  Semi-analytic models (SAMs) systematically predict higher stellar-mass
scatter at a given halo mass than hydrodynamical simulations and most empirical
models. Our goal is to investigate the physical origin of this scatter by
exploring modifications to the physics in the SAM Dark Sage. We design two
black hole formation models that approximate results from the IllustrisTNG
300-1 hydrodynamical simulation. In the first model, we assign a fixed black
hole mass of $10^{6}\, \mathrm{M}_{\odot}$ to every halo that reaches
$10^{10.5}\, \mathrm{M}_{\odot}$. In the second model, we disregard any black
hole growth as implemented in the standard Dark Sage model. Instead, we force
all black hole masses to follow the median black hole mass-halo mass relation
in IllustrisTNG 300-1 with a fixed scatter. We find that each model on its own
does not significantly reduce the scatter in stellar mass. To do this, we
replace the native Dark Sage AGN feedback model with a simple model where we
turn off cooling for galaxies with black hole masses above $10^{8}\,
\mathrm{M}_{\odot}$. With this additional modification, the SMBH seeding and
fixed conditional distribution models find a significant reduction in the
scatter in stellar mass at halo masses between $10^{11-14}\,
\mathrm{M}_{\odot}$. These results suggest that AGN feedback in SAMs acts in a
qualitatively different way than feedback implemented in cosmological
simulations. Either or both may require substantial modification to match the
empirically inferred scatter in the Stellar Mass Halo Mass Relation (SMHMR).
