On learning from "doing the math"

In case you have been living under a rock (yet inexplicably reading this blog) Usain Bolt has now run both the 100 meter and 200 meter track events faster than anyone ever. The margin of improvement in the 100 meter event (which occurred earlier) was sufficient to start the sports world abuzz. Naturally, sports fans are willing to talk endlessly about the most absurd minutia and implications of such an event in terms pedestrian and embarrassingly overwrought.
YHN is no different.

I was struck, however, by one particular approach to analyzing the performance of Usain Bolt in the 100 meter dash. As we see from this discussion, it is possible to take the world record 100 m times over the past several decades and construct a mathematical function which fits, more or less, the data.

source[see update!]This is a not-uncommon approach in science. First, graph your data and take a look. See if there is something orderly about the data that allow you to predict other outcomes or other data in a series. Perhaps use some mathematics to make those predictions somewhat more quantitative, general or precise. All well and good.
Just so long as you don’t forget something important.
This prediction approach has been blogged by Ethan Siegel over at Starts with a Bang. The trouble is I think he does a huge disservice to both sports fans and communicating the essential conduct of science* with his post. How so? Well Ethan generated his own version of the above figure and then made several key observations.

Luckily, simply modeling this mathematically — by an exponential — will tell us what the world record progression ought to look like, and should tell us what the theoretical limit of the human body is. Not only that, but we can predict what the future record ought to be. What do we find?
mathematically, it looks like the theoretical limit of how fast humans can run the 100 meter dash is somewhere around 9.2 seconds, but it looks like we won’t get there for hundreds of years.

Ethan Siegel’s update
Okay, okay, he emphasized the mathematically part. Almost as if the obvious caveats were about to emerge. “Under these conditions”. That is about the most general way to put it. The prediction into the future only holds as long as the conditions under which the data which were used to generate the prediction hold.
Sadly, Ethan fails to make this point and indeed sprints steps right into error (in the post, anyway).

So what do we learn, practically, from doing this math? That watching Usain Bolt run is like watching Bob Beamon’s long jump in 1968; it’s a record that should stand for at least a generation.

Gak. Let me get back to the proper way to look at the world record 100 m dash data and the predictive curve fitting. One of the best parts of science can be to look at your data and find something that looks funny**. To ask: Where do the data violate the trend?
Who cares about performances matching prediction? Violations of the expected are what is absolutely fascinating. Especially to the sports-fan scientists. Because now you get to engage in hypothesis generating. Which, in the sports fan, is otherwise known as bar-stool bullshitting. In science, however, this is what allows you to move forward in new, perhaps unexpected, perhaps fascinating, directions. Looking at the graph here, you might identify some outlier data that makes you wonder.
Why did 100 m dash times stagnate in the late seventies? A drop in public interest in track and field changing contingencies? Technological stall-out? Contingencies in other sporting endeavors poaching what would be the top sprinting talent?
Why did times start dropping again in the 80s-90s? [*cough*doping*cough*]
And now, how do we explain the performances of Usain Bolt?
Leaving pharmacological doping aside, since current testing has been unable to find any evidence of this with Bolt to date, we have a description, if not a mechanistic explanation. In a radio interview I heard on NPR, Professor Peter Weyand, of Southern Methodist University [also quoted on the topic here] pointed out that Bolt is unusually tall for a world-class 100 m sprinter. That he started the race as quickly as the more traditional (shorter) sprinter but then finished the race faster (i.e., consistent with a taller runner). In short this individual sprinter is a violation of previously existing conditions.
So first of all, we get a slap upside the head about the mathematical modeling. Conditions have changed. Our assumptions about a rule of the physiology of elite sprinters have changed. It is possible to find a tall man who starts the race as quickly as the previous 100 m champion phenotype. (Actually, once you accept this, is Bolt really so surprising?) We need to fit a new function.
Will Bolt’s record stand for a generation? Maybe. Maybe not. Perhaps highly promising young runners who coaches “know” are “too tall” to be 100 m runners will not be pushed into the 400 m + events but rather trained for the 100 and 200 m events? Or coaches will focus their runner selection on the start of the sprint in taller runners? Or is Usain Bolt simply an outlier?
Final points from the world of pro cycling. Miguel Indurain absolutely dominated the Tour de France in the early 1990s, winning 5 in a row. He was a violation of type, at 1.88 m (6 ft 2 in) and 80 kg (176 lbs) however it was assumed that a generous cardiovascular endowment that was consistent with type enabled him to excel. Not knowing this, one might assume towards the end of the Indurain era that many subsequent Grand Tour cyclists would be big guys (who, btw, focused exclusively on the Tour events). No evidence of this yet so we must assume he was indeed something of an outlier with his cardiovascular superiority compensating for his large(r) size.
The world hour record is a performance benchmark more similar to track and field in that ultimately it is one person against the clock under more or less fixed conditions. In this case, the 1990s heralded some performances that violated the mathematical prediction of prior data (page down to the bottom of the wikipedia article). The reason in this case was technological advances in the aerodynamic efficiency of bike and rider (clothing and positioning). A change of the conditions under which the data were collected. Ultimately the sanctioning body artificially restored the trendline by outlawing the technological advances.
Okay, irritation with the unthinking application of mathematics in a case which calls for, you know, thinking scratched. These Bolt performances are awesome, aren’t they?
[UPDATE: As Isis kindly points out in a comment, the first graph comes from a much more sophisticated modeling procedure than does the second. I gave an erroneous impression by not detailing this. I would refer you to the website of one Jonas Mureika, Associate Professor of Physics, LMU-LA which even includes some collected sprint-event datasets! I would have to suggest that Mureika’s approach certainly adheres to my main points, even if MSM coverage appropriates graphs for muddled interpretation. Still, none of this excuses Ethan Siegel’s analysis blog post :-)]
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*I am trying very hard not to make this about a certain I-have-a-hammer and I-know-how-to-use-it blindness of particular mathematically oriented scientific disciplines.
**My new favorite is the apparently well worn cliche that science proceeds not through Eureka! but rather through “huh,…that’s funny”
[h/t for some links: Isis]