A while back I ran into this blog post and it made me wonder. I’m not a native speaker but the idiomatic phrases that they note as common don’t strike me as such. I don’t think I have ever encountered them very often in real dialogue.
The blog post lists the 10 most common idioms in English. Idioms, also known less ambiguously as fixed expressions, are units of language that span at least two words. Their meaning, relatively to the individual meaning of the parts of the phrase, are figurative. Despite this, fixed expressions don’t classify as creative language, or exploitations. By definition most speakers will unequivocally be familiar with them.
For example, they cite piece of cake as the most common idiomatic expression. This refers to using the phrase to mean that something is easy, that it isn’t challenging. An example of literal use, however, would be when ordering a piece of cake for desert in a restaurant.
Everyone knows that language is a perpetually changing thing, so to begin with it’s even slightly misleading to discuss of the commonness of a phrase, without giving more context. The blog post doesn’t justify the ranking with any numbers anyway, so let’s take them one by one and find out how common they really are!
The approach we are taking here is known as corpus linguistics. The best way to argue that a certain phrase is common, that something is used with a specific meaning or that some constructions are normal is, under corpus linguistics, not to make up examples that seem reasonable, but to look at representative collections of text (corpora) and trying to find the examples there. The conclusions you get this way are backed by real-world language use.
An argument often brought against generative linguistics is that it focuses on the (hard) border between grammatical and not grammatical, and the border is usually defined by made-up examples. This is inappropriate for studying how the norms are exploited in real language use, for example. I refer the interested to the work of Patrick Hanks [1, 2].
Corpus linguistics is sensitive to the corpus used. For this example let’s use two British English corpora: the British National Corpus and the Oxford English Corpus. Measuring by number of words, the latter is around 20 times bigger. The strong point of the BNC is the attention given to the mixing proportions of various domains. The OEC, on the other hand, is larger and more recent. I have a feeling (but I cannot strongly affirm) that the differences in the following results arise from the inclusion in the OEC of blogs dating from the mid-2000s.
Cognitive salience vs. social salience
One of the key ideas that motivate corpus approaches is the mismatch between these. The cognitive salience of something is the ease with which we can recall it. An example often used in language is the fixed expression kicking the bucket. It is one of the standard examples of fixed expressions that people give very often when asked. It is supposed to mean dying.
However, big surprise: the BNC has only 18 instances of this phrase, out of which only 3 are idiomatic, the rest being either literal or metalinguistic. This is a nice example of the salience contrast, but we mustn’t hurry to conclusions. The OEC has 193 examples (still few, relative to its size) but a lot more of them are idiomatic uses. To save the time I didn’t look at all the examples, but took a random sample of size 18, to compare the relative frequencies to BNC. Here, 15 out of 18 instances are idiomatic and none are meta. Quite a difference!
This goes to show the importance of context when we draw conclusions about language use. Now let’s tackle the list with a similar analysis.
Piece of cake
In BNC, this phrase occurs 51 times. 29 of these occurrences, however, the meaning is literal. In OEC we find 601 occurrences. In a random sample of size 51 we find 12 literal uses.
Costing an arm and a leg
For flexibility we search for the phrase an arm and a leg. In BNC it can be found 29 times: one literal, four with the verb to pay, and 16 with to cost. In OEC it appears 228 times. We take, again, a sample of size 29 and find no literal uses, 16 with to cost, four with to pay, three with to charge and a few different uses. The figurative meaning is the same in all cases: a lot of money.
Break a leg
BNC: 16, 13 of which are literal. OEC: 70 hits, 10/16 literal.
Hitting the books
BNC: 1 occurrence of hit the record books, which has a different meaning. The idiom is never used. OEC: 135, one of which literal.
Letting the cat out of the bag
We just looked for cooccurrences of cat in the context of the phrase out of the bag.
BNC: 19, out of which 3 metalinguistic/literal. OEC: 298, and out of a sample of 19, all were idiomatic.
Hitting the nail on the head
BNC: 12 instances, all idiomatic. OEC: 484, and out of a sample of 12 all were idiomatic.
When pigs fly
We looked for the lemma fly before the word pigs therefore catching multiple variations.
BNC: 17 hits, OEC: 240.
Judging a book by its cover
We looked for the fixed phrase book by its cover, because the leading verb might vary.
In the BNC, 11 instances (1 of them with tell instead of judge). In OEC, 195 instances. Sampling 11, all were idiomatic.
Biting off more than one can chew
BNC: 16 occurences, one of which with “to take” instead of “to bite”. OEC: 231, all idiomatic after sampling 16.
Scratching one’s back
BNC: 23, out of which only 5 idiomatic. OEC: 756, 5/23 idiomatic.
Recalculating the rank
We now have enough data to reorder the expressions and compare. The result will be more approximate for the OEC because of our use of small subsamples to estimate the frequencies, but hopefully it will still be interesting. The way we are estimating the counts for the OEC is as follows: take, for instance, *break a leg*. It was found 70 times, and out of a sample of 16, 10 were literal. The expected number of idiomatic uses is therefore:
We can see that apart from the apparent switching of hitting the nail on the head with costing an arm and a leg, the rankings are not too different. We can quantify this by using the Rank Distance, a metric introduced by Liviu P. Dinu [3, 4]. Here, all our 3 rankings are over the same domain: we are not looking for the most frequent idioms in the corpora, this would be very hard. We are just reordering the proposed rank according to the occurrences in BNC and OEC. In this simple case, Rank Distance reduces to [latex]\ell_1[/latex] distance over rank position vectors. The weighted Rank Distance, bounded on [latex][0, 1][/latex] is in this case given by a scaling factor of [latex]0.5k\^2[/latex] where k is the length of the rankings (10 in our case).
The computed distance between the original ranking and the BNC reordering is 0.52. Between the original and the OEC reordering, it is 0.68. Our two reorderings are much closer: the distance is 0.28. This is mostly because that the permutations between the two reorderings affect the top position, and are therefore weighted more.
It’s also interesting to look at the ratio of the counts. Interestingly, they approximately differ by a constant factor not far from the relative size difference of the two corpora, as would be expected.
We have to throw away hitting the books because its BNC zero count leads to divisions by zero. After this step, the average of the relative counts of the idioms is 19.5, with a standard deviation of 10.1, while OED is supposed to have around 20 times more words than the BNC.
Well, it seems people don’t say break a leg and let’s hit the books as often as the original author claims. The popularity of most of the cited idioms seems supported by the data, but we have no easy way to find other idioms that might turn out to be much more frequent. Corpus linguistics is a reliable way to measure the social salience of language patterns It should always be used to verify and back empty claims of the form X is correct, Y is frequent or Nobody says Z.
 Patrick Hanks, How people use words to make
 Patrick Hanks, Lexical Analysis: Norms and Exploitations. The MIT Press (January 25, 2013)
 Liviu P. Dinu, Florin Manea. An efficient approach for the rank aggregation problem. In: Theoretical Computer Science, Volume 359 Issue 1, 14 August 2006. Pages 455 - 461.
 Liviu P. Dinu, [On the Classification and Aggregation of Hierarchies with Different Constitutive Elements]. Fundam. Inform. 55(1): 39-50 (2003)
[On the Classification and Aggregation of Hierarchies with Different Constitutive Elements]: http://dl.acm.org/citation.cfm?id=937465