We analyze the impact of sensor attacks on a linear state estimation problem subject to variance and sparsity constraints. We show that the maximum impact in a leader-follower game where the attacker first chooses the distribution of an adversarial perturbation and the defender follows by choosing an estimator is characterized by a minimum Fisher information principle. In general, this is a nonlinear variational problem, but we show that it can be reduced to a finite-dimensional mixed integer SDP. Alternatively, the proposed solution can be seen as a lower bound on the maximum impact for a game in which the defender plays first.