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 If you only spend 20 minutes of the rest of your life on economics, go spend them here.
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..... "Any economic unit can emit money. The serious problem is to get it accepted" Hyman Minsky
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. -- $E(X_t|F_s) = X_s,\quad t > s$
But I still doubt that the performance of the human body is repeatable to .1 %...
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 -- $E(X_t|F_s) = X_s,\quad t > s$
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.
