[sampo]

> If the average of the last 10 seasons is 20 home runs, what would be a better predicted value?

You are correct, 20 is the best estimate for this single variable (or similarly for any single variable in isolation).

Only if the objective is to minimize the total MSE (Mean Square Error),

          (Ph - h)² + (Pg - g)² + (Pt - t)²
    MSE = ---------------------------------
                          3

then it pays off to bias each estimate – Ph, Pg, Pt – slightly towards zero. If any of the observed values is larger than the true value, we do improve the estimation by using a correction coefficient slightly under 1. If the observation happens to be smaller than the true value, we do make a mistake. But we make a smaller mistake when the observed value was small because it was small, than what we improve when it was large. A set of 3 independent variables is already large enough that this gamble pays off in average (in the combined total error of the 3 estimates).