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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
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