On a naïve proposal for decathlon scoring

John Barrow was a mathematics professor at Cambridge (he passed away in 2020). Among his many interests was that for mathematics of sports. He authored the book Mathletics 

where he is presenting a collection of most interesting back-of-the-enveloppe calculations that would appeal to every physicist, even those who are not particularly interested in sports. He was the director of the Millenium Mathematics Project. On the project's site one can find a slew of interesting articles. Among the latter one encounters an article entitled "Decathlon: the Art of Scoring Points". It's the one I would like to comment upon in this post.

Barrow had an "on the surface" great idea: "let's do away with the scoring tables". So he proposed to score the combined events by multiplying the lengths of the jumps and throws, dividing them by the product of the times of the races.

Let's see how this (what Barrow calls the "special total") would work for performances that correspond to 1000 and 0 points in the current men's decathlon tables. For 1000 we have the succession of performances

10.39, 7.78, 18.40, 2.21, 46.17, 13.80, 56.17, 5.29, 77.19, 3:53.79 (233.79 in seconds).

The special total in this case is 4.688.

In the case of 0 points (the tables do not list the zero point but it is straightforward to obtain it from the parameters of the scoring formulae) we have

18.00, 2.20, 1.50, 0.75, 82.00, 28.50, 4.00, 1.00, 7.00, 8 min (480 s).

The special score in this case is 0.000003.

Already there is a factor of one million between the highest and lowest score something that would appear exaggerated even to scoring-untrained eyes. But wait, there is more. Had we decided to use empire measuring units (God forbid) for the jumps and throws, we would have obtained a totally different score. This comes from the fact that multiplying arbitrarily numbers that have a dimension does not make much sense, unless one specifies the measuring unit. The special score we obtained above is a number with dimensions m^6/s^4 and its value has a meaning only in these units.

The least one can do when one tries to set up a system for scoring is to give a dimensionless score. The easiest solution to this is to divide each performance by a reference one, for instance the performance corresponding to 1000 points in the scoring table. This would amount to dividing the special score by 4.688. The advantage of this is that the result is independent of the units in which one measures the performances. (It is impossible that Barrow ignored such basic a fact. My guess is that, given that the conversion to a dimensionless unit is an overall factor, he decided not to enter into those details so as to keep his presentation as simple as possible).

Let us now do a real life comparison, using the special score recipe for the 6 best decathletes of all times (the data are available on the World Athletics site). Since the overall factor is the same for all athletes we can simply neglect it. 

We find

Athlete	decathlon	special score
K. Mayer	9126	2.61
A. Eaton	9045	2.03
R. Sebrle	9026	2.29
D. Warner	9018	2.13
T. Dvorak	8994	2.40
D. O'Brien	8891	2.13

While Mayer emerges as the best decathlete ever, A. Eaton is, surprisingly, beaten by all the other decathletes in the top-6 list. This reveals the real inadequacy of the special score recipe: it is the events where large variations are possible that have a bigger effect in the final score. Let us parse this in the case of Mayer versus Eaton. Their overall ratio is 1.28 in favour of Mayer. (In fact, another way to obtain a dimensionless number using the special score is to consider the ratio of the scores of two athletes). We compute now the ratios of throws, jumps and races. We find (Mayer/Eaton for the two first and the inverse for the third) 1.45, 1.05 and  0.83. So the throws are the ones that decide the outcome. In fact this is practically true for all the athletes of the list.

Here is the list of the 6 first where the overall special score and the one obtained from the throws alone are divided by that of Mayer 

Athlete	overall ratio	throws ratio
K. Mayer	1.00	1.00
T. Dvorak	0.92	1.01
R. Sebrle	0.88	0.89
D. O'Brien	0.82	0.87
D. Warner	0.82	0.79
A. Eaton	0.78	0.69

Unsurprisingly, Eaton has the lowest relative score, while Dvorak, who has the best ratio to Mayer's score is even slightly better in the throws. 

