Matchmaking Improvements

[crescendo-ss]

Matchmaking enhancements, with new configuration options are added to optimize team formation.

The matchmaking module can now optionally wait for more players to enter the queue (LookAheadWindow). For example, if the window size is 3, then the next 11 queued players (8 + 3) are chosen from for match formation. Subsets of 8 players are first chosen from the 11 players in the window, with an effort to make sure that the skill level of all players is near each other using Least Trimmed Squares (LTS) selection.

The best subsets (measured with the LTS metric, which minimizes big skill outliers) are then evaluated for team formation. Of the 8 players, we will attempt to create balanced teams from those (using the current snake approach, which I will probably switch out for something more comprehensive in the future).

Important notes from this example is that we chose from the 11 next players in the queue, and only 8 are selected. So three are excluded. The three that are excluded may have been at the head of the queue. To make sure that those three are less likely to be excluded in the next selection, we apply a skill-annealing approach where we will intentionally boost/adjust their skill so it's closer to the mean skill level of other players in the queue next time we match make. This boost/adjustment is proportional to the amount of games they've been skipped.

We additionally allow some players to set a preference that allows them to be avoid being matchmade into games where their skill level is significantly higher than the lowest skill level. Players use the ?matchmaking strict or ?matchmaking casual commands to enable or disable this.

// How many extra players to include when trying to form subsets
LookAheadWindow = 3
// How long we wait after getting 8 players to let into the subset candidates
LookAheadWaitSeconds = 60
// How much we boost/reduce very low/high ranked players to the average skill level whenever they're skipped
SkipNudgeRate = 0.2
// Max open skill ordinal difference that players can request that they won't be placed into games with
StrictMatchmakingMaxDisparity = 3.0