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Duckworth Lewis method infamous for a reason

We turned the Sydney Cricket Ground into a baseball stadium, why can't the Yanks do the same for us? (Image: Javelin Australia).
Expert
20th March, 2014
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3220 Reads

As Major League Baseball prepares to open its season in Australia for the first time, I’m reminded of how Australia’s summer game – cricket – is similar in so many ways.

Baseball is like a cousin to cricket, with both games derived from stick and ball games played throughout the English countryside some time in the 1700s. Their trajectories have been incredibly different, though.

Baseball took root in the United States, and has embraced the ‘franchise’ model of professional sports. Cricket, on the other hand, pursued the ‘national’ path, with the preeminent form of competition waged along country versus country lines.

However, both games are made for TV, with predictable, structured breaks in play perfect for slipping in an ad or two in the midst of the action. Major League Baseball games run for around three hours, while cricket varies from eight hours of TV time over five days in Tests down to just under the three hour mark for T20 matches.

One thing substantially different is the way baseball and cricket deal with the weather.

In baseball, they have rain delays. In cricket, they have rain delays. But baseball doesn’t let a bit of H2O get in the way of ensuring a result. Nope, they wait until the rain clears and then resume proceedings.

In fact, they’ll wait hours for clear skies, and then finish the game without any change to playing conditions.

Cricket, I’m sure you don’t need me to tell you, doesn’t do this. In fact, cricket lets the rain completely change playing conditions – even though the reason given for not playing through rain is it alters playing conditions.

Quick tangent: why cricket can’t deal with rain delays effectively
I’ve got a theory as to why baseball and cricket differ when it comes to rain delays: the length of a game, stadiums, broadcasting, and the number of games in a ‘season’.

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In the MLB, each team plays 162 games, with very few of these broadcast on national TV (unless you’re the Yankees, Red Sox or one of the other large teams).

This means a broadcaster isn’t really thrown out of whack if a game goes for an hour or two longer than it would have otherwise. And the broadcaster can always throw to another game going on, while the length of the season gives commentators enough to talk about to fill in gaps.

The games only go for three hours all up – so a 30-minute rain delay isn’t a big problem for broadcasters or spectators, anyway.

International cricket, on the other hand, is much less fluent when it comes to broadcasting. In the Australian summer there are only, say five Tests, five ODIs and a couple of T20s. They form the backbone of the broadcaster’s summer schedule – it would be a major inconvenience not to have a game finish on a Sunday evening in prime time.

It’s also difficult to imagine a 50-over game being delayed for a few hours and then being played in full; although in saying that, baseball games routinely finish in the early hours of the morning.

Another problem for cricket is they don’t ‘own’ the stadium they are using, and so the logistics of re-running a game the following day are more difficult to pull off than for baseball teams in the US (who typically control their stadia).

So there are certainly reasons for it. But that’s not what we’re here to talk about.

Duckworth Lewis explained
In Test matches, rain delays gets marked down as ‘lost time’, which can hopefully be made up over the course of the rest of the match through earlier starts and later finishes.

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Rain and its friend ‘bad light’ are even used tactically, by sides looking to escape pressure at the end of a day’s play or to hold on for a draw.

I don’t think there is a dramatic problem with how rain delays are dealt with in Test cricket – it adds to the drama, and if we want to preserve tradition there’s not a lot we can do to alter this.

Limited-overs cricket, on the other hand, is a concern to me. In short-form cricket, instead of tackling rain head-on with the patience shown in the MLB, the powers that be buckle to Mother Nature and alter the playing conditions using the infamous Duckworth Lewis Method (DLM).

Did the hairs just stand up on your neck when you read that?

The DLM, for those who aren’t fully aware of the mechanics, seeks to alter the amount of runs a team batting second in a limited overs match has to score in order to win the game, using some reasonably basic maths.

The DLM says a batting side has two resources available when chasing: wickets in hand and overs remaining. Using a multiplier based on the combination of these factors at the end of each over of the innings, a new ‘target score’ is calculated.

As a guy who uses this kind of maths and statistical analysis on a daily basis, I consider myself ‘at one’ with Duckworth and Lewis. So it hurts me to say the system doesn’t work.

What the numbers say
Lets take a look at some high level numbers (scrapped from the Cricinfo database). I’ve pulled the match results for every One Day International played from 1994 to March 2014 – 2,617 in total.

