The growth of supermassive black holes ( BHs ) located at the centers of their host galaxies comes mainly from accretion of gas , but how to fuel them remains an outstanding unsolved problem in quasar evolution . This issue can be elucidated by quantifying the radiative efficiency parameter ( \eta ) as a function of redshift , which also provides constraints on the average spin of the BHs and its possible evolution with time . We derive a formalism to link \eta with the luminosity density , BH mass density , and duty cycle of quasars , quantities we can estimate from existing quasar and galaxy survey data . We find that \eta has a strong cosmological evolution : at z \approx 2 , \eta \approx 0.3 , and by z \approx 0 it has decreased by an order of magnitude , to \eta \approx 0.03 . We interpret this trend as evolution in BH spin , and we appeal to episodic , random accretion as the mechanism for reducing the spin . The observation that the fraction of radio-loud quasars decreases with increasing redshift is inconsistent with the popular notion that BH spin is a critical factor for generating strong radio jets . In agreement with previous studies , we show that the derived history of BH accretion closely follows the cosmic history of star formation , consistent with other evidence that BHs and their host galaxies coevolve .