**Sweat Science**

# How Likely Is a Sub-Two Hour Marathon in 2020?

## A new statistical approach brings sophisticated probability analysis to the future of marathoning

There are two basic approaches to predicting the athletic future. One is to start with the human body, try to understand how it works, and use that physiological insight to estimate what some future human might be capable of. That’s the approach that Michael Joyner, a Mayo Clinic physiologist, used back in 1991 to forecast that an ultimate marathon time of 1:57:58 might someday be possible.

The other approach ignores physiology and simply extrapolates from past trends to predict the future. That, in a nutshell, is what an Australian economist named Simon Angus does in a new paper published in *Medicine & Science in Sports & Exercise*—and the result is a forecast that an ultimate marathon time of 1:58:05 might someday be possible. This apparent convergence is intriguing, and it’s just one of several interesting insights that make Angus’s analysis worth a closer look.

The simplest version of the statistical-historical approach is taking a plot of world records over the years, drawing a straight line through them, and seeing where it leads. That’s how you get predictions like the famous one, published in Nature in 1992, that women would surpass men in the marathon in 1998. But as Angus explains, you can take a much more sophisticated approach to this sort of analysis, by thinking more carefully about which historical data you use, what sort of line you draw through it, and what it actually means to predict a future occurrence.

That last point about the nature of prediction is key. When you draw a graph of world record trends and see where the line leads, what you’re implicitly doing is identifying when events will have a 50 percent probability of occurring. If your line crosses the two-hour threshold in 2036 (as one previous model did), that doesn’t mean there *will* be a sub-two in that year. It means that there’s a one-in-two chance it will happen—which isn’t necessarily what we intuitively mean when we ask the question.

Angus, a professor at Monash University (and trail runner) whose research focuses on data science and complexity, takes official IAAF record data since 1950 for both men and women, and fits a non-linear model to the data. But rather than simply using that model to predict future performances, he uses a statistical approach called “prediction intervals” to reflect the fact that the performance of individual runners in the future won’t conform exactly to some mathematical function. We can’t say with certainty when a future event will happen—we can only say how likely a given event will be at a given time.

Let’s make this more concrete: when will the two-hour barrier be broken? If you set the odds at 1 in 10, Angus’s model predicts May 2032. That means he figures there’s a 10 percent chance of it happening then, but it could easily happen earlier or later. He pegs the odds as 1 in 34 in 2020, 1 in 12 in 2030, and 1 in 6 in 2040. The chances of it ever happening are about 1 in 2.

Here’s what those predictions look like in graphical form. The thick line in the middle is the basic prediction of the model at a probability of 50 percent. The parallel lines below show the times at longer odds like 1 in 4, 1 in 10, and so on. (The smaller inset graph shows the odds of a sub-two marathon by year.)

An interesting side note: if you’d asked the model last fall how likely it was that Eliud Kipchoge would run a 2:01:39 marathon (which is what he did in Berlin), the answer would have been roughly 1 in 4. Unlikely, but not a farfetched possibility, in other words.

Another feature of the model is that its predictions approach an asymptote, which corresponds to a hypothetical ultimate record. This too is subject to given levels of probability: the model doesn’t tell you what record can never be broken, but it tells you what ultimate performance has only a 10 percent (or 1 percent, or whatever you choose) chance of being broken. At the 10 percent level, the ultimate record for men is 1:58:05, strikingly similar to Joyner’s physiological prediction. The corresponding women’s time is 2:05:31.

That women’s time, nearly 10 minutes faster than the current record, should perhaps be a warning. Angus uses the men’s and women’s models to suggest some ideas about the appropriate women’s equivalent of a men’s two-hour barrier. Since a two-hour marathon is 1.62 percent slower than the men’s ultimate 10-percent limit, the equivalent women’s time would be 2:07:33. Rounding up to the nearest convenient round number, he suggests that 2:10:00 should be the benchmark that women’s moonshot marathon goals target. According to the model, there’s a 10 percent chance that this threshold will be crossed in... January 1996.

How is it possible that the model produces such a seemingly nonsensical prediction? Angus stands by his model and argues that the reason top female marathoners are currently so far away from the model’s predictions (relative to the men) is that the talent pool of East African marathoners hasn’t yet been fully tapped to the degree it has been for men. Given the sociological constraints that have traditionally faced female athletes in countries like Kenya, that’s an entirely reasonable hypothesis, but I don’t think it explains anywhere near the whole gap.

Instead, I suspect the problem here is the same one that bedeviled the UCLA researchers who predicted female primacy by 1998. The key question facing any attempt to predict the future based on the past, as Angus himself points out, is whether the same factors that produced past trends are still the dominant factors in the future.

This question is a hot one in the two-hour debate. The men’s record has been dropping like a rock since the late 1990s, and if that rate of improvement—five minutes and 11 seconds since 1998—continues, we would expect to see a sub-two in the next six or seven years. But there have been some major changes in marathoning over that period, like far larger prize purses drawing the best runners away from the track at a younger age, and more recently, advanced shoe technologies making runners more efficient. We can’t assume that there will be comparable advances in the decade to come.

On the women’s side, the elephant in the room is that women mostly weren’t even allowed to run marathons until the 1970s. Angus’s model starts in 1950, and the first record in his dataset is Merry Lepper’s 3:37:07 in 1963. The factors that took women from 3:37 in 1963 to 2:38 in 1975 have very little in common with what will be required for women to go from 2:15 to 2:10, and a model that blindly assumes that the former has something to tell us about the latter is likely to make some false assumptions about how easy it is to get faster.

In the end, of course, the biggest mistake we could make is to assume that any one model can tell us everything we want to know about the future. The closer we get to our hypothetical limits, the more the nuances of individual physiology will matter. But as someone who gets asked pretty frequently when a sub-two will happen, I also really like Angus’s approach. Combining “when?” with “how likely?” gives you more robust and informative predictions. And as an added bonus, it’s easier to weasel out of predictions that go wrong.

*My new book, *Endure: Mind, Body, and the Curiously Elastic Limits of Human Performance*, with a foreword by Malcolm Gladwell, is now available. For more, join me on Twitter and Facebook, and sign up for the Sweat Science email newsletter.*