One factor that I don't think we're considering is risk-taking.
Of those who graduated in my BFA class, the most successful by far is the student who took a massive gamble and got in the ground floor of a newly-established company. After a year or two of awful pay and dying fabrics in her parents' bathtub, the project has grown and grown, and now it looks very much like she has a job for life. (A job she happens to love, and which pays considerably more than a living wage.)
She was never going to get that job (certainly not at her age!) if she'd gone through the ordinary channels. Her success is down in large part to her willingness to take a considerable risk early in her career in the hope that it would pay off down the line.
But this story doesn't always end well, right? For every company formed by young and emergent artists which manages to really knock it out of the park and become a major game-changing phenomenon, there are literally dozens who put on a single show and fold immediately. (If they put on a show at all!)
And we should also consider that risk-taking doesn't exist in a vacuum. This woman had supportive parents who took care of her while she spent hear year-or-two in the wilderness. Those of us who have to immediately start paying back six figures of student debt literally cannot afford to take these sorts of chances.
Do we call this entire phenomenon luck? I'm not sure.
It does often seem that the difference between a wise risk and an unsavvy gamble is little more than good or bad luck. (Especially for emergent artists who haven't yet acquired the chops needed to tell the difference between a promising project with potential for considerable long-term success, and a complete and utter turkey.)
But her willingness to work hard, her contacts (Setting aside her friends in the industry, how do you even meet the sort of ambitious early-career artist who has this kind of vision--and how do you persuade them to make you a part of that vision--without having contacts and knowing how to work them?) and her perseverance are also pretty key.
We're in danger of going wildly off topic here, but I'm going to bite. We can always split into a new topic if we get too far derailed.
To me, luck is winning the lottery. A career break, development, promotion, success - these are the products of any number of factors, but in general terms I reject the notion of luck.
Even your example of your classmate who found success in a startup. Is she lucky that the startup took off? I don't think so. It's the result of hard work, skill, knowledge, preparation, whatever of the entire team, and ultimately capitalizing on opportunity (something many people fail to do). Is she fortunate her family was able to provide security so that she could take a risk? Absolutely. But to call it luck trivializes what it took for her family to get to that position. Is she lucky to be born into that situation? Maybe, but that's an entirely different discussion.
My opinion may seem a bit harsh, but I've found there are generally two types of people who use the word luck to describe success:
1) People who are envious of another's position in life.
2) People who are either more passive and expect something to eventually "come to them", or people who believe in fate. This would be opposed to someone who is active, aggressive, and relentless in the pursuit of success.
Is it this absolute in reality? I don't think so. But it's interesting for the basis of a discussion.