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WE’VE reached the limit for some sports. No matter how hard we train or how much the design of running shoes improves, we’re just not going to get any better.

A mathematical analysis shows that most of our track and field records are being broken by chance rather than by better equipment or increased skill. The researchers looked at the best annual performances in 22 events in German athletics championships during the 1980s and 90s, including long jump, high jump and running races. Only four events showed any kind of systematic increase over that time, while the rest had hit…

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