We perform a systematic study of the 56 Ni mass (M Ni ) of 27 stripped envelope supernovae (SESNe) with both well-constrained rise times and late-time coverage (>60 days) by modeling their light-curve tails. Based on this sample, we find that using "Arnett's rule" with observed peak times (t p ) and luminosities (L p ) will overestimate M Ni for SESN by a factor of ∼2. Recently, Khatami & Kasen (2019) presented a new analytic model relating t p and L p of a radioactive-powered SN to its M Ni that addresses several limitations of Arnettlike models, but depends on a dimensionless parameter β, which is sensitive to details of the progenitor system and explosion mechanism. Using the observed t p , L p , and tail-measured M Ni values for the sample of SESN, we observationally calibrate β for the first time-finding 0.0 < β < 1.71 with a median value of 0.70. Despite scatter, we demonstrate that the model of Khatami & Kasen (2019) coupled with these empiricallycalibrated β values yields a significantly improved measurement of M Ni when only photospheric data is available. However, these observationally-constrained β values are systematically lower than those inferred from numerical simulations, due primarily to the observed sample having significantly higher (0.2-0.4 dex) L p for a given M Ni . We investigate this discrepancy and find that while effects due to composition, mixing, and asymmetry can increase L p none can explain the systematically low β values. However, the discrepancy with simulations can be alleviated if ∼7-50% of L p for the observed sample comes from sources other than the radioactive decay of 56 Ni. Either shock cooling or magnetar spin down could provide the requisite luminosity, with the former requiring that a substantive fraction of SESN undergo late-stage mass loss or envelope inflation. Finally, we find that even with our improved measurements, the M Ni values of SESN are a factor of ∼3 larger than those of hydrogen-rich Type II SN, indicating that these supernovae are inherently different in terms of their progenitor initial mass distributions or explosion mechanisms.