OK so if you click through to the linked Reddit thread, there are some important caveats to the numbers that OP doesn't seem to have accounted for and that I want to drag into the analysis here on Tumblr.
The Prospect Draft Has Changed
The draft worked in substantially different ways in the early days, especially the 60s, when the original 6 teams depended on feeder systems to acquire elite prospects (basically sponsoring juniors teams in order to get first dibs on the cream of the crop). The remaining players who made it to the draft were the ones who hadn't been immediately snapped up, so: decidedly not the cream of the crop. Genuinely, the entire dataset from the 60s should've been excluded.
Also, I don't know anything about how the draft worked in the 70s through the 90s, but given how much the game has changed I wouldn't be surprised if there were confounding factors that make a meaningful comparison difficult, insofar as any kind of meaningful comparison can be made. Like, today's scouting reports are more data-focused than they've ever been, but ultimately, ranking top prospects is an exercise in vibes informed by data. How much more of an exercise in vibes was it back in the 70s and 80s, especially given the lack of readily-available game footage and data-crunching software?
Being the best doesn't matter if everything else sucks
I'm stating the obvious here, but having the best players in the world means nothing if your team is chronically mismanaged and mis-coached (*koff*Oilers*koff*). In fact, hilariously, if you take into account ONLY post-cap era picks and leave out the last ten years to account for growing/rebuilding pains, turns out every 1OA between 2004 and 2015 has won a cup except John Tavares (time to get a new amulet, bud!) and the ones who went to the Edmonton Oilers.
Man I feel bad for McDavid and Draisatl. Their polycule deserves so much better.
How many high draft picks does it take to win a cup?
I wanted to look at numbers from the other end, i.e., how many Stanley Cup winners from the last 20 years had at least one 1OA on the team, and then decided to expand it to 2OA through 5OA. What I found out was:
12 of the 20 winning teams had at least one 1OA pick
But! 14 out of 20 winning teams had at least one 2OA, which was the most
All except one team had multiple top 5 picks. The Pens had six top 5 picks on their roster when they won the Cup in 2009!
Only the St. Louis Blues managed to win the Cup with only one top 5 pick (Brad Stuart, 3OA in 1998 to the Sharks).
These numbers don't ultimately mean much, because you have incredible players like Letang and Kopitar who made a massive impact on their teams who weren't picked top 5 (or even top 10!), plus draft busts also definitely exist (lol once again the Oilers, who picked Nail Yapukov), and I didn't run the numbers on how many high picks all the losing teams had (definitely a nonzero amount!), but. It was fun to poke at the numbers anyway.
Right in Front of My Salary Cap?
I wrote a thing about win rates pre- and post-salary cap and then remembered oh right expansions exist lol. The win streaks between 1965 and 1984 look incredibly silly—the Habs win 10 of the 20 Cups!—but that's in part because there were way fewer teams. Someone better than me at crunching numbers and has better access to data can and no doubt has looked at the effect (if any) the salary cap has had in leveling the playing field and whether that's a stronger effect than having high draft picks on your roster.
The 1OA data from the 60s should've definitely been excluded; personally, I think there's a pretty good argument for excluding the data from the 70s and 80s, too.
Having at least one 1OA pick certainly doesn't hurt when it comes to helping teams win Cups, and having multiple high picks is even better, but the magic sauce appears to be team chemistry + competent coaching and management. Groundbreaking revelations. Wow. Also, way to ruin a lighthearted post that's mostly about Mack's 1OA curse vs. Will's lucky girl syndrome with over-analysis and numbers.
Anyway. Mike Grier and Warso, I have my eyes on you!!! Don't fuck up the Sharks.