The FUMBBL Coach Rating is based on the Glicko-2 system (direct link to the paper), with a few modifications.

This page is not intended to fully explain the Glicko-2 system, and you should refer to the paper linked above for full details. Instead, this page describes the changes and the configuration used on FUMBBL.

Core configuration:

Tau = 0.2
Initial sigma = 0.15
Initial r = 1500
Initial RD = 150

The following modifications and adjustments have been made:

RD is capped to a maximum of the initial RD (150).
The rating period is set to 7 days.

The E formula (Step 3 in the paper) is adjusted to include a CTV factor, which I call rho (added part bolded):

E(mu, mu_j, phi_j, rho) = 1.0 / (1.0 + exp(-g(phi_j)*(mu - mu_j + rho)))

rho = (-4 * g(phi_j) + 5.5) / (1 + exp(delta_CTV / 200000)) - (-4 * g(phi_j) + 5.5) / 2;

To add an element of rating decay, the rating used to compare and rank coaches is based on both the direct rating r' and the rating deviation RD' as follows:

CR = r' - 5 * Max(RD' - 100, 0)