Just found this thread now. I applied to 7 Poli Sci PhD programs, mostly in the Northeast USA (with the exception of one in the south). I was pretty picky about program fit, potential supervisors + location, which is why I narrowed it down so much. I have an MA already, so didn't apply to any MA programs.
I applied to 7 and I'm honestly worried that wasn't enough!! I know there are a few more programs with deadlines Jan 15 but most of those I'm just like ughhhhh idk if I want to move there and also not to mention all of these application fees!!
Sometimes it says on the program website (granted, I guess it depends on your discipline as well). For example, in the FAQ section on the program page they might have a question like "How many people get admitted each year?" with an answer of "Generally we receive 600 applications and hope to admit 10% of the class" which you can then draw your answer from. Other times they are more explicit and say "We hope to admit between 10-12 students each year" or whatever. You can also reach out to a potential supervisor or contact at the school if you feel comfortable asking them directly. In some of my conversations with potential supervisors prior to applying I occasionally asked this question. Hope this helps! Best of luck.