2007 Cricket World Cup Final: How The Duckworth-Lewis-Stern method (DLS) Shaped Australia vs Sri Lanka.
The match between Australia and Sri Lanka, held at Kensington Oval, Bridgetown on 28th April 2007.
- Australia Innings:
- Ricky Ponting won the toss and elected to bat.
- However, the start of play was delayed due to rain, and the match was reduced to 38 overs per side.
- Adam Gilchrist’s score of 149 – the highest in a World Cup final – helped give Australia an imposing total of 281.
- Sri Lanka Innings:
- Sri Lankan batsmen Kumar Sangakkara and Sanath Jayasuriya added 116 for the second wicket, before falling with the score at 123 and 145 respectively.
- Further rain forced the reduction of Sri Lanka’s innings to just 36 overs, with the target revised to 269. (Duckworth-Lewis method)
- At the culmination of the 33rd over, with Sri Lanka still trailing the adjusted Duckworth-Lewis target by 37 runs, the umpires temporarily suspended the game due to bad light.
- The last three overs were played in almost complete darkness, during which Sri Lanka added nine runs, giving Australia a 53-run victory via the Duckworth–Lewis method
Role of DLS:
- This controversial match highlighted the importance of DLS in ensuring a fair result when rain disrupts limited-overs cricket.
- It also sparked debates about the limitations of DLS, particularly when matches are played in difficult conditions like near darkness.
Table of Contents
Pre-DLS Methods in Cricket: A Historical Overview
Before the Duckworth-Lewis-Stern (DLS) method, there were several less sophisticated methods used to determine a result in rain-affected cricket matches:
- Average Run Rate (ARR) method: This simply took the total runs scored by the first team and divided it by the number of overs bowled, then multiplied that number by the number of overs remaining for the second team to get their target. This method was criticized for not considering wickets lost, which can significantly impact scoring rate.
- Most Effective Overs (MPO) method: This method looked at the highest-scoring overs of the first team’s innings and assumed the second team would score at the same rate in their remaining overs. This method was flawed as it ignored the fact that teams often bat more cautiously early on and wouldn’t necessarily maintain the same aggressive pace throughout their innings.
- Last Wicket Stand method: This even simpler method just took the number of runs scored by the last wicket partnership of the first team’s innings and added that to their total score to set a target for the second team. This was obviously a very arbitrary and unreliable approach.
Unlike earlier methods that relied on guesswork (average run rate, last wicket stand) or unrealistic assumptions (most effective overs), the DLS method uses complex statistical analysis to create a fair target score. It considers factors like wickets lost and remaining overs, leading to a more accurate and adaptable approach for rain-affected cricket matches.
The Evolution of DLS: From Duckworth-Lewis to Duckworth-Lewis-Stern
The DLS method was originally named after the two English statisticians who devised it: Frank Duckworth and Tony Lewis. It was known as the Duckworth-Lewis method (D/L) when it was first introduced in 1997.
Later, in 2014, Australian statistician Steven Stern made significant contributions to refining the model, particularly for the fast-paced nature of T20 cricket. In recognition of his work, the method was then renamed to the Duckworth-Lewis-Stern method (DLS) to reflect the combined efforts of all three individuals.
How Does the DLS Method Work? A Step-by-Step Explanation
Data Collection and Analysis:
- The foundation of DLS is a massive database of historical data from limited-overs matches. This data includes details like runs scored, wickets lost, overs bowled, and final match results.
- Statistical techniques are used to analyze this data and identify patterns. This reveals how scoring rates typically change throughout an innings based on wickets remaining and overs bowled.
Resource Percentages:
- DLS considers the two key resources available to a team in a limited-overs match: overs remaining and wickets in hand. Each combination of overs and wickets is assigned a corresponding “resource percentage,” with a full set of overs and all wickets intact being 100%.
- These resource percentages are calculated based on historical data, reflecting the typical scoring difficulty at different stages of an innings.
