I think 4400 MMR places OP in at least Ancient-1 ranking which is approximately the 95th percentile. I'd call that at least semi-pro.
I'm just 3.5k (I think that's 70th percentile), but I know lots of 4.5k players. To describe the average 4.5k player: Probably has regular groups of people they play with at different skill levels (anywhere from 2.5-5k+), regularly plays battle-cup on Saturdays, maybe played amateur JoinDota league, maybe had a laugh and played open qualifiers only to lose in the first couple rounds, and probably log between between 10-20 hours per week into the game.
4.5k players know how to play to a very good standard and beat the vast majority of other players, but are miles away from the weakest of the professional scene. 4.5k doesn't even appear on the leader boards.
Solo - the guy that is the captain of Virtus Pro, was at 4k for the longest time. There's more to dota than just mmr.
There are players at 5.5-6k range that still do not understand the basics of team play, but are just extremely mechanically gifted and are in great gaming shape.