Practice And Probability

Posted on June 15, 2010

Yesterday I read an article by Jason Cohen imploring software entrepreneurs to avoid seeing patterns where none exist. I don’t want to comment directly on that article, but one part seemed relevant to musicians: streaks.

Jason points out that when an athlete goes on a streak, sports commentators notice. As real as the streak seems, it may be an illusive pattern in random noise.  A statistical mirage, if you will.

As a pianist, I’ll often claim to have good days where everything feels right, or bad days when I seem to make lots of simple errors. On the bad days, I frequently analyze my playing intensely, trying to figure out what’s different and what I need to change. But if Jason is right, I’m finding a pattern that doesn’t really exist, and badgering myself needlessly about it.

That alone is a valuable insight. But it got me thinking: can I use probability theory in my practicing?

When have I practiced enough?

Let’s say I’m practicing a piece that’s 200 measures long. And for simplicity’s sake, let’s say that if I can play each measure perfectly, I can play the piece perfectly. What percentage of the time do I need to play each measure correctly to have a good chance of playing the entire piece correctly?

Prob. correct measure Prob. correct piece
50% 6.2*10-59%
90% 7.1*10-9%
99% 13%
99.5% 37%
99.6% 45%
99.7% 55%
99.8% 67%
99.9% 82%

If you only play each of the 200 measures correctly half the time, you’re more likely to win Powerball 6 times than you are to play the piece without error from start to finish.

And in order to have a better-than-even chance of playing the whole piece correctly, you have to be able to play each measure correctly 997 times out of 1,000.

What does this mean?

Two things.

First, perfection is hard. Really hard. You have to work to drive up your success rate, but you can’t get down on yourself for making errors. The numbers just aren’t on your side.

Second, if you’re like me, your standards for when you “know” a passage may have been too low. Many of us have been taught to practice something until you play it right ten times in a row. As the table above shows, that’s a good start, but only a start.

Obviously it’s often unreasonable to play something 997 times in a row. In the absence of that, your standard needs to be not only playing it correctly, but comfortably. There’s a difference between getting it right because you got lucky, and getting it right because it would be unnatural to get it wrong.