I'm a stats newbie, so I have a basic question here:

I'm trying to model a sports simulation where given a batter who has a
X% history of performing some event ( like striking out ) in a single
at bat, and a pitcher who has a Y% history of performing the flipside
of that event ( like striking someone out ), determining what the odds
are of that batter performing that event when facing that pitcher in a
single at bat. One basic way I've thought of this is to treat
striking out / striking someone out as traits that follow a normal
distribution. Thus, I first take league-wide data and calculate what
the mean/stddev is for the league for both traits. Then I establish
what percentile the batter and pitcher have at their respective
traits.

The part I'm wondering is how these should interact in a
mathematically plausible way. The assumption I'm making is that the
pitcher has a Y% chance of striking someone out when facing a batter
at the mean of the curve ( similar logic for the batter ). Also, for
simplicity, I think I want to use just one normal distribution per
event type ( the same one for both batters and pitchers ): so now we
have one normal distribution called "strikeout tendency".

So say a
pitcher is at the 75th percentile at striking guys out, and a batter
at the 50th; then the result should be whatever the strikeout rate is
at the 75th percentile. What about pitcher=75th %ile ( strikes
people out more than average ), batter=25 %ile ( strikes out less than
average )---intuitively this should even out somewhere around the
mean. But pitcher=75th %ile, batter=75th %ile should push the result
further away from the mean. Any ideas would be appreciated!