The puzzle consists of two pieces. First, smoking during pregnancy is linked to lower birthweight. That link was already being reported in the 1950s; for example, Simpson (1957) Simpson, W. J. (1957). A preliminary report on cigarette smoking and the incidence of prematurity. American Journal of Obstetrics and Gynecology. found that smoking mothers were much more likely to have babies in the low-birthweight group, and later prospective work by Yerushalmy (1964) Yerushalmy, J. (1964). Mother's cigarette smoking and survival of infant. American Journal of Obstetrics and Gynecology. again found more low-birthweight births among smokers, with heavier smoking linked to a higher chance of low birthweight.

Second, low birthweight is strongly linked to worse survival. The World Health Organization notes that low-birthweight infants are about 20 times more likely to die than heavier infants.

Put those two facts together and you would expect babies of smoking mothers to do worse. But once researchers looked only at low-birthweight babies, the pattern seemed to flip: babies of smoking mothers sometimes appeared more likely to survive than low-birthweight babies of non-smokers. In later data summarized by Hernández-Díaz, Schisterman, and Hernán (2006) Hernández-Díaz, S., Schisterman, E. F., and Hernán, M. A. (2006). The birth weight “paradox” uncovered? American Journal of Epidemiology. low-birthweight infants born to smokers had lower infant mortality than low-birthweight infants born to non-smokers, even though smokers had higher risks of both low birthweight and infant mortality overall.

That is what made the result so strange. Yerushalmy himself basically said: this cannot be right in any simple biological sense. As he put it "It is difficult to propose a reasonable explanation for this phenomenon of relatively more, but apparently healthier, infants of "low birth weight" among smoking than nonsmoking mothers. "