Average Run Rate method

The Average Run Rate (ARR) method was a mathematical formulation designed to calculate the target score for the team batting second in a limited overs cricket match interrupted by weather or other circumstances. Often matches interrupted by weather would use Reserve Days, bowl outs, or were replayed on another date, but when that could not happen, the ARR method might be used instead.

The ARR method was used from the start of one-day cricket in the 1950s/1960s, until replaced by the Most Productive Overs method in the early 1990s.[1]

Calculation

If an interruption means that the team batting second loses some of their overs, their target score is adjusted as follows.[2]

This means that Team 2 just has to match the average run rate achieved by Team 1 in the overs it has available. For example, if Team 1 made 250 in their 50 overs, which is an ARR of 5 runs per over, and Team 2’s innings is reduced to 25 overs, Team 2's new target is (5 x 25) + 1 = 126.[1]

This formula can alternatively be written as:

In other words, the target is reduced in proportion to the loss in overs. Using the same example as above, with this formula the new target for Team 2 is (250 x 25/50) + 1 = 126.

Criticisms

Very frequently the ARR method alters the balance of the match, usually in favour of the team batting second.[3] This is because:

  • It is easier to maintain a given run rate for a smaller number of overs, as less care needs to be taken to preserve wickets. Therefore an adjusted target is easier to achieve.
  • The method takes no consideration of wickets lost, so a team scoring 126–9 from 25 overs in reply to a score of 250 from 50 overs would be deemed to have won.[4]
  • There is no compensation to the team batting first if they unexpectedly lose some of their final overs which they were expecting to be able to use to score from.
  • If Team 2's innings is interrupted mid-innings, the current match situation is irrelevant in the calculation of the new target. Therefore the balance of the match will be changed.

Notable matches decided by ARR

  • England v Sri Lanka in the 1987 Cricket World Cup. England scored 296 from 50 overs, an ARR of 5.92. Sri Lanka's innings was reduced to 45 overs, therefore their target was 267 (5.92 x 45 = 266.4).
  • In the third final match of the 1988-89 World Series Cup, Australia scored 226 from 38 overs, an ARR of 5.95. Chasing 227 from 38 overs, West Indies were 47−2 after 6.4 overs when rain stopped play. At this point they needed 180 more runs from 31.2 overs, an ARR of 5.74. At the re-start, West Indies' innings was reduced to 18 overs in total. Their revised target was therefore 108 (as 5.95 x 18 = 107.1), so they had 61 more runs to score from 11.2 overs, an ARR of 5.38. The West Indies won the match easily with 4.4 overs remaining and eight wickets in hand.[5]
The revised target therefore gave West Indies a huge advantage, as it significantly reduced the amount of overs they needed to maintain a given run rate, and it also actually reduced the run rate they needed. Australian fans booed this conclusion, which was criticised by the media and Australia's captain, and led to Australia developing the Most Productive Overs method.

References

  1. 1 2 Duckworth/Lewis, Q2. "The D/L method: answers to frequently asked questions". ESPN Cricinfo. Retrieved 16 September 2017.
  2. ↑ Brooker, S.; Hogan, S. (2010). "How fair is the Duckworth/Lewis adjustment in one day international cricket?" (PDF): Section 2.1.
  3. ↑ Duckworth, F.C.; Lewis, A. J. (1998). "A fair method for resetting the target in interrupted one-day cricket matches". Journal of the Operational Research Society. 49 (3): 220–227. doi:10.1057/palgrave.jors.2600524.
  4. ↑ Duckworth, F.C. (2008). "The Duckworth/Lewis method: an exercise in Maths, Stats, OR and communications" (PDF). MSOR Connections. 8 (3): 11–14.
  5. ↑ 3rd Final, 1988/89 Benson and Hedges World Series Cup
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