Vaporflys or how supershoes changed the Marathon forever

Those who follow my blog have noticed that I have a great esteem for Ross Tucker, a renowned sports physiologist. Together with his colleague Jonathan Dugas, Tucker had a blog entitled "The Science of Sport". It was active from 2007 to 2013 and then went silent. The last post in the blog was on the sub-2 hour marathon. And the title expressed clearly the authors reservations: "Is the sub-2 hour marathon imminent? Don't hold your breath". Well, it turned out that they were somewhat pessimistic or rather they didn't predict the revolution that would take hold of long distance running in the years to come. And six years after the Science of Sport article, Eliud Kipchoge ran the first sub-2 marathon in history.

In 2013 the men's marathon world record was held by W. Kipsang with 2:03.23. The women's records were established back in 2003 (mixed race) and 2005 (women only) by P. Radcliffe with 2:15:15 and 2:17:42. Today the men's record is held by the late K. Kiptum with 2:00:35 and the women's records are held by R. Chepngetich (mixed race) with 2:09:56 and P. Jepchirchir (women only) with 2:16:16. Just to put the women's records in the right perspective, the men's 2:10 barrier was broken in 1967 by D. Clayton. (At that time no woman had run under 3 hours). And what is happening it's not only due to some exceptional individuals. We are witnessing a real revolution in long distance running. One can argue that what we observe is due to better training and a ripple effect where the performance of the leaders reverberates through the whole runner community. Maybe so. But there is one factor that has undeniably contributed to the explosion of performances: shoes.

But let us start at the beginning. At the end of the 90s the team of the Human Performance Laboratory of the University of Calgary started interesting themselves in the effect of shoe bending stiffness on jump height performance. In order to increase the stiffness they inserted a carbon fibre plate into the shoe midsole.

The initial studies were targeting high jump but subsequent studies extended the subject to that of running economy. It was well known at the time that the energy put in on the metatarsophalangeal joint (the joint between the metatarsals and he toes) is not returned when pushing off. Using shoes with inserted carbon plates reduces the energy dissipated in these joints. The Calgary research showed running energy savings of approximately 1% when using a stiff midsole as compared to a "normal" one. To put the result in perspective (since the energy expenditure for running is proportional to the athlete's velocity) a 1% gain would mean shaving off more than a minute from the time of a marathon for an elite runner.

Curiously the Calgary study did not have any impact on the shoe industry for more than a decade. It was around 2015, when people from the Calgary lab went to work at Nike, that the new shoe generation saw the light. The first modification with respect to the initial design was a bent plate. The reason is that a flat plate makes it actually harder for the calves to push up. The team of the Locomotion Lab at the University of Colorado studied the prototype of the shoes that would become known as the Vaporflys and found that they lowered the energetic cost of running by 4%.

Kipchoge did attempt an under-2 marathon using Vaporflys in 2016 in the Breaking2 event held in Monza. He came tantalisingly close to the 2-hour barrier, completing his run in 2:00:25. While the course design was legitimate (flat course) the remaining conditions (like the use of rotating pacemakers shielding the star runner and the use of a car projecting a laser beam to aid pacing) made that the record could not be homologated. 

While the people of the Calgary lab attribute the energy gain to the stiff plate, the Colorado team's opinion is more reserved. For them the metabolic savings of the shoes appear to be due to a superior energy storage in the midsole foam, the clever lever effects of the carbon-fibre plate on the ankle joint mechanics, and the stiffening effects of the plate on the metatarsophalangeal joint. Apparently the midsole foam plays an important role. When the foot hits the ground the sole deforms and some energy is lost. However in today's "supershoes" better foams result in diminished energy loss. (And Nike did further improve upon this by introducing air-filled rubber cushioning).

Following these studies Nike came up with a better model, the Alphafly. Kipchoge used them in Vienna in 2019 at the Ineos 1:59 Challenge and this time the 2-hour barrier did fall. Today Alphaflys are available to anybody who can afford the rather stiff price. 

The other brands have caught up with Nike and this explains the explosion of records. World Athletics are trying to put some order in this. They require that shoes be on the market for a month before they can be used in an official competition. Moreover there are limiting the stacking height (the amount of material between the foot and the ground) for track events to 20 mm. However the marathon shoes are allowed to have a 40 mm stack height. Some people are speaking about "shoe doping". I believe that this choice of words is most unfortunate since nobody is cheating and everybody has access to the new shoes. But it remains that they give the athletes a massive advantage. 

