I checked out the recent NASPA 2016 North American Scrabble Championship playlist on Youtube which had ten videos of late round games. I've put the scores of those videos below. Note that competitive Scrabble is only 2 players.
gibson 585 swift 243
eldar 350 francillon 493
gibson 358 li 311
eldar 480 winter 374
gibson 347 swift 333
eldar 461 winter 460
gibson 397 meller 501
gibson 311 weinstein 449
gibson 397 weinstein 371
meller 438 sherman 436
The lowest score was 243, and it was the only one that was under 300. From this I can surmise that to be a top tier Scrabble player, you should be getting 300 a game on a regular basis. And this is against other very good players who will be attempting to limit your moves. Against regular players you would expect this to be even higher, as they will be less likely to take the doubles and triples.
The important thing, however, isn't to judge yourself based on what is a good or bad score. Rather, are you improving your scores? Are you enjoying the game? Do you know what causes you to get more or less points and how to get better? I think these are far more encouraging and productive questions than reducing yourself to a score comparison.