Influence implies causation, and hence the opposite of randomness. I see randomness vs. determinism similar to a parallelogram of forces. Every behavior can be divided into a deterministic component and a randomness component. But that’s the only two components there are. And free will doesn’t fare better with the randomness component than with the deterministic component. Randomness means you are subject to an arbitrary choice. Influence is a causation arrow from you to the thing you influence (like a choice you make). But it says nothing about the arrows pointing to you.