Being Human

I've observed from time to time, half-seriously, that the ambiguity of plural noun-phrase comparison ("women have better hearing than men") causes — as well as results from — the tendency to interpret small group differences as essential group characteristics (e.g. "The Pirahã and us", 10/6/2007; "Annals of essentialism: sexual orientation and rhetorical assymmetry", 6/18/2008; "Pop platonism and unrepresentative samples", 7/26/2008; 'The happiness gap returns", 7/26/2008;. "Reverse Whorfianism and SHAs", 12/23/2008).

But there are other, more lexically specific, sources of confusion about statistical concepts and statements. One that I noticed for the first time yesterday is an ambiguity in the word chance. Its popular use in the sense of probabilistic odds ("little chance of success"; "his chances are good" , etc.) is relatively recent, and has always overlapped with an older meaning that emphasizes complete unpredictability and the lack of any discernable cause.

This history helps explain the shocking sentence that I read yesterday on the online front page of the New York Times; "A longtime trainer uses an actuarial approach to predict injuries, defying the assumption that what happens to players is a matter of chance".

The Society of Actuaries will be surprised to see "an actuarial approach" characterized as "defying the assumption that what happens … is a matter of chance", since their web site tells us that

Actuaries use mathematics, statistics and financial theory to study uncertain future events, especially those of concern to insurance and pension programs. They evaluate the likelihood of those events, design creative ways to reduce the likelihood and decrease the impact of adverse events that actually do occur.

And the American Statistical Association may wonder whether it should reconsider the name of its magazine, Chance.

The OED gives the following etymology for chance:

[ME. chea(u)nce, a. OF. cheance (= Pr. cazensa, It. cadenza):–late L. cadentia falling, f. cadent- falling, pr. pple. of cad-ĕre to fall: cf. CADENCE.]

The ASA's magazine is named for the OED's sense 5.a., "A possibility or probability of anything happening: as distinct from a certainty: often in plural, with a number expressed".

1778 T. JONES Hoyle's Games Impr. 153, I would know how many Chances there are upon 2 Dice..The Answer is 36. 1785 REID Int. Powers 626 The doctrine of chances is a branch of mathematics little more than an hundred years old. 1841-4 EMERSON Ess. xix. Wks. (Bohn) I. 239 Unless the chances are a hundred to one that he will cut and harvest it. 1848 MACAULAY Hist. Eng. I. 215 There was no chance that..the scheme..would be supported by a majority. 1879 LUBBOCK Sci. Lect. i. 7 The chances against any given grain reaching the pistil of another flower are immense.

The NYT teaser is apparently using the OED's sense 6, "Absence of design or assignable cause, fortuity; often itself spoken of as the cause or determiner of events, which appear to happen without the intervention of law, ordinary causation, or providence". This meaning seems to be older:

1526 Pilgr. Perf. (W. de W. 1531) 144b, In cases of chaunce or vncertaynty. 1581 J. BELL Haddon's Answ. Osor. 160b, Those whiche..doe committe the successes of thynges to happe hazard, and blynd chaunce. 1641 BROME Jov. Crew II. Wks. 1873 III. 389, I ha' not so much Wealth to weigh me down, Nor so little (I thank Chance) as to daunce naked. 1722 WOLLASTON Relig. Nat. v. 83 Chance seems to be only a term, by which we express our ignorance of the cause of any thing. 1802 PALEY Nat. Theol. xii. §2 (1819) 198 A conformation so happy was not the gift of chance. 1841-4 EMERSON Ess. xiv. Wks. (Bohn) I. 183 The ancients, struck with this irreducibleness of the elements of human life to calculation, exalted Chance into a divinity. 1846 MILL Logic III. xvii. §2 It is incorrect to say that any phenomenon is produced by chance; but we may say that two or more phenomena are conjoined by chance..meaning that they are in no way related through causation.

The actual NYT article in question (Michael S. Schmidt, "Seeking a Way to Predict Baseball Injuries", NYT, 8/7/2009) presents a clear picture of the issues involved:

The ability to predict how players’ bodies will fare is a holy grail. With an actuarial approach, [Stan] Conte [the Dodgers' head athletic trainer] seems to have a head start in the pursuit. He is trying to build a formula that would give teams a competitive advantage and help them avoid players who spend their days in the training room and not on the field.

“The insurance industry has made millions of dollars off figuring out how, when, where and why people are going to die, and we are trying to figure those things out about injuries,” Conte said.

But: it also explicit suggests that if something is "a matter of chance" or "a matter of luck", then it must be completely random and unpredictable:

Conte believes the long-prevailing belief in baseball that injuries are a matter of chance is misguided.

“I refuse to think we are doing all these things to get them healthy, and it’s a matter of luck whether lightning hits or doesn’t hit,” he said.

[Update: Note that there are plenty of difficult philosophical and practical questions in the area of probability, uncertainty, ignorance, and causation — see e.g. here. But what underlies examples like those cited above seems to be too little thought about such puzzles, rather than too much. ]