It's not "all random", and you can certainly increase your chance of winning, and you can increase your preparation and give yourself more opportunities, but you cannot increase luck. That's, by definition, impossible.
A person who gets lucky will prepare and put themselves in good positions beforehand, and so when they get lucky, they think that the luck was a result of putting themselves in that good position, being prepared, creating opportunities, etc. However, those people forget that just as many people who do the exact same things you did, will not get lucky.
That's what luck is. It's not the preparation and the putting yourselves in good positions. It's the differing outcomes that still come from that.
If we took two teams that were exactly equally prepared and put themselves in the exact same great position, and gave themselves the exact same great opportunities, etc., and we pit them against each other in a playoff series, who wins and why?
They saw a decent player who could fill a role, like any other team with their players. They had no idea that he would score 2 goals in a game 7 they barely even got to. He has 7 points in 15 games, so he's not exactly busting the door down. And they spent a goldmine on Hagel, who has been pretty disappointing for them, so where was this magical machine that showed them the future with Paul when Hagel was being acquired? What if the refs aren't braindead and they don't hand them game 6, or the puck bounces around and one of the 9 OT shots we got went in, and they never get to game 7 for Paul to score 2 goals? How does the Paul acquisition look then? What if the refs aren't braindead again in game 7, and the game is tied and we win in OT? Both teams would have done the same everything that they did, but the outcome would be different.