  Recent cosmological analyses (e.g., JLA, Pantheon) of Type Ia Supernova
(SNIa) have propagated systematic uncertainties into a covariance matrix and
either binned or smoothed the systematic vectors in redshift space. We
demonstrate that systematic error budgets of these analyses can be improved by
a factor of $\sim1.5\times$ with the use of unbinned and unsmoothed covariance
matrices. To understand this, we employ a separate approach that simultaneously
fits for cosmological parameters and additional self-calibrating scale
parameters that constrain the size of each systematic. We show that the
covariance-matrix approach and scale-parameter approach yield equivalent
results, implying that in both cases the data can self-calibrate certain
systematic uncertainties, but that this ability is hindered when information is
binned or smoothed in redshift space. We review the top systematic
uncertainties in current analyses and find that the reduction of systematic
uncertainties in the unbinned case depends on whether a systematic is
consistent with varying the cosmological model and whether or not the
systematic can be described by additional correlations between SN properties
and luminosity. Furthermore, we show that the power of self-calibration
increases with the size of the dataset, which presents a tremendous opportunity
for upcoming analyses of photometrically classified samples, like those of
Legacy Survey of Space and Time (LSST) and the Nancy Grace Roman Telescope
(NGRST). However, to take advantage of self-calibration in large,
photometrically-classified samples, we must first address the issue that
binning is required in currently-used photometric methodologies.
