It's raining, so time for some quick exponential decay maths
April 8, 2020 11:09 AM   Subscribe

Tony Lewis, half of the famous Duckworth-Lewis duo, who created their namesake method for calculating the required score for rain-interrupted limited overs cricket matches, passed away this week at the age of 78.

But what is the Duckworth-Lewis Method? (nowadays actually the Duckworth-Lewis-Stern method) Well surely nothing could be simpler than quickly calculating Z(u, w) = Z0(w)(1- e-b(w)u) in your head as you walk in the rain back to the sheds, but seeing as you asked...

If limited-overs cricket matches (e.g one-day games) are rain-affected, the Duckworth-Lewis method is used to reset targets to attempt to gain a result. The system is based on the percentage of resources (overs and wickets) a team have left. For example, with 50 overs and 10 wickets remaining, a team have 100 per cent of their resources left. But it gets just a little more complicated than that, as described by the authors themselves to the Royal Statistical Society.

Suffice to say whenever a mathematical formula is used to adjust an otherwise evenly contested sports match, there will be...ummm...issues. In the 2007 World Cup Cricket Final, confusion over the method and rules resulted in the teams continuing to play in almost unplayable conditions even though Australia had already won. And South Africa always seemed to be on the wrong end of it at the worst possible times.

Suffice to say fans ever love or hate the method (depending on which side they are on), and it has become an integral part of modern cricket.

There is also the Duckworth-Lewis Method band with their albums "Sticky Wickets" and the self-titled "The Duckworth Lewis Method" (both available on ITunes), if you find yourself in need of some cricket-themed music currently.
posted by inflatablekiwi (10 comments total) 5 users marked this as a favorite
For those of you NOT familiar with this simple English sport (which does involve drinking beer as a compulsory supporter activity and shouting out "Gwarn!" when things do not go their sides way) the rules are explained around the Interwebs as such:

You have two sides, one out in the field and one in.

Each man OR woman OR They that’s in the side that’s in goes out, and when he/she/they is out he/she/they comes in and the next man/woman goes in until he/she/they are out.

When they are all out, the side that’s out comes in and the side that’s been in goes out and tries to get those coming in, out.

Sometimes you get men/women/they still in and not out.

When a man/woman/they goes out to go in, the men/women/they who are out try to get them out, and when he/she/they is out he/she/they goes in and the next batter in goes out and goes in.

There are two men/woman/they called umpires who stay out all the time and they decide when the men/women/they who are in are out.

When both sides have been in and all the men/women/they have been out, and both sides have been out twice after all the men/women/they have been in, including those who are not out, that is the end of the game!

Updated for inclusiveness...
posted by IndelibleUnderpants at 11:33 AM on April 8, 2020 [2 favorites]

Well that may be true for test matches IndelibleUnderpants, but you see for one day games its completely different in that you have two sides, one out in the field and one in......
posted by inflatablekiwi at 11:39 AM on April 8, 2020

As historically important as the formula for calculating Easter. As complicated, as well.
posted by thatwhichfalls at 12:03 PM on April 8, 2020 [2 favorites]

Cricket descriptions always look like word-substitution ciphers to me. It’s like the dictionary has an additional definition for words at the bottom in the UK- well, in cricket this actually means something entirely different...
posted by q*ben at 12:37 PM on April 8, 2020 [2 favorites]

I think there needs to be an international force tasked with flying out from England to areas beset with drought or wildfires. As anyone who follows the game will attest, at a critical moment in a game (N.B. all moments are deemed 'critical') it is absolutely GUARANTEED to rain.

I met John Arlott the noted cricketing commentator once - note I do not say 'I had the pleasure of meeting him' as his private persona was significantly different from that when commentating a match. His radio voice was 'perfect' for the game, labelled the 'Voice of Post War Britain', and several of his quotes are legendary. My favorite being "It is rather suitable for umpires to dress like dentists, since one of their tasks is to draw stumps.". More here. Not quite in the same league as Coleman Balls or Murray Walker. It is what formed my early life.

Now? Now I am coming to terms with the stultifying properties of American Baseball. Which brings me to ask if there are any other games/sports with the equal properties of placing a dead person into a coma or equally incomprehensible rules...
posted by IndelibleUnderpants at 12:44 PM on April 8, 2020 [5 favorites]


Any mathematician who's also a sports fan will tell you it's incredibly rare for any of their complex math-based rule ideas to actually be adopted by a sport (see some of the overtime and kickoff ideas proposed for American football). Lewis and Duckworth got it done.
posted by Ampersand692 at 1:16 PM on April 8, 2020 [4 favorites]

To recycle a comment:
If you don't understand cricket, I can suggest two options.

a) DM's Guide To Cricket is a good starting place.
b) conclude that this thread may not be for you, and move on to the next post.

Option c), 'hurf durf cricket man talk funny' is on a level with 'Is this something I'd need a TV to understand?', 'sports suck anyway', or 'NOPE NOPE NOPE' in a post about spiders.
posted by zamboni at 3:22 PM on April 8, 2020 [3 favorites]

There is also the Duckworth-Lewis Method band

which is as close as I've ever gotten to loving cricket. Two great songs:

The Age of Revolution
Line and Length
posted by philip-random at 5:53 PM on April 8, 2020 [3 favorites]


Like Ampersand692 said; it is really rare to have a academic solution to a sports conundrum be accepted so quickly by the authorities.

I liken the Duckworth-Lewis-Stern method of deciding matches akin to Churchill's description of Democracy. It is the least bad method. But it IS miles better than what was used before. Especially things like scoring 22 runs off a ball nonsense.

But then you realize that even with full matches being played; including extra over; there are things like number of boundaries scored that determine the winner!! :-)

DLS for the win.
posted by indianbadger1 at 7:55 AM on April 9, 2020 [1 favorite]

But then you realize that even with full matches being played; including extra over; there are things like number of boundaries scored that determine the winner!! :-)

That comment should come with a trigger warning for us NZ supporters......
posted by inflatablekiwi at 11:10 AM on April 9, 2020

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