A Statistical Timetable for the Sub-2-Hour Marathon

Introduction Breaking the sub-2 hour 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 hour barrier will be broken are statistically coupled considerations. Methods Using a non-linear limiting exponential model and calculating prediction intervals, a statistical timetable for the sub-2 hour event is produced over a range of likelihoods. Results At the benchmark odds level (1 in 10, or 10% likely), the expected sub-2 hour 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 1hr 58min 5s and 2hr 5min 31s respectively. These times equate to a performance gap of 2.9% and 8.6% respectively. The male estimate has remarkable similarity (~ 7s) to Joyner's 1991 limiting human physiological estimate. Finally, I provide an estimate of the equivalent 'sub-2h' threshold for females, and argue that a threshold of 130min ('sub-130') could be an appropriate choice. Conclusion The study is the first to address all three related aspects of world record marathon performance (sub-2 hour, limits, gender equivalence) in a single, unified modeling framework and provides many avenues for further exploration and insight. This is an open-access article distributed under the terms of the Creative Commons Attribution-Non Commercial-No Derivatives License 4.0 (CCBY-NC-ND), where it is permissible to download and share the work provided it is properly cited. The work cannot be changed in any way or used commercially without permission from the journal. The author declares no conflict of interest regarding the study. The results of the present study do not constitute endorsement by the ACSM. The results of the study are presented clearly, honestly, and without fabrication, falsification, or inappropriate data manipulation. Correspondence: Simon D. Angus Dept. of Economics, Monash University, Wellington Road, Clayton 3800 VIC Australia. E-mail: Simon.angus@monash.edu, Submitted for publication November 2018. Accepted for publication February 2019. © 2019 American College of Sports Medicine

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