Monday, March 16, 2009

Smoothing Free Throw Percentages

I hope you had a nice spring break. My son's tennis team is flying to Florida this week -- I wish I could join him.

Since March Madness is starting, I thought it would be appropriate to talk about basketball data. There was an interesting article about free-throw shooting that recently appeared in the New York Times. See the article here.

The main message was that free-throw shooting in professional basketball has hovered about 75% for many years. Unlike other athletic performances such as running and swimming, basketball players don't seem to be getting better in shooting free throws.

Is that really true? Has free-throw shooting accuracy remained constant for all of the years of professional basketball?

To answer this question, I collected some data. For each of the seasons 1949-50 through the current season 2008-09, I collected the overall free-throw shooting percentage in the NBA.

Here are the shooting percentages graphed as a function of year.

Actually, although the overall free-throw shooting percentage is approximately 75%, there seems to some interesting patterns in the graph.

To better see the patterns, I use the command


to superimpose a 3RSSH smooth on the graph and I get the following:

What patterns do we see?

1. In the early days between 1950-1970, the shooting percentages were relatively low with a valley around 72% in the late 1960's.

2. The shooting percentages increased through the 1970's, had a small valley and hit a peak of about 76% in 1990.

3. Then the percentages decreased again and had a local minimum of 74% around 1995.

4. In recent years, the percentages are increasing. It is interesting that the current free-throw shooting percentage 77.2 is the highest in NBA history.

So in reality, the shooting percentage has not stayed flat across years. But it is surprising that NBA players haven't learned to shoot free throws better in the last 60 years.

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