one_win = 30 mmr
10000 mmr - 1 mmr = 9999 mmr
9999 mmr / one_win= 333.3 (wins)
If we say one game takes on average 45 minutes to complete:
333 wins x 45 minutes = 14985 minutes
14985 minutes / 60 minutes (1hr) = 250 hours
and finally
250 hours / 24 hours (1d) = 10.4 days
A week and a half, playing non-stop without eating or sleeping, assuming you're winning every single game, which is a lot to assume, and I've been trying since 2014 so it's basically an impossible feat, except for the 1% of players that have immortal.
Funny...all these years I never did this calculation again. If the above is correct, and assuming a person has 10000 skill at dota, they could go from 1mmr to immortal in 3 months.
For a 9k player i think its safe to say that:
0-2k MMR = 100% winrate - amount of games required = 67 (67 wins *30 ~ 2000 MMR )
2-3k MMR = 95% winrate - amount of games required = 37 (35 wins = 1050 + 2 loses ~ 1000)
3-4k MMR = 90% winrate - amount of games required = 40 (37 wins = 1110 + 3 loses ~ 1000)
4-5k MMR = 85% winrate - amount of games required = 47 (40 wins= 1200 + 7 loses ~ 1000)
5-6k MMR = 80% winrate - amount of games required = 55 (44 wins = 1320 + 11 loses ~ 1000)
6-7k MMR = 70% winrate - amount of games required = 81 (57 wins = 1710 + 24 loses ~ 1000)
7-8k MMR = 65% winrate - amount of games required = 111 (72 wins = 2160 + 39 loses ~ 1000)
8-9k MMR = 60% winrate - amount of games required = 153 (93 wins = 2790 + 60 loses ~ 1000)
Total RANKED games required = 591
Assuming that the guy plays around 10 games per day (every day) he will need 59.1 days ~ 2 months , thats my guess.
After 15 wins in a row, you get put in a "smurf mmr gain" and you gain 100 MMR for a win.
It means, all of your calculations are wrong.
You could do Herald1 > Immortal in less than 20 days.
Why would you? It could be very well be that your MMR decayed as mine did.
2018 I'm around 5500.
2019 I find a job and slowly start falling to 4500. I quit dota for a year.
2020 I come back and I'm uncalibrated. Still play like shit. I fall down fast to 3500.
2021. I wanna play serious again. I easily win 15 games in a row. I start getting 100 MMR per win, which is enough to not get matched with the same people in the next game.
Very fast I'm back to 5000 where my winrate gets closer to 50% because I'm close to my skill level. I only get 30 MMR per win again.
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Been watching a first-person shooter guy, iitztimmy, he did this lowest to highest rank for Apex Legends and Valorant. Bronze 4 to Apex Predator(top 500 of region) in a single stream of about 50-something hours, he did ~55 hours for Valorant and got from Iron 1 to Immortal 3, low rank 500s but the highest rank of Radiant is top 500. He was at the minimum threshold for Radiant (300 Rank Rating) but the lowest rank Radiant was already at ~450 RR.
Assuming someone tried this and didn’t get banned by Valve while attempting it, how long do you think it would take a top player to take a 10 MMR account all the way to rank 500(is this 8K or 9K MMR? I don’t know the MMR situation at immortal). Or maybe more reasonably for Dota, rank 1000(around 7K)?