| George John 2005-04-11, 5:59 pm |
| Mike Nolan wrote:
Mike,
[SNIP]
quote:
> I believe the non-linearity of the expected results function (a bell
curve)
quote:
> goes all the way back to the Elo formulative work, it's just that
earlier
quote:
> versions of the ratings software (prior to 2000) tended to use a
linear
quote:
> approximation of the formula because it was easier to program.
For non-provisional players, the calculation of 'expected score' did
not change. The formula remained We = 1/(1 + 10^(([opponent
rating]-[player rating])/400). Note: We = 'expected score'
What did change is the calculation of K which in the previous system
was linear within three bands (100-2100, 2100-2400, and 2400+.
Interpolation was used when ratings crossed 2100 and 2400). As you
have already pointed out, in the new system K is a function of rating
and/or number of prior games played).
One reason I mention this is because of complaints about how the old
system allowed accurate calculation of rating change estimates by hand.
How many people can calculate 'We' (see above) by hand?! ;-) OTOH,
there was a linear approximation that was good enough in many cases.
Now, I recommend people use
http://georgejohn.bcentralhost.com/tca/ktable.htm.
quote:
> Having spent several weeks in January making sure the new programming
came
quote:
> up with the same results as the old programming, the linear
approxmation
quote:
> has to have been much easier to program.
I guess it would have, if a linear approximation had been in use, but
it wasn't. BTW, I prefer the new method of computing K because it
doesn't have to deal with discontinuities, and therefore avoids
interpolations.
[SNIP]
Best regards,
George John
|