My eyes were opened to the SABR approach to watching baseball after
(like so many others) reading Moneyball five years ago.
I hope you've had the chance to read Nassim Taleb's eye-opener, The
Black Swan. His general theme is that Gaussian probability is flawed.
The distribution of of so called "outliers" in a dynamic system (he
focuses on financial markets) is not as remote as traditional
statistical theory tells us.
Taleb describes a "Black Swan" as a completely unexpected event
that humans try to explain (rationalize) after the fact by a series of
logical and, in his mind, statistical fallacies. Taleb favors the
idea of scalable probability based on fractal mathematics, i.e., large
deviations from the "mean" are certainly more rare, yet they occur
much more frequently than the bell curve dictates.
So since baseball is a dynamic system (insofar as there are a massive
amount of things that can happen with every pitch) this brings to mind many potential "black swans", like Brady Anderson hitting 50 HRs in 1996 and Shawn Chacon's Yankees pitching performance in 2005...or Johnny Damon tearing it up so far this season.
Taleb's concepts might (that's might) describe baseball outcomes better than Jamesian/SABR normalized (bell curve) assumptions.