From: Edward J Glamkowski (eglamkowski@ANGELFIRE.COM)
Date: 08/26/98

Ok, I just did up the cleric saving throws and have
some interesting results.  First of all, the only
two types of equations that yielded consistently
high R^2s are linear and polynomial (I only used order
three to maintain sanity :)
The polynomial yielded better fits, but not usually
by a lot.

For example, breath (x-axis = level, y-axis = saving
y = -1.4788x + 80.621  R^2 = .9908
y = -.0012x^3 + .0664x^2 - 2.4745x + 84.082 R^2 = .9952

So, since the linear equations are much easier to use
and program, I will put forward the linear equations
and ignore the polynomials.

In fact, the coefficients for the equations for most of
the [cleric] saving throws are sufficiently close that
we can probably reduce all five to one single equation:

Para:   y = -1.6033x + 52.218  R^2 = .9599
Rod:    y = -1.4788x + 70.621  R^2 = .9908
Petri:  y = -1.4785x + 65.717  R^2 = .9916
Breath: y = -1.4788x + 80.621  R^2 = .9908
Spell:  y = -1.4785x + 75.717  R^2 = .9916

I would tend to reduce this to one equation:
save:   y = -1.5x + 70

It is reasonably close to all the individual equations
(only on para is it really off), and it fairly trivial
to program.

The polynomial equations also tended towards one
single equation:
y = -0.0016x^3 + 0.09x^2 - 2.9x + 74
or, even more simply:
y = -0.002x^3 + 0.1x^2 - 3x + 74

I expect the other classes will all show this same
tendency. Do you all want one equation?  Five
equations?  Linear?  Polynomial?
I'd like to know what direction I should go before
crunching the rest of the number ;)

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