Archive for sport statistics

gender-neutral Olympics?!

Posted in Mountains, Running, Statistics, University life with tags , , , , , , , , , on May 16, 2012 by xi'an

As usual, reading the latest issue of Significance is quite pleasant and rewarding (although as usual I have to compete with my wife to get hold of the magazine!). This current issue is dedicated to the (London) Olympics. With articles on predictions of future records, on whether or not the 1988 records can be beaten (the Seoul Olympics were the last games before more severe anti-drug tests were introduced), on advices to Usain Bolt for running faster (!) and on the objective dangers of dying from running a marathon (answer: it is much more “dangerous” to train!).

However, a most puzzling (and least statistical) article is Stephanie Kovalchik’s proposal for a gender-neutral Olympics.  The author’s theme is that, in most sports (the exceptions being shooting, yachting, and horse riding, where competitions are mixed), raw performances of women are below those of men for physical and physiological reasons. Stephanie Kovalchik thus “question[s] whether a sex-stratified Olympics is the product of groundless stereotypes about male athletic superiority or could be justified by gender differences at the elite level of sport” (p.20). Unsurprisingly, she concludes that no amount of training seems capable to bring both sexes at the same level: indeed, for instance, Paula Radcliffe, the fastest female marathon runner (2:15:24), is still 11 minutes beyond Patrick Makau, the fastest male marathon runner (2:03:38). They are both super-terrific athletes, the top ones in their categories. Now, Paula runs half-marathon and marathon faster than the best male runners in my team (Insee Paris Club). Where’s the problem?! And why should we try to rank Paula against Patrick?!

A parenthesis: the author mentions a most bizarre (but eventually inappropriate) exception: in the Badwater Ultramarathon, a crazy race covering 135 miles and going from Badwater, Death Valley, at 280’ (85m) below sea level, to the Mt. Whitney Portals at nearly 8,300’ (2530m), with a total of 13,000’ (3962m) of cumulative vertical ascent, four women won over the 25 occurrences of the race. I found this phenomenon quite curious and went to check first the records of the comparable ultra-trail du Mont Blanc, another even crazier race (168km, 9,600 metres of positive height gain, at mostly higher altitudes, between 1000m and 2500m), and saw that last year the first woman in the race was 13th in total, with a difference of four and a half hours with the winner (20:36 hours, believe it or not..!). Going back to the Badwater Ultramarathon, checking the results showed that the race actually attracts a very limited number of runners, from 17 finishers the first year to 83 last year (where the first woman was 7th, about 5 hours from the winner), with a huge variation between runners and between years. So I would not draw so much of a conclusion from this example, certainly not that “in an event where sheer dogged endurance, guts and determination must count for almost everything, we may be there already”. It is rather a law of small numbers: such extreme events attract a very small number of participants with incredibly variable finishing times, e.g. two of the four winning women won out of…5 (1988) and 2 (1989) finishers, while the two other victories were achieved by Pamela Reed over 45 (2003) and 57 (2002) competitors, a much more remarkable feat. Meaning that one or two runners missing or giving up brings a huge change in the final time. The ultra-trail du Mont Blanc now involves a thousand runners and there, numbers count. End of the parenthesis (with total respect to all those runners, I wish I could do it!).

Going back to the paper proposal, Stephanie Kovalchik considers that “credit merit apart from hereditary luck will favour individuals who possess the best genes for sport. Thus, prejudice – in the true sense of pre-judging – at the Olympics runs deeper than gender lines. Geneticism more than sexism is to blame for making the possession of a Y chromosome an advantage at the Games” (p.21). She suggests to instead rank athletes by a “statistical adjustment [that would]  remove the confounding factor of genetic inheritance, to provide a standard of achievement that all could aim at, no matter what their hereditary luck” (p.22). In essence, the winner would be the one that had gained the most compared with a “demographically matched sample of untrained individuals” (p.24). If I may, this sounds perfectly ridiculous! First, the whole point of the Games and of any sporting competition is to determine the “best” athlete. This is not an egalitarian goal and can and does lead to poor outcomes such as cheating, drug enhanced performances, nationalistic recuperations, commercialisation, bribery, and so on. It is thus perfectly coherent to be against those competitions. (I am not a big fan of the Olympics myself for this reason. However, without competition, even at my very humble level, and with little hope of winning anything, I would certainly train much less than I currently do.) But to try to reward efforts to counteract physical differences sounds like political correctness pushed to the extreme!  Second, and this is why I find the paper so a-statistical!, the adjustment must be with respect to a reference population. If we carry the argument to its limit, the only relevant population is made of the athlete him/herself. Indeed, genetic, sociological, cultural, geographical, financial, you-name-it, elements should all be taken into account! Which obviously makes the computation just impossible because then everyone is competing against him/herself.

