## Duckworth Lewis and Sprinting a Marathon

How would you like it if you were running a marathon and someone were to set you targets for every 100 meters? “Run the first 100m in 25 seconds. The second in 24 seconds” and so on? It is very likely that you would hate the idea. You would argue that the idea of the marathon would be to finish the 42-odd km within the target time you have set for yourself and you don’t care about any internal targets. You are also likely to argue that different runners have different running patterns and imposing targets for small distances is unfair to just about everyone.

Yet, this is exactly what cricketers are asked to do in games that likely to be affected by rain. The Duckworth Lewis method, which has been in use to adjust targets in rain affected matches since 1999 assumes an average “scoring curve”. The formula assumes a certain “curve” according to which a team scores runs during its innings. It’s basically an extension of the old thumb-rule that a team is likely to score as many runs in the last 20 overs as it does in the first 30 – but D/L also takes into accounts wickets lost (this is the major innovation of D/L. Earlier rain-rules such as run-rate or highest-scoring-overs didn’t take into consideration wickets lost).

The basic innovation of D/L is that it is based on “resources”. With 50 overs to go and 10 wickets in hand, a team has 100% of its resource. As a team utilizes overs and loses wickets, the resources are correspondingly depleted. D/L extrapolates based on the resources left at the end of the innings. Suppose, for example, that a team scores 100 in 20 overs for the loss of 1 wicket, and the match has to be curtailed right then. What would the team have scored at the end of 50 overs? According to the 2002 version of the D/L table (the first that came up when I googled), after 20 overs and the loss of 1 wicket, a team still has 71.8% of resources left. Essentially the team has scored 100 runs using 28.2% (100 – 71.8) % of its resources. So at the end of the innings the team would be expected to score 100 * 100 / 28.2 = 354.

How have D/L arrived at these values for resource depletion? By simple regression, based on historical games. To simplify, they look at all historical games where the team had lost 1 wicket at the end of 20 overs, and look at the ratio of the final score to the 20 over score in those games, and use that to arrive at the “resource score”.

To understand why this is inherently unfair, let us take into consideration the champions of the first two World Cups that I watched. In 1992, Pakistan followed the principle of laying a solid foundation and then exploding in the latter part of the innings. A score of 100 in 30 overs was considered acceptable, as long as the team hadn’t lost too many wickets. And with hard hitters such as Inzamam-ul-haq and Imran Khan in the lower order they would have more than doubled that score by the end of the innings. In fact, most teams followed a similar strategy in that World Cup (New Zealand was a notable exception, using Mark Greatbatch as a pinch-hitter. India also tried that approach in two games – sending Kapil Dev to open).

Four years later in the subcontinent the story was entirely different. Again, while there were teams that followed the approach of a slow build up and late acceleration, but the winners Sri Lanka turned around that formula on its head. Test opener Roshan Mahanama batted at seven, with the equally dour Hashan Tillekeratne preceding him. At the top were the explosive pair of Sanath Jayasuriya and Romesh Kaluwitharana. The idea was to exploit the field restrictions of the first 15 overs, and then bat on at a steady pace. It wasn’t unlikely in that setup that more runs would be scored in the first 25 overs than the last 25.

Duckworth-Lewis treats both strategies alike. The D/L regression contains matches from both the 1992 and 1996 world cups. They have matches where pinch hitters have dominated, and matches with a slow build up and a late slog. And the “average scoring curve” that they have arrived at probably doesn’t represent either – since it is an average based on all games played. 100/2 after 30 overs would have been an excellent score for Pakistan in 1992, but for Sri Lanka in 1996 the same score would have represented a spectacular failure. D/L, however, treats them equally.

So now you have the situation that if you know that a match is likely to be affected by rain, you (the team) have to abandon your natural game and instead play according to the curve. D/L expects you to score 5 runs in the first over? Okay, send in batsmen who are capable of doing that. You find it tough to score off Sunil Narine, and want to simply play him out? Can’t do, for you need to score at least 4 in each of his overs to keep up with the D/L target.

The much-touted strength of the D/L is that it allows you to account for multiple rain interruptions and mid-innings breaks. At a more philosophical level, though, this is also its downfall. Because now you have a formula that micromanages and tells you what you should be ideally doing on every ball (as Kieron Pollard and the West Indies found out recently, simply going by over-by-over targets will not do), you are now bound to play by the formula rather than how you want to play the game.

There are a few other shortcomings with D/L, which is a result of it being a product of regression. It doesn’t take into account who has bowled, or who has batted. Suppose you are the fielding captain and you know given the conditions and forecasts that there is likely to be a long rain delay after 25 overs of batting – after which the match is likely to be curtailed. You have three excellent seam bowlers who can take good advantage of the overcast conditions. Their backup is not so strong. So you now play for the rain break and choose to bowl out your best bowlers before that! Similarly, D/L doesn’t take into account the impact of power play overs. So if you are the batting captain, you want to take the batting powerplay ASAP, before the rain comes down!

