Close elections are important for many reasons, including that consequent election disputes can weaken democratic legitimacy and risk political violence. We quantify the probability of close outcomes in U.S. presidential races with novel applications of empirical election models from several sources. We show that razor-thin margins are very likely under the Electoral College (EC). And we establish that the EC causes this closeness: It would not occur under any plausibly comparable popular vote system. The tendency of the EC to generate close elections is found today and throughout U.S. presidential voting history.