Note: This will probably come off as bragging, but I don't really care.
I play Scrabble...a lot. Probably enough so that I can be called something more than a casual player, but I don't engage in tournament or club play.
Scrabble uses what's called an Elo rating system similar to the one used for chess. Generally the rating system calculates the relative strengths of each player based on their record, the quality of their opponents, and the skill of those opponents. It's pretty fair because wins aren't the end all be all to the ratings, you have to play well. Losing to a good player may still cause your rating to increase while barely beating a bad player might cause it to go down.
From what I can tell Scrabble starts each new player at a rating of 1200, which seems to be the average for tournament and club players (though a bit higher than the average for all players) and moves your score up or down as you continue to play more games.
On the Scrabble app for droid, I have a current record of 44-5 and a rating of 1573. Generally a rating of 1600 and up is considered expert level (which is what I typically play at). Most people on there seem to be in the 1100-1300 range for ratings which has led to my somewhat bloated record. (At least two of my losses are forfeits before I realized I could force idle players to forfeit.) Right now my high play is 100 (Quitted) and my high game score of a complete game is 454.
The thing I like about Scrabble is that each game is vastly different, and that there are a multitude of things that go into playing well. You need to have a good vocabulary for sure, but you also need to be able to spot good plays on premium tiles. Great words do you no good if you're not doubling and tripling your points. You also need to have a good memory, knowing a lot of two and three letter words will be crucial to your success. Plus your mind has to be active on every turn. It's not like Monopoly where you can buy a bunch of premium properties and sit around rolling dice mindlessly. A crappy play could kill you, either setting up your opponent, leaving you with god awful letters in your rack, or just not advancing your score enough.