To state the validity of my answer, some small facts about myself:
- I have almost 3k hours of Dota 2.
- I have been playing Dota 2 since 10/2011.
- I have a solo MMR of 3900.
- I often watch alot of tournaments, pro streams and other stuff about dota.
Now for your question:
When Valve introduced the Ranked Matchmaking system they released a blog post about what they were using to establish the rank of each player which can be found here.
They count in all games you've played until you entered the ranked matchmaking for the first time (in my case that was like 1000 normal games) and add to that the 10 calibration games (which are valued equally to the previous games, so in my case had close to zero relevance on my solo MMR). Even before you have an official matchmaking rating you will have an unofficial one for your normal games (what you suspected).
So let's say you played 100 games and got an unofficial MMR of 1500. Now you play your ten placement matches. Let's say that all companions and opponents you get have the same MMR as you. This means that you will gain 25 MMR for every win and lose 25 MMR with every loss. so with the 10 placement matches you can gain a maximum of 250 points and you can lose a maximum of 250 points as well. after that you have between 1250 and 1750 MMR.
The +/- 25 MMR is the default value for even teams. What is and isn't even is explained in that blog post, but in general they compare the MMR of all players and if the numbers are roughly the same, it's an even game. A higher ranked player can have more positive impact on his team than a worse ranked player can have a negative effect, thus a group of "1500-1500-1600-1400-1400" would be close to equal to a "1500-1500-1500-1500-1500" team. Additionally a party of two 1500 MMR players will be evaluated as stronger than two separate 1500 MMR players, since they generally have better communication and might even be synchronized in a way. The following table shows the relation between MMR and the amount of players worse than you:
5% 1100
10% 1500
25% 2000
50% 2250
75% 2731
90% 3200
95% 3900
99% 4100
Given the fact that this was the situation at the time they released the ranked matchmaking system the numbers might be slightly off now, but should be close (iirc 3900 is now the 99% border, but who cares for the exact numbers).
You see that in lower MMR areas there are way more players. Thus you will get games faster and your games will theoretically have more even teams (not accounting for smurfs or other things). This results in mainly +/- 25 MMR games. Once you get higher up the MMR ladder (professional players have between 5k and 7k MMR you will have less players eligible to play with you, thus waiting times for games increase and you will have less even games. This is adjusted by the amount of MMR you will get for winning and losing. If you play a game that according to the MMR system you should win, since your team has a higher team MMR than your enemies, you don't get the 25 MMR for winning, but instead might get 23 (if at a slight advantage) or even just 2 (if highly favoured, this generally opens happens to the guys with highest MMR (top 200 on the server). At the same time, if you lose a game that you're statistically supposed to win you will lose more than the 25 MMR (27 for slight advantages going up to 50 for games in which you were highly favoured).
So basically the MMR is based upon Win/Loss with whom against whom. Personal stats like K/D/A and LH/D are highly irrelevant for your MMR.
P.S.: Please note that if you are better than your teammates and enemies, you will have an easier time climbing in MMR if you play a snowball hero in the midlane, since you can have the biggest game impact with those. By playing hard support for people that can't efficiently farm and don't know who to focus during a fight and generally when to fight you lower your chances of stomping. At the same time, try looking for a couple of players to play pubs with that are around your MMR (i think 1500 is the maximum span of MMR that you can queue with others) and then pick some easy combos like Leshrac + Sand King, Venomancer + Juggernaut or Bane + Mirana. Because winning more lanes than the enemy almost safely assures you the victory in lower MMR regions, since people lack the understanding of when to fight and when to avoid fights. Also try to pick what is best for your team.
Best Answer
So the main MMR change will be for the selected role. Lets say you selected core role, and win, you'll get around +25 for this win on your core MMR. But your support MMR will also adjust somewhat, although to a much lesser degree.
The aim of this is to prevent people with great support skills from having a much lower core MMR (or vice versa), when many skills are transferable.