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In the literature on authoritarian elections, there are multiple interpretations of the fact that rigged elections often win by wide margins. However, since the ballot box blends the illegitimate votes with the legitimate ones, it is hard to know whether the documented irregularities reversed a defeat, widened a winning margin, or were only cosmetic modifications to an overwhelming victory. In this paper, I use an original estimation technique to demonstrate how fraud can widen an incumbent's margin of victory that was already wide. Using original data from Mexico, I apply this new method to the magnitude of fraud in Mexico's infamous 1988 presidential election. Consistent with conventional wisdom, I find that the winner committed large-scale fraud, inflating his vote share by more than 1.5 million votes or about 20% of its legitimate vote earnings. However, I also find that the irregularities did not determine the outcome: the perpetrator would have won anyway, by a considerable margin. By estimating counterfactual fraud-free vote shares, the proposed method provides new insights into the conditions under which incumbents engage in fraud.