To be fair, Barrow was aware that his system was biased and thus, in his article, he did not pursue the issue and went on to discuss the World Athletics tables. I have two versions of his article and curiously the one in the Millenium Math project site does not contain the last part of the first where the author argued that "in each event (with the possible exception of the 1500 m) whether sprinting, throwing or jumping, it is the kinetic energy generated by the athlete that counts". I beg to differ. As I have repeatedly explained, what should count, when it comes to scoring, is the energetic cost of the effort. And while for jumps the energetic cost is closely related to the kinetic energy (things are somewhat more complicated for the throws) when it comes to races, the energetic cost is roughly proportional to the first power of the velocity and not the second one as in the kinetic energy. (To be fair, there is a small velocity-squared contribution in the case of sprints but the dominant term is the one linear in velocity).

Anyhow, scoring is a delicate business, and Barrow's idea, although exceedingly naïve and not really applicable, had the advantage of being a zero-parameter one, a kind of a black swan in the complicated world of sports modelling.

I couldn't resist the temptation

I was visiting the World Athletics page where the Szekesfehervar Continental Tour Gold, to be held on July 18, was announced. And since I try to follow the meetings on the World Athletics YouTube channel (a vpn is often needed) I scrolled down on the page and there I was surprised. Let me explain.

When opening the page on the Szekesfehervar meeting one, is greeted by a photo of various world champions who will be present in Hungary. And most prominent, in the center of the photo, is Shericka Jackson, who has the world leading 100 m time this year with 10.65 s.

But then, when one scrolls down on the page, one finds the very same photo with one (major) change: Shericka Jackson is replaced by Sha'Carri Richardson. The photo is used in announcing the livestream of the competition on the World Athletics YouTube channel. 

I must say that I was surprised by the switch between the two sprint superstars. But then I got it. In a great race during the Diamond League meeting, held on July 16 in Silesia, Richardson beat Jackson,  10.76 to 10.78 s, in a race decided in the last few meters.

So the World Athletics staff decided that the sprint queen of the moment was Richardson and, in an act reminiscent of the stalinian photo retouching, they evicted Shericka and replaced her by Sha'Carri. When I saw this I felt that I had absolutely to share it with you. As to who is the sprint queen, I'm afraid that we'll have to wait till the World Championships of Budapest in order to know the answer.

The Pheidippides myth

The marathon race is considered as the crowning moment of modern Olympics. It has been present since the very first, 1986, Athens, Games. In fact it was during those Games that the race was introduced. The idea came from a french linguist, Michel Bréal. He was a personal friend of de Coubertin and he convinced him to incorporate into the olympic program a race that would commemorate the feat of Pheidippides. Unless you have been living under a stone, you have heard about the battle against the Persians and how Pheidippides ran all the way from Marathon to Athens in order to announce the athenian victory, expiring upon arrival, just after crying out "Νενικήκαμεν" (we have won).

Well, things are not that simple. While working on the amateurism series I came upon the writings of D. Young. He was great hellenist, who published several treatises among others on the Olympic Games. (One day I will tell the story of how the modern Olympics came to be, based on Young's writings). In an Appendix of his book on the history of the (ancient) Olympics he dispels the Pheidippides myth. I found his arguments more than convincing and I decided to write this short article.

The story of the battle of Marathon, where the Athenian army defeated the much larger Persian one, is told by Herodotus, who is a reliable historian and, moreover, gave his account just half a century after the battle. Herodotus explains that the Athenians, fearing the superiority in numbers of the Persians, sent a runner, named Philippides (in some manuscripts the name is given as Pheidippides), to Sparta to ask for assistance. The Spartans agreed to help the Athenians but their departure was delayed because, for religious reasons, they could not leave before the full moon with as a result their arriving after the battle. Anyhow, Phillipides ran the close to 500 km, Athens-to-Spartan distance and came back in time to participate in the battle. There is no other mention of Philippides or Pheidippides in the writings of Herodotus. In fact, after the battle, the whole of the Athenian army, and not just a single envoy, marched swiftly back to Athens, where they feared an attack of the remaining Persian forces.

