Despite numerous enlightening studies of the hiring and retention of academic faculty, relatively little is known about the rates, patterns, and causes of mid-career moves (MCMs). Here, we analyze 10 years (2011-2020) of an annual U.S. faculty census to characterize MCMs. Although MCMs are rare in academia, we find a rich heterogeneity in the annual MCM rate by field and domain. Younger faculty, faculty at elite institutions and rural institutions are at a higher risk of moving, self-hires are at a much lower risk, while we do not find a significant gender effect on MCM risk. MCMs tend to move faculty to institutions that are closer in prestige to their origin institution than we expect, exhibit significant assortativity between public and private institutions and effectively increase the number of self-hires and faculty at private and urban institutions. Faculty experience prestige advantages when they move to their alma mater, to private and urban institutions, while women gain slightly more prestige than men over MCMs. Finally, we find that faculty tend to trade prestige for a promotion when they move, prompting us to develop a utility theory of faculty MCMs. These findings quantify large-scale patterns in faculty MCMs in tenure-track/tenured faculty in PhD granting universities in the US at an unprecedented scale, enriching the grounds for further research to determine causal mechanisms that drive these patterns.