunton, and won by 157 runs as Sri Lanka collapsed to 216 all out. What passed quite unnoticed was that if Sri Lanka had scored 120 for no loss in the first 25 overs, and rain had washed out the rest of the match, they would have emerged winners. One can argue that wickets in hand made all the difference, but winning with an asking rate of 10 for the last 25 overs is stretching it way too much.


The reason for this absurd target was that D/L was just not geared for an exceptionally high score. The average innings score considered was 235. There is a reason I mentioned the birth years of the veteran duo. They took a while to come to terms with the faster rate of scoring.


There were other quite glaring loopholes.


1.    It assumed that scoring rates increased continually as the innings progressed. The idea was still rooted to the 10 slog-overs of the late 80s. When asked about the field restrictions of the first 15 overs, and later the power-plays, the casual and often evasive answer was that increasing run-rate put wickets in peril. While it may be so in English conditions, the argument did not seem to hold water as Mark Greatbatch, Sanath Jayasuriya and others started belting it from the word go.


2.    When the innings of Team Two was interrupted, the revised target was derived by using the scale down ratio (Resources available [overs and wickets] for Team 2)/ (Resources that were available to team One). However, if Team One’s innings was curtailed, a similar scale up ratio was surprisingly not used. The quite peculiar alternative invoked was called G50, average score in ODIs, which started with 225 and was later revised to 235.


In stark contrast, VJD faced no such problems because of sticking to elegant but inflexible mathematical equations.  Ironically, this lack of Mathematical equations that was quoted as a reason when ICC rejected VJD in 2004.


Tweaks and Changes


After the 2003 final discussed above, Duckworth and Lewis were forced to look into the problems. The resulting enhancements resulted in a computer-based Professional Edition.  According to the Journal of Operational Research (JORS) paper of 2004, D/L had added additional variables to the mathematical model, so that more weight was given to overs than wickets. The Professional Edition now generates a new D/L table for every score by the team batting first, as opposed to the previous ploy of using one table for all conditions.


Using this method, Sri Lanka’s target in the Taunton match would have been 150 for no loss in 25 overs, which is exactly the same as evaluated by the original VJD method.


D/L also claimed to have done away with the G50 anomaly, moving to scale up and scale down methods. However, their JORS paper of 2004 does not mention this. Jayadevan is of the opinion that the scale up method did not work due to the rigid mathematical model, and they surreptitiously went back to G50. The annoying part is that the Professional Edition is not available in the public domain.


In the meantime, VJD has also been tweaked and computerised. The Professional Edition of D/L and the current version of VJD produce almost identical revised targets. Most of it, however, remains black box, with interactive menus asking the user to enter match details and providing the target scores.


The seven criteria


While evaluating systems for fixing revised targets, ICC mentions seven criteria:


1.    Reasonability of adjusted targets under a wide range of match scenarios.


2.    Consistency between sequential targets following multiple interruptions.


3.    A suitable method for describing the result of an interrupted match.


4.    Compatibility with current or prospective playing regulations.


5.    Usability of calculations routines required to generate adjusted targets.


6.    Practical impact on a match in progress.


7.    Overall mathematical robustness of the underlying theory and formulae.


Jayadevan points out quite a few discrepancies in D/L with respect to these criteria.


For example, discussing the consistency of set targets, he states that Team One scores 40 for no loss and 41 for no loss  in 20 overs, the D/L target for Team Two in 20 overs is 134 and 133 respectively – lower for a score of 41 than for 40! VJD computes these targets as 93 and 95.


Statistican and cricket analyst Srinivas Bhogle, however, puts D/L slightly ahead against the second criterion when faced with Team Two innings interruptions, while stating that D/L may struggle in the case of multiple Team 1 interruptions.


It is while discussing point 4, compatibility with correct or prospective playing regulations, that Bhogle puts VJD way ahead of D/L – particularly for Twenty 20.


T20 scenario – caught with pants down


In the ICC T20 World Cup encounter on May 3, 2010, England scored 191 for five only to lose to West Indies who ended up with 60 for 2 in six overs. Following this, Bhogle, with fellow Indian Statistical Institute alumni Rajeeva Karandikar, professor at Chennai Mathematical Institute, wrote a detailed article stating why D/L is not suited for T20.


The major drawback is that D/L considers T20 to be a 50 over game where not a single wicket has fallen for 30 overs, and 20 overs remain. Karandikar and Bhogle used the analogy of cutting off daddy’s trousers to fit the son. The same model just does not fit both formats, and T20 scores have not been analysed properly enough to adapt D/L to the shortest version. The exponential decay curves used in D/L simply don’t work well, and the disgruntled captains can testify as much.


Since VJD does not keep track of the number of overs, going by percentages of overs completed, wickets remaining and required runs, it suffers no such problems.


It seems that in the T20 scenario, there had been more than a case for VJD to be tried out.


Unfair game


The Board of Control for Cricket in India (BCCI) has been using the VJD method for Domestic tournaments since 2007, after the likes of batting legend Sunil Gavaskar strongly voiced the need of alternate systems. It has also been used in the now defunct Indian Cricket League (ICL). However, in spite of talks of using the system for Indian Premier League 4, the BCCI has stuck to D/L.


Jayadevan maintains that the 2004 evaluation by ICC had been unfair. He has especially strong words about the comments publicised by David Kendix, the ICC representative who evaluated VJD. According to him, VJD conforms to all the seven conditions stipulated by ICC, while D/L fails to satisfy most.


On the other hand, in Duckworth Lewis: The Method and the Men Behind It, Frank Duckworth says that his colleague Lewis had demonstrated some illogical results produced by VJD.


While the two parties may have their own view of things, what is surprising is that this time Jayadevan’s suit has been dismissed by ICC on grounds that his system does not offer any improvements. In view of the shortcomings of D/L in the T20 format, the verdict is most surprising.


Sunil Gavaskar feels that the game’s governing body could at least have tried the solution. D/L after all has had a long run.


Statistician Karandikar sounds worried, “I think that more than D/L vs VJD, it is the attitude of ICC that bothers me. It seems from the reports that they are not even willing to examine the issue.”


Appendix: Jayadevan’s Open Letter To ICC President Sharad Pawar


Disappointed at the ICC response to his suggestion, Jayadevan wrote to ICC President Sharad Pawar. “I am Jayadevan, who developed the VJD system for setting target scores in interrupted limited over cricket matches. I am fully confident in saying that this is the best available system for the purpose today. For the last 12 years, I am trying to convince this to the authorities. Last week the cricket committee of the ICC rejected my proposal in the final round. I am really unhappy about the neutrality of the evaluation conducted by ICC.”


(Arunabha Sengupta is trained from Indian Statistical Institute as a Statistician. He works as a Process Consultant, but purifies the soul through writing and cricket, often mixing the two into a cleansing cocktail. The author of three novels, he currently resides in the incredibly beautiful, but saD/Ly cricket-ignorant, country of Switzerland. You can know more about him from his author site, his cricket blogs and by following him on Twitter)