Ange1o DePa1ma wrote:
"Kenneth Sloan" wrote

Sloan may be right that the scale is arbitrary, and we may employ
negative numbers, fractions, or even imaginary numbers if we like. We can
make an average rating zero instead of 1500.
Wherever did you get that the average rating was 1500?
Have you been talking to Dubeck?

Jesus, Ken, I was just picking a number out of my hat. 1200. Whatever.


The point is: the "average rating" is not an interesting concept when
specifying the rating system. It depends more on the demographics (who
chooses to play in your system) than on anything else.

The reason I complained is that there *are* people out there who believe
that the rating system is designed to produce a specific "average
rating" (and surprisingly many of these people think that the magic
number is 1500).


I get the point. I'm not sure if it's mathematically relevant if you simply
define a know-nothing rating as zero.

It may be 'relevant' - but if so, it's flat out wrong!

In any Elo-based system, the only "correct" rating for a player who
truly knows nothing is: -infinity.

I'm not sure what the system gains by
going into negative numbers because as soon as you score 1/2 a point out of
100 games against players rated ELO 100, you have a positive rating. It may
be closer to zero than to one, but it is positive.

that's not correct. If you score 0.5-99.5 against 0100 opposition, your
proper Elo rating is most definitely NOT positive. Do the math.

But, at least it's no longer -infinity!

Remember - what matters is the rating DIFFERENCE between you and all
those 0100 players who are beating up on you. What rating DIFFERENCE
predicts a score of 99.5-0.5 (look it up!). Your new rating after going
0.5-99.5 against 0100 competition is 0100-thatDifference. Which, I
assure you, is a negative number.

Why, exactly, do you think that your rating would be greater than 0000
after that performance? Because USCF has an Absolute Floor of 0100?
That's an administrative twiddle (mostly meant to pacify innumerate folk
who believe that ratings must be positive).




USCF does not assign negative ratings (even though some players earned
them) - but only because the politicians think that innumerate Americans
can't handle the complication of the '-' sign. Alas, they are probably
right. One need only read this thread to see that innumeracy reigns.

Americans' stupidity re math notwithstanding, there is no practical reason
for a negative rating.

Do you know the real reason that the USCF minimum rating is 0100, and
not 0000?

You wouldn't believe me if I told you - it's too silly for words.

In any event, there is indeed a "practical reason for a negative
rating". That reason is: the negative rating more accuratly predicts
the future performance of that player (e.g., that player will score 0.5
out of 100 against 0100 competition).

USCF has decided that this valid reason is counterbalanced by other
reasons (that's how you run a real system - you end up compromising).
But...you'd really laugh if you heard the *real* reason that the minimum
USCF rating is 0100.

HINT: it's closely related to the reason that the minimum USCF rating
used to be (many years ago) 1000.






--
Kenneth Sloan
Computer and Information Sciences +1-205-932-2213
University of Alabama at Birmingham FAX +1-205-934-5473
Birmingham, AL 35294-1170 http://www.cis.uab.edu/sloan/