Runs Per Win

Runs Per Win (RPW) is a general term that refers to estimates of the number of additional runs it would take for a given team to win one more game. Thus, it is usually an estimate of marginal runs per marginal win. Often, RPW is stated for a hypothetical average team, although it could be figured for any combination of team runs scored and allowed. Formulas for RPW can be derived from Winning Percentage Estimators. A common rule of thumb is that 10 runs = 1 win.

Methods of Estimating RPW

• Pete Palmer estimates RPW as 10 times the square root of (runs per inning by both teams). In a typical context in which each team scores 4.5 runs per game, the runs per inning for both teams is 1, and thus RPW = 10. This formula for RPW is used in his Linear Weights System to convert a player’s runs above average into wins above average.

• A common assumption is that RPW = RPG, where RPG is Runs per Game by both teams (figured for any specific team as (R + RA)/G). This assumption is used by Base Wins method, and can also be shown to be a consequence of using the Pythagorean Theorem with an exponent of 2.

• Using the Pythagorean Theorem, it can be shown that for a .500 team with R = RA, RPW = (2*RPG)/x, where x is the exponent used. Thus, with an exponent of 2, the equation simplifies to RPW = RPG. For PythagenPat, the equation simplifies to 2*RPG^(1 - z), where z is the exponent to which RPG is raised, generally in the neighborhood of .27-.29.