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Except that in many of these sports, the margins are so low as to be completely laughable. The 100 m swimmers this year, for instance, have a spread between first and second place of a fraction of a second. There is no way that the measurement of the time it takes a swimmer to cross a 100 m basin is accurate to one tenth of a second.

I did the calculation once for similarly ridiculous differences, and it turned out that to measure the difference between gold and silver in the 100 m swimming Olympics, you have to have a swimming course with a length that is accurate to about a millimeter, nevermind the accuracy of the clocks...

A reasonable interpretation of those data is that the two guys arrived simultaneously and should share a first place. Or flip a coin for the gold medal - that'd be about as reasonable.

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Mon Aug 25th, 2008 at 01:37:21 PM EST
[ Parent ]
Then you are measuring the wrong quantity, no? The winner isn't the fastest in the water, it's the first who hits the plate at the finish line. How you get there is irrelevant, although you obviously have to be fast enough through the water to make it.

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$E(X_t|F_s) = X_s,\quad t > s$
by martingale on Tue Aug 26th, 2008 at 01:04:08 AM EST
[ Parent ]
Well, they're supposed to be competing in similarly sized basins... And if the margin is on the order of a tenth or a hundredth of a second, "similarly sized" becomes a very precise criterion indeed.

But in either case, I would argue that even if we drop the argument about measurement accuracy, a difference of a tenth or a couple of hundredths of a second still comes down to luck - it's hardly credible to claim that either is the better athlete based on such a thin margin.

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Tue Aug 26th, 2008 at 02:27:27 AM EST
[ Parent ]
Isn't there some confusion here between who is fastest in a particular Pool, and the validity of "World Records" calculated to 100 th's of a second when Pools may be imperfectly measured?

A case in point being the huge amount of money currently being expended (stripping tiles, planing concrete etc)to extend London's Crystal Palace Pool from its current 49.98m to 50.00m.....

"The future is already here -- it's just not very evenly distributed" William Gibson

by ChrisCook (cojockathotmaildotcom) on Tue Aug 26th, 2008 at 03:55:21 AM EST
[ Parent ]
Not really. My argument is that the ends of the pools are not perfectly parallel to the millimeter, so the courses are not equally long even in the same pool.

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Tue Aug 26th, 2008 at 04:11:33 AM EST
[ Parent ]
There are two different issues: For comparing competitors in a single race, only the variation of the pool size over the various lanes matters (and the quality of time keeping). For comparing competitors over several races (eg over time in different olympics) the variation over different swimming pools also matters. Generally, since swimming pools in different countries are built by different contractors, it's plausible that the variation between pools is higher than the variation between individual lane lengths. The time keeping tolerances are much smaller, so can be ignored, at least over the last 30-50 years I'd say, and anything older is not worth bothering with.

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$E(X_t|F_s) = X_s,\quad t > s$
by martingale on Tue Aug 26th, 2008 at 05:08:04 AM EST
[ Parent ]
The FINA olympic size is precisely defined as 50.0m with a tolerance of plus/minus 1cm, ie 1/5000th of the size of the pool (*). Since it takes about 20s to cross 50m, the variation in time taken is on the order of 20s/5000 = 0.004s, less than half a hundredth of a second.

The crystals in your computer or mine measure billionths of a second reliably, and separating swimmers to within four thousandths of a second with literally negligible margins of error is easy with touch panels. There's really no issue at all of margin of error in time measurement to speak of.

When athletes are selected, it's safe to say that they are believed to be able to reliably repeat their performances. It would not do to send an athlete whose performance has a huge random variation from race to race, and since the olympic performers are practically constantly monitored during training, such variation does show up.

I have little doubt that a 0.01s difference is meaningful on the day of the race.

(*) I believe Beijing was boasting a tolerance of 2mm rather than 1cm, but if you're comparing against other olympic races in other countries, 1cm is needed.

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$E(X_t|F_s) = X_s,\quad t > s$

by martingale on Tue Aug 26th, 2008 at 04:59:52 AM EST
[ Parent ]
I stand corrected on the measurement, then.

But I still doubt that the performance of the human body is repeatable to .1 %...

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Tue Aug 26th, 2008 at 05:16:40 AM EST
[ Parent ]
It's an interesting question, isn't it? The kind of data which can truly decide this is hard to come by. Here's a list of world records in 50m freestyle, which shows a typical improvement of 1/10th of a second or so. If this was all there is to it, then you'd be right.

What is true is that world records only happen a few times a year during championship meets yet swimmers do pretend races every day during training. Moreover, records have a different statistical distribution compared with the underlying time series, so the list above says nothing about how the daily improvements would look for a typical top swimmer.

At this level of competition, all bodily functions are controlled and training happens every day for most of the day so there's plenty of scope for steady progress with tiny improvements of the order of 1/100th second every couple of days, which add up to 1/10th progress by the time that the next big race occurs.

However, I couldn't find a time series supporting this with casual googling, and in truth I expect it's too valuable to be found on the web. At this level of competition, the swimmers are measured daily, and all their bodily functions are controlled. A complete time series of daily improvements is likely worth a small fortune. Swimming coaches at this level of competitionare unlikely to give out daily timing progress

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$E(X_t|F_s) = X_s,\quad t > s$

by martingale on Tue Aug 26th, 2008 at 06:09:40 AM EST
[ Parent ]
... of a human body is repeatable to within 0.1% ... no swimming contest is making the claim that the result would be repeated with exactly the same finish and times if repeated ... its only making the claim that that was the finish on the day.

Indeed, if it were repeatable to that precision, there would be little point in racing.

In Oz, where they take their Olympic swimming coverage quite seriously, you not only hear the winning time and whether it broke a World Record or Olympic Record, but also the PB's (personal best time) of the individual ozzie swimmers and whether they did a new PB at the Olympics.


I've been accused of being a Marxist, yet while Harpo's my favourite, it's Groucho I'm always quoting. Odd, that.

by BruceMcF (agila61 at netscape dot net) on Tue Aug 26th, 2008 at 10:13:39 AM EST
[ Parent ]

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