A statue of Pheidippides near Marathon. 

(Why did the sculptor depict him carrying a torch? 

The olympic torch relay was invented by the nazis)

And, why on earth, does a runner, able to run 500 km, die after running just 40? The writings of ancient historians give accounts of athletes who, having won in Olympia, ran all the way to their hometowns in order to announce their victory. Pausanias is telling the story of Ladas from Sparta, who, after winning in the Games, ran the 150 km to Sparta and died upon his arrival. This may be the origin of the Pheidippides myth. Writing in the first century AD, Plutarch tells the story of Eukles who participated in the Marathon battle and ran to Athens, dying just after having announced the victory. Lucian, writing a century after Plutarch conflates this story with that of Herodotus and uses the name Pheidippides instead of Eukles. So, the Marathon story, as is known today, dates from seven centuries after the facts.

I prefer, and by far, this representation of Pheidippides

The infatuation with the Pheidippides story stems most probably from the homonymous poem by Robert Browning written in 1878. And with Bréal's lobbying, the marathon race was born. The first marathon was run over a distance of 40 km. It would have been much simpler had the distance being fixed to this simple, metric, one. Instead we are now stuck with the 42195 m which was, totally arbitrarily, inflicted upon us by the organisers of the 1908, London Olympics. The first marathon races were, to say the least, eventful. The Athens, 1986, was won by Spyros Louis who became instantly a national hero. (But things are not always as they appear and I will tell the story of the Athens marathon some other time). The Paris, 1900, marathon was a disaster (just as the whole 1900 Olympics). It took place in the streets of Paris and there are strong suspicions that the French runners, and in particular the winner, M. Théato (announced as French but being actually a native of Luxembourg) took shortcuts. The St. Louis, 1904, marathon, was another disaster. F. Lorz arrived first but it soon became known that he had covered part of the distance in a car. The official winner T. Hicks was carried part of the way by his support crew. (You can see the photo in my article on the history of doping). His trainers had to carry him over the finish line. Still, he was not disqualified. Had he been so (quite deservedly), F. Carvajal would have won the bronze medal. (You can read the story of Carvajal in the wikipedia page dedicated to him). The 1908 marathon was marred by the Dorando Pietri incident. He entered the stadium first but, utterly exhausted, took the wrong direction. He was redirected by the judges and then fell down for the first time. He fell three more times and was helped by umpires in every occasion, taking 10 minutes to cover the last 350 metres. He was subsequently disqualified for an error committed not by himself but by the judges. 

So, it is a disputable and rather improbable myth that led to the creation of the marathon race. Given that there is no historical foundation for this event wouldn't it have been better if we have stuck to the metric distances, say 40 or 50 km? Well, World Athletics appears to think otherwise. As the IOC rejected the proposal for a women's 50 km race-walk, they proposed a two-athlete mixed race-walk relay over a marathon distance. Why on earth did they opt for this distance that has nothing to do with race-walking instead of choosing something simple like a 40 km? Once more the argument, far from being sports-based, is one of marketing, trying to capitalise on the popularity of the marathon, a race introduced by a misguided dreamer and which survives and flourishes thanks to a self-sustained tradition. (And just to make things clear: I have a great admiration for the great marathon runners, who are superb athletes. It is the choice of the race that I am criticising and, to some extent, the use of the word "marathon" that has created a slew of "-thon" ending linguistic atrocities).

The amateurism myth (part five)

Or how Samaranch set the cat among the pigeons (professionals in the Olympics)

At the 1981 olympic congress, J. Holt (we have already met him in this blog, when it was question of the proposal of G. Purdy of new scoring tables) who was the secretary general of IAAF stated clearly that athletes should be compensated in order to be able to train.

