The distribution of the 'expert adivsors' or whatever they actually are, their accuracy, and the actual events being predicted. I recognize this is difficult to compute (maybe Solomonoff hard), and bounding the error is a good, very-computable proxy. But it's just a proxy; we care about the expected result, not the result assuming that the universe hates us and wants us to suffer.

If we had a bound for the randomized case, but no bound for the deterministic one, that would be different. But we have bounds for both, and they're within a small constant multiple of each other. We're not opening ourselves up to small-probability large risk, so we just want the best expectation of value. And that's going to be the deterministic version, not the randomized one.