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Language Log: "The odds of X are large": likely or unlikely?

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Murray Smith asks about a phrase in Joe Drape, "Looking for Zenyatta's Mr. Right", NYT 1/13/2011: How Zenyatta will fare in her new career as a broodmare at Lane's End Farm is anyone's guess. She was a once-in-a-generation princess on the racetrack, winning 19 of 20 starts […] Breeding, however, is more magic than math. […] The Mosses and the people they have entrusted Zenyatta to know that the odds of coming up with another horse like her are long. Murray observes that "The context makes clear that it is considered somewhat unlikely that Zenyatta will produce offspring of her calibre (the odds are against it), but the quote seems to say that it is likely (the odds of it are long)". Any idea what's happening? Any way to tell whether 'odds of' has always been ambiguous between "'for' and 'against'?" In fact, "long odds" has always traditionally been used to mean "the odds placed on an outcome that has little or no chance of success". ("Short odds" is the opposite, though it is much rarer: 126 to 1 in the COCA corpus.) But confusion results when the traditional meaning of "long odds" is combined with the default association of long and large, along what the OED lists as sense 6.a. of odds, "The chances or balance of probability in favour of something happening or being the case; probability, likelihood. Now usu. in (the) odds are: the likelihood is". As a result, some people use large ("enormous", "huge", etc.) odds of X to mean that X is unlikely. Here are some examples from Google Books : On the other hand, you might say that the odds of something happening are a million to one. Such odds might strike you as being so large as to rule out chance or coincidence. However, with over 6 billion people on earth, a million-to-one shot will occur frequently. It would seem the odds of this [extraordinary coincidence] actually happening are impossibly large. Since then, hunting for stratigraphic traps has been regarded as "elephant hunting" and the odds of finding them are equally large. With different designs fitted on so many different makes over different years the odds of having the one asked for are large indeed. They understand that they won't always succeed, that the odds of overcoming transience are enormous, and that every institution they build is fragile. The odds of winning are enormous, yet many of us dream of it. and inevitably someone will succeed. But, can we expect children to have interest in life's real substance — in the arts, books, politics, philosophy, etc. — if parents have no interest? I think the odds of overcoming parental lack of interest are enormous. I mean, as you well know, just playing in the big leagues, the odds of playing there and staying are so enormous. The odds of all those things happening are huge, I'll admit, but not impossible. Even if you don't believe in a higher power, the odds of you being conceived and born are huge, which makes you remarkable no matter what. In fact, for those who think of odds in a mathematical sense, those examples are all backwards. Instead, large odds of X should mean that X is likely, as in these examples: The fact that the odds of survival are greater for species better fitted to their environment gave rise to the well-known phrase "survival of the fittest." Because surveys are endeavors that are ( 1 ) customized to each problem, and (2) constructed from thousands of detailed decisions, the odds of imperfections in survey statistics are indeed large. For, if interpreters are confused about what it is they are interpreting, the odds of their producing incoherence are enormous. With only a few seconds of drop time, no time for a backup parachute to open, and a real chance of slamming into the building or mountain from which you jumped, the odds of injury and fatality are enormous, far greater than with regular parachuting. Death, injury, and/or impairment are consequences that occur very frequently to impaired drivers; the odds of these happening are enormous. No matter how creative and careful a programming job you do, the odds of your being wrong are large, and in the health field, the odds are enormous. … the odds of younger drivers experiencing accidents are twice as large as those for older drivers On the other hand, where the odds of X are "tiny", "minuscule", or "small", the phrase always seems to mean "the odds in favor of X".  I believe that this is due to the fact that "short odds" is hardly ever used, and so the confusion arises entirely at the large/long end of the scale. This suggests that people are somewhat confused about what odds really are, or perhaps they're simply using the word in fixed expressions without thinking of the technical meaning even if they know it perfectly well. They're used to expressions like "a thousand to one shot" being used to mean that something is very unlikely to happen, and so they may think that if the odds of X are a thousand to one, then X is very unlikely to happen and has "large odds" — although technically, if they mean that the odds are a thousand to one against X, the odds in favor of X ought to be expressed as one in a thousand, which is a small number (relative to 1) rather than a large one. It's possible that "the odds of X" is coming to be ambiguous between "the odds in favor of X" and "the odds against X". But I don't think so, because it this were happening, we'd expect to see evidence at the small end of the odds scale as well as at the large end. Murray also points out that the "odds of" phrase seems to increased recently in frequency, as suggested by this Google n-grams plot The COHA corpus supports the same conclusion: Indeed, many of the pre-1970 instances of "the odds of" are in phrases like "what's the odds of two shillings more or less", "a man to whom even a first-class player can afford to give the Odds of a Rook and Knight has no claim to be ranked among Chess-players", "thou hast the odds of me", etc. Perhaps this coincides with the spread of a more figurative use of odds, though it might alternatively reflect increased amounts of quasi-statistical language in the sources included in those collections. (I know that these explanations point in opposite directions — please feel free to investigate and to determine whether either of them is correct.) [Update — a comment by Ian Preston is worth promoting: I am not convinced that "odds" is a "a betting term originally" or just an extension of "betting talk". Looking at the history of its use in the OED, I get the impression that it began as a general term denoting unevenness which became attached some time in the 16th century to any inequality in the probabilities of an event occurring and not occurring and which was then picked up both in discussion of betting and of probability. The way the term is used has then diverged in those two contexts (presumably with influence in both directions) but it is not as if either set of users has any priority or is misapplying a term that originates with the other. If you look at the early formal writings on probability in English then you find the use of the "odds of X" or "odds that X" as the preferred terms on one side and the "odds against X" on the other seems already well-established. (That looks to me to be the way terms are used by Abraham de Moivre in The Doctrine of Chances in 1718 and in his writings on annuities and by Thomas Simpson in The Nature and Laws of Chance in 1740, for example.) This certainly accords with what I've been able to find out. But this leaves open the question of what has been happening in the past few decades, both to make "the odds of" (sometimes) ambiguous, and also to make it so much more common.]

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