  With the advent of space-based precision photometry missions the quantity and
quality of starspot light curves has greatly increased. This paper presents a
large number of starspot models and their resulting light curves to: 1) better
determine light curve metrics and methods that convey useful physical
information, 2) understand how the underlying degeneracies of the translation
from physical starspot distributions to the resulting light curves obscure that
information. We explore models of relatively active stars at several
inclinations while varying the number of (dark) spots, random spot
distributions in position and time, timescales of growth and decay, and
differential rotation. We examine the behavior of absolute and differential
variations of individual intensity dips and overall light curves, and
demonstrate how complex spot distributions and behaviors result in light curves
that typically exhibit only one or two dips per rotation. Unfortunately
simplistic "one or two spot" or "active longitude" descriptions or modeling of
light curves can often be highly misleading. We also show that short "activity
cycles" can easily be simply due to random processes.
  It turns out to be quite difficult to disentangle the competing effects of
spot lifetime and differential rotation, but under most circumstances spot
lifetime is the more influential of the two. Many of the techniques tried to
date only work when spots live for many rotations. These include
autocorrelation degradation for spot lifetimes and periodograms for both global
and differential rotation. Differential rotation may be nearly impossible to
accurately infer from light curves alone unless spots live for many rotations.
The Sun and solar-type stars its age or older are unfortunately the most
difficult type of case. Further work is needed to have increased confidence in
light curve inferences.
