Phys. Rev. B 55, 9007 (1997).
Despite many years of intense theoretical effort it is still not possible to predict whether a material will be superconducting or not at low temperatures by measurement of its physical properties at higher temperatures. Nor is it possible in general to estimate the magnitude of the superconducting critical temperature $T_c$ from measurements of normal state properties. Here we address these questions from a statistical point of view. The metallic elements in the first six rows of the periodic table are assumed to be a ``representative sample'' drawn from a larger set of materials, and various statistical measures of correlations between the magnitude of $T_c$ and a normal state property, as well as between a normal state property and the fact whether the material is or is not a superconductor, are considered. Thirteen normal state physical properties are studied, some of which are believed to be important to determine superconducting properties within conventional BCS theory and others not. It is found that properties assumed to be important within BCS theory rank lowest in predictive power regarding whether a material is or is not a superconductor. Instead, properties with highest predictive power in this respect are found to be bulk modulus, work function and Hall coefficient. With respect to the magnitude of $T_c$, it is found to be positively correlated with electronic heat capacity, magnetic susceptibility and atomic volume, and negatively correlated with electrical and thermal conductivity and Debye temperature. No significant correlations with ionic mass and ionization potential are found. Consequences of these findings for the theoretical understanding of superconductivity are discussed.