We need a fairer system for deciding rain-affected games in Twenty20 cricket

In all versions of cricket, a team’s ability to score runs is limited by two factors
We need a fairer system for deciding rain-affected games in Twenty20 cricket
We need a fairer system for deciding rain-affected games in Twenty20 cricket
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The sixth World Twenty20 cricket tournament begins in India this March and the competition comes at a time when the shortest version of the game is gaining popularity at a remarkable rate.

But there’s a potential dark cloud hanging over the tournament’s intrinsic fairness – literally – when it comes to deciding who’s the winner if a game is cut short.

In all versions of cricket, a team’s ability to score runs is limited by two factors: the number of wickets remaining and the maximum time available. In Test cricket, the time is limited by a clock and a calendar.

In shorter versions of the game, it is limited by a maximum number of possible deliveries. Difficulties arise in limited-overs cricket when sides have their innings shortened, usually because of a rain delay or bad light.

In the history of limited-overs cricket, various formulae have been used to calculate what is intended to be a fair total for a team to reach when (at least) one innings is truncated.

Since the 1990s, a system first proposed by British statisticians Frank Duckworth and Tony Lewis has been accepted as standard for all major competitions. Despite generally being seen to produce fewer unfair or absurd outcomes than some of its predecessors, the Duckworth-Lewis method (sometimes the Duckworth-Lewis-Stern method after its later revision by Steve Stern) is not without its critics.

Adding to the confusion is the fact that several international captains have gone on record to admit that they don’t fully understand how the method works.

Stumped by statistics?

The Duckworth-Lewis System combines the remaining wickets and deliveries into a single resource. In the event that the regulated number of overs cannot be bowled, the target that a team needs to reach is recalculated to account for the resources lost during the break.

Graph showing the Duckworth-Lewis calculation for combining remaining wickets and deliveries into a single resource.

For example, consider a 50-over game in which Team A bats first and scores a total of 200 runs in 50 overs. Team B then begins its innings, and scores 50 runs in ten overs while losing three wickets. The game is then abandoned for whatever reason with Team B unable to complete its innings.

The Duckworth-Lewis method would say that Team A had used 100% of its available resources (since it faced all 50 possible overs) whereas Team B had used only 30.4% of its resources. The game would then be decided by which team had scored the most runs, allowing for Team B’s lost resources.

Team A’s score of 200 would then be multiplied by the ratio of each team’s available resources (30.4/100) to give a target of 60.8 runs to be reached by Team B. As Team B scored only 50 runs, Team A would be declared the winners.

Critics of the Duckworth-Lewis method in Twenty20 cricket focus on two issues. First, by focusing on preserving resources, the system does not directly attempt to preserve winning probabilities.

That is, a team’s chances of victory before and after a delay might be greatly different because of the formula alone. This is seen by many critics as rather a perverse idea, but it is one that Duckworth and Lewis admit was intentional and have vocally defended. Alternative metrics, including some that seek to preserve winning probabilities have been proposed.

The bigger issue with applying the Duckworth-Lewis method to Twenty20 is more simple: it was not developed or calibrated for this shorter version of the game. The calculations assigning relative importance to wickets and remaining deliveries have been developed for the 50-over format.

It is often argued that wickets are relatively less valuable in Twenty20, as most teams are ultimately limited by the number of deliveries before they run out of wickets. In longer versions of the game, the need to avoid losing wickets is more important.

What do the record books say?

The issues and criticisms discussed are all reasonable in theory, but we wanted to see whether the history books supported these concerns.

Breaking out our copies of Wisden Cricketers' Almanack, we looked at the results of of more than 1,700 recent Twenty20 matches.

Excluding a small number of matches that ended in ties or were abandoned, we analysed the results of every game from the World Twenty20 (since 2007), Australian Big Bash League (since 2011-21), Indian Premier League (since 2008), English t20/t20 Blast (since 2010), South African T20 Challenge (since 2011-12) and Australian Women’s Big Bash League (since 2015-16.)

From this dataset, we calculated what proportion of games had been won by the team batting first and proportion by the team batting second. If the order of the teams’ batting does not bias the winning probabilities, then the observed proportions of wins should be close to 50/50.

Even in cases where one team is clearly stronger than the other, whether or not they bat first is decided by a coin flip and a subsequent captain’s decision.

For the 1,628 games that did not require the Duckworth-Lewis method to be employed, we found that approximately 51% were won by the side batting first. From a sample of this size, there is insufficient statistical evidence to reject the belief that these games were unbiased.

For the 84 games that required the Duckworth-Lewis method, the picture was very different. For the rain-affected games, barely more than 39% of games were won by the first team to bat.

So the history books support the critics' view that the current adjustment formula is unfair and ripe for review. The records show that the win rate of teams batting second is more than 50% greater than that of the team batting first when Duckworth-Lewis method is required.

What improvements can be made?

A full examination of ball-by-ball datasets for recent Twenty20 matches should shed some light on exactly how scoring patterns and rates differ from the longer version of the limited-overs game.

As Twenty20 grows ever more popular, it clearly demands its own adjustment system, not the ill-fitting hand-me-down from the 50-over game.

Whatever methods might be developed, such revisions will not be implemented in time for this year’s tournament. In the interests of sporting fairness, you might have to simply cross your fingers are hope for clear skies over India.

If the rain clouds arrive, the most influential figures in the tournament might turn out not to be the game’s premier batsmen or bowlers, but two ageing British statisticians.

That, as they say, is just not cricket.

Honours student Ignatius McBride co-authored this article.

Stephen Woodcock, Senior Lecturer in Mathematics, University of Technology Sydney

This article was originally published on The Conversation. Read the original article.

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