"Do people improve when they don't have to look at the audience?"
Different musicians are different. Many performers play much better when in front of an audience. Or at least, they play with more emotion, although it may be less common for them to get more notes right. In fact, that's part of what drives some musicians to become professional performers -- the thrill of performing for people.
Other musicians have problems with nerves. Some take medications for it, but this in turn can cause problems performing (and with other aspects of life and health). Many musicians have to quit performing because of their nerves. Or, in some cases, they quit performing in public but continue to record. IIRC, that was the case with Glenn Gould.
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Different musicians are different. Many performers play much better when in front of an audience. Or at least, they play with more emotion, although it may be less common for them to get more notes right. In fact, that's part of what drives some musicians to become professional performers -- the thrill of performing for people.
Other musicians have problems with nerves. Some take medications for it, but this in turn can cause problems performing (and with other aspects of life and health). Many musicians have to quit performing because of their nerves. Or, in some cases, they quit performing in public but continue to record. IIRC, that was the case with Glenn Gould.