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

Equation 2 · Pokémon Formal Measurement

A Showdown Ladder Rating Measures the Ladder, Not the Player

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

​ 1 ​ , q = 400 ln 10 ​ ≈ 0.0057565 r' = r + $\frac{q}{1/\mathrm{RD}^2 + 1/d^2}$ $\sum_{j=1}^{m}$ g($\mathrm{RD}_j$)$\left(s_j - E(s \mid r, r_j, \mathrm{RD}_j)\right)$ 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 published c = 6.6775026092 and the schedule is fully determined: it is not a metaphorical “uncertainty,”…

Meanings in this article

• $d^2$: a variance term built from the same g($\mathrm{RD}_j$) and expected-score factors, $s_j$ $\in$ \{0, 0.

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