Prior information is essential for statistical seismic inverse problems to quantify uncertainties of unknown subsurface parameters. Conventional prior knowledge is based on empirical observations of subsurface structures like the smoothness of the subsurface image. However, such hand-designed prior knowledge is too generic to describe detailed subsurface structures. Deep generator priors are a recent encouraging development, where a high-quality prior can be crafted solely from existing data and a deep neural network. Such deep generators can create detailed subsurface models from Gaussian vectors in a lowdimensional latent space. Alongside this potential advantage, comes the major risk that the prior might be too restrictive to give physically meaningful solutions a high enough likelihood. In this work, we attempt to mitigate this risk by presenting a measure to evaluate the quality of the learned deep generator prior, which can then be leveraged to tune its hyperparameters. Given a testing model and a generator, we first find the best generated model that minimizes the `2-norm misfit between the generated and testing models. To measure the quality of the generator, we suggest two criteria: (1) the `2-norm model error should be small; and (2) the `2-norm of the corresponding latent vector should be bounded and within a pre-defined reference range. Numerical examples show that a good prior generator in the sense of the proposed measure can help produce more accurate results for statistical seismic inverse problems.