## How many players in the NBA are "above average"?

A seemingly simple question (duh, about half!) with a not so simple answer.

The talent level in the NBA is not bell curved, with most players being average and a small number of really bad players and a small number of really good ones. If that were the case yes, half of the players would have above average talent. But we don't select NBA players randomly from the population at large. We select players from the top end of the talent distribution.

Since we're selecting a pretty decent sample of players (about 360), the probability distribution of talent in the NBA is approximately exponential:
Exponential Distribution on Wikipedia
where the highest concentration of players is actually at the lowest level of talent that can get you on a roster (the CBA structure may skew this a little, but basically that's what's going on). Because of this "skewness" in the distribution of talent, the "average" talent level will be above the median. So actually less than half of the players would have "above average" talent -- if the average talent level = 1, the median player will have a talent level of about 0.7. Or to put it another way, the median player's talent level is actually one standard deviation below the mean!

The cumulative distribution function for an exponential distribution with a mean of 1 is F(x)=1-exp(-x). What that means in English is that the probability of having talent greater than average is exp(-1)=36.8%. So a little more than a third of the players in the NBA have "above average" talent. If there are 30 teams with 12 players each (360 players total), about 132 players are above average.

This represents the view of the user who wrote the FanPost, and not the entire Bullets Forever community. We're a place of many opinions, not just one.

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