If you wish to learn more on supershoes, I suggest that you read an excellent article on Runners World.

Speaking of the advantage offered by the shoes reminds me of a controversy going back to the 50s. In 1957 Yuri Stepanov, a soviet high jumper, broke the World Record with a 2.16 m jump. When photos of the record attempt were circulated people noticed that Stepanov was wearing a shoe with a thick sole on his take-off leg. 

People cried foul (some were talking about a 4 cm "trampoline" but a closer examination of the photo, as well as other photos of Stepanov in competition, point at a thickness not exceeding 2 cm). In absence of specific rules the IAAF homologated the record and proceeded to limit the shoe sole thickness to 13 mm. This limit has been raised today to 20 mm. (But as P.J. Vazel is pointing out, it is not clear that an elevated shoe offers any advantage in the Fosbury style, it might even present some risk due to the quite different take-off technique). While Stepanov's sole thickness would have been acceptable with today's rules, back in 1957 he was heavily criticised by the media. Being mentally fragile he foundered into depression, alcoholism and committed suicide in 1963, at just 31 years of age.

PS And when we thought we had seen everything, along came the running sandals. 

B. Kiplimo won a Marathon in Thailand running with carbon-plated sandals. Now, how can anybody run 42 km with this kind of shoes is a mystery to me. But Kiplimo did it and won the race in a respectable 2:18:55 time. 

A bizarre theory on world records

Some time ago I stumbled upon an article, on BBC of all things. The title was "Why world records seem to be getting harder to beat - according to maths". I was intrigued and I decided to read the article. And once I read it I was really annoyed. How can one pretend, using bogus premises, that mathematics are explaining the new records paucity? 

But let us start at the beginning. The article starts with the, by now almost mandatory, tribute to M. Duplantis, who, by the way is the living proof that records are not getting harder to beat. The author of the article feels compelled to explain the pole vault records, who are in clear contradiction with the title and the thesis he will present later. He does this by invoking improvements in diet, technique or equipment. (Perhaps Mama Duplantis was feeding her offspring a special diet?). And then we goes on to remark that the long jump record is standing unbroken since 1991. Up to that point things are more or less acceptable, in particular, if one  complements "diet" by medical monitoring and aftercare. But the worse is still to come.

The author segues his introduction with a short paragraph where he presents his main argument. In his own words:

 "We refer to these sorts of situations (in which further improvement is impossible and differences between an athlete's performances come down to "luck") as "stationary", in the sense that the overall trend in average behaviour is unchanging. Given a stationary system, we can ask how often we should expect records to fall due to random fluctuations". 

And, just so that people get to understand what he means by this, he presents an example of rain records in various cities ending up with a harmonic series. (The later is the series one gets by adding the inverses of the successive integers 1+1/2+1/3+ 1/4 and so on). A graphic is also given which, supposedly, justifies the authors assumptions.

Well, what are these assumptions? First the stationarity one. It is a clear abuse of the term, in particular when one invokes mathematics. Neither the record situation nor the harmonic series are stationary. But, let us accept that the author decided to simplify the situation in order to make it palatable to us mere mortals. (Referring to the increase of the harmonic series as logarithmic would have probably discouraged the majority of his readers). But the really faulty premise is attributing the establishing of new records to random fluctuations. Nothing is further from the truth. What it takes for a new record is to have a talented athlete. Once the latter matures one expects a series of records by the same person a scenario that we have seen time and again in Athletics. The difficulty is to find the really gifted individuals, but, pretending that the process is random, is pure heresy. 

Now let's get serious. What do real, scientific, analyses say about the evolution of records? A team of researchers of various universities in the Paris region addressed the question (and in fact in a broader setting, as evidenced by the title of their article "Are we reaching the limits of Homo sapiens?"). They analysed a vast amount of data from various sports. In the figure below they show the evolution of the 10 best women's performances for 800 m, high jump and shot put. It is clear from the graphic that starting from the late 80s the performances stagnate and even decline in the case of shot put. But may one draw a sound conclusion based on this graphic? Definitely not. The 80s marked the beginning of a strict anti-doping control era and this changed dramatically the performances. 

The next graphic, where they show the evolution of the world record relative improvement is more instructive. The downward trend of the mean confirms that records are indeed more difficult to break as time goes by.