Who’s #1?

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , , , , , , , , on May 2, 2012 by xi'an

First, apologies for this teaser of a title! This post is not about who is #1 in whatever category you can think of, from statisticians to climbs [the Eiger Nordwand, to be sure!], to runners (Gebrselassie?), to books… (My daughter simply said “c’est moi!” when she saw the cover of this book on my desk.) So this is in fact a book review of…a book with this catching title I received a month or so ago!

We decided to forgo purely statistical methodology, which is probably a disappointment to the hardcore statisticians.” A.N. Langville & C.D. Meyer, Who’s #1? The Science of Rating and Ranking (page 225)

This book may be one of the most boring ones I have had to review so far! The reason for this disgruntled introduction to “Who’s #1? The Science of Rating and Ranking” by Langville and Meyer is that it has very little if any to do with statistics and modelling. (And also that it is mostly about American football, a sport I am not even remotely interested in.) The purpose of the book is to present ways of building rating and ranking within a population, based on pairwise numerical connections between some members of this population. The methods abound, at least eight are covered by the book, but they all suffer from the same drawback that they are connected to no grand truth, to no parameter from an underlying probabilistic model, to no loss function that would measure the impact of a “wrong” rating. (The closer it comes to this is when discussing spread betting in Chapter 9.) It is thus a collection of transformation rules, from matrices to ratings. I find this the more disappointing in that there exists a branch of statistics called ranking and selection that specializes in this kind of problems and that statistics in sports is a quite active branch of our profession, witness the numerous books by Jim Albert. (Not to mention Efron’s analysis of baseball data in the 70’s.)

First suppose that in some absolutely perfect universe there is a perfect rating vector.” A.N. Langville & C.D. Meyer, Who’s #1? The Science of Rating and Ranking (page 117)

The style of the book is disconcerting at first, and then some, as it sounds written partly from Internet excerpts (at least for most of the pictures) and partly from local student dissertations… The mathematical level is highly varying, in that the authors take the pain to define what a matrix is (page 33), only to jump to Perron-Frobenius theorem a few pages later (page 36). It also mentions Laplace’s succession rule (only justified as a shrinkage towards the center, i.e. away from 0 and 1), the Sinkhorn-Knopp theorem, the traveling salesman problem, Arrow and Condorcet, relaxation and evolutionary optimization, and even Kendall’s and Spearman’s rank tests (Chapter 16), even though no statistical model is involved. (Nothing as terrible as the completely inappropriate use of Spearman’s rho coefficient in one of Belfiglio’s studies…)

Since it is hard to say which ranking is better, our point here is simply that different methods can produce vastly different rankings.” A.N. Langville & C.D. Meyer, Who’s #1? The Science of Rating and Ranking (page 78)

I also find irritating the association of “science” with “rating”, because the techniques presented in this book are simply tricks to turn pairwise comparison into a general ordering of a population, nothing to do with uncovering ruling principles explaining the difference between the individuals. Since there is no validation for one ordering against another, we can see no rationality in proposing any of those, except to set a convention. The fascination of the authors for the Markov chain approach to the ranking problem is difficult to fathom as the underlying structure is not dynamical (there is not evolving ranking along games in this book) and the Markov transition matrix is just constructed to derive a stationary distribution, inducing a particular “Markov” ranking.

The Elo rating system is the epitome of simple elegance.” A.N. Langville & C.D. Meyer, Who’s #1? The Science of Rating and Ranking (page 64)

An interesting input of the book is its description of the Elo ranking system used in chess, of which I did not know anything apart from its existence. Once again, there is a high degree of arbitrariness in the construction of the ranking, whose sole goal is to provide a convention upon which most people agree. A convention, mind, not a representation of truth! (This chapter contains a section on the Social Network movie, where a character writes a logistic transform on a window, missing the exponent. This should remind Andrew of someone he often refer to in his blog!)

Perhaps the largest lesson is not to put an undue amount of faith in anyone’s rating.” A.N. Langville & C.D. Meyer, Who’s #1? The Science of Rating and Ranking (page 125)

In conclusion, I see little point in suggesting reading this book, unless one is interested in matrix optimization problems and/or illustrations in American football… Or unless one wishes to write a statistics book on the topic!