UCCOM FIFA

Everyone starts at \(R_0 = 1000\). Before a game, player \(A\)’s expected score against \(B\) is

$$E_A = \frac{1}{1 + 10^{(R_B - R_A)/400}}, \qquad E_B = 1 - E_A$$

With actual score \(S_A \in \{1, \tfrac12, 0\}\) for a win, draw or loss, \(K = 40\), and rounding to the nearest 2:

$$\Delta_A = 2\cdot\operatorname{round}\!\left(\frac{K\,(S_A - E_A)}{2}\right), \qquad R_A' = R_A + \Delta_A, \qquad R_B' = R_B - \Delta_A$$

So drawing someone better than you still gains points, and an upset win is worth more. The margin doesn’t change the rating, and total points are conserved.

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