Chess One wrote:

"Wlodzimierz Holsztynski (Wlod)" wrote in message
ups.com...

Thanks for offering to sample a range - my suggestion are maybe not the best
ones [too close together?] and maybe better to take 1000, 1200, 1500, 1500,
1700 and 2,000 as sample players. Your comments on new player
intedeterminate strength / fluctations, noted.

Phil, Elo at least got the translation invasriance,
meaning that the expected result of a match
depends only on the difference of the Elo ratings
of the two players and not on the ratings as such.

Thus if you are interested in the 100pt difference
or 200pt or 300pt difference... and if someone
will tell me the predicted match result then I can
tell you how fast the Ockham ratings will converge
from the initial ratings, which perhaps do not reflect
their relative strength properly, to the relatively
proper ratings when the two play a match.

Now, let someone try to do it for Elo :-) :-)
They would have to run a simulation :-)

I think that Elo would be extremely happy if he got
not just the translation invariance but also additivity
(which is equivalent to the multiplicativity). He would
do it if he knew how.

***

In the scientific applications (to economy etc)
the multiplicativity is actually called **consistency**
(not transitivity, as I said earlier).

***

Regards,

Wlod