Can anyone summarize calculations that have been done about the **theoretical** probability of a detectable black hole collision happening in the observable universe within the time that LIGO has been operating?

I mean, given what we know about processes and parameters in the universe - about densities of black holes, rate of explosion of stars etc - how often would we expect an observable event?

This question is looking for an analysis **independent of observations of actual GW events**. It's the scientific "what does theory predict" question.

If we just think for a moment about black hole mergers (as opposed to other GW events), the types of thing that obviously need to be taken into account is "what is the density of black holes throughout the lifetime of the universe?", to determine what is the chance that they merge. This is a complicated question in itself, because the relevant density comes from earlier and earlier in the universe's life the further away the event is (obviously?).

But interestingly, there's also the problem if the planar nature of GW wave fronts. What is the chance that Earth happens to be in the plane of the GW event at the time - it seems to me that this aspect alone must dramatically reduce the number of probable observations...

It appears to be an obvious question, but googling the exact question, and creative variants I could think of, does not uncover anyone else asking it or addressing it. Similarly, ligo.org does not appear to have any material talking about this topic.

The consideration is alluded to in [this question and answer](https://physics.stackexchange.com/a/235778/37626), but not given any direct elaboration that I could find.

Interestingly, the answers in [this similar question](https://physics.stackexchange.com/questions/10161/is-there-a-good-chance-that-gravitational-waves-will-be-detected-in-the-next-yea?rq=1) are massively different. One says "possibly daily" and the other says "should see one by 2020". Neither offer any justification.