What does this equation mean?

The mechanism is two coupled numbers, not one. A player’s rating R changes only from game outcomes; the rating deviation RD changes from game outcomes and from the simple passage of time — RD shrinks as a player competes and grows as a player sits idle, because “the more games played, the more information is learned about a player’s ability… as time passes, we become more uncertain about the player’s strength” [ 3 ] . The update equations, stated with Showdown’s own configured constants substituted in, are $g(\mathrm{RD}) = \frac{1}{\sqrt{1 + 3q^2 \mathrm{RD}^2 / \pi^2}}, \qquad q = \frac{\ln 10}{400} \approx 0.0057565$. 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 top of Showdown’s own configured uncertainty range, since that range tops out exactly where the starting value sits — which is the algorithm’s honest way of stating that it knows nothing about a new player yet, before either the player or their opponents log a single result.