Probably 3000
Heard alot of good players that tried to calibrate as low as possible with feeding on all 10 calibration games still ends up on 3000ish
So even if your in very high skill? Is it possible to calirate less than 3.7 k??
I would Imagine the lowest possible MMR would around the 2700 Range. VHS bracket starts at 3700, In my experience (3-4 smurf account calibrations) calibration generally works as a +/- 100MMR depending on whether or not you won the game. Therefore 3700 -1000 MMR (10 lost calibration games) = 2700.
However Id imagine there is some sort of standard deviation of your unranked MMR as well as some sort of performance indicator factored in for each of your calibration games that prevents you from either loosing 10 games unfairly or being carried in 10. So perhaps it is more like 3000 MMR.
Thank you @trollpigeon
Some says that you better played more than required games b4 solo ranked can be qued to avoid bigger deviation:)
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SURVERY : Lowest calibrated mmr in very high skill bracket?