As is customary for quite some time now, the IAAF published a special edition of their Statistics Handbook as a bedside (or is it tv-side?) reading for the Rio Olympiad which is just one month away. The book, produced in collaboration with the Association of Track & Field Statisticians (ATFS), is a goldmine of data. And since one can download the pdf for free, there is no reason why one should deprive oneself of such a precious guide for the Games.
While perusing the Handbook, one thing drew my attention. On page 12 one finds the chronology of the Olympic Games
and there, to my surprise, the 1906 Athens Games did figure in the same list as the remaining Olympics. This spurred my curiosity and I searched the IAAF website. And, of course, the Athens Games do figure among the Olympics. They are given as Intercalated Games without number but still they figure in the same list as the other Olympiads. It goes without saying that in the IOC website there is no mention whatsoever of the 1906 Olympics. So, there you have it: this is one more reason I love Athletics.
I have written about the wrongdoing of the IOC concerning the recognition of the Athens 1906 Olympics in my article on the man who orchestrated this (perhaps channeling the infamous de Coubertin) but so as to hammer home the scurrilous fact here are the names of the commission that decided to shamelessly delete a page of the olympic history:
Avery Brundage (USA)
Sidney Dawes (Canada)
Miguel Angel Moenck (Cuba)
While Dawes was a skier (and thus one can understand why he wouldn't care about the 1906 olympics), Brundage and Moenck were T&F athletes. A real shame!
While following the Jamaican trials (the exact tile is a mouthful: Supreme Ventures Jamaica Athletics Administrative Association (JAAA) National Senior Championships) I was shocked by Bolt's absence from the 100 m final. What did happen? Bolt himself did explain in a tweet
And of course he withdrew from the 200 m as well. In a photo posted also on twitter we can see that Bolt is not losing time and is undergoing a treatment that will, hopefully, allow him to compete at the Olympics.
A second shock came a day later when Elaine Thompson, who won the 100m in a blazing 10.70, as well as Shelly-Ann Fraser-Pryce who finished second in 10.93, had withdrawn from the 200 m final. Thompson won a silver medal over 200 m in last year's World Championships while Fraser-Pryce was world champion in 2013.
The reasons evoked was that Fraser-Pryce continued to be in great pain as a result of her injured toe, and Thompson’s hamstring was hurting. Just as in the case of Bolt, a medical exemption was submitted for Thompson while Fraser-Pryce decided to forgo her participation in the 200 m.
So what will happen in Rio? Will Bolt run or are we condemned to see double doping offender Gatlin win another olympic medal (which will definitely spoil the 2016 Olympics for me)? Shall we be deprived of another fabulous duel like the one between Schippers and Thompson in last year's World's, this time arbitrated by the 2012 olympic gold medalist Allyson Felix?
But first things first. How can Bolt and Thompson participate in the Rio Olympics? The Jamaican trials are not like the US ones where you have to finish among the three first of else. The JAAA has a special provision in its selection policy:
Athletes who are ranked/listed in the top three in the world for their event who are ill or injured at the time of the National Championships and are granted an exemption from competing at the Championships may still be considered for selection provided that they are able to prove their world ranking form prior to the final submission of the entries for the competition. Where an athlete has been granted an exemption and the Selection Committee has determined that such an athlete should be selected among the entrants for the event that athlete shall be selected above the athlete placing third at the National Championships or in place of an athlete finishing in either of the first two places of the event where that athlete has been determined by a medical panel appointed by the JAAA to be ill or injured and not being in a satisfactory physical condition to warrant being entered to compete.
There is however a small problem. Bolt will try to prove that he is back in shape at the July 22, London Diamond League competition. I do not know what are the plans of Thompson but it is probable that she will choose the same competition. In any case the only other major, non-European, competition in this coming month is the July 15th, Monaco, Diamond League. Choosing the later date will provide the athletes with an extra week of recovery time. But, and this is a non-trivial but, the deadline for entries to the Olympics is fixed at July 18. And contrary to the World Championships where a nation can enter four athletes and select the three who will actually compete at the very last moment, in the Olympics there is no convenient proviso for reserves. So, what can be done?
One possibility is to replace one of the three entered athletes on medical grounds. In this case the athlete who is replaced cannot participate in any other event and, in fact, must leave the olympic team. In fact when something like this is foreseeable the national team can even enter the name of the athlete who may replace some other team member but this athlete is not member of the team until the final late-replacement decision (always on medical grounds) is taken. Such a late replacement can take place until 24 hours before the final confirmation of participation at a given event.
The alternative, which applies to the case of both Bolt and Thompson, is for athletes who are already members of the team to be considered as reserve for some other event. Thompson is already in for the 100 m and Bolt minimally for the 4x100 m relay. So, they can replace some other athlete at the moment of the final confirmation of participation and the athlete replaced does not lose his/her rights as member of the olympic team.
