Why do you have to play placement matches still?
I play this game since 2010 and I guess there is enough information available to pretty sharply determine my skill level in all matchups.
Instead there should be a general skill level for each player that applies to all games. That way playing fixed team games with alternating members would make sense.
What makes no sense is to play placement matches again and again in 3v3 and 4v4 whenever just one player switches.
1v1 skill decisive for all game types 100% 1v1, 50% 2v2, 33% 3v3, 25% 4v4
2v2 skill decisive for 2v2 50%, 3v3 33%, 4v4 25%
3v3 skill decisive for 3v3 33%, 4v4 25%
4v4 skill decisive for 4v4 25%
if no information available, fill gaps with higher priority available information or then make him play placements.
Example:
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Player has only played 2v2 yet and now starts to play 1v1: He has to play placement matches.
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Player has only played 1v1 and 2v2 yet and now wants to play 4v4
his 4v4 rank is determined by 25% 1v1, 25% 2v2, 25% 1v1 (as 3v3 is gap), and 25% 1v1 (as 4v4 is gap)
alternative a: create priority to fill gaps in this relation:
1v1 = 100 + 50 + 33 +25 = 208
2v2 = 50 + 33 +25 108
3v3 = 33 + 25 = 58
4v4 = 25 = 25
alternative b: delete gaps
alternative c: use β with gaps.
And so on, it is pretty easy for little above average brain to figure all situations out and implement them. It will be maybe 200 to 500 situations. Put 3 developers on it to rewrite the matchmaking. 3 monthes should be enough to have 80% result. Rest can be added in time after step by step.
As well as implementing decay for inactivity and new player implementation and all that. Be creative. Create a penalty for players found to abuse the new system until you reach the required level of quality.
Go figure it out blizzard and stop sucking.