“It’s not what you don’t know that hurts you; it’s what you know that just ain’t so.”–Satchel Paige

Question #86: In both 1995 and 1996, David Justice of the Atlanta Braves had a higher batting average than the New York Yankees Derek Jeter. Who had the higher two-year average over the same two-year period?

The answer is Derek Jeter. The anomaly, known as Simpson Paradox, occurred because in the first year Jeter had only 48 at-bats and 12 hits for average of .250, while Justice batted 411 times with an average of .253. The following year Jeter batted 582 times and hit for a .314 average, while Justice hit .321 but had only 140 at bats.

In other words, when you combined the players totals for both years Jeter comes out on up as the table below demonstrates.

The sporting world is ripe with unlearning examples. One of my favorites occurred on December 30, 1936 when over 17,000 fans packed into the old Madison Square Garden to watch Long Island University, the country’s top-ranked basketball team, take on Stanford University. It was slated to be a great game. Long Island was putting up its 43-game winning streak up against the reigning Pacific Coast Conference champions.

More than that, though, people were eager to watch Hank Luisetti, Stanford’s star sophomore. He was the only player known for shooting the ball with one hand while jumping up in the air. At the time, every other basketball player in the country shot with two-hands or took hook shots.

Luisetti’s “jump-shot” was so radical, in fact, that it caused Nat Holman, the legendary coach of City College of New York—and a man known as “Mr. Basketball”—to remark, “That’s not basketball! If my boys ever shot one-handed, I’d quit coaching.”

Luisetti and Stanford went on to crush Long Island University and, two years, later, Luisetti became the first college player ever to score 50 points in a game.

Today, it is impossible to find a single player at either the collegiate or professional level who shoots two-handed.

It took a long time for basketball players (and their coaches) to unlearn the two-handed shot but the story and Jeter/Justice anomaly remind us that unlearning can be both counter-intuitive and paradoxical.

To this end, while it is true that a return to two-handed shooting is unlikely, it might make sense on one area of the basketball court: the free-throw line. Consider the case of Rick Barry. Although he used an unorthodox under-handed “granny-style” style to shoot free-throws, Barry is the National Basketball Association’s second most accurate free-throw shooter of all-time with an average of .900. Today, not a single player shoots free-throws under-handed. This is in spite of the fact that the average accuracy rate in the NBA is roughly 75% and many games are determined by just a few points.  

For those players and coaches with the courage to unlearn their current free-throw shooting style, it could lead to an “above average” outcome because even a modestly higher free-throw average could result in a handful more victories each season.

Homework Assignment: Explain why you think no one in the NBA shoots under-handed free-throws. For extra credit: Name at least two NBA players who might want to unlearn their current form and consider shooting “Granny-style”? (Hint: At 52.4%, Shaquille O’Neal is only the second worst free-throw shooter.)