If you read the books “Rare Earth & Privileged Planet”, one of them does a plausibility argument on how common extraterrestrial intelligent life might be given known physical constraints. (I forget which book and I m too lazy to dig it out. Anyway they are both worth reading!) Constraints like age of the universe, position in the galaxy, star type, star volatility, etc. Life possible systems (forget intelligent for a minute!) have to be out on the galactic rim, way too much radiation as you move inward, this means such systems have to be roughly the same age given some +/- X amount of millions of years. You say should that be enough time for a Mr Spock visit. Maybe and maybe (more likely given what we currently know!) interstellar space travel is really really hard to do! So maybe they haven’t come because they haven’t figured interstellar space travel out yet and maybe its impossible to do like in Star Trek. Maybe the best you can do is the occasional long lag time chat in RF. And maybe they’re not there! So far that fits the known facts, fact change then possibilities change!
... A big unknown in the original Drake Equation is the average lifetime of a civilization during which they might be available to communicate with us. This window might be very short, especially if technological species are typically replaced by machines. Or it could be very long.
Reframing the question makes longevity a moot point. Frank and Sullivan ask: What is the chance that we are the only technological species and always have been? If we put the question this way, the Drake Equation boils down to A = Nast * fbt, where A is the number of technological species that have ever formed over the history of the observable universe, Nast are all the astronomical unknowns (which we now have a much better handle on than we did in 1961), and fbt are the biological unknowns, which are still many—including the fraction of suitable planets on which life actually appears, the fraction of those planets on which intelligent life emerges, and the fraction of civilizations that develop a technology that releases detectable signs of their existence into space.
Based on recent exoplanet discoveries, Frank and Sullivan assume that one-fifth of all stars have habitable planets in orbit around them. This leads them to conclude that there should be other advanced technological civilization out there, unless the chance for developing such a civilization on a habitable planet in the observable universe is less than 1 in 1024 (a 1 with 24 zeros!). For our own Milky Way galaxy, the odds of being the only technologically advanced civilization are 1 in 60 billion. Thus, it’s very likely that other intelligent, technologically advanced species evolved before us. Even if only one in every million stars hosts a technologically advanced species today, that would still yield a total of about 300,000 such civilizations in the whole galaxy.
The Archilles’ heel of these statistical estimates is of course the biological uncertainties; Earth is still the only planet where we know life exists. The appearance of life may be extremely unlikely, and so might the evolution of technology. After all, there are many intelligent species on our planet, including dolphins, octopi, apes, parrots, and elephants, but only once in 4.6 billion years has a technologically advanced species evolved. And life cannot have appeared in the very early Universe until heavier elements produced by the explosions of many supernovas became abundant.
Still, Frank and Sullivan think their 1 in 1024 estimate constitutes a “pessimism line”—a lower bound on the probability that one or more technological species has evolved over time. And that’s good news for SETI, even if it doesn’t help us know where to look.