$$\mathrm{RD}_{\text{new period}} = \sqrt{\mathrm{RD}_{\text{old}}^2 + c^2}$$

Equation 7 · 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.

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,” it is a specific number computed the same way every 24 hours for every account on the ladder. A brand-new Showdown account starts at RD = 130 — already at the…

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