# Inferring an unmeasured value

Suppose we have a table of finishing times for an number of 100 metre races where each competition has a different mix of entrants. We suspect that some races are slower than others due to, say, a headwind, but this wasn't measured. How do I find the underlying time for each runner and the correction for each race?

I have devised my own crude technique to solve this problem. I assume

Tobs(e,c) = Tund(e) + Tcor(c) + E(e,c)

where

Tobs(e,c) = observed time of entrant e in competition c
Tund(e) = underlying time of entrant e
Tcor(c) = time correction for competition c
E(e,c) = error matrix

sum of all Tcor = 0
sum of all rows in E(e,c) = 0
sum of all columns in E(e,c) = 0



I then iteratively choose values for Tcor until the above relations are satisfied.

Is there a better way? Using R? Please be gentle. As you might have guessed by now, I don't much much about stats or maths. Thanks!