Holy shit the answers in this thread are terrible. OP: This is still very much an open question.

Okay, so you're asking very broadly what determines the abundances produced by the r-process?

The answer? Not the astrophysics.

The r-process produces heavy elements like gold in (possibly) supernova and (probably a bit more likely) neutron star mergers.

Backing up now. The 'r-process' stands for the rapid neutron capture process. Basically, when ejecta is getting shot out, it's super hot, full of proton and neutrons, which first clump to form 'seed nuclei' which then capture a shitton of neutrons very quickly before beta decaying back to stability.

When we look out into the universe, we see metal-poor stars enriched with r-process elements that pretty much all have the same relative abundance pattern. What does this mean? It means when you look at almost any given star that formed from gas polluted by only one r-process event, you'll see the same pattern of stuff made (e.g. twice as much of element X than element Y).

This is because the r-process abundances are determined by the nuclear physics at work. The neutron capture rates, beta decay rates, masses and half-lives of unstable elements - all of these are parameters that determine the yields in the r-process. Presently, we have a decent guess how these things work, but it's far from solved.

There are simply too many knobs - lots of work is being done to measure the relevant nuclear physics, but it's simply not known yet, and we rely a lot on theory at the moment.

So can we predict how much of a certain element will be made? Sorta. We have models, but the best way to know how much is made in an event is to just go out and observe low metalicity stars, and try to work backwards from there.