W. Daume was even more explicit : "If the Olympic Movement, expects the athletes to pursue excellence, it should not discriminate against them”. It is not clear whether this liberal attitude costed Daume the presidency of the IOC. Be that as it may in the 1980 election J.A. Samaranch was elected with 44 votes while Daume obtained just 6 (out of a total of 78).

Samaranch and Daume

During the 21 years of his presidency Samaranch put all his energy into transforming the IOC into a full-fledged corporate entity. The main danger were the professional sports and the fact that several olympic sports had developed professional circuits. The presidency of Samaranch was marred by bribery, bidding scandals, and a culture of corruption but one must recognise that it was him who brought the IOC back from the brink of bankruptcy.

Starting from 1981 the IOC worked towards more liberal eligibility rules removing existing anti-profiteering restrictions. Still football, ice-hockey and tennis continued to dissent with the IOC line. The FIFA for instance insisted that players from Europe and South America who participated in the World Cup be excluded from the olympics. The reason for this was to have the best national teams present only in the FIFA World Cup but the IOC members could see through the ruse. In fact the FIFA had started pushing for limiting the age of players in olympic teams to 23 removing any professional–amateur distinction. (As a consequence the football teams participating in the 1984 Olympics were composed mainly by professional players). Tennis had left the Olympics in 1924, but for Samaranch that was something unacceptable and  he decided that tennis would return to the 1984 Olympics and to hell with amateurism. In fact at that time hardly anyone was caring about who was amateur and who was not. 

For many years the IOC had lived with the fear that money would doom the Olympics to failure. But it was becoming apparent that the opposite was true. The fear of debt had grown strong to the point that cities, who would have liked to host the Olympics, abstained from even bidding for them. The Olympics was facing disaster. Samaranch understood that the only salvation would come from the commercialisation of the Olympic Games. 

But even then there are traditions that die hard and even Daume, at the 1985 iOC session, argued in favour of a modernisation of the eligibility code but made clear that “open Olympics had to be avoided at all costs”. Brundage had left the presidency 13 years before but the IOC inertia was making progress really sluggish.

Pound and Samaranch

With the help of D. Pound, Samaranch obtained record-breaking television deals and lucrative commercial sponsorship arrangements. Pound pushed for open Olympics arguing that many things have changed since the birth of the modern Olympics and that “professionals had proved themselves as capable of observing the Olympic spirit and fair play as anyone”. The question of allowing professional tennis players in the 1988 Games was discussed in the 1987 session. Some members were still reluctant fearing that if the IOC legalised the breach of amateur status it would not be able in the future to reverse the vote to approve professionals. They were right, but they were also a minority. Professionals would come to the Olympics to stay. And the IOC shifted its efforts towards the enforcement of anti-doping rules.

In 1989 the IOC accepted the decision of the international basketball federation for an "open" olympic tournament. And while the professional tennis players were admitted in 1988 as a unique exception, the arrival of the US Dream Team in 1992 was heralded as one of the major moments in the Olympic history. In the meantime the olympic charter had purged the term amateur and Daume, as head of the Eligibility Committee, made sure that professional athletes could participate in the Olympics, provided their federation approved that.

As for Dick Pound, who had been a champion of professionalism in the Olympics, he lost his bidding for the presidency in 2001 when J. Rogue was elected with 59 votes, Pound obtaining 22 out of a total of 110.

This concludes the series I set out to write on the myth of amateurism promoted by de Coubertin and his successors. (But there will be at leat one more "bonus track" on some point I have not yet addressed). 

Reading the story of amateurism, which is in good part the story of the IOC, one may wonder how the IOC continues to thrive. D. Chatziefstathiou, a de Coubertin specialist I have mentioned in my post "de Coubertin unmasked", points out that today, Olympism blends the twenty-first-century demand for elite sport, with multiculturalism, inoffensive moral dictates such as fair play and healthy competition, and a subtle dose of antiquity thrown into the mix. Those are the values that have substituted amateurism. As for the latter? Well, it was equal parts ideology, mythology, and nostalgia. And gone for good. And we will not miss it.