Of course the important question is not whether Bolt will participate but rather whether he will be in top shape and able to add a few more gold medals to his collection. I guess we shall have to wait till August for this.
As you may have noticed by now, I am always searching the web for sites specialising in athletics. This time I fell upon a dutch site which has several very nice analyses. What attracted my attention was a recent post on the high jump records as a function of age covering a huge span, in the case of men from ages of 2 to 98 and for women from 7 to 95. It was a real treasure trove. I was particularly interested in those data since I had, in 2009, written an article in New Studies in Athletics on "Scoring the athletic performance for age groups" (volume 24:3, pages 63-75) where I was lamenting the dearth of data.
While it is not a matter of repeating the calculations of that publication I was tempted by the appearance of these data into seeing what one can do what I called in my paper the toy model. In this model I assume that an athletic performance is the resultant of several physiological factors, technique as well as psychoemotional factors. The latter lie totally outside the scope of a toy model: they represent the most fickle component since for the same person they may vary within the few hours of a competition. No detailed studies do exist (at least to my knowledge) concerning the evolution of technique with age. Schematically one can distinguish three stages in this evolution. Young athletes spend years acquiring a technique and adapting it to their growing body. When adulthood is reached the technique becomes quasi-optimal for every athlete (but the question of an optimal execution during a given event or attempt is always a crucial one). Finally for aging athletes a decline of technique is to be imputed to the decline of physical qualities. Still, one should keep in mind that an experienced athlete performs with the technique that is best suited to his physical qualities and thus the question of optimality is a delicate one.
In what follows I will neglect the impact of technique to performance (making thus the toy model even more toy-ish) and assume that the performance in a given discipline are maximal aerobic capacity, alactic anaerobic capacity (directly related to speed) and strength. If one considers for instance a 400 m race we may assume that the physiological factors influencing the performance are 40 % aerobic, 40 % anaerobic and 20 % strength (your percentages may vary; mine are given just as an illustration). I represent these qualities by a,l,s and their contributions by α=0.4, β=0.4 and γ=0.2. The total performance q is given by
q=αa+βl+γs
What one needs now is the dependence aerobic and anaerobic capacities as well as strength on age. In fact, since I am going to analyse only the data on high jump for which I do not expect the aerobic capacity to play any role, I will concentrate on just the alactic anaerobic capacity and strength. The two figures below show the data that will be used in the model. They were taken from the book P. Ceretelli and P.E. di Prampero, Sport, ambiente e limite umano, Ed. Montadori, 1985, p.69,
as far as the anaerobic capacity is concerned and from the paper of S. Israel, Age-related changes in strength and special groups, in Stength and power in sport, edited by Komi. P.V., Blackwell, 1992, p.322
in the case of strength and they give the dependence of said qualities on age. The literature of these subjects is vast but since we are presenting just a toy model the data that can be found in those two monographs do suffice.
The model I will be using is a simple one where the performance is achieved by a simple combination of strength and anaerobic capacity. I did not attempt any sophisticated optimisation but opted for a rough 60 %-40 % combination of these two factors. The height of the jump is given thus by
h=αs+βl
where α=0.6 and β=0.4. The strength and anaerobic capacities are expressed as a percentage of their maximum and thus the resulting quantity h is a number smaller than 1. Next, h is multiplied by the adequate factor so that at its maximum it coincides with the existing world record. This results to the following diagram of the variation of the best high jump performance with age (thick line) compared to the existing data (points linked by a thin line).
The agreement of the toy-model with the data is quite impressive. The overall shape of the curve is reproduced both in the junior and master's age brackets. One can also use the details of the curve in order to explain on a physiological basis the evolution of the performances. It would appear thus that the observed "plateau" between ages 20 and 30 is due to the fact that a strength increase balances the loss in anaerobic capacity, an equilibrium that cannot be maintained beyond the age of 30, whereupon the decline begins.
However one should not misinterpret the nice agreement as the proof of the validity of the toy model. First, one may remark readily that I have limited my application to the age bracket [10-70]. An application of the model to younger and/or older athletes could (and most certainly would) lead to disagreements. Second, while the model was capable to represent the existing data there is no doubt that alternative models could do equally well. The main virtue of my model is its simplicity in the sense that it captures the basic mechanism underlying the performance in high jump.
One point that I still find a little bit worrying is that one has the impression that the technique does not play an important role, since it was possible to fit the data with the tacit assumption that the technique was optimal at all ages. I am aware of the fact that it is very difficult to quantify the technique. Also one should make the fine distinction between technique and style. The first is a rather abstract notion: for every athletic gesture there exists an optimal technique for its execution. Style is the application of this technique by each athlete adapted to his physical and physiological capacities. What we see when we watch a performance is style and not technique. Given these difficulties the decision to neglect, as far as the toy-model is concerned, the influence of technique in the performance is just an application of Ockham's razor (or of lex parsimoniae, for those who, like myself, prefer Latin expressions over Saxon ones).
