A Scrabble Luck Calculator
nautil.us
nautil.us
"What specifically causes this advantage" is, to put it briefly, playing first. The first player will have about 0.5 more opportunities to score. In fact, since it's legal to pass, it's a trivial game theory result that any advantage in Scrabble belongs to the first player.
IIRC simulating an AI-AI game only took a short period of time (maybe a few seconds to a minute), so replicating the study with this scrabblebot wouldn't be too difficult.