| George John 2005-04-11, 5:59 pm |
| Angelo De Pa1ma wrote:
Angelo,
quote:
> Ahhh, I get it now.
>
> Performance rating doesn't enter this calculation in any shape,
manner, or
quote:
> form.
Bingo! Correct!
quote:
> Since the expectation curve is not linear you can't get an
expectation
quote:
> for the event by averaging the ratings, then looking up the
expectation for
quote:
> that "game". Instead, you must calculate the expectations
individually.
Correct!
[SNIP]
quote:
>
> Now my question is, what is the philosophic/mathematical basis for
*not*
quote:
> normalizing average opponent ratings during a tournament as in my
fantasy
quote:
> formula? Just curious.
Looking at it from the POV of what impact each rating point difference
has, I think the idea behind this is the results of games become
increasingly less significant, proportionately speaking, as the rating
differences grow greater. IOW, as rating differences change it becomes
more uncertain what the result of that game means relative to 'true'
rating strength. If a player starts losing a lot to players rated
exactly the same, that means quite a bit more than if they lose to
players rated 400 points higher, and a whole lot more than if they are
losing to players rated 800 points higher (as examples).
And, while it is true a player does lose more points as they lose to
players with increasingly lower ratings, the incremental impact
decreases for each additional increase in rating differences. For
example, the number of points lost to losing to a player rated 800
points less is not much more than against one rated 400 points less.
The largest incremental difference in rating change is between someone
your own rating and one rated one point less.
You provided a good example when you said that scoring 4.5 against your
opponents was much easier than scoring 2.5 against 5, 2300 rated
opponents. Five games played by only 2300 rated players have more
significance (rating-wise) than games played with significant rating
differences like the ones you played. So, your 2300 result has
correspondingly less 'meaning' WRT to adjusting your rating.
I hope this helps more than hurts your understand. ;-) I'm not a
statistician, so please consider this a layman's perspective.
BTW, another quick tip on the rating system which you may or may not
already know, the expected score formula is calibrated on differences
of 400. For example:
Rating Difference, Expected Score
-1200, 1.0 out of 1001 games
-800, 1.0 out of 101 games
-400, 1.0 out of 11 games
0, 1.0 out of 2 games
400, 10.0 out of 11 games
800, 100.0 out of 101 games
1200, 1000.0 out of 1001 games
Best regards,
[SNIP]
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