I've been getting back into the groove of ranked lately and my friend told me he jumped from Tier 3 to 1. Is this because of his mmr being higher than the league he's in? If so, how would you accomplish getting a high mmr? Win more games? Lose less?
It is mainly you winning a lot. In S3 I went from S4 -> S2 -> S1 -> G5 -> G3 -> G1 -> P5. All you need to do is win a majority of your games. I feel the thing that causes people stop climbing quickly is usually losing during their promo series. Since you rise/fall pretty quickly the less ranked games you played, you winning your earlier games benefits you.
