Author: Ricardo Gibert
Date: 19:48:22 08/28/00
Go up one level in this thread
On August 28, 2000 at 16:32:46, Peter Skinner wrote:
>In comparing a PIII 450 vs let's say an Athlon 750, what would the expected game
>win/loss % be for the PIII 450.
>
>For testing purposes, let's say we are using Crafty.
>
>Would the 450 get absolutely killed?
To compute the effective rating difference between 2 machines with speeds S1 &
s2:
Rd = 72*ln(s1/s2)
The constant 72 assumes that a doubling of speed is worth about 50 rating
points. If you don't like that, the constant (C) can recomputed with:
C = R2/ln(2)
where R2 is equal to the expected rating difference for each doubling of speed.
The following table gives a different C for each different values of R2:
R2 C
-------
30 43
40 58
50 72
60 87
70 101
80 115
Now the win expectation (We) can be calculated with:
We = 1/(1 + 10^(-Rd/400))
Where ^ denotes exponentiation, e.g. x^y is equal to x to the yth power.
Using your example:
Rd = 72*ln(750/450) = 37
We = 1/(1 + 10^(-37/400)) = .55 or 55%
so the winning expectation of the 750 Athlon over the 450 PIII is about 55%.
Despite the large difference in speed, they should remain fairly competitive,
which is contrary to what most people would assume. I've assumed that an Athlon
is equivalent to an PIII at the same clock speed.
One thing that could throw things off is, since you are using the same program,
a "I know what you are thinking" type of situation is present. The faster Crafty
version sees _everything_ that the slower Crafty version sees plus more by
virtue of its speed advantage. This is different from the situation of comparing
2 different programs of the same strength. I don't have any experience in this
type of comparison where a significant differential in speed is present. Perhaps
someone else can be more enlightening.
The other problem affecting the above is the rating system was not intended for
comparing one individual with another individual. Ratings are a measure of one
individuals _past_ performance against a _population_ of players.
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