Political actors often manipulate redistricting plans to gain electoral advantages, a process known as gerrymandering. Several states have implemented institutional reforms to address this problem, such as establishing map-drawing commissions. Estimating the impact of these reforms is challenging because each state structures its processes and rules differently. We model redistricting as a sequential game whose equilibrium solution summarizes multistep institutional interactions as a univariate score. We argue that this score measures the leeway political actors have over the partisan lean of the final plan. Our differences-in-differences analysis demonstrates that reforms reduce partisan bias and increase competitiveness by constraining partisan actors. We perform a counterfactual policy analysis to estimate the effects of enacting recent reforms nationwide. Though commissions are likely to reduce bias, reforms that restrict partisan actors in multiple ways, such as removing veto points (Michigan), are more effective than commissions where parties retain some control (Ohio).