A Random Walk down FIBS Street ;-)

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Ed Rybak x84336

Sep 27, 1994, 6:35:54 PM9/27/94
A few weeks ago I became curious about the variability in FIBS ratings
that I was seeing among a number of players: for example, when I began
playing on FIBS, fatboy was in the low 1600's, climbed to the low 1700's,
fell to the high 1600's, rose to about 1770, and now is in the mid-to-low
1600's again. What kind of variability should one expect in one's FIBS
ratings based on chance?

This is important because so many of us base our estimation of improvement
on our FIBS ratings! And many of us have changed our play in frustration
over having lost the fourth or fifth match in a row? Can we really
measure our progress with our FIBS rating?

So I ran a series of Monte Carlo simulations using the FIBS ratings
formula. In the first series I had two players of equivalent skill
and FIBS ratings (1700) play one another 1000 5 point matches. I made
the assumption that the players skill remains constant whereas the
rating varies with the results of the match. The results were
fascinating: the ratings of the players varied tremendously often
changing by over a hundred points over a few hundred matches. I ran
100 simulations of 1000 5 point matches and the average minimum and
average maximum of the ratings were 1626 and 1780 respectively.

So a 1700 player, playing with no improvement/diminishment of skill,
can expect to see their rating fluctuate by plus or minus 80 points
in the course of play. Add in some variability due to fatigue, or
steaming, or "bathwater" adjustments to the skill level and it could
be even greater.

I ran a whole bunch of other simulations. One simulation asked: if I'm
a 1700 player (ranked and skilled) and I miraculously improved my play
(re: skill) by 100 points, how long before it will be reflected in my
rating? The average number of 5 point match required to reach the true
rating of 1800 was about 280.

The length of the match doesn't seem a difference. Nor does the true
rating of one's opponent...it's all adjusted for in the ratings formula.

One interesting result: the fastest way to improve one's rating is by
playing players that are overrated (i.e. those who's ratings are higher
than their skill). This assumes, of course, that you can differentiate
overrated players. I ran one simulation where you played only players
that were 50 points overrated; the simulations converged much more
quickly than a 100 point skill increase, allowing a 1700 skilled player
to be rated in the high 1800's. The only readily identifiable class
of overrated players is new players (statistically speaking) which
explains why they are played so readily by some ;-)

It appears to me that FIBS rating is not a very good indicator of skill
except in the broad sense. If I lose four matches in a row to players
of my level, I probably shouldn't adjust my game and I definitely
shouldn't lose my composure. I have taken to using other indicators:
matchquiz, analysis of my play, etc. to measure myself.

Ed Rybak
Sequent Computer Systems
15450 SW Koll Parkway
Beaverton, OR 97006
phone: (503) 578-4336
fax: (503) 578-3811


"You see, one thing is, I can live with doubt and uncertainty and not
knowing. I think it's much more interesting to live not knowing than to
have answers which might be wrong. I have approximate answers and
possible beliefs and different degrees of certainty about different things,
but I'm not absolutely sure of anything and there are many things I don't
know anything about..."

-Richard Feynman


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