exp formulas

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

So, now that I have the saving throw formulas down,
and the THAC0s are no-brainers for converting to
formulas, I took at look at the exp tables.

First glance they might look exponential, and while
that is generally true at low levels, you lose it at
high levels.  Using a general power function yields
reasonable results, however.

cl:  22.479x^3.9437  R^2 = .9445
mu:  27.672x^3.9055  R^2 = .9415
th:  13.332x^3.0685  R^2 = .9632
wa:  26.869x^3.936   R^2 = .9406

Not great fits, but a lot better than the .6-ish
R^2s that an exponential function yields.  Linear
models are possible, but again the fits are lower
than the power functions.  Also they aren't as
interesting ;)

Simplified versions that are easier to use:
22.5x^4, 27.7x^4, 13.3x^3, 26.9x^4
This doesn't require the pow() function, but yields
slightly steeper exp curves for all but the thief.

Obvious consequences of this:  players will shoot
up through the low levels very quickly, but will take
longer to reach the higher levels than is currently
the case.

I'm not sure these functions are particularly
desirable, and something more along the lines of
Nic's exp patch is probably better:
(exp = GET_LEVEL(ch) * modifier * 4000).
While I'm not sure I like that system exactly as
written (no offense, but 4000?!), it is that type of
idea that should be used.

http://www.angelfire.com/nj/eglamkowski/null.html <- Null webring
http://www.angelfire.com/nj/eglamkowski/eia.html  <- EiA webring

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