log10P1Pref

log10P1Pref is a term used in some statistical and machine learning codebases to denote the base-10 logarithm of a first-choice preference probability, abbreviated as P1Pref. In this context, P1Pref represents the probability that option 1 is chosen or preferred over alternatives. The quantity log10P1Pref is defined as log10(P1Pref). Since P1Pref lies in the interval (0,1], log10P1Pref takes values in (−∞,0]. When P1Pref equals 1, log10P1Pref is 0; as P1Pref approaches 0, log10P1Pref decreases without bound, which can pose numerical challenges in some applications.

In typical modeling workflows, log10P1Pref is used to perform computations in log space to improve numerical stability, such as in log-likelihood calculations, posterior updates, or ranking scores. If P1Pref is estimated from data via a link function (for example, a logistic or probit model), log10P1Pref can be computed after obtaining P1Pref by applying the base-10 logarithm.

An example: if P1Pref = 0.5, then log10P1Pref ≈ log10(0.5) ≈ −0.3010. If P1Pref = 0.01, log10P1Pref ≈ −2.0.

Because log10P1Pref depends directly on P1Pref, changes in the underlying probability map into log space, illustrating how small probability differences can produce larger negative values in the log scale. See also log10, logit, log-likelihood, and probability.