Oh Duckworth-Lewis, you loveable rogue – why are you treated like the creepy cardiologist uncle of the stats family?

Duckworth and Lewis don’t get a lot of love for their invention, a fact which seems to point to a collectively short memory for cricket fans. Without DL’s clever method for resolving rain-interrupted (or abandoned) matches, we had to put up with a steady stream of one-day international controversies, including the the 1992 world cup semi final (full video horror from the 20 minute mark here). The results were – to describe them just one way – weird, disappointing and counter intuitive. (Another way is, they were bullshit.)

And yet, whenever rain falls or darkness moves in, officials have a heart attack and have to turn to the creepy uncle to fix it all and prevent yet another controversy (or, at least, prevent a statistically indefensible one).

What would we find if we unearthed some of the repressed pre-DL memories? From the 1970s to the 90s, players in fifty-over matches enjoyed such scenarios as:

1) Team B bats for 25 overs, moseying along to 0/75. Then, gracious me, it rains for two and a half hours! Time enough for lunch, and by the time the outfield dries, just enough time for 25 more overs. Team A – go ahead and chase a target of 76. They fumble their way through it, getting to 9/76 for the win. (DL says – revised target 173.)

2) Team A bats and crumbles to pieces for 150. Against the fierce bowling, half the time, all they could do is duck, weave and block. Team B bats and makes 0/120 after 30 overs – well ahead of the pace, with the openers batting beautifully. But then, gracious me, it rains for three and a half hours! It gets dark and the game is over. So Team B’s target is revised by removing A’s twenty lowest scoring overs, which were a collection of maidens, ones and twos, totalling 20. The new target is 150 – 20 = 130, and Team A wins by 10. (DL says – 0/46 is enough to win.)

3) Team B bats and makes 249. Team A performs fairly well, scoring fast but losing wickets regularly. After 30 overs, A is at 9/210, with numbers 10 and 11 struggling. But then (oh, gracious me), the rain tumbles down yet again. The target is revised as in example 2, and – wouldn’t you know it – Team B scored 40 runs in its 20 worst overs, so the new target is 210 and Team A wins again. (DL says – for the loss of 9 wickets, target is 240.)

4) Team B decides to give up cricket. (DL agrees.)

The problem, to state the obvious, is the systems used ignored some facts about cricket that are… well… bleeding obvious. Here’s the sell job, at the ICC circa 1987:

ICC maths person: “I know how to solve limited overs rain outs!”

ICC manager person: “Mate! You’re a genius! Tell me.”

Maths: “Well, it’s not perfect.”

Manager: “I’ve got a meeting in five minutes.”

Maths: “Ok, but it doesn’t to take into account that teams score better if they have more batsmen left.”

Manager: “Four and a half.”

Maths: “Or that teams bat slower if they don’t realise their innings is about to be ended by rain.”

Manager: “Four.”

Maths: “But it has a stab at the idea that teams score quicker towards the end of the innings.”

Manager: “Genius! Again! Three minutes.”

Maths: “But not in a way that’s supported by actual data. Easy to calculate though.”

Manager: “Look, mate, do you want that raise or not? The Board are busting my protector to figure this out before summer. Can’t you just put it in a memo and I’ll make sure the right people get Whitney Houston tickets so it’ll get approved? I mean, how bad can it be?”

Well, it wasn’t that bad. But it was pretty ordinary at times.

So why is the replacement the creepy uncle? This blog’s suggestion is that it’s because most people’s understanding of statistics is limited to the law of averages. DL sits in the wings, waiting for a cloud to cross the sky, whilst commentators speculate about a team’s likely total or who might win a game and TV graphics people put up charts like this.

Wow, the longer each team bats, the closer its run rate edges to its final run rate… for both teams! Stunner.

Or, screens like this.

Projected total at current run rate? Who’s saying they’re going to do that for the last 36 overs? Don’t teams usually accelerate or something? I’m sure I remember reading that somewhere. Why would they score 4, or 5, or 6 runs an over? If only we had a tool for predicting how many runs a team will score *sigh miserably* … oh, hold on. What’s that Duckworth thing again?

According to DL, 1/79 after 14 overs in the second innings of a fifty-over match would beat a beat a score of 334. Actual score in this instance? Just 252, after a stunning batting collapse of 9 wickets for the last 82 runs.

Boohiss to DL, then? Well, not quite. For starters, the usual minimum input is 25 overs before the results are meaningful enough to provide a winner for an abandoned game. And second, obviously, is that DL is a mathematical calculation, not a crystal ball. The best it can do is to suggest the most likely winner (or innings score) if the match ends at any given point. That will become evident after lots of matches, not just one.

A comparison between DL’s prediction for the innings total, and one based on current run rate.  DL quite correctly reacts to the batting collapse. Number of overs and actual score along the bottom.

A comparison between DL’s prediction for the innings total, and one based on current run rate. DL quite correctly reacts to the batting collapse; the run rate-based prediction stays suspiciously flat. Number of overs and actual score along the bottom.

So, this summer, The New Statsman will put DL to the test, during the international Generic Beer Series, and the Power Tool Domestic One Day series, with graphs and on ongoing DL predictions throughout each international match. The action starts in September and runs through to March 2014. Stay tuned!

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