I've heard that description before and find it more ad hoc than intuitive. Is there some valid mathematical object K such that often times you will normalize un

I've heard that description before and find it more ad hoc than intuitive. Is there some valid mathematical object K such that often times you will normalize unbiased estimators by N/(N-K)? Is this K sometimes equal to some measure of the number of equations/constraints you have? Does this seem to hold a lot of force in ANOVA especially? Sure, sure, sure. I still don't see why this normalization is required to make a better estimate (excepting when you define "better" as an unbiased estimator, maybe the MVUE).