What do we learn by mapping dark energy to a single value of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>w</mml:mi></mml:math>?

We examine several dark energy models with a time-varying equation-of-state parameter, $w(z)$, to determine what information can be derived by fitting the distance modulus in such models to a constant equation of state parameter, ${w}_{*}$. We derive ${w}_{*}$ as a function of the model parameters for the Chevallier-Polarski-Linder (CPL) parametrization and for the Dutta-Scherrer approximation to hilltop quintessence models. We find that all of the models examined here can be well described by a pivotlike redshift, ${z}_{\text{pivot}}$, at which the value of $w(z)$ in the model is equal to ${w}_{*}$. However, the exact value of ${z}_{\text{pivot}}$ is a model-dependent quantity; it varies from ${z}_{\text{pivot}}=0.22--0.25$ for the CPL models to ${z}_{\text{pivot}}=0.17--0.20$ for the hilltop quintessence models. Hence, for all of the models considered here, a constant-$w$ fit gives the value of $w$ for $z$ near 0.2. However, given the fairly wide variation in ${z}_{\text{pivot}}$ over even this restricted set of models, the information gained by fitting to a constant value of $w$ seems rather limited.