Who is the best decathlete?

Well, everybody knows that the best decathlete ever is the legendary Jim Thorpe. But it is interesting to ask the same question concerning the contemporary decathlon heroes. This post of mine was inspired by a post in Jon Mulkeen's blog who is comparing five of the greatest decathletes of our times: Eaton, Sebrle, Dvorak, O'Brien and Thompson. Mulkeen's blog is one of the two blogs that I follow regularly (the other one is that of J.P. Vazel, a blog I am frequently referring to here).

Reading Mulkeen's analysis I started thinking and making some calculations. When you compare the world records of Eaton and O'Brien event by event you realise that O'Brien was leading this imaginary competition up to the 8th event. It was only because of below par performances in the last two events that he lost ground in the end. 

In my blog post  on Eaton's potential I was comparing the decathlon score of Eaton and Sebrle to their possible maximum, finding that they performed at 95 % and 97 % respectively. I hadn't thought at O'Brien at the time but Mulkeen's post made me repeat the calculations for him. By the way, Dvorak is at the same level as Sebrle, a 97 % performer (8994/9265), while Thompson's performance stands at 96 % (8847/9218). Concerning Thompson I cannot resist the temptation to report what a commentator on Mulkeen's post said about the great british decathlete. When asked recently about Eaton, Thompson said “Eaton’s terrific – I wouldn’t have beaten him by much”. It seems that Thompson apart from excelling in athletics is also recordman of chutzpah.

Coming back to O'Brien, here are his personal records

Event	Record	points
100 m	10.23	1040
Long Jump	8.08 m	1081
Shot Put	16.69 m	894
High Jump	2.20 m	992
400 m	46.53	982
100 m Hurdles	13.47	1044
Discus Throw	52.71 m	927
Pole Vault	5.20 m	972
Javelin Throw	66.90 m	842
1500 m	4:36.63	702
Total		9476

His world record of 8891 is less than 94 % of his maximum of 9476 points. 
Even Karpov whom I consider one of the biggest wasted talents in the decathlon has a 95 % score, 8725/9186, (but had he managed a decent javelin throw, things could have been different). 

Had O'Brien succeeded to perform at 96 % of his maximum we would have registered a whopping 9100 world record and been the first man over 9000. Well, to be fair, this honour belongs to the chinese decathlete Yang Chuan-kwang, who under the 1950 tables registered an impressive 9121 performance (which, in any case, is the first over 8000 points record with the current table).

Of course, had Eaton performed at 96 % of his maximum, when he established his world record, the latter would stand today at 9160 points (but then we wouldn't have had the occasion to enjoy his fantastic effort in the 1500 m). On the other hand Eaton is still active and, who knows, one day he may break the 9100 points barrier. 

So, for me the question of who is the best decathlete will remain unanswered. Eaton has probably a very slight advantage over O'Brien but I would wait for more before awarding him the title.

A fabulous blog, but ...

Only recently I came accross a blog that has great posts on the (ancient) Olympic Games but also some rare pearls like the article on the colombian goalkeeper Rene Higuita Zapata (a.k.a. el Loco). Here is the link:

Dino Retrosportivo

It is maintained by the greek journalist, writer and old comics expert extraordinaire G. Vlachos. The only drawback... it is in greek and thus it can only be appreciated by those who can read my maternal language. But if you are among the happy few, do not hesitate. This blog is a must.

Record prediction: an absurdity

In a previous post of mine I discussed the inadequacy of the logistic extrapolation for the prediction of the record evolution in athletics. I concluded that post saying that I did not believe that the logistic approximation was to blame. Thus I decided to perform the analysis of the data used in the aforementioned post using different mathematical expressions.

The first expression I am going to analyse here is the four-parameter logistic which has the form

where L is the length of the throw, t is the time and A,B,b,c are parameters. The standard, three-parameter, logistic expression corresponds to A=0, so adding this term brings an extra freedom which might improve the situation. The figure below shows the best fit of a four-parameter logistic expression to the data. Indeed a small improvement with respect to the extrapolation of the three-parameter logistic used in the previous post is obtained. While previously we found a prediction for the 2015 record of circa 83 m, with the four-parameter expression we obtain a prediction of 81 m, still way off.

Next I turn to another expression widely used in various domains of biology or finance, the Gompertz law. While the logistic expression is a symmetrical sigmoïd, the Gompertz function has a rapid initial growth and a slower approach to the final asymptote. The precise expression of the Gompertz law is 

again a four parameter function. It turns out that the Gompertz law leads to a much stiffer fit and an extrapolation of the record for 2015 beyond 85 m.

What is the conclusion one can draw from this analysis? To sum it up in a catchy way: "garbage in, garbage out". It is not the mathematical tool used for the analysis that is at fault. It is the fact that we are attempting an analysis based on the past trend that is to blame. No prediction can be made unless one takes into account the reality of the discipline. In the case of women's discus the fact that the record did stagnate, with the best performances of the past decade several meters behind those of the late 80s, should essentially be attributed to the better antidoping controls introduced in the 90s. Thus it is not the mathematical analysis that is inadequate but its use with inappropriate data.

At this point I cannot resist the temptation to make a remark, based on the analysis presented in an article, co-authored with Y. Charon, and published in New Studies in Athletics  29:4 (2014) page 37. The world record, despite its absolute and gripping character, should not be used in order to assess the progression of a discipline. In the figure below we show the progression of the 50th performer for women's triple jump since 1992 (shortly after the IAAF recognised officially this event) till 2012. While the world record has remained unbeaten since 1995, the performance of the 50th performer is increasing steadily, representing faithfully the progress of the discipline. 

Given the smooth progression one would be tempted to use the data on the 50th performer and extrapolate towards the future. The dashed line in the figure does just that using a three-parameter logistic formula. And, once more we obtain an absurd result. The asymptotic value we find is a mere 14.73 m, a performance I am convinced will be reached (and surpassed) by the 50th performer before the end of the decade. 

The whole point of this post is that record prediction is a very subtle business and no mathematical approach will ever work even for short-term predictions. The situation is slightly better if one considers the performances not at the very top (like the first 5) of the discipline but rather those of the elite (say the 50th performer) provided one limits oneself to really short-term predictions. But this is something any competent coach can do without using any mathematics.