Monday, July 18, 2011

Excellent duck soup

Duckworth and Lewis. Sound familiar? Our expert reviews a book by the two gentlemen who gave the cricket world the formula for revised targets in rain-affected games.

What could you do on a United Airlines flight to Hawaii? Reading a book seems like a good idea; sipping wine as you read is an even better idea.

But hardly anyone would choose to spend his time thinking up a formula that looks like Z(u,w) = Z0F(w)[1-e-bu].

Unless your name is Frank Duckworth, and you are trying to model the average number of runs one can score in an ODI match with u overs left and w wickets lost.

This formula would undergo more twists and turns. After a big scare, when Ganguly’s India almost conspired with Joberg’s dark clouds to grab the 2003 World Cup from Ponting’s Australia, the equation would turn even more complicated with creepy s entering the fray.

But we’re still in 1995; we’re still with Frank Duckworth and Tony Lewis as they share their “Eureka!” moment. This formula is so enticing that they affectionately call it the ‘Waikiki formula’.

The formula was indeed magical. It argued that to set fair targets in ODI matches with curtailed overs we must consider the combined effect of ‘overs left’ and ‘wickets lost’.

Sadly, few could appreciate the real Duckworth-Lewis (D/L) magic – of being able to effectively handle multiple interruptions during either ODI innings, and not just between innings. Instead, everyone commented on the seemingly preposterous situation where D/L could ask Team 2 to score 245 runs in 40 overs to win, even though Team 1 had only scored 200/2 in their curtailed 40 overs.

BBC called the Duckworth-Lewis method ‘bizarre’, The Times called it ‘complicated’. The unkindest cut was when Matthew Engel’s 1998 Wisden editorial called the concoction ‘Duck soup’.

All this hurt – and puzzled. Duckworth and Lewis therefore decided that they would never respond, arguing that they are “answerable to the cricket authorities, not to the press”. But they did express their gratitude when Steve Waugh told Tony Lewis at a Buckingham Palace reception that the D/L method was the best rain rule.

Yes, Tony Lewis was actually at Buckingham Palace, and Frank Duckworth would have been there too but for that ill-timed holiday in France! The 1999 World Cup was on in England, and Duckworth and Lewis were enjoying the fame, adulation and recognition coming their way after the early years of mistrust and ridicule. As designated ‘Duckworth Lewis Match Managers’ (DLMMs) they could walk in and out of press boxes and generally have a rollicking time. Why, someone even asked Frank for his autograph!

Some of the most enjoyable passages of the book are in these middle chapters. Duckworth and Lewis, who failed to sparkle in their cricket playing days (for the record, Frank’s best was 11 not out and Tony only calls himself a dour opening batsman who couldn’t score runs quickly, but doesn’t mention if he scored any runs at all!), are genuinely delighted to rub shoulders with the legendary Sir Clyde Walcott (3798 Test runs, average 56.7) at an ICC annual meeting. But Jagmohan Dalmiya (0 Test runs) gives them the cold shoulder.

Then there was that wonderful 2003 Caribbean holiday at Almond Beach flying first class on BeeWee aircraft, with a chauffeured stretch limo and complimentary champagne on the ground. And all this simply to teach West Indian scorers how to set D/L targets!

As someone sufficiently familiar with the D/L method, it was interesting to read how the method evolved after that 1995 Eureka moment. There was a lot of work to do after running out of that apocryphal bath tub: Duckworth’s original curves had to be flipped, the rain rules had to be captured in the computer program named CODA, the formula to reset targets when Team 2 had more resources than Team 1 had to be reworked, ‘intelligent guesses’ had to be made on the relative value of each of the ten possible ODI innings partnerships, and there was this uphill task of ‘selling’ the D/L method to the different cricket boards and, eventually, the ICC. It was therefore helpful that Duckworth and Lewis lived only a few miles apart in Gloucestershire and there was a pub mid-way called Pickwick Inn that served excellent ale to stimulate discussion and debate.

As I read about these travails of Duckworth and Lewis, I couldn’t help admiring my ‘compatriot’ V Jayadevan who must have gone through the same tortuous process, without recognition or ale, to come up with an equally good rain rule. Jayadevan briefly pops up on pages 102-103; and I pop up too as his Indian compatriot. There is some respect for Jayadevan, and an acknowledgement that his VJD method is D/L’s only serious challenger. But Jayadevan’s method is first dismissed as being internally inconsistent, and when he fixes these inconsistencies – that D/L themselves pointed out – his corrections are derisively described as ‘artful patches’.

It is easily possible to describe the D/L method itself as a wonderful artwork of patches built around a basic exponential decay model. All those creepy s we mentioned earlier were essentially ‘patches’ needed to eliminate the shocking possibility of India winning a rained out World Cup final by scoring just 157/3 in 25 overs in reply to Australia’s 359/2! Even the G50 idea was an after-thought – after D/L discovered that while targets could be reset by using the ratio R2/R1 when R2 < R1, there would be inconsistencies if R2 > R1. When the Professional Edition came along in 2004, D/L declared on the official ICC website that G50 was no longer needed. And then, in 2009, they smuggled G50 right back (see page 98) without even a whisper. Artful, very artful!

Duckworth and Lewis also write: “Bhogle came down marginally in favour of Jayadevan – perhaps out of loyalty to his countryman and maybe also to his website readership.” I don’t find that very flattering, but I do agree that being loyal to a fellow countryman is a good thing. Duckworth and Lewis too handle their compatriot David Kendix with kid gloves. Before Kendix became ICC’s in-house statistical expert (who picked him?), his only cricketing claim to fame was that he had devised the ICC Test and ODI rankings. While Duckworth and Lewis do mention (page 149) that the ‘main weakness’ of the Kendix scheme is its abnormal love for the month of August, they conveniently overlook its real weakness … that the method doesn’t give a higher weight to ‘away’ wins!

There are times when Duckworth and Lewis seem to suggest that the D/L method is cricket’s new magic wand: Use D/L as an alternative to net run rate (makes a lot of sense); use it to create national ODI rankings (maybe, certainly D/L can estimate the comfort of victory well); use it for player one-day ranking (possible, but are we getting too ambitious?). However, insisting that the D/L method works fine in T20 cricket is very hard to accept! No single analytical tool or technique can hope to be the ultimate panacea. I have no doubt at all that a vastly superior T20 rain rule is round the corner; read, for example, T20 is a different animal .

Towards the end of the book, Duckworth and Lewis, now 70-year old pensioners, turn pensive and a trifle wistful: “We cannot, of course, go on for ever”. They then suggest that Steven Stern, who developed the Windows version of CODA, and David Kendix could be possible successors (I wouldn’t anoint Kendix at this stage. He is on the ICC expert committee that will decide if the VJD method can replace D/L. So there is an obvious conflict of interest).

But I would most enthusiastically join the applause in honour of these two venerable professors, especially because the D/L method was the outcome of honest academic curiosity, not crass commercial consideration. For the record, Duckworth and Lewis haven’t become millionaires after D/L, and probably never will. But I’m sure they don’t mind. They have pop groups, and a racehorse, named after them. They appear on crossword puzzle clues and there is evidence that the D/L method performs just as well in the bedroom as on the cricket field (see page 169). So what more, indeed, can they want?

Duckworth Lewis The method and the men behind it by Frank Duckworth & Tony Lewis. SportsBooks Limited, £12.99. An earlier version of this review appeared on Yahoo! Cricket.

Tuesday, June 28, 2011

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.