From Infamy to Ingenuity: The Evolution of Duckworth-Lewis Method
How the Duckworth-Lewis method revolutionized cricket match outcomes
22 March 1992, Sydney Cricket Ground
A date that will forever be imprinted in the memory of cricket fans all over the globe. It was the day of the dramatic World Cup semi-final clash between England and South Africa, which would later be regarded as one of the most contentious and heart-wrenching moments in the history of the sport.
South Africa needed 22 runs off 13 balls to beat England in Sydney when rain stopped play. When the players returned after a ten-minute break, the revised target showed that South Africa now needed an impossible 22 runs off just one ball due to the lowest-scoring-over rain rules. It was a heartbreaking end for South Africa perhaps the beginning of what was later known as Chokers.
This controversial ending to the match led to widespread criticism of the existing rain rule, which was deemed to be inadequate and unfair. The International Cricket Council (ICC) subsequently appointed a panel of statisticians, including Frank Duckworth and Tony Lewis, to develop a new method for determining revised targets in rain-affected matches.
The Creation
At the time, the rain rule in place was considered to be insufficient and unjust., as it only took into account the total number of runs scored by the team batting first, and did not factor in the number of overs played or the wickets lost. This meant that a team that batted first and scored a large number of runs in a limited number of overs could effectively win the match if rain interrupted play during the second innings.
Duckworth and Lewis recognized the need for a more accurate and fair method of determining revised targets in rain-affected matches and set about developing a system that would take into account the number of overs played by each team, the number of wickets lost, and the run rate required for the team batting second to win the match.
Their efforts led to the development of the Duckworth-Lewis (DL) method, which was initially employed in 1996. Since then, it has undergone various modifications and improvements to become the current version of the Duckworth-Lewis (DL) method, which is utilized in limited-overs matches to determine revised targets in rain-affected games.
The Duckworth-Lewis method was first used on 1 January 1997 during the Zimbabwe versus England ODI series, where Zimbabwe won by seven runs. It was later adopted by the ICC in 1999 as the standard method for calculating target scores in rain-affected one-day matches.
The Duckworth-Lewis (DL) method is used to determine the target score for the team batting second in a match affected by rain or other interruptions. The technique employs a complicated mathematical formula to determine the score depending on a variety of factors, including the number of overs delivered, the number of wickets lost, and the run rate of the side batting first.
The DL method takes into account the par score for the team batting second, which is based on the number of overs remaining and the number of wickets lost. The par score is the score that the team batting second is expected to achieve at that stage of the game.
It then modifies the par score in accordance with the team batting second’s current run rate. The target score will be greater than the par score if the team batting second is scoring higher than the par score. The score will be lower if the team batting second falls short of the par score.
The Improvement
As of 2014, the Duckworth-Lewis approach is now known as the Duckworth-Lewis-Stern (DLS) method. The system was updated to increase its precision and reactivity to changes in the game. Steven Stern, a statistician who helped design the approach, was honoured with the new version’s name.
The inclusion of a new resource termed the “resource availability” factor was the primary modification made when DL became DLS. This calculation takes into account both the number of remaining wickets and the number of remaining overs. The target score that the side batting second must reach in order to win the game is determined by the resource availability factor.
The DLS system adjusted the par score calculation to account for teams’ tendency to score more runs in the closing stages of an inning. In a limited-overs match disrupted by rain, the DLS technique uses this revised par score computation to establish the target score for the side batting second.
These changes were made to address some of the criticisms of the original DL method and to make the system more accurate and fair in determining target scores in rain-affected matches.
The Formula
The formula for the DLS method is complex and takes into account several factors such as the number of overs played, wickets lost, and the resources remaining. Here is a simplified version of the formula:
Team 1 Target Score = Team 2 Score + (Team 2 Resource Percentage — Team 1 Resource Percentage) x Par Score
In this formula, the par score is determined by calculating the average score of the first innings, adjusted for the number of overs lost due to rain. The resource percentage is calculated by dividing the number of overs remaining by the total number of overs in the innings.
Let’s take the example let’s say a match is played between India and South Africa.
In this match, South Africa batted first and scored 227 runs for the loss of 9 wickets in their allotted 50 overs. Due to rain interruptions, India’s target was revised to 231 runs in 47 overs under the DLS method.
To calculate the revised target, the following formula was used:
Revised Target = Total Runs scored by the team batting first x (Par Score/Total Overs available for the team batting first) x (Overs available to team batting second/Par Overs)
Here, the par score is the score that the team batting first was expected to achieve at the end of their innings based on the conditions, pitch, and opposition. It is calculated using a complex statistical model.
In the match, the par score at the end of the 50th over for the first innings was calculated to be 223 runs. Since the first innings was played over 50 overs, the Par Overs were 50.
Now, to calculate the revised target for India, we need to determine the number of overs they would have had if there were no rain interruptions. In this case, the match was reduced to 47 overs. So, the overs available to India is 47.
Plugging in these values in the formula, we get:
Revised Target = 227 x (223/50) x (47/50) = 231.76
Therefore, the revised target for India under the DLS method was 232 runs, which was rounded down to 231 runs.
A Controversial Tool?
