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What is the probability of
getting heads ten times in a row? It is a little under one in one thousand.
That's about as often as you'd expect to see someone like Shaquille O'Neal or
Ben Wallace

What is the probability of someone like Reggie Miller missing ten free throws in a row? It is a little less than one in ten trillion. That means that for all intents and purposes, you would win the Powerball lottery about 10,000 times in a row before Reggie were to miss ten consecutive free throws. (I'm being a little less than perfectly formal here, just to give a flavor. Technically, it would take about ten trillion trials of ten free throws each for Reggie Miller to expect to miss all ten in a row, assuming his free throw percentage is 95 percent).

For your own free throw shooting, here's how I like to use these numbers. If you've ever tried to improve your game or your shot, then certainly at one point you must have attempted to shoot ten free throws. You probably counted the number of times you made the shot. Perhaps you do it on a regular basis.

Sometimes the shooting goes well and you make ten in a row. Sometimes it's only nine. Sometimes, heaven forbid, it's only three or four. Those are bad shooting days. But how can you keep in your head some numbers that will help you determine what your true percentage is, if you don't want to resort to memorization or a notebook?

Here's a tip. If you're aiming to be a 90% free throw shooter, then you should know this: the chances of you getting seven or less out of ten is only about 7%. In other words, it should happen so rarely it's not even worth thinking about.

The human mind remembers things in a very particular way. It remembers the last thing, sometimes the first thing, and often the most extreme things. So you remember the times you got all ten in a row very well. And you may also remember the time you got zero or one or two out of ten. And you remember how you did on your last outing. Your first outing was far too many years ago to recall.

So what to do? Go shoot. If you make seven or less, most likely you are not a 90% free throw shooter. You may well be a 75% free throw shooter, because you'd expect about half the time to get seven or less, and about half the time to get eight, nine, or ten. But you're almost certainly not a 90% free throw shooter.

This little calculation helps me when I shoot. How? It focuses my attention on really making sure to get the ball in the hole. Otherwise, I could be deluding myself thinking I am a 90% free throw shooter when it counts (sound familiar, Shaq?) even though I consistently shoot only seven or eight out of ten.

Each miss is huge when you're aiming to be a 90 percent guy. At 90 percent, you should be getting 10 out of 10 about a third of the time. You should be getting 9 out of 10 about a third of the time. And you should be getting 8 out of 10 about one fifth of the time. The remaining times, statistically speaking, pretty much never happen. If you repeatedly get 7 out of 10, and only occasionally 9 or 10 out of 10, then you are not a 90% free throw shooter.

The problem with probabilities is you never know if you're really discovering new information or just repackaging obvious things. I have simply found that a recognition of some of these ancillary numbers really make it clear how devastating each miss is to your free throw percentage.

And how potentially devastating it can be to your team.

Is it safe to predict that the team whose center hits the highest free throw percentage will win each game? It doesn't seem like a bad bet. If I told you Shaq hit 92% of his free throws in a particular game, wouldn't you think the Lakers won? Note my sly use of a number like 92% instead of 80% which might imply Shaq only got to the line five times, a bad omen. We are indeed omitting the number of attempts here, and looking at just the probabilities. Is it safe to say that if Ben Wallace shoots a significantly higher percentage than Shaq that the Pistons are likely to have won?

It may not be a perfect bet, mainly because of questions about free throw attempts and lots of noise from the performance of other players, but it may not be a bad bet either. So let's go for it. What the hey. A bold prediction for a bold series:

The team whose All-Star center (Ben Wallace for Detroit, Shaquille O'Neal) hits the highest free-throw percentage over the series will win the championship.