By estimating a statistical model for male and female marathon world record progressions a study found that 1:58.05 is likely the fastest time that any living human being will be able to run this distance.

Published today in Medicine and Science in Sports and Exercise, the American College of Sports Medicine’s flagship journal, results show that the chance of a female athlete ever breaking the two-hour mark is less than 1 in 100, with the fastest all-time female marathon time estimated to be 2:05.31.

The study by Monash Business School is the first to address all three related aspects of world record marathon performance in one modelling framework – the sub-two hour limit, the limits of human physiological running capacity and gender equivalence.

It also highlights the potential barriers elite female athletes face in marathon running resulting in a something of a “world record drought”, with Paula Radcliffe’s 2:15.25 mark, set in 2003, still standing. A ‘sub-130 minute’ project (2:10.00), advocated in this study, would empower female long-distance athletes.

The marathon has an official distance of 42.195 kilometres (26.219 miles) and was one of the original Olympic events in 1896. More than 800 marathons are held across the world each year, with tens of thousands of participants taking part in this physically gruelling event.

As part of the study, Dr Angus, Associate Professor of Economics at Monash Business School and ultramarathon runner, applied a robust non-linear economic model to all official IAAF world record marathon performances of men and women since 1950 in order to calculate record-breaking prediction intervals.

From there, Dr Angus was able to reconceptualise the ‘sub-two hour question’ as one of odds – for example, when will a given time be run with 1 in 10, or 10% likelihood.

Using these figures, Dr Angus was then able to determine the limits of human performance for the male and female marathon; the performance gap between the current male and female world record to the limiting times; and the equivalent of the ‘sub-two hour’ threshold for women and when this will be achieved.

The economic model is, on average, accurate to within 1% for men – or around 70 seconds – across a 66-year period which saw a 19 minute reduction in the world record time. For women, accuracy is within 3% – or roughly 200 seconds – across the same period where the world record dropped by one hour and 22 minutes.

A statistical findings for the sub-two hour male marathon are noted as:

The current male world record holder, Eliud Kipchoge from Kenya, is just a fraction outside the sub-two-hour mark with a time of 2:01.39 – a record he set at the Berlin Marathon in 2018. By inspecting the prediction lines on the economic model, there was only a 2% chance that the sub-two-hour record would be broken at that point in time.

Using the same economic model and 10% likelihood approach, Dr Angus calculated that the likely human performance limit for male and female marathon times is 1:58.05 (performance gap to current world record of 2.9%) and 2:05.31 (performance gap of 8.6%) respectively.