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Gary Wong wrote:
> How do we convert between FIBS ratings and expected points per game?
> To the best of my knowledge this is an open question. However, here's
> a simple model. Assume 1-point matches are being played on FIBS.
> FIBS expects that between players ranked 94 +/- 34 points apart (as
> Chuck found JF 7 to be above JF 5), the favourite will win 52.7% +/-
> 1.0 of the games. If we assume this constant factor is also correct
> in money games, and assume a win in a money game is worth 2 points on
> average (see my other article for justification), then this 2.7% +/-
> 1.0 CPW is worth 0.108 +/- 0.04 points per game.
I looked at this a few months ago, but I used a much more complicated
model than Gary's. Instead of just going with the one point match
win percent, here is what I did:
- set a probability distribution for the points won for each player,
when they win. (for example: each player might win 1 point 38%,
2 points 38%, 4 points 20%, 6 points .5%, 8 points 2.5%,
and 16 points 1%)
- set a probability for how likely it is one player will beat the other.
- play a "long" match between these two players, assuming that the
results for each game will follow the money distribution until the
players get "close" to the end of the match.
- at this point, settle the match using a match equity table.
(An important refinement: use a skill-adjusted match equity table,
like those in _Can a Fish Taste Twice as Good_.)
- repeat this many times and determine overall match winning chances
for the two players
Based on the match winning chances, it is easy to get the rating
difference. Based on the probabilities you set, you have the money
points per game.
I did this for a lot of different probability distributions and
edges in probability of winning, along with a lot of different
definitions of "long" and "close" above.
The overall results are:
A rating difference of 40-50 points corresponds to about a .10ppg
money edge.
The key assumption is that play is like money until you get "close"
to the end of the match. This is pretty true most of the time.
When the score gets real lopsided, it's not. Also, there might be
some changes in the low frequency distributions (8-point and 16-point
wins) even fairly early in a match. I don't think this swings
much.
*Much* more important are many other factors. Some money players
don't play matches. And vice versa. Certain styles of play are
better suited to money or matches. And so forth. So this
result, even if valid, is *only an approximate rule of thumb*.
Data from my own real-life money play conforms to this rule. I think
I have about a 150 point rating edge over my average local opponent,
based on watch FIBS ratings go up and down, and my long-term money
result is about +.30ppg.
David Montgomery
monty@cs.umd.edu
monty on FIBS
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