The D/L is a good system no doubt, else it would have not survived for 14 years. However, it creates a game that is unfair to both teams, and forces them to play according to a formula. We can think of alternatives that overcome some of the shortcomings (for example, I’ve developed a Monte Carlo simulation based system which can take into account power plays and bowling out strongest bowlers). Nevertheless, as long as we have a system that can extrapolate after every ball, we will always have an unfair game, where teams have to play according to a curve. D/L encourages short-termism, at the cost of planning for the full quota of overs. This cannot be good for the game. It is like setting 100m targets for a marathon runner.

PS: The same arguments I’ve made here against the D/L apply to its competitor the VJD Method (pioneered by V Jayadevan of Thrissur) also.

## Sachin’s 100th

In the end it was quite appropriate. That the needlessly hyped “false statistic” of Sachin’s 100 100s came about in a match against a supposed minnow, in an inconsequential tournament, which didn’t even help India win the game. The hype surrounding this statistic had become unbearable, both for normal cricket fans and also for Sachin, perhaps. And that could be seen in his batting over the last one year, in England and in Australia. There was a distinct feeling that every time he just kept playing for his century, and not for the team cause, and the only upshot of his “100th 100” is that the monkey is finally off his back and hopefully Sachin can go back to playing normal cricket.

Unfortunately, there are a couple of other milestones round the corner. He now has 49 ODI 100s, so now people will hype up his 50th. And as someone pointed out on facebook yesterday, he has 199 international wickets! Hopefully that means he starts turning his arm over once again, with his lethal spinning leg-breaks and long hops.

The thing with Sachin is that he has always seemed to be statistically minded (irrespective of what he says in his interviews). The mind goes back to Cuttack during World Cup 1996, when he played out two maiden overs against Asif Karim while trying to get to his 100 (against Kenya). Even in recent times, including in 2007 when he got out in the 90s a large number of times, it is noticeable how he suddenly slows down the innings once he gets into the 90s. He gets nervous, starts thinking only about the score, and not about batting normally.

In that sense, it is appropriate that this meaningless statistic of a hundredth hundred came about in a game that India lost, to a supposed minnow. It was a “batting pitch”. As Raina and Dhoni showed in the latter stages of the innings, shotmaking wasn’t particularly tough. And yet, what did Sachin do? Plod at a strike rate of 75 for most of the innings, including in the crucial batting powerplay just so that he could get to his 100. I don’t fault his batting for the first 35 overs. He did what was required to set up a solid foundation, in Kohli’s company. But in the batting powerplay, instead of going for it, the only thing on his mind was the century. Quite unfortunate. And appropriate, as I’ve said a number off times earlier.

Again, I want to emphasize that I’m NOT an anti-Sachintard. I’ve quite enjoyed his batting in the past, and there is no question that he is one of the all-time great cricketers. I’m only against meaningless stat-tardness. And it was this retardation about a meaningless stat that prevented Sachin from giving his best for the last one year.

## Ranji nostalgia

It was the winter of 1991-92. I had just got introduced to this wonderful game called cricket, and about a month earlier had seen my first ever full one day international (on TV, of course). India had thrashed Australia at Perth. Ravi Shastri had taken 5-15 but still the man of the match award went to Srikkanth who made 60. This was two days after I had turned nine.

India was touring Australia and cricket craze hit me. It hit me so bad I couldn’t have enough of cricket. In a few days’ time I’d pulled out all the newspapers in my house and rummaged through them for cricket scorecards and stories. I remember getting fascinated reading about the England-West Indies series of 1991. And while going through the newspapers I saw that there was a Ranji trophy match on, and it was being broadcast live on radio. Out came my grandfather’s ancient pocket transistor.

The game was being played at Kolar Gold Fields (an ironic choice considering the Cauvery riots were on – the reason I had holidays from school and could indulge in luxuries like listening to Ranji commentary). On the first day, Karnataka had bowled Goa out cheaply, with Anil Kumble (i think) doing most damage. Goa had this left arm spinner in their line-up called Arun Shetty, and on the second day, he was spinning webs around the Karnataka batsmen. He took a 5-for that day, most of them bowled. Only one man was able to resist him. That also happened to be the day Rahul Dravid made his first first-class century.

Karnataka duly won the game by 10 wickets, with Dravid’s 100 being the difference between the teams in the first innings. Karnataka would go on to massacre Kerala and Andhra, while they drew Hyderabad after conceding a large first innings lead. Tamil Nadu were beaten by one wicket, but some silly points system in the Ranji meant that Karnataka, with four wins and a draw didn’t go through while Hyderabad and TN, with three wins each made it to the knockouts.

