Equation 20 · A Showdown Ladder Rating Measures the Ladder, Not the Player
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Glickman’s RD is this same object, derived from a different starting assumption but converging on an identical use. He states the correspondence in his own words, not as an analogy this article is imposing on his work: a Glicko rating and RD together are “usually more informative to summarize a player’s strength in the form of an interval… report a 95% confidence interval. The lowest value in the interval is the player’s rating minus twice the RD, and the highest value is the player’s rating plus twice the RD” [ 3 ] . Line up the two constructions and the correspondence is not loose: . This is the article’s original contribution: not the observation that a rating has…
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Glickman’s RD is this same object, derived from a different starting assumption but converging on an identical use. He states the correspondence in his own words, not as an analogy this article is imposing on his work: a Glicko rating and RD together are “usually more informative to summarize a player’s strength in the form of an interval… report a 95% confidence interval. The lowest value in the interval is the player’s rating minus twice the RD, and the highest value is the player’s rating plus twice the RD” [ 3 ] . Line up the two constructions and the correspondence is not loose: . This is the article’s original contribution: not the observation that a rating has “uncertainty,” which anyone who has seen a percentage sign after a GXE could guess, but the derivation that Showdown’s published RD update schedule is doing formally, on Glickman’s own stated terms, exactly the job Novick’s 1966 axioms assign to a standard error of measurement — no metaphor, no rounding of two different ideas into looking alike, one construction restated in the other’s notation.
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