Okay, my turn to throw in 2 cents or a nickle if someone can make change.
The only part of poker that involves luck is the order in which the cards come out. Which comes in two parts really. First are your hole cards, second are the board cards. No amount of skill will ever affect the order in which the cards come out. That order is defined by the shuffle (whether live or by online algorithm is irrelevant).
Everything else you do is based on your personal skills. Your skills include, but are not limited to:
1. evaluating your hole cards for starting value
2. knowing and understanding your position at the table
3. viewing your stack size proportional to others
4. reading your opponents
5. recollection of previous
hands and the play in them
6. knowing/understand
odds of making your hands
7. counting outs
8. putting opponents on a range of hands
9.
pot odds and implied odds
10. I'd keep going, but you should get the picture.
All these things mentioned (and all the other stuff that didn't make the list for sake of space) are skills and have nothing to do with luck, not at all. Some things you may be good at, some you may suck at, but they are skills with levels that can be changed. Maybe you've heard those sayings where good players get luckier, etc. Well there is some truth to that. Not because they are actually luckier, but because they are making more skilled decisions than others (based on odds and such). They seem to make their hands more often, and if fact they do because they are typically in a better situation than someone else that is complaining how the cards are coming back to haunt them. In reality, it is the skill level winning out. As for the bad beats, that is back to the luck factor as to the order of the cards coming out. You can't fix that. So in my opinion, the luck factor is much smaller than 40%, more like 10% overall. But luck appears to be a much larger factor because everyone harps on their bad beats (of which many aren't bad beats, but bad plays) and forgets about all of the winning hands that held up like they were supposed to.
/whew. Glad I got that off my chest.