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The Duckworth-Lewis-Stern method: how does it work to ensure a result in an interrupted cricket game?

Cricket

Rebecca, Year 9, looks at how the Duckworth-Lewis-Stern method works to calculate the required score in a cricket match interrupted by the weather.

Raining at Cricket Match
A rain delay at the cricket at the Oval

With the arrival of summer comes the Cricket World Cup in England and Wales. Although England are the favourites, there is no guarantee that they will win. One thing that is pretty much guaranteed though is rain. After all, it is England! But how do you calculate the revised target score in a rain-interrupted match?

The Duckworth-Lewis-Stern method (DLS) is a mathematical formula designed to calculate the target score for the team batting second in a limited over cricket match interrupted by weather or other circumstances. It is an attempt to set a statistically fair target for the second team’s innings, which is the same difficulty as the original target. It was devised by two English statisticians, Frank Duckworth and Tony Lewis, and is generally accepted to be the most accurate method of setting a target score.

This method is needed as there are so many cricket matches that experience rain delays. Without DLS, there may not be a result from the game or the incorrect result (statistically) may occur. There were many other methods set up before DLS, but none of these took into account both the wickets lost/remaining and the revised number of overs remaining. For example, the Average Run Rate method took no account of how many wickets were lost by the team batting second, but simply reflected how quickly they were scoring when the match was interrupted. So, if a team felt a rain stoppage was likely, they could attempt to force the scoring rate without regard for the corresponding highly likely loss of wickets, skewing the comparison with the first team. Therefore, the DLS method was created.

What is the DLS Method?

The basic principle is that each team in a limited-overs match has two resources available with which to score runs (overs to play and wickets remaining), and the target is adjusted proportionally to the change in the combination of these two resources.

The Duckworth-Lewis-Stern method converts all possible combinations of overs (or, more accurately, balls) and wickets left into a combined resource remaining percentage figure (with 50 overs and 10 wickets equalling 100%), and these are all stored in a published table or computer. The target score for the team batting second (‘Team 2’) can be adjusted up or down from the total the team batting first (‘Team 1’) achieved using these resource percentages, to reflect the loss of resources to one or both teams when a match is shortened one or more times.

In the version of DLS most commonly in use in international and first-class matches (the Professional Edition), the target for Team 2 is adjusted simply in proportion to the two teams’ resources i.e.


The actual resource values used in the Professional Edition are not publicly available, so a computer which has this software loaded must be used.

Table of results
A published table of resources remaining percentages,
for all combinations of wickets lost and whole overs lost

If, as usually occurs, this ‘par score’ is a non-integer number of runs, then Team 2’s target to win is this number rounded up to the next integer, and the score to tie (also called the par score), is this number round down to the preceding integer. If Team 2 reaches or passes the target score, then they have won the match. If the match ends when Team 2 has exactly met (but not passed) the par score then the match is a tie. If Team 2 fail to reach the par score then they have lost.

References:

https://en.wikipedia.org/wiki/Duckworth–Lewis–Stern_method#Target_score_calculations

http://www.espncricinfo.com/story/_/id/19577040/how-duckworth-lewis-stern-method-works

https://thenortheasttoday.com/archive/the-saga-of-south-africa-and-duckworth-lewis-method/

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How is climate change impacting the planet?

Abhini, Year 10, looks at some of the issues surrounding climate change, and the potential impacts this will have on our lives.

During the Easter holidays, London and other parts of the UK witnessed a significant protest against the government with over 1,000 people being arrested for blocking streets. The wave of protest began with Swedish born 16-year-old Greta Thunberg who, every Friday, would sit outside government buildings in September, accusing her country of not following the Paris Climate Agreement.

What are the concerns?

So what is it that everyone is worried about in terms of climate change? The world is seeing more extreme temperatures being recorded increasingly across the globe. The 21st century has seen records broken with increased temperatures all through the season and the rise in temperatures also has an impact on the Arctic and melting ice caps. 2016 was the hottest year on record since 1880, with average temperatures measuring 0.99 degrees Celsius warmer than the mid-20th century mean. Since the 1950s, every continent has warmed substantially.

New Scientist graph on global temperature change


An additional impact that climate change is having on the earth is on sea levels, as they are rising at their fastest rate in 2000 years and currently changing at a rate of 3.4 mm per year, causing major impacts such as increased flooding. If sea levels continue to rise, countries like Bangladesh will cease to exist, leading to a refugee crisis, as an average of 21.5 million people have already been forcibly displaced since 2008 due to climate change-related weather hazards. Not only are our water levels increasing, but the ocean is now 26% more acidic than before the Industrial Revolution. This also means that the waters are now more acidic than at any other point in the last 300,000 years.

NASA data on sea rise change from 1880-present

Another shocking fact that is due to climate change, is the damage of two-thirds of the Great Barrier Reef. In April 2017, it was revealed that two-thirds of Australia’s Great Barrier Reef has been severely damaged by coral bleaching, usually a result of water temperatures being too high. However, there are many more important and recent events due to climate change such as last week’s cyclone attack in Mozambique and the wildfires that took place in California late last year. The pictures below show these significant, global events.

Is climate change real?

What about the people who deny climate change? A large proportion of the public in Western democracies deny the existence of climate change[1]. Some climate change denial groups say that because CO2 is only a trace gas in the atmosphere, it can only have a minor effect on the climate. Climate denial groups also argue that global warming stopped recently, or that global temperatures are actually decreasing. However, these arguments have been made clear to be false and are only based on short term alternates. Climate change deniers are often those who are economically making a financial interest in it and, in some cases, their generation is not necessarily going to be impacted by it.

We all know about ‘being green’ by walking to school or unplugging electronics when we are not using them. However, it is not enough anymore to just switch our light off as times now call for drastic change. The energy sources in our home need to be renewable, gas must go, and people should start investing in an electric or hybrid vehicle rather than using petrol or diesel.

climate change

We cannot sit and wait on the government to change. Change is in the hands of the people. We need to force the government’s hand and can only do so if we unite to try and save a world which we are currently destroying. Change occurs when we take action.

References: 

[1] See https://www.theguardian.com/environment/2019/may/14/germanys-afd-attacks-greta-thunberg-as-it-embraces-climate-denial