One other proposed factor: the laws of physics may vary across the universe, so stars in faraway galaxies may not be eligible. But there's a lot of evidence that the laws of physics are the same as far away as we can see, so this seems unlikely to me.

There are good reasons to believe that intelligent civilizations are short lived (compared to cosmological time scales). So the absence of radio signals from nearby planets doesn't mean it's not worthwhile to send a probe there to see if there are ruins or something.

"So the absence of radio signals from nearby planets"

Whoa there... The SETI people whom are only occasionally telecom engineers have a thing about scanning for the simplest carrier waves and that's it.

Note that we only broadcast vestigial sideband amplitude modulated video signals which had a lovely strong stable carrier for oh maybe 50 years and we don't broadcast analog TV anymore. Lets be honest that the future for broadcast radio/TV doesn't look particularly bright so even if the aliens had the bright idea to use 8VSB modulation when the USA is in view or OFDM when the euros are in view then they still would see total radio silence from us in "a couple years". Terrestrial broadcasting is pretty much done.

You need to add a term to the SETI equation that your average civilization is only going to broadcast "SETI@HOME" compatible radio signals for maybe a century, probably less.

There's a section of Kraus classic radio astronomy textbook indicating that detecting Earth during the peak of the analog TV era would still have been pretty tricky if the aliens used our own "SETI@HOME" modulation.

You feed a baseband thru the wrong demod and you just get distorted noise.

Broadcast seems kinda dead as a concept in a packet switched social media era. The aliens and us are not going to understand each other on some rather fundamental levels making USA 2050 compared to USA 1950 look fairly trivial. Wait... you still use radio waves for communication instead of high frequency short range gravitic waves? You broadcast to a significant fraction of your unified population instead of social media via low power point to point systems? How... retro.

Good point: a moderately advanced civilization is likely to have no high-power baseband communication. Only intentional alien interstellar transmissions are likely to be powerful enough and decodable.

Earth has made several intentional transmissions (https://en.wikipedia.org/wiki/Active_SETI) but it's unclear if we'll send any more, because they might attract hostile aliens.

> there's a lot of evidence that the laws of physics are the same as far away as we can see

This could be a relativistic effect, just like the speed of light appears the same irrespective of frame of reference.

I don't really see how it could be missing terms. Chance of A. Chance A becomes B. Chance B becomes C. etc. It's intentionally very simple, with very broad terms. It should have no gaps by definition, unless there was a wording error.