Technical Annex 9 - Replace tables by formulas in FMJD rating system

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clp
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Real name: Kees Pippel
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Technical Annex 9 - Replace tables by formulas in FMJD rating system

Post by clp » Thu Feb 03, 2022 17:50

Today computations are carried out by software. Therefore replace tables by formulas.

In Annex 9 2. General Principles, page 76 replace:
table [IX-1]Conversion table from the result in percentage P to the rating difference D (P)

by the logit function with base sqrt(10):

D(P) = log(P/(1-P)) * 2C / log(10), for percentage score P in interval (0, 1), class interval C = 200.

In Annex 9 – FMJD rating system and its application rules, page 87, replace:
table [IX-2] Expected percentage as function of the rating difference

by the logistic/Verhulst distribution with base sqrt(10):

P(D) = 1 / (1 + 10^(-D/2C)), for rating point difference D, class interval 200.

Bronnen
Mark E. Glickman, Introductory note to 1928, url = http://www.glicko.net/research/preface-z28.pdf.
Arpad E. Elo, The Rating of Chessplayers, chapter 8.4 Logistic Probability as a Ratings Basis, p141-143, New York, 1978.

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