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Friday Press Clippings:
Simpson's Paradox in Basketball Statistics

From Kent State University
By Darci L. Kracht
Download source here: ' Simpson's Paradox in Basketball Statistics ' by Darci L. Kracht

"... What's going on here? Let's look at the numbers to find out. The first row of the table has the data for two-point field goals.
We see that Huffman made 57 out of 127 attempts for an average of 57/127 = 0.449, while Bedford made 13 of his 30 attempts for an average of 0.433.

The second row of the table contains the same statistics for shots taken from the three-point range. Here, Huffman made 35 of 100 for an average of 0.350 while Bedford missed his only attempt for an average of 0.000. Thus, Huffman outshot Bedford in both categories. ..."

"... Now combine the categories to find the players' overall field goal shooting percentages.

Adding down the columns of the first table, we see that Huffman made 57+35=92 out of 127+100=227 attempts, giving him an average of 0.405.

On the other hand, since Bedford made 13 of his 31 attempts, his average is 0.419, beating Huffman's! ..."

"... This is an example of an unusual statistical phenomenon known as Simpson's Paradox, after the statistician who described it in 1951. It can occur whenever data from two or more distinct categories are combined into a single category.

Simpson's Paradox is more likely to occur if there is some "lurking" variable that makes the subcategories rather different from one another. ..."

"... There are a couple of lurking variables in this example. First is the level of difficulty of the shots. Shooting from beyond the three-point arc is considerably more difficult than shooting closer to the hoop, as shooting percentages reflect. ..."

"... Finally, we should ask just how useful these statistics are. In other words, how accurately does a player's average reflect the probability that he will make the next shot?

With 100 or more attempts in each category, an extra hit or miss would change Huffman's average by at most one percentage point. Therefore, his shooting percentage is probably a fairly accurate predictor of future performance--- not so for Bedford, as can be seen most dramatically in the statistic for three-point field goals.

With only one three-pointer attempted, his accuracy in this category must be perfect (100%) or dismal (0%). Such a statistic is clearly of little predictive value. Indeed, Bedford has proven to be one of the more accurate shooters on the team this season. ..."

Read more articles in Kent State University.

To read today's 'Press Clippings' in Spanish,
click this week above on the 'Español' tab or afterwards click here:
' La acumulación de victorias en la NBA aumenta la probabilidad de ganar el siguiente partido '
by S. Triguero.

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