Tomspeople says:
Zscores are simply just saying how many standard deviations away from the mean a certain observation is

There's a real notation but in simple words the formula is..

(Raw score - mean of all scores) / Standard deviation



I've never personally used Zscores in sports betting so I couldn't tell you how to apply it to systems. Although I'm working on a system related to standard deviation which of course as you know, is related to Zscores. You can find my thread for that a bit lower.

jarhead60 says:
Z scores are not a measure of reliability. Theu are mostly used to find where a stat falls on a normal bell curve. They can be used to put different series on the same scale for comparison.

An example would be football if you have a system that will forecast the margin of victory. Generally, one would take your estimate of MOV, subtract the point spread, and see if you have a bet. A problem develops because there are four variables--1) your estimate, 2)the betting line,3) the overlay, and 4)the actual MOV-- which all have different means and different standard deviations. If you have history of a few years of each series, you can compare z scores instead of raw numbers. Give it a try and you will find that  this method will be a little better than the raw numbers. You may also find that you may only want to bet the overlays that are 1  or 2 STD's above or below average.

A spread sheet like excel should do most of the math.