rating calculation
Sheldon Richter
I really do not understand the ratings calculations.
I thought that the ratings would change more for
longer matches, and less for shorter matches.
Can anyone please explain the logic of the following:
rating calculation:
rating difference D=1190.934235
match length N=64
Experience: magic_one 6961 - wes 7871
Probability that underdog wins: Pu=1/(10^(D*sqrt(N)/2000)+1)=0.000017
P=0.000017 is 1-Pu if underdog wins and Pu if favorite wins
K=max(1 , -Experience/100+5) for magic_one: 1.000000
change for magic_one: 4*K*sqrt(N)*P=0.000551
K=max(1 , -Experience/100+5) for wes: 1.000000
change for wes: -4*K*sqrt(N)*P=-0.000551
rating calculation:
rating difference D=1187.363751
match length N=3
Experience: magic_one 6967 - wes 7874
Probability that underdog wins: Pu=1/(10^(D*sqrt(N)/2000)+1)=0.085668
P=0.085668 is 1-Pu if underdog wins and Pu if favorite wins
K=max(1 , -Experience/100+5) for magic_one: 1.000000
change for magic_one: 4*K*sqrt(N)*P=0.593523
K=max(1 , -Experience/100+5) for wes: 1.000000
change for wes: -4*K*sqrt(N)*P=-0.593523
--
Please e-mail me at the address above or sric...@capaccess.org
Ron Karr
The theory is: in a longer match, the lower-ranked player is less likely
to win than in a shorter match. The points awarded to the favorite, if
he wins, are proportional to this probability. It's also proportional to
the square root of the match length. In most cases, the favorite will
get more points for winning longer matches; it's just that the amount
increases less than linearly as the match length increases.
This is a very odd case, where the ratings difference is unusually huge
(and wes is known as a player who deliberately throws matches). So in a
64-point match, the odds of the "underdog" winning are calculated as
infinitesimal, so the favorite will not get very many points for winning
the match. (If wes had won, he would have gotten a ton of points.) In
the 3 point match, the favorite "only" has an 85% chance of winning, so
even though the match is shorter, he gets more points for winning.
Technically, this could be considered a "flaw" in the ratings formula,
but in reality I wouldn't even try to have the formula be accurate in the
ridiculous case of an 1190-point ratings difference between players.
It's more important to be accurate in the normal cases of a few hundred
points difference.
Ron
Ron
Lou Poppler
On 26 May 1996 17:58:58 GMT, Ron Karr (ka...@best.com) wrote:
: ric...@uspto.gov (Sheldon Richter) wrote:
: >
: >rating calculation:
: >rating difference D=1190.934235
: >match length N=64
: >Experience: magic_one 6961 - wes 7871
: >Probability that underdog wins: Pu=1/(10^(D*sqrt(N)/2000)+1)=0.000017
: >P=0.000017 is 1-Pu if underdog wins and Pu if favorite wins
: >K=max(1 , -Experience/100+5) for magic_one: 1.000000
: >change for magic_one: 4*K*sqrt(N)*P=0.000551
: >K=max(1 , -Experience/100+5) for wes: 1.000000
: >change for wes: -4*K*sqrt(N)*P=-0.000551
: 64-point match, the odds of the "underdog" winning are calculated as
: the match. (If wes had won, he would have gotten a ton of points.) In
If we change P to equal 1-Pu above (as though wes had won), then
P=0.999983. This makes 4*K*sqrt(N)*P = 4*1*8*0.999983 = 31.999456 points.
A tidy sum certainly, but I don't know if it's a ton....
-- Spider
Sheldon Richter
Sheldon Richter (ric...@uspto.gov) wrote:
: I really do not understand the ratings calculations.
: I thought that the ratings would change more for
: longer matches, and less for shorter matches.
: Can anyone please explain the logic of the following:
: rating calculation:
: rating difference D=1190.934235
: match length N=64
: Experience: magic_one 6961 - wes 7871
: Probability that underdog wins: Pu=1/(10^(D*sqrt(N)/2000)+1)=0.000017
: P=0.000017 is 1-Pu if underdog wins and Pu if favorite wins
: K=max(1 , -Experience/100+5) for magic_one: 1.000000
: change for magic_one: 4*K*sqrt(N)*P=0.000551
: K=max(1 , -Experience/100+5) for wes: 1.000000
: change for wes: -4*K*sqrt(N)*P=-0.000551
: rating calculation:
: rating difference D=1187.363751
: match length N=3
: Experience: magic_one 6967 - wes 7874
: Probability that underdog wins: Pu=1/(10^(D*sqrt(N)/2000)+1)=0.085668
: P=0.085668 is 1-Pu if underdog wins and Pu if favorite wins
: K=max(1 , -Experience/100+5) for magic_one: 1.000000
: change for magic_one: 4*K*sqrt(N)*P=0.593523
: K=max(1 , -Experience/100+5) for wes: 1.000000
: change for wes: -4*K*sqrt(N)*P=-0.593523
: --
> The theory is: in a longer match, the lower-ranked player is less likely
> to win than in a shorter match. The points awarded to the favorite, if
> he wins, are proportional to this probability. It's also proportional to
> the square root of the match length. In most cases, the favorite will
> get more points for winning longer matches; it's just that the amount
> increases less than linearly as the match length increases.
>
> This is a very odd case, where the ratings difference is unusually huge
> (and wes is known as a player who deliberately throws matches). So in a
> 64-point match, the odds of the "underdog" winning are calculated as
> infinitesimal, so the favorite will not get very many points for winning
> the match. (If wes had won, he would have gotten a ton of points.) In
> the 3 point match, the favorite "only" has an 85% chance of winning, so
> even though the match is shorter, he gets more points for winning.
>
> Technically, this could be considered a "flaw" in the ratings formula,
> but in reality I wouldn't even try to have the formula be accurate in the
> ridiculous case of an 1190-point ratings difference between players.
> It's more important to be accurate in the normal cases of a few hundred
> points difference.
>
> Ron
>
So, if the ratings difference were less, say for example a few hundred
points, then the winner, even if (s)he were the favorite; more points
would be rewarded for winning a 64 point match, than a 3 point match, but
the factor would not be 64/3, but only 8/square root of 3??? I understand
that the factor is proportional to the square root of the match length.
However, I was not expecting a linear relationship. I only expected
a direct relationship. I did not expect an inverse relationship.