vjdcricket

A comprehensive scientific analysis of the flaws in D/L system (Wincoda 2.0,

 2009 version) and a comparison with the VJD-system (March-2011 version).

By: V. Jayadevan. http://jayadevan.yolasite.com

 

The Duckworth and Lewis system was introduced to the international cricket well back in 1998.  It has undergone several revisions since then.  But the question on its reliability and accuracy still remains. In many a cases the targets fixed with the system has been under fire.  Whether the international cricket council is aware that the D/L system actually does not satisfy more than a few criteria laid by them is a question mark. In this section it is tried to expose the flaws in D/L system in a scientific way based on the criteria laid by ICC and also it is tried to compare it with the proposed system.

The international cricket council has introduced certain specific guidelines a system for fixing revised targets should have. The seven criteria laid by the ICC are:

       1.      The reasonability of adjusted targets under a wide range of match scenarios

2.      The 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.      The practical impact on a match in progress

7.      Overall mathematical robustness of the underlying theory and formulae

While criteria 3-5 are statements more of a general nature, criteria 1, 2, 6 and 7 do require a detailed and methodical evaluation.

The reasonability of adjusted targets.

Cricket is a game of glorious uncertainties, and no mathematical model can capture these uncertainties and hence no method will be totally foolproof.    However it will be interesting to look into the 10 results (first three, hypothetical and the remaining seven, actual) shown in the table below.

                 Table-1: Reasonability of targets

The results clearly indicate that the vjd-system gives much more reasonable targets.  In many of real the cases shown above (in fact except #7 which occurred before the introduction of D/L), the D/L targets were severely criticized by the affected teams.

Consistency of set targets.

The ICC-criterion is about the consistency in targets in cases of multiple interruptions, but let us have a look at some single interruption cases themselves.

               Table-2:          Consistency of set targets 

The scores like 40/0, 50/0 in 20 overs may not occur in actual situations, similarly 150/0 also; but in order to check the consistency of targets these situations are also considered.  The following defects can be easily noticed in D/L targets.

1.             The target for 41 is less than that of 40!  Similarly target for 62 is less than that of 56!

2.             There is a steady desirable increase of 10 runs for the targets of 40 to 50 runs.  But there is only 5 runs difference for the targets of 50 and 73.  Only 14 runs difference between the targets of 50 and 100.  Just 30 runs difference between the targets of 50 and 130.  Needless to explain that 50/0 in 20 is a below-par score while 130/0 in 20 is a huge score, which might lead to a mammoth total.

3.             For 130/0 the D/L target is 174.  But 174 is also the D/L target for team-2 in in 20 overs if team-1 makes 320 in 50 overs.  That means from this angle D/L expects a team scoring 130/0 in 20 to make just 320 runs in 50.  But see the D/L-par-score table for a score of 320.  87/0 is the par-score (not 130) in 20 overs.  If you look at from the other angle, 130/0 is the par score in 20 overs when team-1 makes a score of 414.  That means from that angle D/L system expects a team to make 414 runs from a score of 130/0 in 20.  For a score of 414, the target in 20 would have been 204 (not 174).  A total inconsistency of the system is exposed here.  On the other hand for the vjd-method, for 130/0 in 20, the 50 over expected score is 399.  The target in 20 for a score of 399 in 50 is 195.  Here in the table it can be seen that the target is 194. Such small differences are justified as vjd-system allows overlaps (i.e. many of the overs within first 20 is considered more productive than many overs in the next 20)

4.             From the table it can be seen that the target remains the same for team-1’s scores of 56 & 67.  It is also seen that if team-1 makes 67 in 22,5 overs and then team-2 plays 20 overs then also target for team-2 will be 148.  Common sense says that it should have gone down as 67/0 in 20 overs is a much better score than 67/0 in 22,5.  The interesting thing is that if team-1 had played 20,3 overs then the target goes up by one run (149)! And for 21,4 the target is 147 (less than that of 22,5).