Does this mean that we are approaching some limit? This is a question that a team of the Guanghan university in China has addressed in an extensive statistical analysis, spanning 23 sports and involving the performances of more than 6000 athletes. If you are interested in the question, you can download freely their article at the url https://www.nature.com/articles/s41598-024-65350-4. But, to put it in a nutshell, they conclude that "...human beings have not yet reached sports limits in athletic performance, suggesting a continuous improvement over time". 

Will this mean that we will see new world records? Definitely, yes. Will breaking records become more difficult? Certainly. Will the process be a random one? Only in the sense that exceptional individuals (the ones that can break world records) cannot (yet) be produced on demand. But invoking the harmonic series in order to explain what is happening is, to my eyes, pure clickbait.

On bad scoring tables

As my regular readers know, I am a fan of scoring tables. And that has been true since a very tender age of 10. I cannot explain why this subject fascinates me, but there we are. Whenever I see a scoring table I feel immediately an attraction. From the outset in this blog, scoring was at the centre of interest. Already the fourth published article talks about scoring, and a whole series entitled "Theories of Scoring" appeared in 2021-22. Scoring was the subject of several articles of mine published in the New Studies in Athletics (alas, now defunct, killed by the belt-tightening measures of Lord Sebastian). And it is, of course, the origin of my collaboration with G. Purdy. While writing these lines I realise that I have never published the article I had promised in "A brief history of the IAAF/WA scoring tables" explaining the relation of the World Athletics scoring tables to the Weibull distribution and moreover I have never presented the results of my collaboration with G. Purdy. One day I will keep my word and explain in detail the relation between performance distribution and scoring.

But let's go back to the current business. As you may know, I am a subscriber to the newsletter of Art of Manliness. Contrary to what woke-brainwashed persons might think, the site is anything but macho. Of course it caters to men's interests and lifestyle, and some people find that they tend to romanticize older stuff, but, frankly, most of its articles (shaving excluded) would be useful to women too. From time to time they publish Army-related articles and they always attract my interest. In case you didn't know, I am a big Army fan. I like the Army discipline, even when it verges on the absurd. Discipline, even exaggerated one, is better than no discipline at all. (I just hope that you are not taken aback by my militaristic tendencies). 

No, it's not modern pentathlon

In an article entitled "Are you combat ready?" (reprinted from one published in 2016) AoM were talking about the "Physical Combat Proficiency Test" of the US Army. The test was designed to assess the soldiers' agility, coordination, and ability to perform what the Army calls “warrior tasks”. The test was introduced in 1969 and was replaced by the Army Physical Fitness Test in 1980. Several iterations and modifications of the latter existed up to 2025 where the Army Fitness Test was introduced (but some people consider the PCPT to be the high-water mark for the Army’s physical training tests).  

What was most interesting in the AoM article was the inclusion of the scoring table for the mile run (the last of five events of the PCPT). Mind you, the mile was to be run in uniform pants and boots, so don't be hard on judging the times.

Once I saw the table I could not resist the temptation. I read off the points and the times and I converted the latter to mean velocity. As I have explained in my article "Theories of scoring: the energetic cost approach", the energetic cost of running is essentially proportional to the velocity, in particular for middle-distance running. But this is something that scoring-table builders are systematically ignoring. As a consequence, the creators of the PCPT mile-run scoring table produced a perfectly regressive table where the points grow roughly as a power 2/3 of the velocity. 

But they are in very good company. In fact, since the introduction of the 1985 tables, that were meant to repair the damages done by the Ulbrich tables, we are living with tables that are regressive for track events. Below I give the corresponding fit for the 1500 m of the decathlon scoring tables.

Apart from the initial part of the curve corresponding to very low velocities, the scoring is regressive, the points growing roughly as a power 3/4 of the velocity. 

I mentioned Ulbrich in the previous paragraph. In fact, he was the one who understood that the quantity in which the tables must be cast for track events is the velocity. His fatal mistake was to assume that velocity was the quantity that was determining the performance in field events. Well, it is, but not the velocity itself. The energy expenditure for field events is proportional to its square. By introducing a scoring proportional to the velocity for field events, Ulbrich introduced a counter-productive regressivity. You can read about this in my post on theories of scoring.

The scoring tables I proposed in collaboration with G. Purdy are strictly progressive for all events. On the same point of progressivity, my Décapassion friends, F. et P. Gousset, make the remark that the current tables for throws are only slightly progressive and this lack of strong progressivity throws the tables off balance. I have promised the Gousset that one day we'll write a joint article on this point. (And when this is done I will give here at least an "executive" summary).