Re: Doitsuyama's ratings after Haru 2000

[Alexander Nitschke <alexander.nitschke@ww.tu-berlin.de>]

TAKAYAMA Kazuhisa wrote:
> 
> >Here is the banzuke for next tournament as I would put it together
> >with the help of my ratings. The numbers are simply indicators of
> >their strength as it was in the past bashos. The higher the rating,
> >the better the rikishi with it; the higher a rating difference
> >between two rikishi is, the bigger is the probability of victory of
> >the higher rated rikishi.
> 
> How did you calculate about the numbers? What's the calculating
> formula?
> 
> ----
> TAKAYAMA Kazuhisa

The rating calculation for the new rating of a rikishi after a bout needs 
four parameters: 

1) The old rating of the rikishi (Ro)
2) The rating of the opponent (Rc)
3) The result of the bout (w)
4) The number of rated bouts of the rikishi ("experience") (Eo)

The new rating (Rn) and new experience (En) then calculates as follows:

Rn = Ro+800/Min(40;E/3+15)*(W-NormDist(Ro-Rc;0;286))
En = Eo + 1

The expected points (=probability of winning) are calculated with 
NormDist(Ro-Rc;0;286) where 0 is the mean and 286 the deviation of a 
normal distribution. (Btw, NormDist is an Excel function)

The change of the rating is dependent of the experience Eo. The greater
the experience the slower the change. At the first bout (Eo=0)the difference
between win and loss is about 53 points. This gets lower and lower. After 
75 bouts the Min-Function in the equation above kicks in and the experience 
Eo is not important anymore. Then the difference between win and loss is 
always 20 points (=800/40).

In the next bout this new rating will of course be the old rating again.

The start rating for new rikishi (meaning coming up from Makushita) is
always 1800. With this value the average rating of all sekitori tends
to be pretty stable over the years. The line between Juryo and Makuuchi
is almost constant at about 2000.

--
Alexander