Equation 2 · Part 18 · A Showdown Ladder Rating Measures the Ladder, Not the Player

Starting index or lower bound: j=1

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=1

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

j=1 appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Full expressionStarting index or lower bound: j=1Article meaning

The passage around this formula

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,”…

Read this part in the article →

Learn the underlying idea

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

Open the illustrated sums and products: repeat an operation over an index guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.