Runs Per Wicket Ratio (RpW ratio, also called the Quotient) is a method of ranking teams in league tables in

cricket Cricket is a bat-and-ball game played between two teams of eleven players on a field at the centre of which is a pitch with a wicket at each end, each comprising two bails balanced on three stumps. The batting side scores runs by striki ...

who are equal on other criteria, including points.

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 The Sheffield Shield (currently known for sponsorship reasons as the Marsh Sheffield Shield) is the domestic first-class cricket competition of Australia. The tournament is contested between teams from the six states of Australia. Sheffield Shi ...

, under the name Quotient. It was used to determine the champions in 1910–11, 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 The Ranji Trophy (also known as Mastercard Ranji Trophy for sponsorship reasons) is a domestic first-class cricket championship played in India between multiple teams representing regional and state cricket associations. Board of Control for Cr ...

and

Duleep Trophy The Duleep Trophy, also known as Mastercard Duleep trophy due to sponsorship reasons, is a domestic first-class cricket competition played in India. Named after Kumar Shri Duleepsinhji of Nawanagar (also known as 'Duleep'), the competition wa ...

, under the name Quotient.

Calculation

It is the number of runs scored per

wicket In cricket, the term wicket has several meanings: * It is one of the two sets of three stumps and two bails at either end of the pitch. The fielding team's players can hit the wicket with the ball in a number of ways to get a batsman out. ...

lost, divided by the number of runs conceded per wicket taken:

\text=\frac \div \frac.

Mathematically, this is equivalent to:

\text = \frac .

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

reciprocal Reciprocal may refer to: In mathematics * Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal'' * Reciprocal polynomial, a polynomial obtained from another pol ...

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

dimensionless quantity A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...

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 In cricket, a player's bowling average is the number of runs they have conceded per wicket taken. The lower the bowling average is, the better the bowler is performing. It is one of a number of statistics used to compare bowlers, commonly use ...

, or with

batting average Batting average is a statistic in cricket, baseball, and softball that measures the performance of batters. The development of the baseball statistic was influenced by the cricket statistic. Cricket In cricket, a player's batting average is ...

References

{{Cricket statistics Cricket terminology ICC World Test Championship Sheffield Shield