You're calibrating smurfs. What happens is the system wants to place us higher if we show the potential but it no longer can put us past 3500 so it just gives you a higher medal (something is obviously wrong with the algorithm) and the cap of mmr.
I calibrated this account at exactly 3500 and I got Legend 4 which is supposed to be near 4k mmr. Out of the 100 games of Normal I had to do before I could rank, Over 85 of those 100 were Immortal level games (Over 200 immortal players encountered total ranging from top 1,000 to top 50). The system was trying to recognize where I really should be (way higher), but the hard cap kicks in during your calibration process. I think the game somehow STILL has your old "medal" even though it was hidden due to evaluation and that's why new smurfs can end up with legend medals higher than their actual mmr.
Both of you calibrating in low 3k but with legend 3 are simply experiencing what I described in my post, except you're both a much lesser degree of that in the system than I am on this account. Not maxing at 3500 and only a barely slightly higher medal than normal for that mmr rating means your smurfing difference is not very much above 3k.
Its not broken, it just has inaccuracy this early on in an account's life because of the stupid hard cap being enforced.
Response to the Not-Even-Divine-Level retard posting just below this,
Hey, go learn basics on how the system works before commenting because nobody who knows anything would say what you just did.
Where did the info that you can only calibrate at 3500 come from? I calibrated both times around 4k
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I made a smurf account and gave a shot to see if I stand a high rank after learning some lessons from youtube. I got Legend 3* at solo mmr and my solo mmr is 3160. I expected Archon 4* according to this list https://dota2.gamepedia.com/Matchmaking/Seasonal_Rankings but this is weird. Here is my account : https://www.dotabuff.com/players/883663437
Did they changed something? I mean my friend re-calibrated at Legend 1* with 3.4k mmr. (original account)
I don't know if this might help but my old account had Archon 1* (party mmr - 2.5k, solo mmr - 2k)