Batting average factors exactly as BA = c [h + (1-h) b], where c is the rate of avoiding a strikeout, h is the home-run rate among non-strikeout at-bats, and b is batting average on balls in play (BABIP). The bracketed term is the rate f at which non-strikeout at-bats become hits, so the composition nests the two-factor identity BA = c f. Using the 256 major-league hitters with at least 300 at-bats in 2025, every season from 2004 to 2025, and 20,357 qualifying seasons from 1901 to 2019, we ask which rates behave like skills and how the corresponding abilities are related. Over 19 consecutive-season pairs the median year-to-year correlation is 0.86 for c, 0.74 for h and 0.41 for b; batting average (0.44) is no more repeatable than BABIP. A trivariate logistic-normal random-effects model gives single-season reliabilities of 0.91, 0.76 and 0.30, and a talent correlation between contact and power of -0.67 (95% profile interval -0.75 to -0.57), while BABIP talent is only weakly related to either. Historically, the negative covariance between c and f, which was near zero in the dead-ball era, explains why batting averages have become less dispersed, and so why no one has hit .400 since 1941. That covariance runs almost entirely through home runs: removing the contact--power channel from the 2010s covariance recovers 72% of the gap between modern and dead-ball dispersion in batting-average talent.
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