Do basketball players tend to improve at shooting free-throws over the course of their career?

Today on Khan Academy there was a probability tutorial on how to figure out the likelihood of a given player making 10 consecutive free-throws.

1 Answer
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Like almost everything in life practice makes perfect, but the questions is if the player indeed practice of his free throws..

you can read the following very interesting post written by Kevin Pelton‬ (NBA analyst for Basketball Prospectus and ESPN Insider) that did research about free throws – http://www.basketballprospectus.com/article.php?articleid=1611

His conclusion was:

To answer the question of whether practice helps at the line, I looked
for pairs of seasons where the same player shot at least 100 free
throws both years, then used statistics to evaluate how often the
change in their percentage was larger than would be expected from
random chance alone. As it turns out, players do seem intrinsically
different at the line on a fairly regular basis–but this is true in
both directions.

We would expect, based on the normal distribution, that 2.5 percent of
players would either improve or decline by at least two standard
deviations from one year to the next. In fact, nearly three times as
many players made such a big jump (7.2 percent). But more than twice
as many (5.5 percent) saw their shooting decay at the line. Free throw
shooting, for whatever reason, is more random than chance would
suggest.

There are more players taking sizeable leaps forward than backward,
which suggests that practice is paying off for some players. However,
the difference between the two groups is relatively small. We’re
talking about 90 players over the last three decades–about three per
year. This is not something that is happening on a routine basis.

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