Each year in the past three decades has seen hundreds of thousands of runners register to run a major marathon. Of those who attempt to race over the marathon distance of 26 miles and 385 yards (42.195 kilometers), more than two-fifths experience severe and performance-limiting depletion of physiologic carbohydrate reserves (a phenomenon known as hitting the wall), and thousands drop out before reaching the finish lines (approximately 1-2% of those who start). Analyses of endurance physiology have often either used coarse approximations to suggest that human glycogen reserves are insufficient to fuel a marathon (making hitting the wall seem inevitable), or implied that maximal glycogen loading is required in order to complete a marathon without hitting the wall. The present computational study demonstrates that the energetic constraints on endurance runners are more subtle, and depend on several physiologic variables including the muscle mass distribution, liver and muscle glycogen densities, and running speed (exercise intensity as a fraction of aerobic capacity) of individual runners, in personalized but nevertheless quantifiable and predictable ways. The analytic approach presented here is used to estimate the distance at which runners will exhaust their glycogen stores as a function of running intensity. In so doing it also provides a basis for guidelines ensuring the safety and optimizing the performance of endurance runners, both by setting personally appropriate paces and by prescribing midrace fueling requirements for avoiding the wall. The present analysis also sheds physiologically principled light on important standards in marathon running that until now have remained empirically defined: The qualifying times for the Boston Marathon.