13 positions in basketball? Muthu Alagappan makes the argument with topology

Can Topology Teach Us Anything About Basketball?

Can Topology Teach Us Anything About Basketball?

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Slate's Culture Blog
May 2 2012 12:34 PM

Does Basketball Actually Have 13 Positions?

Do LeBron James, right, and Carmelo Anthony, left, play the same position?

Photo by Mike Ehrmann/Getty Images

Back in March, after the Sloan Sports Analytics Conference was held at MIT, I wrote about a paper by Kirk Goldsberry called “Court Vision: New Visual and Spatial Analytics for the NBA.” Goldsberry persuasively argued that NBA teams could use maps to improve, for instance, their scoring efficiency. The maps he produced distilled huge amounts of information into quickly understandable visual guides, and struck me as a notable new tool for savvy NBA teams.

David Haglund David Haglund

David Haglund is the literary editor of NewYorker.com. 

On Monday, Wired published a piece about another paper from the same conference. In “From 5 to 13: Redefining the Positions in Basketball,” Muthu Alagappan, using data from last season, groups players according to the points, rebounds, assists, steals, rebounds, blocks, turnovers, and fouls they accumulated per minute, then creates topological maps that render these groupings visually. Guided by these visual “clusters,” Alagappan concludes that there are 13 positions in basketball, rather than five. His paper won a conference award for “best Evolution of Sport.”


The Wired piece is headlined “Analytics Reveal 13 New Positions,” a credulous take echoed by kottke.org (“Basketball has 13 positions, not just 5”). But is Alagappan’s paper actually persuasive?

Positions in basketball are a subject of endless debate. While the baseball diamond, with its four bases and wide outfield expanse, more or less demands the traditional alignment (occasionally tweaked) that all Major League teams use, the basketball court makes no such demands. A team can, in theory, use any arrangement, and what we think of as the traditional five positions have evolved over time.

NBA teams already approach the question of positions with greater nuance than the box score does. General managers look for defensive-minded bigs, volume scorers, wing defenders, and other player-types that are not listed in the box score. Many of Alagappan’s “new” positions reflect this thinking: His list includes roles like “offensive ball-handler,” “3-point rebounder,” and “paint protector.”

It also includes categories like “NBA 1st-Team” (described by Wired as “a select group of players so far above average in every statistical category that the software simply groups them together regardless of their height or weight”), “NBA 2nd-Team” (players who aren’t “quite as good” as 1st-teamers, but are “still really, really good”) and “One-of-a-Kind” (players “so good they are off the charts—literally”). These are positions… how, exactly? It’s not clear. The problem of outliers is a common one in statistical analysis, and it appears to severely weaken Alagappan’s approach. These categories reflect the quality of the player, not the position he plays.

Another red flag: Alagappan’s methods lead him to group players whose similarities are superficial. For instance, the “role player” category includes not only Shane Battier but also Rajon Rondo. Battier and Rondo may accumulate the statistics Alagappan measures at a similar rate, but their roles on the court could hardly be more different. Rondo dominates the ball like few players in the NBA, while Battier rarely touches it. If a coach was trying to decide who should be on the court together, the idea that Rondo and Battier played the same position would confuse the issue, not clarify it.

Of course, an NBA coach would never be confused in this way. Which is another problem with Alagappan’s paper: He claims that because Shane Battier and LeBron James are listed as playing the same position, it is “very difficult” for their coach “to make intelligent in-game substitutions.” This is baloney. Eric Spoelstra knows that James and Battier have very different skill sets, and he employs these players accordingly.

I don’t mean to pick on Alagappan, a college senior who is attempting to tackle an interesting and complicated problem. What worries me is the susceptibility of a certain breed of sports fan, the sort who, rather than fleeing from numbers and graphs, flocks to them. As someone who grew up on Bill James, I love statistical analysis, but such analysis is only valuable when it tells us something new and true about the game in question. If there is such illumination to be found in  “From 5 to 13,” I haven’t seen it.