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BGonline.org Forums
The FIBS rating formula : why sqrt(n) ?
Posted By: Daniel Murphy In Response To: The FIBS rating formula : why sqrt(n) ? (Fabrice Liardet)
Date: Thursday, 15 September 2011, at 4:42 a.m.
You've had some fine responses here. In the link Michael gave, I thought Billings' and Kring's comments worth reading among others, besides Trice's. Also, there must be a lot of other discussions about this topic elsewhere in r.g.bg -- look there and at bkgm.com before reinventing the wheel. Also, the problem with 1-point matches is well known and often discussed, as has the way the formula treats short (i.e. 1-point) matches vs. long matches. Finally, Rich's mention of "range of common match lengths" deserves a highlight -- face to face backgammon match lengths are 5 points to (rarely more than) 17 points, so that's the range a formula needs to be faithful to, for face to face play.
@Jake, on FIBS the formula has not changed. I believe the Grid used the FIBS formula at the start, but changed it, perhaps in 2002, to treat 2-point matches as if they were 1-point matches. I believe the exact GG formula was available on their website for a while (not when it started, and it was later removed, but I remember that Richard McIntosh did a write-up explaining the formula in detail). According to this 2002 r.g.bg comment by Douglas Zare: "On GamesGrid, the rating system now treats 2-point matches the same as 1-point matches for the purposes of deciding by how much one should be the favorite and the rating points at stake. Both are given roughly the value of a FIBS 1-point match. I think both should be given the values that the FIBS formula gives a 2-point match."
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