Tango Distribution

The Tango Distribution, developed by Tangotiger, is a means of estimating the runs per inning distribution of a team based on their average runs scored per inning. Using the runs per inning distribution as a starting point, a runs per game distribution can be estimated. This in turn can be used to estimate team winning percentage.

The formulas are as follows, starting with average runs per inning (R/I):

a = c*RI^2, where c is the control value, typically set to .767 if looking at one team independently, or .852 if looking at two teams in a head-to-head game

f(0) = RI/(RI + a), where f(n) is the probability of n runs scored in an inning

DropRate = 1 - c*f(0)

f(1) = (1 - f(0))*(1 - DropRate)

f(n) = f(n - 1)*DropRate for n>= 2