Equation 2 · Part 4 · A Showdown Ladder Rating Measures the Ladder, Not the Player

Symbol j

r' = r + \frac{q}{1/\mathrm{RD}^2 + 1/d^2} \sum_{j=1}^{m} g(\mathrm{RD}_j)\left(s_j - E(s \mid r, r_j, \mathrm{RD}_j)\right)

j

What this part means

j appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Its job in the formula

j appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Full expressionSymbol jArticle meaning

The passage around this formula

… $\sum_{j=1}^{m}$ g( $\mathrm{RD}_j$ ) $\left(s_j - E(s \mid r, r_j, \mathrm{RD}_j)\right)$ 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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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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