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truth, trust, insight and statistics

You may get an impression from GR weekly that I’m preoccupied with the statistics of the everyday life and society around me. And, yes, in a way that’s true, but it is not because I blindly believe in statistics, on the contrary, it is because I enjoy searching for the meaning of any particular statistical approach to social life. From my physics’ freshman days, starting with the average value of some simple measurements, I carry a shadow skepticism on statistics in general and I never got read of it. (This may sound deviant to those who know that I, as a part of my university career, lectured on statistical physics for many years; however, I’ve never shuffled the practical, technical success of statistical calculations over the justification of those methods.)

I’ve made a peace with myself realizing that I can accept a result of statistical approach only if I understand the assumptions of that particular approach and if I agree with them (or at least, have no objections). That is, if my insight on the subject is along the same guidelines. Well, the truth could be somewhere else, but I don’t trust ‘else", currently.

My ‘preoccupation’ with tennis statistics is a good example of my dilemmas. Although I compliment myself for recognizing a power law in players’ ranking to justify a set of ranking bins used for the world of professional tennis by country, something is not along my insight when I examine the later graph. Is the dominance of Russian women really so pronounced?

Here is another look at WTA rankings : among the top 512 players, as of Feb. 26, 2007, Russia has 41 vs. 40 of USA (2.4% lower) with 21,442.5 total ranking points vs. 8,625.75 (59.8% lower); the average ranking points are 523.0 and 215.6 (58.8% lower), respectfully. So, from the ranking points of view, the Russian dominance is overwhelming. However, the points superiority is not across the board, it is from the few top players (see the graph on the right) while the gap in main field (below 1024 points) is not conclusive at all: 7670.5 vs. 7356.75 (4.1% lower) total points, and 219.2 vs. 188.6 (14.0% lower) average points. Is this the cause of my reservations?

Not likely: I understand that sport is about winning, not welfare. My insight deviates from the statistical picture probably because I perceive tennis rankings as a process while statistics presents a state, a frozen picture at a given time. If the main field is not reigned, how ‘secure’ are leading Russian positions?

WTA rankings : RUS & USA : Feb. 26, 2007

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