His coaches and teammates, though, noticed that he could jump even higher. Every time he cleared the pole, he had about a foot to spare. But if they moved the bar up even an inch, the vaulter would hit it every time. One day, when the vaulter was not looking, his teammates raised the bar a good six inches. The man vaulted over it, again with a foot to spare.

The moral of the story? No matter how high you jump, how fast you run or swim, how powerfully you row, you can do better. But sometimes your mind gets in the way.

“All maximum performances are actually pseudo-maximum performances,” Dr. Morgan said. “You are always capable of doing more than you are doing.”

The problem for many athletes is how to make a pseudo-maximum performance as close as possible to a maximum one. There are some tricks, exercise physiologists say, but also some risks.