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\section{Introduction}  While investigating the $\sim 7\%$ bias Nick was seeing in his velocity dispersion plot, it became obvious that this bias is a result of binning a sample with scatter in the observables and inherant functions in mass. Originally we thought these relationships would not manifest themselves in the median or mean values of the true observables (table values) that we compare with, but this walk through shows otherwise.  Our ultimate goal is There are several key probabilities we need to know in order  to fully accurately predict the scatter/bias of some observable with mass. In more statistical language, we must  know $P(\textbf{O}|M).$ $P(\hat{\theta}|M)$. That is, given a cluster of mass $M$, what is the probability the observable is detected as $\hat{\theta}$.