Here are the instructions for starting a match during Intermission. It’s pretty easy to get matches going—anyone can play for any faction, so it shouldn’t be hard finding Summoners.
Do remember: the captain (pick/bans person) of the winning team has the responsibility for sending in the results. They can either do it themselves or delegate. We’re keeping track of match results for a few reasons. For one thing, it lets us build an all-factions BoP that shows how all the various factions stack up against each other. It also gives us more data for balancing.
Intermission matches are a fun way to try different factions. It’ll also perhaps help introduce some new people to Factions: there’s no need to “sign up” before playing Intermission matches, so it’s easier to get started.
By the way, if you’d like to quickly check how balanced a given matchup is, you can use the winrate calculator to get an estimate. It uses the same database of matches that the BoP uses.