Simpson’s Paradox can make sports stats look weird

Let’s look at two NBA legends, Larry Bird and Reggie Miller.

• When it came to two-point shots, Larry shot 50.9% and Reggie shot 51.6%, so Reggie was better there.
• When it came to three-point shots, Larry shot 37.6% and Reggie shot 39.5%, so Reggie was better there as well.

However, when you add them together Larry was the better overall shooter (49.6% to 47.1%)! How is that possible?

Simply put, Larry shot many more two-point shots than three-pointers, at least compared to Reggie, so his total average was closer to the (higher) two-point number.

It’s weird, I know.

This old video from “singingbanana” helps explain it using a medical example:

As James says in the video, it’s a case that shows how important it can be to pay attention. Initial logic says that Reggie was a better overall shooter or that “Drug B” was more effective, but the math just doesn’t play out that way.

This can apply to medical data or website stats or a variety of other things you might come across. People will often try to show numbers in a way that supports a particular agenda, so knowing about little oddities like this can help you to always be able to sniff out the truth.