  It is commonly argued that an undesirable feature of a theoretical or
phenomenological model is that salient observables are sensitive to values of
parameters in the model. But in what sense is it undesirable to have such
'fine-tuning' of observables (and hence of the underlying model)? In this
paper, we argue that the fine-tuning can be interpreted as a shortcoming of the
explanatory capacity of the model: in particular it signals a lack of
explanatory depth. In support of this argument, we develop a schema -- for (a
certain class of) models that arise broadly in physical settings -- that
quantitatively relates fine-tuning of observables to a lack of depth of
explanations based on these models. We apply our schema in two different
settings in which, within each setting, we compare the depth of two competing
explanations. The first setting involves explanations for the Euclidean nature
of spatial slices of the universe today: in particular, we compare an
explanation provided by the big-bang model of the early 1970s (where no
inflationary period is included) with an explanation provided by a general
model of cosmic inflation. The second setting has a more phenomenological
character, where the goal is to infer from a limited sequence of data points,
using maximum entropy techniques, the underlying probability distribution from
which these data are drawn. In both of these settings we find that our analysis
favors the model that intuitively provides the deeper explanation of the
observable(s) of interest. We thus provide an account that relates two
'theoretical virtues' of models used broadly in physical settings -- namely, a
lack of fine-tuning and explanatory depth -- and argue that finely tuned models
sacrifice explanatory depth.