Practical impact on a match in progress

Let us also discuss the impact of this anomaly in a multiple interruption case.  Suppose team-1 is 57/0 in 20 overs when an interruption shortens the match to 30.  Now, consider the following situations (the targets by the vjd-method are given in square brackets):

                    i.            Before team-1 face another ball another interruption terminates team-1’s innings.  Now the target for team-2 in 20 overs is 148. [vjd: 118]

                  ii.            Suppose 1 ball was played by team-1 before the next interruption and they do not score any run in that, target remains as 148, fair enough. [vjd: 118]

                iii.            Suppose team-1 scores 1 run in that ball.  The target goes down to 147 [vjd: 119].  If they score 3,4 or 5 runs in that ball, the target will be reduced to 147.  But if they make 0, 2 or 6 runs in that ball, the target will remain as 148.

                iv.            If the first ball after he interruption were a no-ball in which the batsman adds 3 runs (total-4) and for the next free-hit ball the batsman hits six, making the total to 67 in 20,1 overs, the target will remain unchanged as 148! [vjd: 129]

                  v.            Suppose the second interruption occur after 20,5 overs and all the five balls were hit for boundaries, making the total to 77, the target will be 150 [vjd: 135], just 2 runs more.  If all the five balls were hit for 6, the target will be 153 [vjd: 145], just 5 run more.

Mathematical robustness of the system.

The points discussed in sections 4.2 & 4.3 above themselves are sufficient to underline that the system has serious mathematical anomalies and the argument that it is mathematically robust is absurd.  The basic concept of the D/L system that every higher over is more productive than the lower one does not stand especially when the power-plays exist. In reality the scoring rate in the first 15 is invariably higher than the scoring rate in the next 15-20 overs. The attempt to manage this inherent defect with a very unscientific concept of G-50 provides such terrible inconsistencies in the system.  A careful examination of the example cited in sections 4.2 & 4.3 will reveal that for working out the target of team-2, D/L system relies more on the magic number “G50” than the performance of team-1 in their innings. 

Another example to show the mathematical anomaly of the system.

Team-1 makes 150/3 in 40 overs.  Target for team-2 in 40 is 206.  Traget in 20 overs is 131.  Suppose it was a 40 over match and team-1 had scored 205 in 40. The situation is the same as for team-2 the target in 40 overs is 206.  Now if the match is reduced to 20 overs, their target would be 136.  A difference of five runs in target for the same physical situation.

Analysis of the T20 situations

The discussions will not be complete, unless we look into some T20 situations as well.  D/L results shows inconsistent results in cases of T20 matches as well, though in a lesser dimension compared to 50:50 format.  Please refer to the table below.  The explanations are given inside the table itself.  It can be seen that the results of the proposed method is much reliable and consistent.

                     Table-3: Inconsistencies in T20 situations

It will be interesting to go a bit more deep into it. Have a look at the table to follow:

             Table-4: A more detailed analysis

From Table-4 it can be seen that from 8 overs to 7 overs there is a difference of 7 runs (against 3 in the other system) and then from 7 to 6 overs the difference is of 5 and then from 6 to 5 it is 4.  This is disproportional and needs a detailed consideration.  Hence look at also the table-5 below.

            Table-5

A careful examination will show that in the case of D/L, when team-1 makes 50 in 8 overs and when team-1 makes the same in 7 overs, the target for team-2 in 7 overs vary by just one run (65 to 64).  Scoring 50 in 7 overs is much better than scoring the same in 8 overs, especially in T20 hence a proportional change was expected.  In the proposed method it can be seen that it is again quite proportional 67 to 61.  So it will be interesting to scrutinize it further (ball by ball). See table-6.

           Table-6:  Inconsistency exposed

On a casual look, both the systems can be seen producing almost comparable results in almost all T20 cases.  But on checking the consistency aspect one can easily identify the deficiencies in D/L system and superiority of vjd-system.  It is hard to believe that the International Cricket council relies on such anomalous system over the past so many years, saying that there are no alternatives. From the discussion above, it is so clear that there is an alternative system, the vjd-system proposed here.  It is fairer, consistent and more reliable. 

Two more examples to underline the inconsistency in D/L system.

Team-1 are 35/2 in 10 overs when the interruption terminated their innings.  Target for team-2 in 10 is 57.

Suppose team-2 gets only 5 overs when resumes.  The target will be 26.

Please note that target in 5 overs cannot be less than 57/2 i.e. it has to be at least 29.

Suppose the match was originally for 10 overs and team-1 had scored 56 runs from 10.  Then the situation is exactly the same.  Target for team-2 in 10 overs is 57.  Now if the match is shortened to 5 overs D/L target is 31.

On exactly similar two occasions, the difference is 5 runs

[When the computed par score can be something like 56.72 (say), not exactly 56 as when it is actually scored, one run difference is permissible, but then also it has to be more than that of the second case]

If team-1 were 50/2 instead of 35 (a more probable situation), target in 10 overs is 71 and that in 5 overs is 36.  But for a 10-over score of 70 runs of team-1, the target of team-2 in 5 is 39, 3 runs difference.

An internationally used system should not have such anomalies.