I am reading about the idea of bagging (boostrap aggregating). I have no trouble understanding how the variance of prediction can be reduced. The simple picture is if you have prediction Z_1 through Z_n for each boostrapped sample, the standard error of the mean will be the reduced by sqrt(n).
However, if this picture is true, Mean of boostrapped sample mean should be unbiased estimate of mean of each Z. Then how can the accuracy be improved as well?