If you reduce everything to atoms and motion in a straight line, people think that that would lead to a totally mechanistic result, and so a straight line materialist such as Democritus would conclude that everything is in the grip of an iron "fate" that allows no room for personal decisions whatsoever. Cicero made this argument against Epicurus in criticizing the swerve as a departure and regression from Democritus.
Ok, so this is where the Epicurean "swerve" comes in to introduce some level of chance. Looking at this from the vantage point of the modern science, we know for a fact that the small-scale world operates on probability (quantum mechanics) and not linearly. Additionally, complex systems, Mandelbrot sets (fractals) all demonstrate how you can get from simple predictable small elements into extreme unpredictable complex whole. This suggests that absolute determinism cannot be defended. In this sense, I suppose "compatibilism" is probably the best description of the reality, though I somewhat dislike the notion of describing a certain feature of universe by accepting co-existence of two extreme and improbable ideas.
Free will has the connotation of a supernatural soul. In materialism without hard determinism, "agency" is the preferred term to replace the term "free will" to get rid of that supernatural connotation. This leaves enough room for anything from the little "free will" of Onfray to a lot of "free will" and is flexible enough to not be refuted by future research results on how far agency actually goes unless those results prove hard determinism. A proof of hard determinism in the real world as perceived by us appears to be not conceivable as of now.
Thank you Martin, I now understand the connotation of a supernatural soul coming from "outside the system". I have been raised in a completely non-religious environment and developed scepticism later in life, so I did not develop a radar for theological red flags. I like the term agency!