The Drake equation provides a way of determining the probability N(c) of us communicating the extra-terrestrials. Carl Sagan mentioned it in his wonderful 'Cosmos' programmes many years ago, I seem to recall. In particular,
N(c) = R(s) x f(p) x n(e) x f(l) x f(i) x f(c) x L(t) x f(e)
where
R(s) = rate of star formation in the Milky Way galaxy,
f(p) = fraction of stars with planets,
n(e) = mean number of planets that could support life per star with planets,
f(l) = fraction of these planets that do develop life,
f(i) = fraction of planets where developed life has intelligence,
f(c) = fraction of planets with intelligent life with communication skills,
L(t) = mean overall length of time during which we will be able to communicate with extra-terrestrials,
f(e) = fraction of extra-terrestrials with English-speaking communication skills.
(The f(e) term is my extra factor, included because most extra-terrestrials seem to speak English, judging by what happens in science fiction!)
Given that we can estimate all of the factors reasonably accurately with the help of the JWT, N(c) must be vanishingly small.
Maybe NASA should be beaming a non-stop radio signal across the galaxy of a dimensionless numerical constant such as pi or e, or the fine structure constant, to let other inhabitants of the Milky Way know that we're here.