However, the method is not without criticisms, One of the main criticisms is that the DLS method is too complex for many fans to understand. While the formula used to calculate revised targets is based on statistical analysis and takes into account various factors, such as wickets lost and overs remaining, it can be difficult for the average viewer to follow. This can lead to confusion and frustration, especially when a match is decided by DLS and not by the actual runs scored by the teams.
Another criticism of the DLS method is that it can lead to unfair outcomes in certain situations. For example, a team that loses early wickets and is behind the run rate when rain interrupts play may end up with a higher revised target than a team that is batting well and on track to score a big total. This can make it harder for the second team to win the match, even though they may have been in a stronger position before the rain.
Critics argue that the DLS method relies too heavily on projections and assumptions, which can lead to outcomes that are not reflective of the actual match situation. There have also been concerns raised about the complexity of the DLS method, which can be difficult for fans, players, and even commentators to understand.
Another criticism of the DLS method is that it may disadvantage teams that are in a strong position before rain interrupts play. For example, a team that has already scored a high total may see its advantage diminished by the DLS method, which could lead to a closer match or even a loss.
A look at alternative approaches
Several alternative methods have been proposed to replace or supplement the DLS method.
VJD method
One such method is the “VJD method,” named after its creators, V. Jayadevan and D. Lakshminarayanan. It was developed in response to the limitations of the DLS method. It is a revised version of the PAR score system and takes into account the resources (wickets and overs) available to both teams.
The VJD method adjusts the target score based on the number of overs lost due to rain and the number of wickets in hand at the time of interruption. The formula for the VJD method is:
Adjusted target score = (Total runs scored by the batting team/Total overs available) x (Overs remaining for the batting team when play is stopped + D/L par score for those overs)
The DLS-S
This is a modification of the DLS method that takes into account the chasing team’s performance in the previous overs. It aims to make the target score more realistic by considering the impact of the chasing team’s wickets and overs remaining on the match situation. The formula for the DLS-S method is:
Adjusted target score = Target score x (Team 2’s scoring rate in previous overs/Team 1’s scoring rate in corresponding overs)
The BWS method
The BWS (Binomial Weibull System) method is a new alternative method that uses a binomial distribution to predict the number of runs a team would score in a given number of overs. It also uses a Weibull distribution to account for the uncertainty of the result. The BWS method is still being developed, and its formula is not yet publicly available.
Kubrick Method
Another alternative is the “Kubrick method,” named after its creator, Australian mathematician Frank Kubrick. This method is based on a probabilistic approach and claims to be more accurate than the DLS method, particularly in low-scoring matches. However, the Kubrick method is still in its early stages of development and requires further testing before it can be considered a viable replacement for the DLS method.
Is the Playing Field Leveled after DLS?
The DLS method has had a significant impact on the game of cricket, particularly in limited-overs matches where rain interruptions are common. Since its adoption as the standard method of calculating target scores in 1999, the DLS method has changed the way limited-overs matches are played and has impacted the outcomes of matches.
One notable example of the impact of the DLS method was the 2019 Cricket World Cup final between England and New Zealand. In a rain-affected match, England’s target was revised to 242 runs from 50 overs after a delay. However, after a dramatic tie in the final over of the match, the match was decided on the boundary count rule, which was controversially criticized by many. Despite this, the use of the DLS method was instrumental in ensuring that a result was achieved in a match that would have otherwise ended in a no-result due to rain.
The DLS method has also led to a change in the way teams approach their innings in rain-affected matches. Teams are now more conscious of the need to score quickly in the early part of the innings to ensure that they are ahead of the DLS par score if the match is interrupted by rain.
The impact of the DLS method can also be seen in matches where teams have successfully chased down revised targets after rain interruptions. One such example was the 2015 World Cup quarter-final between Australia and Pakistan. After rain reduced the match to 47 overs per side, Pakistan’s target was revised to 213 runs from 41 overs. However, Australia’s excellent use of the DLS method to chase the revised target ensured that they won the match by six wickets with 16 balls to spare.
An Effective Tool or a Controversial Solution?
On the one hand, supporters of the DLS method argue that it provides a fairer and more accurate way of determining the target scores in rain-affected matches, as it takes into account the changing match conditions and provides a revised target based on the resources available to the batting team. They also argue that it has reduced the number of matches that end in no result, which can be frustrating for both teams and fans.
On the other hand, critics of the DLS method argue that it can be complicated and difficult to understand, especially for casual fans. They also argue that it can unfairly penalize the team that is ahead at the time of the rain interruption, as the revised target may be higher than what they would have needed if the match had continued uninterrupted.
Overall, while the DLS method may not be perfect, it has become an important part of limited-overs cricket and has helped to reduce the number of matches that end in no result. Whether or not it is the most effective way of determining a fair result in rain-affected matches remains a matter of debate, but it is clear that it has had a significant impact on the way limited-overs matches are played and decided.
Whether you like it or not, the DLS system is as much a part of cricket as the infamous semi-final from the 1992 World Cup. The approach has not been without controversy and criticism, but it has also shown to be a huge improvement over the prior system. The par scoring system and other improvements developed over the years, such as DLS, have given a new level of intricacy to the game and had a big influence on how rain-affected matches are played and determined.