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Of these games, excluding the no results (presumably because it kept raining) and tied games (there are 25 of them), the data shows the team batting second (or chasing) wins 50.9 per cent of the time.

What this says at a very high level is the order of play doesn’t have a role in determining the outcome of a match.

Pretty much what you’d expect, and a good baseline. Let’s plot this on a chart (because charts are cool):

Based on my calculations, there have been 280 international matches affected by the DLM. I say my calculations because the Cricinfo database doesn’t have a flag which tells us when a game was rain reduced, so I’ve had to estimate based on a number of factors present in the overall match figures. So in reality, there may be more than this.

But 280 is a workable sample. What ‘chance’ do we give the chasing team in DLM games?

60.7 per cent.

That’s right, in games affected by rain, the team batting second is expected to win almost 20 per cent more often. Cricket fans have always been skeptical at the Duckworth Lewis Method, but the fact it alters the outcome of the game so dramatically should be a major concern.

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What this comes down to is that the Duckworth Lewis system doesn’t adjust the runs required effectively on the wickets side of things. As the number of overs in the innings reduces, the value of every wicket in the shed goes up, and goes up at a pretty dramatic rate.

Think of it this way: a team starts its inning with 50 overs to bat, and 10 wickets with which to bat with. So in theory it can lose a wicket every five overs and still make it through the innings.

Now, if the innings is shortened to, say, 30 overs, all of a sudden it can now lose a wicket every three overs and still bat out the innings.

So the team can lose wickets 40 per cent faster and still have enough to finish its overs. As a result, the batting side can be significantly more aggressive, take greater risks and probably score faster.

Need a number to back this up? In the overall sample of 2,617 games, the average second innings run rate (win or lose) is 4.86. The average second innings run rate in Duckworth Lewis affected games is 5.29. Over 50 overs, this works out to be roughly an extra 20 runs.

As I said, the DLM seeks to take this into account, but I don’t believe it does so very well. To illustrate this, lets do another couple of tests.

First, what happens in those games where both sides lose overs as a result of rain?

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The expected win rate drops to 57.7 per cent. So the ‘Duckworth Lewis effect’ is reduced, but the chasing team still has a 13 per cent stronger chance of victory.

But let’s see what happens when only the chasing team’s inning is affected by Duckworth Lewis. As you’ll see, if the first team bats its full 50 overs (or is bowled out despite having the full 50 available to them), the chasing team wins 63.1 per cent of the time. That equates to almost a 25 per cent increase in the likelihood of victory, which is significant in itself.

What does this mean?
It says the Duckworth Lewis system doesn’t work as intended. It gives the chasing team a substantial advantage, owing to the trade-off between wickets and overs.

This means we should have a realistic debate about whether using the Duckworth Lewis Method is the best way we can ensure a game of limited overs cricket affected by the weather is not adversely affected. The data shows its not doing a great job.

But what’s the solution? In 50 over games, I’ve always thought a simpler way of accounting for fewer overs is simply to reduce the number of wickets granted to the team chasing. For every five overs lost, the batting team loses one available wicket.

So if the game is limited to 40 overs, the chasing team has eight wickets; 30 overs, six wickets and so on.

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But what of multiple delays? I’d say you continue to adjust the available wickets anyway. If the game was reduced to 40 overs before the start of the inning, and then a further five overs are lost once the inning is underway, the team only has seven total wickets. And if its already lost seven wickets, we say the next wicket to fall means the team is all out.

As for T20s, I can’t fathom why they don’t just delay the game and ensure both sides get to bat and bowl their 20 overs.

While I haven’t compiled the statistics, I’d hazard a guess the Duckworth Lewis effect in the game’s shortest form is even more dramatic; particularly in games that end up going for five overs (as in 30 deliveries).

T20 is already a game of who can hit the most boundaries, and this effect is amplified as the length of the game is made shorter and shorter.

T20s go for a maximum of three hours, maybe more if one of the captains is really pedantic about his field placements. What about if there was a rule that said if there is a rain delay of more than two hours overall, the game is called off and replayed the following day? Otherwise, the game is simply halted until the rain passes, and resumed henceforth.

Perhaps the only problem would be ensuring the field is safe for play – particularly if its been raining for two hours, I guess – but this is something that could be overcome.

I mean, baseball does it. Why can’t cricket?