# Runs Per Wicket Ratio

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Runs Per Wicket Ratio (RpW ratio,[1] also called the Quotient[2][3]) is a method of ranking teams in league tables in cricket who are equal on other criteria, including points.[4][5]

## Usage

It was used in the 2019–21 ICC World Test Championship, under the name RpW Ratio.

It is used in Australia's Sheffield Shield, under the name Quotient.[2] It was used to determine the champions in 1910–11,[6] and a number of times after that. It has not been required to determine final league positions since fractional bonus points for each run scored and wicket taken were introduced (in 2014–15).

It is used in India's Ranji Trophy and Duleep Trophy, under the name Quotient.

## Calculation

It is the number of runs scored per wicket lost, divided by the number of runs conceded per wicket taken:[7]

${\displaystyle {\text{RpW ratio }}={\frac {\text{total runs scored}}{\text{total wickets lost}}}\div {\frac {\text{total runs conceded}}{\text{total wickets taken}}}.}$

Mathematically, this is equivalent to:

${\displaystyle {\text{RpW ratio}}={\frac {{\text{total runs scored}}\times {\text{total wickets taken}}}{{\text{total runs conceded}}\times {\text{total wickets lost}}}}.}$

For example, if in one match Sri Lanka scored a total of 535 runs for the loss of 14 wickets, then they scored 38.214 runs per wicket. If they conceded 534 runs while taking 20 wickets, then they conceded 26.7 runs per wicket. So their RpW ratio = 38.214 ÷ 26.7 = 1.431.

The RpW ratio for their opponent (New Zealand) is the inverse of this: 26.7 ÷ 38.214 = 0.699. So if two teams have played only each other, their two RpW ratio figures are reciprocals.

As the units are the same either side of the division (runs/wickets), they cancel out, so RpW ratio is a dimensionless quantity.

## Interpretation

It is the average number of runs scored per wicket, for each run per wicket conceded:

• If RpW ratio is less than 1, then the team scored fewer runs per wicket than it conceded. In the example, New Zealand scored 26.7 runs per wicket but conceded 38.214 runs per wicket. So they scored 0.699 runs per wicket for each run per wicket conceded.
• If RpW ratio equals 1, then the team scored exactly the same number of runs per wicket as it conceded.
• If RpW ratio is greater than 1, then the team scored more runs per wicket than it conceded. In the example, Sri Lanka scored 38.214 runs per wicket and conceded 26.7 runs per wicket. So they scored 1.431 runs per wicket for each run per wicket conceded.

RpW ratio is not to be confused with the ratio of runs conceded to wickets taken by individual bowlers, known as bowling average, or with batting average.

## References

1. ^ "Standings". International Cricket Council. Retrieved 19 August 2019.
2. ^ a b "2019-20 Marsh Sheffield Shield and Toyota Second XI Playing Conditions". Cricket Australia. Retrieved 8 November 2019. 16.9.5.3 Should there be equality in both total points and outright wins, the positions shall be determined by quotient calculated thus: 16.9.5.3.1 Divide the total number of runs scored by a team by the total number of wickets lost by it. 16.9.5.3.2 Divide the total number of runs scored against a team by the total number of wickets taken by it. 16.9.5.3.3 Divide the former (16.9.5.3.1) by the latter (16.9.5.3.2).
3. ^ "Ranji Trophy Table - 2018-19". espncricinfo. Retrieved 8 November 2019.
4. ^ "What's new - World Test Championship playing conditions". ESPN. Retrieved 21 August 2019. If at the end of the group stage, two or more teams are level on points, the team with more series wins will take the higher spot on the table. If they are level on that front, runs-per-wicket ratio - defined as runs scored per wicket lost, divided by runs conceded per wicket taken - will be factored in.
5. ^ "ICC World Test Championship 2019-2021 - Points Table". howstat.com.au. Retrieved 21 August 2019. If at the end of the league stage, two or more teams are level on points, the team with more series wins will take the higher spot on the table. If they are level on that front, the team with the highest runs-per-wicket ratio (runs scored per wicket lost, divided by runs conceded per wicket taken) will take the higher spot on the table.
6. ^ "Sheffield Shield Table - 1910-11". espncricinfo. Retrieved 11 August 2021.
7. ^ "World Test Championship Playing Conditions: What's different?" (PDF). International Cricket Council. Retrieved 19 August 2019.