A method that relates winning percentage to points scored, points allowed,
the standard deviations of points scored and allowed, and the correlation
between points scored and allowed. Points scored can be replaced with
offensive rating and points allowed can be replaced
with defensive rating.
This method applies in a straightforward manner to teams and probably
applies in a similar manner to individuals.
| (Rtg-Opp.Rtg) |
Win% = NORM |-----------------------------------|
| SD(Rating Difference) |
SD(Rating Difference) = SD(Rtg - Opp.Rtg)
NORM means to take the percentile of
a mean-zero variance-one normal distribution
corresponding to a value given by that in
the brackets I faked.
Rtg: Points scored per 100
possessions (offensive rating)
Opp.Rtg: Points allowed per 100
possessions (defensive rating)
SD(): Statistical standard deviation
of quantity in parentheses ()
Var(): Statistical variance of
quantity in parentheses ()
Cov(): Statistical covariance of
quantities in parentheses ()
See Basketball's Bell Curve
for a discussion of this method. It has also been used in other
articles, such as The Effect of
Controlling Tempo and What
Strategies Are Risky?
This method accomplishes the same thing as the
Pythagorean Method, providing more insights, but also
requiring more information.