  The number of millisecond pulsars (MSPs) observed in Milky Way globular
clusters has increased explosively in recent years, but the underlying
population is still uncertain due to observational biases. We use
state-of-the-art $N$-body simulations to study the evolution of MSP populations
in dense star clusters. These cluster models span a wide range in initial
conditions, including different initial masses, metallicities, and virial
radii, which nearly cover the full range of properties exhibited by the
population of globular clusters in the Milky Way. We demonstrate how different
initial cluster properties affect the number of MSPs, for which we provide
scaling relations as a function of cluster age and mass. As an application, we
use our formulae to estimate the number of MSPs delivered to the Galactic
Center from inspiralling globular clusters to probe the origin of the
Galactic-Center gamma-ray excess detected by Fermi. We predict about $400$ MSPs
in the Galactic Center from disrupted globular clusters, which can potentially
explain most of the observed gamma-ray excess.
