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Equation 23 · A Showdown Ladder Rating Measures the Ladder, Not the Player

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R±2⋅RDR \pm 2 \cdot \mathrm{RD}

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RR

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multiplication

multiplication

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​ Rating deviation RD\mathrm{RD} , bounded to Showdown’s 25–130 range 95% interval: X ±\pm 1.96 ⋅\cdot SEM\mathrm{SEM} 95% interval: R ±\pm 2 ⋅\cdot RD\mathrm{RD} [ 3 ] Reliability rises with more independent items RD falls with more games played in a period [ 2 ] Reliability falls with time since calibration RD rises with time since the player’s last game [ 3 ] 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…
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​ Rating deviation RD\mathrm{RD} , bounded to Showdown’s 25–130 range 95% interval: X ±\pm 1.96 ⋅\cdot SEM\mathrm{SEM} 95% interval: R ±\pm 2 ⋅\cdot RD\mathrm{RD} [ 3 ] Reliability rises with more independent items RD falls with more games played in a period [ 2 ] Reliability falls with time since calibration RD rises with time since the player’s last game [ 3 ] 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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