# Extrapolated Runs Calculator & Formula

Extrapolated Runs Calculator
1B = SB =
2B = CS =
3B = AB =
HR = K =
HBP = GIDP =
BB = SF =
IBB = SH =

Extrapolated runs, abbreviated XR, is a sabermetric that measures the number of runs a player contributes to his team. Developed by Jim Furtado, extrapolated runs is an alternative to the runs created sabermetric, RC, created by Bill James. One advantage of the XR formula over the RC formula is that it is linear. If you add the XR values of each player on a team, you arrive at the total runs estimator for the team. In contrast, RC has a multiplicative formula; if you add the RC values of each player on a team, you won't obtain a total team runs estimator.

### Formula for XR

Although the extrapolated runs formula is linear, it is still somewhat complex because it includes over a dozen variables. The raw form is

XR =

0.50*1B + 0.72*2B + 1.04*3B + 1.44*HR
+ 0.34*(HBP + BB - IBB) + 0.25*IBB
+ 0.18*SB - 0.32*CS - 0.09*(AB - H - K)
- 0.098*K - 0.37*GIDP
+ 0.37*SF + 0.04*SH.

By expanding terms in parentheses, combining like terms, and writing H as 1B + 2B + 3B + HR, we can write this equation in a completely equivalent, but more efficient form:

XR =
0.59*1B + 0.81*2B + 1.13*3B + 1.53*HR + 0.34*HBP + 0.34*BB - 0.09*IBB
+ 0.18*SB - 0.32*CS - 0.09*AB - 0.008*K - 0.37*GIDP + 0.37*SF + 0.04*SH

Example: In 1998, Sammy Sosa's stats were

1B = 112
2B = 20
3B = 0
HR = 66
AB = 643
BB = 73
IBB = 14
HBP = 1
SB = 18
CS = 9
SH = 0
sF = 5
GIDP = 20
K = 171

His extrapolated runs for that year was then

XR =
0.59(112) + 0.81(20) + 1.13(0) + 1.53(66) + 0.34(1) + 0.34(73) - 0.09(14)
+ 0.18(18) - 0.32(9) - 0.09(643) - 0.008(171) - 0.37(20) + 0.37(5) + 0.04(0)

= 142.732, or 143 rounded to the nearest integer.