Unfortunately I don’t think I followed any other Ranji season as closely as that one, until cricinfo came along that is. Forget international matches (India’s tour of Australia, world cup, etc.), I would know the scorecards of most Ranji matches. At the ripe age of ten, I was able to provide insightful commentary on domestic cricket, on Indian team selections, and so forth. Sadly, I would never play the game.

Nowadays occasionally when I’m trying to take a break from work, I pick a random Ranji season from the 1990s and start looking up the scorecards. First the scorecards of all the South Zone matches (remember that Ranji was zonal in those days)., and then the knockouts. I remember that in one of the seasons in the early 90s, there were no draws at all in the knockouts (or maybe there were one or two here and there) – a far cry from nowadays when hardly one innings gets completed. And then I go on to look at the Duleep Trophy scorecards from the season – and these are the most interesting since I’m likely to know more players there.

It’s an awesomely good feeling to find a scorecard of a match that I remember, and I don’t know why but each time this happens I’m reminded of that game at KGF, the first one I followed, when Rahul Dravid made his first first-class century.

## Studs and Fighters and Form

It’s been a long time since I wrote about the Studs and Fighters framework. I had overdosed on it a few months back, when I’d put some 3 posts in 4 days or something, but that was when I was hajaar enthu about corporate affairs.

It’s been almost two months since I quit my last job, and in this period, among other things I’ve lost all enthu for anything corporate. I don’t find Dilbert funny anymore. I usually just put well left to the office-politics posts that some of my friends on Google Reader share. And since the S&F theory was mainly meant to deal with corporate situations, that too has gone to the backburner.

I was thinking about Mitchell Johnson’s inclusion in the Aussie team in the Third Test. Given how badly he has been bowling all tour, and given that Stuart Clark hasn’t been bowling badly at all, it seems like a surprising selection. But dig deeper, and employ my favourite framework, and you’ll know why he’s still in the team.

It seems like Johnson is a stud bowler (as I’d remarked earlier, Test match bowling in general is stud). And the theory goes that form matters so much less for the stud. This is mainly because studs are significantly more inconsistent than fighters, which makes forecasting one data point based on historical data a nightmare. This also means that the last few data points say much less about a stud’s next data point than they do for a fighter’s case.

All that a stud needs to do to make amends for his hitherto bad form is to come up with one, or maybe a handful of moments of inspiration/insight. And that can happen any time. In fact, theory says that it is more likely to happen when the stud is defocussed on what needs to be done.

So even in the first couple of Tests, you could see Johnson occasionally coming up with the totally awesome delivery, which would produce wickets. Most of the time he was crap, but the occasional moments of brilliance were enough for him to make an impact. So the thinking in persisting with him is that sooner or later, he will produce enough moments of brilliance in a game that no one will look at all the crap he has bowled, and even that the moments of brilliance can push up his confidence which can lead to less crap.

This kind of thinking doesn’t apply to a traditional fighter, who isn’t capable of that “moment of brilliance”. He usually relies on consistency, and accuracy, and process to do what he needs to do. For the fighter, it has to be a steady rise from one “form situation” to another. And so persisting with the fighter doesn’t make sense. So for example, if Mike Hussey continues batting in the same way as he has been this series, there is a case of sending him to domestic cricket.

The problem with a lot of fighters is that they refuse to acknowledge the existence of studs and treat them too as fighters (on the other hand, most studs understand the existence of fighters). And this treatment of studs (assuming they are fighters) can have disastrous effects.

## IPL

It’s day one of the second edition of IPL and I’m already loving it. As has already been said by several people several times on Twitter today, it’s quite fitting that the three best performances of the day have come from Tendulkar, Dravid and Kumble. The second match was extremely strong, even from a neutral perspective, and was very refreshing after the batfest that had been the first edition of the IPL.

One major blessing in disguise of moving the tournament to South Africa is the change in conditions – which is likely to lead to better cricket – in the sense of a better contest between bat and ball. Last year’s tournament was a joke in terms of the quality of cricket. There was absolutely nothing in it for the bowlers, and then they put NED after that and made things worse for themselves. Hopefully this promising start will lead to a better effort by bowlers this time round and we’ll have more games like the second one.

I’ve always maintained that the best ODIs are defences of low to moderate scores. The ideal ODI, in my opinion, will have the team batting first making 200-225, taking early wickets and putting pressure on the second team so that it ends up as a tight game (don’t care who wins). Sadly, the pitches they have been making nowadays seem to be creating 300+ games only which is why I’ve stopped watching ODIs.

