Thanks for doing the math!
It would be fun to really really look into this. Run some controlled experiments (alas no multi universe engine to do that correctly), deep dive into what each fund actually does to find positive or negative correlations, etc.
It would be interesting for instance to do back testing on many of these things - if someone is declared a ‘winner’, vs not declared a winner (but doing the same things), is the likelyhood the winning streak holds up greater or lesser?
Does a large amount under investment change odds of success? (Big pockets make it easier to win?) Does a change in amount under investment change odds of success? (People flock to perceived winners, both investors and opportunities, increasing their odds of success)