We investigate the rubrene triplet sensitization by perovskite thin films based on methylammonium formamidinium lead triiodide (MAFA) of varying thicknesses. The power-law dependence of both the MAFA photoluminescence (PL) intensity and upconverted emission is tracked as a function of the incident power density. Bimolecular triplet-triplet annihilation (TTA) exhibits a unique power-law dependence with a slope change from quadratic-to-linear at the threshold I-th. The underlying MAFA PL power-law dependence dictates the power law of the upconverted P: (1) below I-th, the slope of the upconverted PL is twice the value of the MAFA PL; (2) above I-th, it follows the same power law as the underlying recombination of mobile electrons and holes in the MAFA films. We find that the I-th shifts to subsolar incident laser powers when increasing the MAFA thickness above 30 nm. For the thickest MAFA film of 380 nm we find an upconversion threshold of I-th = 7.1 mW/cm(2).