Precision: Defines generally how close to the aiming point the ball will land based on where you hit on the swing meter
Yes, the lottery element definitely exists. It's been in the game since day 1and is represented wholly by the Precision stat on your sticks. Some know it as the 'beast'. Others will call it a 'precision deviation.' Whatever name fits your fancy, it's the same thing.
Assuming a 1mph on Kiawah's first tee, you can hit your 'perfect' tee shot 20 times in a row and it will land in 20 different places every time. Some will be right down the middle, some will be down the sides, 1 or 2 might even stray into the rough.
Now, assuming that meter is struck 'perfect' and the conditions are exactly the same (let's not forget this a game for a second, not real golf), then what accounts for the fact that 1 or 2 of those balls are in the rough?
Some rounds you play, you will find your 'perfect' shots in the rough more often than other rounds. You'll find your 'perfect' approaches are flying offline at a larger percentage than other rounds. Again, a random element built into the shot to stray the ball offline.
This is a fact, not supposition. It's even in the FAQ, just not in so many words.