While we do want to keep track of join and ready times, we really don't
care about those stats for players who join the lobby _and leave_ prior
to the arena actually starting.
Coincidentally, _not_ storing stats for players that don't actually pick
a class means we don't end up trying to insert a `null` value into the
class name column, which should solve the error thrown when trying to do
just that as a result of the auto-start timer kicking players or players
themselves leaving prior to starting.
Fixes#16