First of all, it doesn't need to be a proven fact. This thread is about the labelling of the luck factor, so we need to find our best judgement. I'd say that almost any experienced player with Elo>300 will agree that there is luck in the setup.
See this strategy thread on BGG.
https://boardgamegeek.com/thread/170395 ... -stalemate
One of the highest rated players on the Patchwork App argues (by his juggement) that "... probably 25% of the games give one player a fairly significant advantage based on turn order (fairly significant is ambiguous, so let's take it to mean 4 to 7 buttons). Finally, maybe 10% of the games will give one player a quite substantial advantage (8+ buttons with extreme cases being upwards of 15+ button advantages)."
Second,
it is more or less proven that there are unbalanced setups and usually you can identify them. The programmer of the super-hard AI for the Patchwork App stated (and I quote from the thread linked above): "The starting configuration matters a great deal and can bias the game quite a bit. And it doesn't take a perfect combo to do it either. I've had the AI play several thousand games against itself. Overall, player 1 won 53% of the time (about the same as chess's first player advantage). However, if the 0-cost cross piece is in the first 3 available, the first player wins 77% of the time! A few other pieces can give a strong advantage too."
