| George John 2005-04-07, 6:08 pm |
| Angelo De Pa1ma wrote:
Angelo,
quote:
> I was recently browsing the MSA and noticed that one of my buddies in
quote:
> Hackettstown had recently gained 52 rating points in a quad (not run
at the
quote:
> H'town club). This fellow had a performance rating (PR) of 2194 over
3 games
quote:
> (2.5/3), which is pretty decent for a 1789 player but jeez, it's only
3
quote:
> games. His PR was 405 points above his pre-tournament rating.
The actual opponents' post-event ratings are necessary to correctly
compute the rating change. Many combinations can result in a 2194 PF,
but they will not all result in the same rating change (see below).
quote:
> I then visited my own MSA page and looked up my result from the
USATE. My PR
quote:
> over five played games (4.5/5) was s a healthy 2303 but I "only"
gained 41
quote:
> points, from 1853 to 1894. My PR was about 450 points higher than my
> pre-tournament rating.
Using post-event ratings, I get a PR of 2300, and a new rating of 1895.
[Note: MSA shows 1894. I don't know why there is a difference of 1
point. One reason why is MSA does not round away. My rating
calculator does. Another possible reason is MSA uses non-rounded
post-event ratings, and defers rounding until later].
quote:
> I thought the discrepancy -- +450 over five games with a 41 point
gain, vs.
quote:
> +405 over 3 games and a 49 point gain -- was odd so I did a little
> experiment.
>
> I plugged 2303 (my PR from the USATE) into five of the opponent
rating boxes
quote:
> in the rating calculator, 1853 (my pre-USATE rating) into the
"current
quote:
> rating" box, and 2.5/5 as my score. Of course I get the same 2303 PR
but
quote:
> instead of 1894 my "new rating" is 1920, a nearly 30-point increase
over the
quote:
> same 2303 performance achieved with a range of opponent ratings.
>
> Can anyone explain why and how this can happen? I always thought
equal PRs
quote:
> were, well, equal. Are some PRs more equal than others?
Rating changes are not based on PR (although they do correlate to some
degree of course). Rating changes are based on the difference between
expected score and actual score multiplied by the K Factor + Bonus.
Especially important is the fact the expected score function is
non-linear.
For example:
Using ratings of 1680, 2068, 1201, 1556, and 2108,
Your expected score was 2.96624, actual score 4.5 (the bye is ignored),
K is 20.68, and bonus threshhold 23.36
Your raw rating change is 20.68 * ( 4.5 - 2.96624 ) = 31.7181
Bonus is 31.7182 - 22.3607 = 9.3574
Total rating change = 41.0755 or 42 (the rating system rounds away, or
so I was told).
New rating is 1853 + 42 = 1895 (or 1894 if you don't round away, but
round normally).
Now try this with 5, 2300 rating players.
The expected score is .354436, actual score 2.5
The raw rating change is 20.68 * ( 2.5 - .354436 ) = 44.3703
Bonus is 44.3703 - 22.3607 = 22.0096
Total rating change = 66.3798 or 67
New rating is 1920.
That's a difference of +25.
quote:
> Please don't say the calculator is only approximate
I won't. -smile- Actually, the calculator should be very close to
exact (if it's not, I need to be notified of that fact), but it's only
as good as the data given to it.
quote:
> because it's predicted
> our club members' ratings to within 1-2 points every time I've used
it.
quote:
> Besides, the calculator quirks don't explain my basic scenario since
these
quote:
> are actual, USCF-calculated ratings.
I hope this makes some sense. I left out the computation of expected
score. If you would like to see that, I would be glad to add it.
Best regards,
George John
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