I manually recorded the "points for" and "points
against" for each post
position and for each result for many
many games and thousands of points.
I then took an average. I know that if
post 2 finishes out of the money then
post 2 scored ON AVERAGE 0.69 times
and failed to score 1.48 times. Post
2 , when finishing out of the money,
plays 2.17 (0.69+1.48) times per game.
Skiena, in his book, shows a chart for
the percentage times that various posts
score depending upon if they W-P-S-OUT.
But he does not show the breakdown. He
keeps this information unavailable. He
says that "Averaging averages yields a
meaningless number whenever the denominators are different". In other
words, one cannot arrive at a meaningful
number when one totals only the averages alone.
In other words, a 70.7 % winning average
when 5 points are played is different
than a 70.7% average when 2 points are played.
This is why the breakdown is necessary.