The problem with your edit how do you do that when you have 2 lighthouse vets and one newbie or 2 newbies and 1 lighthouse vet?
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Well, if the Fireteam was rated on a simple system of having gone Flawless, and each fireteam member that has gone Flawless is +1 to a group rank, then there would be 4 grades of Fireteam; Rank 0 Fireteams of 0 vs 0 (nobody on either team has gone Flawless), 1 vs 1 (one member on each team has gone Flawless), then 2 vs 2, and finally Rank 3 Fireteams of 3 vs 3. Then, the system just needs to prefer matching like rank to like rank.