# Equivalent Runs

Equivalent Runs (EqR) is a run estimator developed by Clay Davenport, with figures published by *Baseball Prospectus*. It is the major input in the calculation of Equivalent Average, a companion rate stat.

## EqR Formula[edit]

The first step in calculating EqR is to figure what Davenport calls Raw EqA (REqA) for both the individual/team and the league in which they played:

REqA = (H + TB + 1.5*(W + HB + SB) + SF + SH)/(AB + W + HB + SH + SF + SB + CS)

REqA is the converted into EqR by this formula:

EqR = (2*REqA/LgREqA - 1)*Lg(R/PA)*PA

## Nature of EqR[edit]

EqR is essentially a linear weights formula--the only cause of non-linearity in the formula is the presence of SB and CS in the denominator of REqA. Otherwise, since PA = AB + W + HB + SH + SF (the same as the REqA denominator ignoring SB and CS), PA cancels out when REqA is multiplied by PA. Thus, if one ignores SB and CS, EqR can be rewritten as:

EqR = (2*(H + TB + SF + SH) + 3*(W + HB))*Lg(R/PA)/LgREqA - Lg(R/PA)*PA

Using the 2007 AL as an example, the LgREqA (without SB and CS) was .774 and the Lg(R/PA) was .127. Plugging these values into the above equation simplifies to (rounding to two decimal places):

EqR = .53*S + .85*D + 1.18*T + 1.51*HR + .36*(W + HB) + .20*(SF + SH) - .13*(AB - H)