Let's think about this logically.
If the difference between a major and a private 1st class is that a major is luckier, consider this. A major would have to be 4 times as lucky to be a major because majors win half the points private 1st classes do, and lose double the points. So, let's assume that you win 50% of your rolls. I would have to win 80% of my rolls according to you. However, no one wins that many rolls. You would be unable to find someone who wins 65% of the time he/she rolls the dice.
Download the dice analyzer plug in and see for yourself. There is plenty of skill involved in the game, even on bs maps and settings. After 100s of games I have a win rate that is 9% higher than it should be on doodle assassins. Trust me, no one is that lucky for that long a time.