# Why is it the case that off-policy evaluation using importance sampling suffers from high variance?

The average return for trajectories, $$V^{\pi_e}$$(s) is often computed via the importance sampling estimate $$V^{\pi_e}(s) = \frac{1}{n}\sum_{i=1}^n\prod_{t=0}^{H}\frac{\pi_e(a_t | s_t)}{\pi_b(a_t|s_t)}G_i$$ where $$G_i$$is the reward observed for the $$i$$th trajectory. Sutton and Barton gives an example whereby the variance could be infinite.

In general, however, why does this estimator suffer from high variance? Is it because $$\pi_e(a_t|s_t)$$ is mainly deterministic and, therefore, the importance weight is $$0$$ for most trajectories, rendering those sample trajectories useless?