Coming to the games today, the main mistake that Chennai Super Kings made was with respect to their batting order. A lot of people maintain that they messed up their team selection, and I agree with them – I would definitely have put in Vijay and Balaji instead of Parthiv and Joginder. But even the team that they started off wiht wasn’t too bad, where they messed up was in the chase.

When you are chasing a reasonably moderate total like 166 (equivalent to 250 in ODIs), you don’t need to pinch hit. I know Sri Lanka did that when they won WC96, but I’m more of a fan of Pakistan’s method in WC92 which is to first build a base and then have hitters coming in lower down the order to capitalize. Similarly, chasing 166 with Hayden at one end, what was required was a proper batsman at the other, and Dhoni sent in Flintoff. I think the match might have been sealed there.

It is all about slotting people into the right roles. Having Badrinath and Flintoff in the same team makes sense, but the role for each needs to be well-defined. Badrinath is an excellent “holding batsman” (the same role in which Dravid and Tendulkar excelled in today – and the role that Tendulkar plays in ODIs nowadays) – someone to hold one end up and rotate the strike while batsmen at the other end go for it, but he is incapable of slogging if he comes in with a large required run rate and not much time. And CSK didn’t desperately need to slog when Raina got out – all they needed was some consolidation and for one guy to stay while Hayden accelerated.

Similarly, when you look at Rajasthan’s lineup, you will notice that there are very few “proper batsmen” in the line-up, and a large number of “hitters”. How many people in the Rajasthan XI would you count on batting for you within the first 30 overs of an ODI? I can count Smith, Asnodkar and NK Patel, and maybe Ravindra Jadeja. The rest of the “batsmen” in their lineup (Pathan, Henderson, Mascarenhas) are all essentially hitters. And when conditions are not ideal for hitting, you can come unstuck.

If things continue to go the way they did today, teams will need to re-think their strategies. The slam-bang approach of last year won’t work and they will need to move towards “proper cricket”. Have proper batsmen and proper bowlers and proper keepers rather than having bits and pieces guys, and fill-in guys. Let’s see how things pan out.

I hereby predict that if things continue to go this way, Rajasthan Royals will recall Mohammed Kaif. Also, you might have noticed Uthappa shouting out to Kumble in Kannada about what to bowl (he frequently shouted “kaal muri” which literally translates to “leg break”). And that the Bangalore team has 5 guys from Bangalore – which perhaps enables them to indulge in this kind of “cipher”.

## Fighter Batsmen and Stud Bowlers

Insight of the day: Batting is inherently fighter and bowling is inherently stud. Of course there are severral stud batsmen (eg. Sehwag) and fighter bowlers (eg. Giles) but if you look at it broadly – a batsman needs to get it right every ball, while a bowler needs only one ball to succeed.

The fundamental idea is that bowling success can be more lumpy than batting success – for example the maximum that a batsman can do if he has one great over is to score 36 runs – whcih in the context of the average game won’t amount to much. However, if a bowler has one great over and picks up six wickets, the impact is tremendous.

The bowler can afford to be much more inconsistent than the batsman. He might get a few balls wrong, but he can suddenly make an impact on the game. For a batsman to have a significant impact, however, he should be able to carry it on for a significant amount of time. An “impulse”  (a large force acting for a small time period) will do the batting team no good, while it can be a tremendous boost for the bowling team. On the other hand, steady unimaginative play by the batsman is good enough, while a bowler needs to necessarily show patches of spectacularity to have an impact.

Hence, batting is fighter and bowling is stud.

However, what the advent of one day cricket has done is to invert this. By limiting the number of overs, and creating conditions where a team need not be bowled out, it has turned things upside down. Of course, a stud performance by a bowler (say a hat-trick) can have a significant impact on the game, but inconsistent and wayward bowling is likely to cost the bowling team significantly more than it does in Test cricket.

Similarly, with the game getting shorter, an impulse by the batsman (say a quick 40 by Sehwag) has a much larger impact on the game than it does in Test cricket. And on the other hand, dour batting  – which is so useful in Tests – may actually be a liability in ODIs. Similarly the mantra for bowlers has become containment, and thus fighterness in bowlers has a greater impact – and so people now do respect bowlers who can bowl long spells without taking wickets, but just containing.

Remember that even now, to succeed in Test cricket, you need to have the correct characteristic – Sehwag’s batting might appear stud and risky, but he has the ability to play really long innings which is why he is a really good Test batsman. If he didn’t have the “longevity gene”, he would’ve still remained a one-day wonder. Yes – now teams do pick a fourth bowler to do the “holding role” – keeping one end tight while others attack. Still, the holding guy needs to have some ability to pick up wickets by himself.

Preliminary reading on studs and fighters theory:

Studs and Fighters

Extending the studs and fighters theory