I'm working on a hobby project that involves tournament-style player rankings, and I'm using the TrueSkill system developed by Microsoft for online gaming. It's a great system, but much of the math is far above my head. Even without understanding it, I've got most of what I need figured out, except for two equations which are never explicitly defined. The document that best outlines them is http://research.microsoft.com/pubs/67956/NIPS2006_0688.pdf.
(1) On the first page, equation 1 references psi, which denotes "the cumulative density of a zero-mean unit-variance Gaussian."
(2) In the preceding paragraph, there is mention of a function, N, representing player performance.
Having never taken a day of statistics in my life, and certainly not the graduate-level math that it seems is necessary for understanding this paper, it'd be great if somebody who does understand could just give me a numerical formula for these two functions that I could plug into my code (programming project). If you're curious, or it helps to answer the question, another great article about the system which is a little more approachable is http://research.microsoft.com/en-us/projects/trueskill/details.aspx.
Thanks for whatever help anyone