Improve Coaching Efficiency

[uberfastman]

Currently coaching efficiency is calculated by taking your total score and dividing it by your optimal score, giving you a percentage rating for how close to picking the correct players to sit/start you were. However, this metric can be both gamed (picking up backup players who play or suit up but don't play much or at all), and is not robust against later weeks when lots of players are on bye or are injured.

As such, thought has gone into the appropriate way to improve this metric. The current working plan is to use joint probability calculations, such that we calculate n choose k for each starting lineup position (one QB slots w/3 QBs on the roster -> 3c1), and then multiplying that by each other starting lineup probability to get the joint probability of correctly picking an entire perfect lineup.

Additionally, in order to translate these probabilities into a usable ranking, some sort of weighting based on combining how close your selected position player's points were to the best points possible at that position and the probability of correctly selecting that player for that slot could be used to create a cumulative score.

Alternatively, the full joint probability could be combined with your actual points divided by optimal in some way to weight your coaching efficiency percentage by how hard it was to actually get that percentage.

This is an open issue, and will hopefully eventually result in a reliably robust coaching efficiency metric.