Frank Drake’s 1961 expression for the number of civilisations in the galaxy whose transmissions could be detected now, written as N equals the rate of star formation, times the fraction of stars with planets, times the number of habitable planets per system, times the fraction on which life appears, times the fraction on which intelligence appears, times the fraction that transmit, times the mean lifetime of a transmitting phase. Drake composed it to organise the agenda of the Green Bank meeting of November 1961, which had about a dozen attendees, and not as a prediction.
PURSUE Release 06 record DOW-UAP-D127, a Defense Intelligence Reference Document of 11 March 2010 (DIRDs), recasts the equation statistically, replacing each factor with a random variable. For its worked example the classical equation gives 3,500 communicating civilisations in the galaxy and the statistical version a mean of about 4,590, with a 75 per cent probability that the nearest lies between 1,361 and 3,979 light years; the paper says the numbers hold only for the input values it assumed, and that fifty years of searching had found no extraterrestrial civilisation.
What it can and cannot do
It is an identity rather than a model: multiply the terms and the answer follows, so its entire content is in the values chosen. Three of the seven terms are now measured rather than guessed, the star formation rate and the planet counts having been settled by transit surveys, and one of the remaining four, the lifetime term, dominates everything. Move that term alone between a century and a hundred million years and the answer moves by six orders of magnitude with no measured input changed. The honest use of the equation is as a list of the things nobody knows, in the order in which they would have to be learned.
Why it stays in use
Because it survives its own misuse. Every argument about the Fermi Paradox is a claim about one of these terms, and stating which one is being pushed is a discipline that keeps the discussion falsifiable. SETI search strategy has been priced against it for sixty years, and the Kardashev Scale does the same job for the detectability question that the equation does for the counting question.
Connections
SETI · Fermi Paradox · Arecibo Message · Kardashev Scale · Wow! Signal · The Three-Body Problem · DIRDs · Nonlocal Signalling