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.

Stud and Fighter Instructions

My apologies for the third S&F post in four days. However, this blog represents an impression of the flow of thought through my head, and if I try to time my thoughts to suit readers’ interests and variety, I’m afraid I may not be doing a very good job.

I came across this funda in one of the “sub-plots” of Richard Dawkins’s The God Delusion, which I finished reading two days back. Actually, there is another post about the main plot of that book that I want to write, but I suppose I’ll write that some other day, maybe over this weekend. So Dawkins, in some part of the book talks about two different ways of giving instructions. And thinking about it, I think it can be fit into the stud and fighter theory.

I must admit I’ve forgotten what Dawkins used this argument for, but he talks about how a carpenter teaches his apprentice. According to Dawkins, the carpenter gives instructions such as “drive the nail into the wood until the head is firmly embedded” and contrasts it to instructions which say “hold the nail in your left hand and hit it on the head with a hammer held in the right hand exactly ten times”. By giving instructions in the former way, Dawkins argues, there is less chance of the apprentice making a mistake. However, in case the apprentice does err, it is likely to be a significantly large error. On the other hand, with the latter kind of instructions, chance of error is higher but errors are likely to be smaller.

A set of “stud instructions” typically tell the recipient “what to do”. It is typically not too specific, and lists out a series of fairly unambiguous steps. The way in which each of these smaller steps is to be accomplished is left to the recipient of the instructions. Hence, given that each instruction is fairly clear and unambiguous, it is unlikely that the recipient of the instructions will implement any of these instructions imperfectly. What is more likely is that he goes completely wrong on one step, maybe completely missing it or horribly misunderstanding it.

“Fighter instructions”, on the other hand, go deep into the details and tell the recipient not only what to do but also how to do what to do. These instructions will go down to much finer detail than stud instructions, and leave nothing to the reasoning of the recipient. Obviously the number of steps detailed here to do a particular piece of work will be significantly larger than the number of steps that a set of stud instructions. Now, the probability that the recipient of these instructions is likely to make a mistake is much larger, though the damage done will be much smaller, since the error would only be in a small part of the process.

Dawkins went on to give a better example than the carpenter one – consider an origami model of a boat on one hand, and a drawing of a boat on the other. Origami gives a set of precise and discrete instructions. Drawing is as good as a set of “continuous instructions”. Dawkins talks about experiments where kids are made to play a version of “chinese whispers” using the origami and the drawing. I won’t go into the details here but the argument is that the stud instructions are much easier to pass on, and the probability of the tenth kid in line producing a correct model is really high – while in case of a drawing, there is a small distortion at each and every step, so each final model is flawed.

Stud and fighter instructions have their own set of advantages and disadvantages. Fighter instructions require much more supervision than do stud instructions. Stud instructions enable the recipient to bring in his own studness into the process and possibly optimize one or more of the sub-processes. Fighter instruction sets are so-finegrained that it is impossible for the recipient to innovate or optimize in every way. To receive a set of stud instructions, the recipient may need to have certain prior domain knowledge, or a certain level of intelligence. This is much more relaxed in case of fighter instructions.

I personally don’t like supervising people and hence prefer to give out stud instructions whenever I need to get some work done. However, there was one recent case where I was forced to do the opposite. There was this IT guy at my company on contract and I was supposed to get a piece of code written from him before his contract expired. Given the short time lines in question, and given that he didn’t have too much of a clue of the big picture, I was forced to act micro and give him a set of fighter instructions. He has ended up doing precisely what I asked him to do, the only problem being that he has  written code in an extremely inflexible and non-scalable manner and I might have to duplicate his effort since this bit now needs generalization.

I have noticed that a large majority of people, when they have to give out instructions spell it out in the fighter manner. With a large number of micro steps rather than a small number of bigger steps. And until the recipient of the instructions has got enough fundaes to consolidate the set of micro-instructions he has received into a natural set of bigger chunks, it is unlikely that he will either be very efficient or that he will produce stuff that will be flexible. It might also be the case that a large number of people don’t want to let go of “control” and are hence loathe to give out stud instructions.

In the general case, however, my recommendation would be to give stud instructions, but have a set of fighter instructions ready in case the recipient of the instructionss wants things to be more specific.

Preliminary reading on studs and fighters theory:

Studs and Fighters

Extending the studs and fighters theory


The story begins with this slightly old blog-post written by Ritesh Banglani, a guest faculty at IIMB. Banglani writes:

In the first class of my course at IIM, I asked students a simple question: What is strategy?. The most interesting response came from a rather cynical student: “Start with common sense, then add some jargon. What you get is strategy”.

I didn’t say so at the time, but that is precisely what strategy is not. If anything, strategy is uncommon sense – making choices that may not appear intuitive at the time.

The cynical student in question mentioned this during a conversation earlier today, and I thought the discussion that followed merited a blog post. I thank the cynical student for his contribution to this thought.

Innovation happens when someone gets an insight, which, by definition, is a stud process. The person innovating, naturally, is a stud. For a few years after the innovation, the idea is still in development, and it is still very tough for other people to do what the pioneer stud has done. The first wave of people to do what the pioneer has done will also naturally be studs.

However, after the idea has been established, the market for it grows. The pool of studs that are then involved in the idea won’t be able to service the entire market. Also, being studs, they are prone to get bored easily with whatever they are doing, and will want to move on. The increased size of the market as well as the gaps left by the leaving studs will attract fighters to this idea.

Now, fighters are not natural when it comes to generating insight. However, they are excellent at following processes. And once an idea has been developed beyond the initial stage, it makes itself amenable to processes. And thus, a set of processes get established. Soon enough, thanks to the processes, the fighters are able to do a much better job of implementing this idea as compared to the pioneering studs, and studs get driven out of the industry.

This generalized process that I have just described applies to all fields, or “domains” if you would like to call it that. Let us now leave the generalization and come to one specific profession – strategy consulting. Strategy consulting started off as an insight-driven process, a stud process. Industrialists would go to consultants in order to get insights, and out of the box ideas, in order to take forward their business. Soon, the business became profitable, and the consultants, like any good capitalists wanted to expand.

There was one problem, however – talent. It wasn’t easy for them to attract similarly insightful wannabe consultants to work for them. Similarly insightful people would either not want to work in strategy consulting, or they would start their own consulting shops. Thus, there was a need to bring in the fighters into the mix.

It was to facilitate the entry of the fighters that the various consulting models and frameworks came into being. A large set of processes were drafted, and all that the fighter consultants had to do was to identify the appropriate processes for the situation and then implement them along with the client. Insight and out-of-the-box thinking were thrown out of the window. Hourly billing became the industry standard.

Strategy consulting has come a full circle now. It has been “fighterized”. Clients nowadays don’t expect insight. They expect processes. They expect to be led down the “correct” path, and they want to make sure they don’t make obvious mistakes. And thus, the “strategy” that the consulting firms offer are mostly common sense which has been appropriately packaged. And this has percolated down to business schools. And so the cynical student’s cynicism is valid.