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).

The best of the best of 2025 (according to Athletics Podium)

On several occasions I mentioned in this blog the excellent site "Athletics Podium". It is run by the turkish sports journalist S.F. Erbay, accompanied by a team of contributing editors. I cannot think of any better athletics-oriented site on the web. My Turkish neighbours are really the best and, on several occasions, they have pleasantly surprised me with the originality of their articles. (I must confess that quite often I am jealous when I compare the quality of their site to my blog, but, I console myself with the thought that I am a one-man operation).

At the end of the year they published their year's best athletes list and I must say that I found it original to the point that I had to share it with you. 

They did not follow the World Athletics classification of track, field and out-of-stadium, neither one like mine that lists, roughly, the ten best of each sex. The Athletics Podium people decided to list the best by continent, with America split, as usual to South America and NACAC (which stands for North America, Central America and the Caribbeans). They ended up with the following lists

WOMEN

Melissa Jefferson-Wooden (NACAC) and World
Maria Perez (EUR)
Beatrice Chebet(AFR)
Salwa Eid Naser (ASI)
Natalia Linares (S.AM)
Nicola Olyslagers (OCE)

MEN

Armand Duplantis(EUR) and World
Busang Kebinatshipi (AFR)
Sang-Hyeok Woo (ASI)
Caio Bonfim (S.AM)
Geordie Beamish (OCE)
Ethan Katzberg (NACAC)

I find the list interesting but also somewhat surprising. M. Jefferson-Wooden best of the World?  I would put at least three athletes ahead of her. At least B. Chebet gets plaudits for Africa, but this left no place for F. Kipyegon. (Sometimes choices are hard). N. Linares instead of J. Angulo, M. Perez instead of F. Bol or D. Kambundji would have also been my choices but, frankly, how can one ignore S. McLaughlin?   On the men's side I was happy to see that B. Kebinatshipi did get a mention (although that was at the expense of E. Wanyonyi).

The "Rising Stars" are called "Prospects" by the Athletics Podium people. And out of the 12 names I had to look up almost half of them.

Europe: Kelly-Ann Douala Edimo and Jarno van Daalen 
Africa: Prestina Ochonogor and Justice Oratile 
Asia: Puripol Boonson and Yan Ziyi 
NACAC: Liranyi Alonso and Kamari Kennedy 
South America: Maria Maturana and Ricardo Montes de Oca 
Oceania: Reki Selita Roberts and Gout Gout 

As you may have noticed I am not very good when it comes to the Rising Stars list (although I feel that I have made some progress these last years). So, I don't have major objections to the list above. But, still, I think that if there is one young European athlete who merits the distinction that's Hubert Trościanka. (But then, I am a combined event aficionado, so this explains that). 

I mentioned F. Kipyegon, S. McLaughlin and E. Wanyonyi as being left on the shelf. Well, apart from F. Kipyegon, the other two got a mention in the "Top Performances" list. I reproduce it below but I don't know if the order means something.

MEN

1) Armand Duplantis - 6.30m (PV)
2) Emmanuel Wanyonyi - 1:41.86 (800 m)
3) Mykolas Alekna - 75.56m (DT)
4) Rai Benjamin - 46.52 (400 m H)
5) Jacob Kiplimo - 56:42 (Half Marathon)

WOMEN

1) Beatrice Chebet - 13:58.06 (5000 m)
2) Sydney McLaughlin-Levrone - 47.78 (400 m)
3) Anna Hall - 7032 pts (Heptathlon)
4) Ditaji Kambundji - 12.24 (100 m H)
5) Valarie Allman - 73.52m (DT)

It is my feeling that F. Kipyegon's 1500 m 3:48.68 World Record (and her 3000 m 8:07.04 one) should have secured her a place in the Top Performances list. But where I strongly disagree with the AP list is with Rai Benjamin 46.52 s performance trumping the 46.28 of K. Warholm. We are talking performance here and world champion or not, Benjamin does not have the best performance of the year. At least I console myself seeing two throwers and one combined-event athlete included in the top-5 list, as well as J. Kiplimo who was totally ignored by World Athletics in their out-of-stadium choices.

Although I do not agree with all the Athletics Podium choices, I find their approach most interesting and very well researched. But, of course, this is not astonishing: as I said already, they are the best in what they do. So, if you haven't already done so, bookmark their site and think about visiting it regularly.