A Statistical Timetable for the Sub–2-Hour Marathon

Abstract

Breaking the sub-2-h marathon in an official event has attracted growing interest in recent times with commercial and international momentum building. Here it is shown that predicting how likely and when the sub-2-h barrier will be broken are statistically coupled considerations. Using a nonlinear limiting exponential model and calculating prediction intervals, a statistical timetable for the sub-2-h event is produced over a range of likelihoods. At the benchmark odds level (1 in 10, or 10% likely), the expected sub-2-h arrival time is found to be May 2032. By estimating the model for male and female world record progressions, I find that limiting marathon times for males and females (at 1 in 10) are 1 h 58 min 5 s and 2 h 5 min 31 s, respectively. These times equate to a performance gap of 2.9% and 8.6%, respectively. The male estimate has remarkable similarity (~7 s) to Joyner's 1991 limiting human physiological estimate. Finally, I provide an estimate of the equivalent "sub-2-h" threshold for females and argue that a threshold of 130 min ("sub-130") could be an appropriate choice. The study is the first to address all three related aspects of world record marathon performance (sub-2 h, limits, gender equivalence) in a single, unified modeling framework and provides many avenues for further exploration and insight.