Target Setting Algorithm:
- When a rain interruption occurs, the DLS method uses the resource percentages of both teams (before and after the interruption) to calculate a revised target score for the team batting second.
- The algorithm factors in the lost resources of the team batting second due to the rain and adjusts the target score accordingly, aiming to create an equivalent challenge compared to the full innings of the first team.
Continuous Improvement:
- The DLS method is not static. New data from every season is incorporated into the analysis, allowing the model to adapt to evolving batting strategies and pitch conditions.
- This ongoing development ensures the DLS method remains statistically sound and reflects the ever-changing nature of the game.
The calculations behind DLS
Basic Principles of DLS
1. Resources: The method considers two primary resources in a cricket match: Overs remaining and Wickets in hand
2. Resource Table: The DLS method uses a resource table that assigns a percentage value to every possible combination of overs remaining and wickets lost. This table quantifies the remaining scoring potential of a team given the state of the match.
3. Calculation of Resources: Before the interruption, the resources available to each team are calculated. After the interruption, the new resources available to the team batting second are recalculated based on the number of overs remaining and wickets in hand.
Steps in Applying the DLS Method
1. Determine Total Resources Available to Both Teams– Team 1’s Resources (R1): Resources available to Team 1 based on their full allocation of overs. Team 2’s Initial Resources (R2_initial): Resources available to Team 2 before the interruption.
2. Calculate Resources Lost Due to Interruption: Calculate the resources lost due to the interruption for Team 2 by comparing the resources available before and after the interruption. Remaining Resources for Team 2 (R2_final): Resources remaining after the interruption.
3. Compute Resource Ratio: The resource ratio is calculated by dividing Team 2’s remaining resources by the total resources of Team 1.
– Resource Ratio (RR) = (R2_final) / R1
4. Adjust Target Score:
– The target score for Team 2 is adjusted based on the resource ratio.
– If Team 1 scored S1 runs, the revised target T for Team 2 is calculated as:
T = S1 * (Resource Ratio) + {par score adjustment}
Example Calculation of DLS Method: Simplifying the Complex
Suppose: team 1 scores 250 runs in 50 overs. Team 2 has an interruption after 20 overs, reducing their total to 30 overs.
Using the DLS method:
1. Team 1’s Resources: 50 overs, 10 wickets: 100% resources.
2. Team 2’s Initial Resources: 50 overs, 10 wickets: 100% resources.
3. Team 2’s Resources After Interruption: 30 overs, 10 wickets: Suppose 75% resources (as per the DLS resource table).
4. Resource Ratio:
– Resources available to Team 2 after interruption = 75%.
– Resources used by Team 1 = 100%.
– Resource Ratio (RR) = (R2_final) / R1 = {75} / {100} = 0.75
5. Adjusted Target:
– Using the ratio, the adjusted target score “T”
T = 250 * 0.75 = 187.5
– Rounded up: 188 runs.
Duckworth Lewis Stern Methodology : a guide by ICC
Clippings from the DLS table, used to determine the resource% directly
Recent examples in which DLS was used
2023 Indian Premiere League – Chennai Super Kings vs Gujarat Titans
- Rain interrupted the match after CSK’s chase innings began, causing a delay. The DLS method was then used to set a new target for CSK. With GT scoring 214/4 in their 20 overs batting first.
- CSK were given a revised target of 171 runs to chase in just 15 overs. The powerplay was also shortened to 4 overs and there were bowling restrictions implemented. CSK went on to win the match by 5 wickets using the DLS method.
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2023 Cricket World Cup – Pakistan vs New Zealand
- New Zealand batted first and scored a massive 401 runs.
- Rain interrupted Pakistan’s chase when they were at 200/1 in 25.3 overs.
- DLS set a revised target of 263 runs for Pakistan in 39 overs.
- The match couldn’t continue because of the rain.
- By DLS Pakistan won by 21 runs.
