Equation 6 · Part 1 · A Showdown Ladder Rating Measures the Ladder, Not the Player

Symbol j

j

j

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j is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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j is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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The passage around this formula

where $d^2$ is a variance term built from the same g( $\mathrm{RD}_j$ ) and expected-score factors, $s_j$ $\in$ \{0, 0.5, 1\} is the outcome of game j , and between rating periods the deviation itself grows on a fixed schedule, $\mathrm{RD}_{\text{new period}}$ = $\sqrt{\mathrm{RD}_{\text{old}}^2 + c^2}$ , clamped to Showdown’s own configured ceiling of 130 rather than Glickman’s generic default ceiling of 350 [ 2 , 3 ] . Substitute Showdown’s…

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