T20 is a different animal

The D/L method applied in rain-interrupted ODI games has its flaws when adapted to the T20 version. Our expert talks of a suitable alternative.

Ask Paul Collingwood, or ask Stephen Fleming. They’ll tell you that the Duckworth-Lewis (D/L) rain rule performs poorly in T20 cricket. But ask them (or anyone else) which rain rule to use instead and there is no easy answer.

The VJD rain rule proposed by V Jayadevan could be a candidate. But in T20 matches, the VJD and D/L targets tend to be very similar; so that won’t get us very far.

Currently, D/L assumes that a T20 match evolves exactly like the last 20 overs of an ODI match; so when Sehwag and Gambhir come out to open India’s T20 innings they are supposed to pretend that it is the 31st over of an Indian ODI innings.

Or think of it this way: Imagine that you are 20 inches tall and someone gifts you a trouser meant for a person that is 50 inches tall. How do you wear the trouser? D/L recommends that you cut the trouser so that it at least kind of fits you.

Last year, Rajeeva Karandikar (now the Director of the Chennai Mathematical Institute) and I looked at this problem and proposed a variant: we said that instead of ‘cutting’ the trouser, we should probably ‘shrink’ it down to the required size. We were in effect suggesting that a T20 match evolves just like an ODI match except that things happen faster.

To be honest, our proposal didn’t improve things too much. The shrunk trouser too was clumsy and ill-fitting. The only correct way was to call in the tailor and stitch a new pair of trousers.

But where would we find this tailor? To my surprise, I find that a team of tailors have created a very promising prototype of the T20 trouser at Canada’s Simon Fraser University (SFU) just last year.

It would be too tedious and too technical to explain what the SFU team did. Very briefly, they looked at data from about 90 T20 international matches and tried to create a new and complete D/L-type resource table. It is hard to create such a table (if it was easy, D/L would have done it by now!) essentially because of two problems: the table entries must be both ‘consistent’ and ‘complete’.

By ‘consistent’, we mean that the resource must continually diminish as the overs and wickets deplete. As an example, imagine that the resource remaining after 5 overs are bowled and 2 wickets are lost is 75.3%. Then after ‘6 overs bowled and 2 wickets lost’ the resource remaining must be less than 75.3%. Likewise the resource remaining after ‘5 overs are bowled and 3 wickets are lost’ too must be less than 75.3%.

By ‘complete’, we mean that every cell in the resource table must be filled up. We must know the resource value for every ‘overs bowled-wickets lost’ combination (actually, every ‘ball bowled-wicket lost’ combination!)

Now it is intuitively clear that once a very large number of T20 matches are played, it should be possible to create a really accurate, consistent and complete resource table. But that’s going to take very long. So what do we do in the interregnum? We seem to know no way; that’s why we are trying these ‘fixes’ using cut or shrunk trousers.

This is where the SFU team has been clever. They embed criteria in their estimation model to force consistency. For missing resource values, they impute D/L’s resources as priors. And to generate large datasets they use simulation (it is like telling the computer: “here’s a resource table based on the first innings score of 90 actual matches; now use this data to create a vastly superior resource table based on 50,000 simulated matches!)

Of course any resource table that you create using fancy Bayesian sampling and analysis must eventually pass the acid test on the cricket field! At the end of this blog, we will look at some real examples, but before we do that, let’s look at a ‘heat chart’ reproduced from the SFU research paper.

A heat chart is used to compare two datasets. This chart compares the D/L resource table with SFU’s proposed resource table. The darker the red, the greater is the difference between the two resource tables.

We see a lot of red at the bottom left and the top right, but this is not a serious concern. The dark red at the top right simply says that D/L and SFU ‘strongly disagree’ when 20 or 19 overs are remaining and 7-9 wickets are lost. But it is practically impossible to lose 7-9 wickets in the first 6-9 balls of a T20 innings. Likewise, it would be very rare to have all 10 wickets intact with only a handful of overs left (at the bottom right corner).

It is the red in the middle that’s more interesting, and if you look up the two resource tables you’ll find that the red is essentially telling that, at the half-way stage, D/L thinks that there are about 5% more resources available for the chasing team than SFU. That means, based on the mid-innings score, D/L expects the end score to be rather more than SFU.

Now we know that D/L adapts an ODI model to fit T20 while SFU is a ‘truer’ representation of the real T20 scoring pattern; so the considerable red in the middle suggests that T20 is quite a different animal! Here are two examples that suggest that SFU may be closer to the truth.

In the 2009 T20 World Cup game, in reply to England’s 161/6 in 20 overs, D/L required West Indies (WI) to only score 80 in 9 overs to win. WI reached 82/5 in just 8.2 overs to win easily much to Paul Collingwood’s dismay. The SFU model would have set WI a higher target of 94 runs in 9 overs (because it expects WI to use more resources at this stage than D/L).

In another South Africa (SA)-England game in 2009, England scored 202/6 in 20 overs. After a rain interruption, SA were required to score just 129 in 13 overs; at a run rate marginally lower than England’s! The SFU model would’ve set SA a higher target of 145. It is of course another matter that SA still lost.