A universal law of decline for running, swimming… and chess?!


As of September 2017, new Sweat Science columns are being published at www.outsideonline.com/sweatscience. Check out my bestselling new book on the science of endurance, ENDURE: Mind, Body, and the Curiously Elastic Limits of Human Performance, published in February 2018 with a foreword by Malcolm Gladwell.

- Alex Hutchinson (@sweatscience)


Which do you lose first as you get older: speed or endurance? Swimming speed or running speed? Athletic ability or cognitive ability? There have been dozens of studies investigating these questions, often with conflicting results. But all these processes of decline follow the same basic mathematical rules, according new study in the journal Age by researchers in France (press release here; full text freely available here).

The abilities of all living things follow a basic pattern: (1) you start at zero when you’re born; (2) as you get bigger, stronger and more experienced, your abilities increase exponentially; (3) as your body starts to age and wear out, an exponential decline kicks in; (4) you end up back at zero when you die. During your peak years, the balance between the rising and falling exponential curves gives you a brief plateau.

Now, this seems like a fairly bland set of statements. After all, they’re not taking into account loss of muscle mass with aging, and shortening of telomeres, and loss of tendon elasticity and so on. They’re just wrapping all the details into a general curve. And in fact, their argument is even bigger than that: this curve doesn’t just describe your 100-metre dash time. It describes the life of cycle of individual cells; of human beings; and of species in general. They claim.

To explore this theory, the researchers studied the career trajectory of more than 11,200 individual track athletes, swimmers and chess players. Here’s some sample data: track is at the top (Ato Boldon, 100m, blue; Sandie Richards, 400m, red), swimming is middle (Peter van den Hoogenband, 100m free, blue; Martina Marcova; 200m free; black), and chess is the bottom (Jonathan Simon Speelman in blue, Jan Timman in black).

Convinced? Yeah, me neither, to be honest. But statistically, they claim that this model accounts for 91.7% of the variance at the individual level, and 98.5% at the species level. For “species level,” they looked at age-class bests. The data below shows curves for (top) men’s 100m free, women’s 200m free and women’s 400m run; (middle) best chess performance by age; (bottom) men’s marathon. The marathon graph is the most interesting, because it shows the two exponentials — rising and falling — that are added together to produce the model.

So what does this all mean? I’ve got to be honest: I found the paper pretty hard to understand. (Fortunately, the full text is freely available online, so you don’t have to rely on my attempts to decipher it!) I don’t think we’re supposed to look at those graphs and assume that Ato Boldon is going to be either dead or paralyzed when he turns 64. Rather, I think this model is intended to help us understand what the future evolution of sport (and other human capabilities) as a whole might be. As the researchers conclude:

The study of the world records progression and top performances revealed a plateau in a majority of studied events. We extended the studied data and the model to a broader context: the development of physiological performance in the process of ageing. This questions the upcoming evolution of the biphasic pattern presented here: will the phenotypic expansion continue, plateau or decrease? Do we have the ability to maintain our development in a sustainable way?

Good questions — but of course, they don’t know the answers. Let’s see what Usain Bolt does this year and next, then we’ll talk.

[BONUS: Here’s a link to the appendix where they list the fitting parameters for the 11,200 careers they analyzed. Interesting tidbit: the average ages of peak performance for different events. E.g. for running: 23.3 for men’s 10,000m, 31.6 for men’s marathon. That’s a big gap!]

5 Replies to “A universal law of decline for running, swimming… and chess?!”

  1. Maybe the top performers are just tired of performing after a number of years and they’ve lost motivation. It would be interesting to see the graph of someone who became serious at the age of 35. Would the curve look the same but shifted over by 15 years or would it begin to decline immediately to match the data of the earlier starters?

  2. I haven’t read this closely, but a Yale economist named Ray Fair did a similar study a few years back. Fair has also charted his own running times through several decades, as well as other performances, and produced interesting curves and factors quite similar to the World Age/Gender-Graded tables. Good stuff at http://fairmodel.econ.yale.edu/aging/index.htm

  3. I think Richard is right, top athletes started young and peak early, from my 20 to 49 years i run 2 or 3 times a week, 10k around 40 min.
    becoming a master at 50. i started to train and diet seriously. 5 days a week. and since then i break all my pr.s 10k 36.12 next year when i am
    55 I hope to run my first sub 3hour marathon.
    when i keep this going i will be dutch champion master 60+ in a few years.
    nice curve would that be.
    But statistics will alway neutralise the individuals like me.

  4. @Richard: Yes, I think one of the assumptions implicit in the analysis is that the performances in the fit are more or less maximal (they only used data from yearly world lists) — which obviously isn’t necessarily true, particularly for those of us not on the world lists. 🙂 My naive guess is that (according to this theory, at least) each of us conforms to a “virtual” curve with the same general shape (though, as their data shows, different people and different types of performance peak at different ages). If you’re not “maximizing” your potential during a given period of your life, then your performances fall below that virtual curve, but don’t change its shape.

    @Amby: Thanks for the link — interesting stuff. And interesting that both groups use running and chess to study the issue. I guess they’re both easily quantifiable. Makes me want to start tracking my chess performance… which way does the horsey move again?

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