There are some research (instead of cherry picking/anecdotes). I don't have any links right now but basically half of the funds lose compared to the index (by law of nature - averages and all that). Furthermore, taking fees into account, just a few percentages make anything more (over time) - which is probably within scope of randomness.

In general hard working prudent value investors are able to beat the index. It's just that those are very few. I mean Buffet has done it for half a century, that's not a coincidence.

Given the statistics and number of investors involved, it seems like an absolute certainty that a few people would beat the index for the entirety of their lives simply by chance.

Yes some people might do it by chance. Some other people, they do it by knowledge.

Find me the one who knows they got there by chance alone...

It's very easy to create a narrative around random movements. I expect that anyone who is ahead of the market creates such a narrative, and declare themselves a genius. And then half of the geniuses underperform each year, same as every year...

How do you tell one from the other?

You learn enough about value investing to know who is actually following that framework and then you just hope it works. Note: it works.

Half will beat index by definition. The key is to beat it including the cost of beating - and we've also seen that the extra value have generally been captured by the fund managers - not the fund buyers.