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.
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