  The bolometric properties (nickel mass, ejecta mass and kinetic energies) of
61 Ibc supernovae (SNe), including 20 Gamma-Ray Burst and X-Ray Flash
(GRB/XRF), 19 Ib, 13 Ic and 9 Ic-BL (broad-lined) SNe are presented. All of the
available $BVRI$ photometry in the literature have been collected and used in a
new method that utilizes a template supernova (SN 1998bw) and an analytical
model based on Arnett (1982) to accurately estimate the bolometric properties
of each SN. A statistical analysis of the bolometric properties is then
performed, where it is found that GRB/XRF SNe are the most energetic, and eject
more mass (including nickel content) than Ib, Ic and Ic-BL SNe. The results are
then compared to the existing progenitor models of Ibc SNe, where it is
concluded that it is highly likely that at least two progenitor channels exist
for producing a Ibc SN: most Ibc SNe arise via binary interactions, where the
mass of the stellar progenitor is less than what is attributed to a Wolf Rayet
star. Conversely, the progenitors of Ic-BL and GRB/XRF are more massive than
those of Ib and Ic SNe, though a key difference between them is progenitor
metallicity, with Ic-BL SNe arise from more metal rich progenitors. As mass
loss in massive stars is influenced by metal content, the progenitors of Ic-BL
SNe lose more mass, and therefore more angular momentum, before exploding. It
is expected that the explosion mechanism in Ic-BL and GRB/XRF SNe is
``engine-driven'' (i.e. an accreting black hole, or a millisecond magnetar),
but the increased mass loss of Ic-BL SNe means the central engine is less
powerful than in GRB/XRF SNe. Finally, it is found that the SNe that accompany
GRBs and XRFs are statistically indistinguishable, and some mechanism other
than metallicity is needed to explain the differences in the high-energy
components in these events.
