Index of coincidence
The probability that two characters drawn at random from a text are the same — a single number that tells you whether a ciphertext hides a language or only noise.
The measure was set out by William F. Friedman in Riverbank Publication No. 22 in 1922, routinely named as the single most important paper in modern cryptanalysis. The point is that natural language is lumpy. Pull two letters at random from English text and the chance they match is about 6.7 percent; from a uniformly random string of 26 letters, only 3.8. A monoalphabetic cipher relabels the letters but leaves the distribution alone, and so keeps its index — which is itself the leak.
The application is mechanical, and therefore automatable. A low index says the cipher is polyalphabetic. Slice the text into every n-th character and test n = 1, 2, 3 …, and the index snaps back towards the language's value exactly when n is the key length, reducing Vigenère to a handful of simple substitutions. The same underlying idea — count coincidences, compare against chance — reappears twenty years later in Turing's Banburismus, this time with Bayesian weighting and on a rather larger scale.