I am a player with a mean skill of 30 and a skill variance σ2 of 4 but my friend is only a player with a mean skill of 10 and a skill variance σ2 of 2. If we play as a party, what people will we be matched with?
If you play as a party, the mean skill of every party member will be the average of all the mean skills and the skill variance is the average of the skill variances of all party members. Thus, for the purpose of matchmaking only, your mean skill will be 20 and your skill variance will be 3; the same is true for your friend. Hence, together you make a team of skill 40 = 2 * 20 with a joint skill variance of 6 = 4 + 2. But, when you finish a game the update will use your actual mean skill and skill variance; thus, your mean skill will grow/shrink faster (why?) depending on the outcome of the game.
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