The Watchmaker: my fav argument

[Angrboda]

As a result, most times the simpler explanation will be more probable simply because of its lack of complexity.

I agree with your overall argument and use of probability, but I don't know if I agree with this particular sentence. As an example, the original heliocentric model assumed that orbits were perfect circles rather than ellipses. This oversimplification was arguably as "improbable" as the overcomplication of Ptolomy's epicycles.

I would also like to forward the perspective that complexity can be interpreted as increasing the resolution of our models, allowing for a clearer image.

Yes, like I said, it's more a heuristic than a rule. With the heliocentric model in particular, they were dealing with unknowns such as what held the planets in place (I believe God was the answer). Though I think you miss the point that it be necessary that the simpler theory account for all the facts, which the heliocentric model with perfect circles didn't do because it wasn't in accord with all the facts but only with some of them. It's a question that I'd have to consider at length as to whether that made the circle model more or less probable, as you're dealing with the principle of insufficient reason again in which circles are just as probable as ellipses or moreso. It's also worth noting that accounting for the orbits of planets without appealing to God would have resulted in a complex or even hopeless explanation at the time. Again, I'd have to mull the matter for some time, as there's a lot going on with the example of the heliocentric model.

As an addendum, it also bears pointing out that an explanation may appear simple because of one cause or another when it is not simple. The God explanation hides an enormous amount of assumptions behind the simple expression that God did it. So many in fact that people struggle to this day to reconcile them with the facts. I, myself, am convinced they cannot be reconciled, but that depends on the particulars being attributed to God. Needless to say, if it's such an open question as to whether God fits the facts or not, he must be anything but simple.