For as long as basketball has been played, it's been played with five positions. Today they are point guard, shooting guard, small forward, power forward and center. A California data geek sees 13 more hidden among them, with the power to help even the Charlotte Bobcats improve their lineup and win more games.

Muthu Alagappan is a Stanford University senior, a basketball fan and an intern at Ayasdi, a data visualization company. Ayasdi takes huge amounts of info like tumor samples and displays it in interactive shapes that highlight patterns like genetic markers that indicate a likelihood of ovarian cancer. It's called topological data analysis, and it can be applied to sports, too.

That is exactly what Alagappan did.

Dallas Mavericks' Dirk Nowitzki (41) is not a forward and Jason Terry (31) is not a guard, but rather a scoring rebounder and an offensive ball handler under an analytics model that reveals 13 new positions. Photo: David J. Phillip/Associated Press

He used the company's software to crunch a data set of last season's stats for 452 NBA players. He discovered new ways to group players (.pdf) based on performance after noting, for example, that Rajon Rondo of the Boston Celtics had more in common with Miami Heat forward Shane Battier than with fellow point guard Tony Parker of the San Antonio Spurs.

After reading his map, Alagappan came up with 13 new positions based on the three typical roles of guard, forward and center:

Offensive Ball-Handler. This guy handles the ball and specializes in points, free throws and shots attempted, but is below average in steals and blocks. Examples include Jason Terry and Tony Parker. Defensive Ball-Handler. This is a defense-minded player who handles the ball and specializes in assists and steals, but is only so-so when it comes to points, free throws and shots. See also: Mike Conley and Kyle Lowry. Combo Ball-Handler. These players are adept at both offense and defense but don't stand out in either category. Examples include Jameer Nelson and John Wall. Shooting Ball-Handler. Someone with a knack for scoring, characterized by above-average field goal attempts and points. Stephen Curry and Manu Ginobili are examples. Role-Playing Ball-Handler. These guys play fewer minutes and don't have as big a statistical impact on the game. Hello, Arron Afflalo and Rudy Fernandez. 3-Point Rebounder. Such a player is a ball-handler and big man above average in rebounds and three-pointers, both attempted and made, compared to ball-handlers. Luol Deng and Chase Budinger fit the bill. Scoring Rebounder. He grabs the ball frequently and demands attention when on offense. Dirk Nowitzki and LaMarcus Aldridge play this position. Paint Protector. A big man like Marcus Camby and Tyson Chandler known for blocking shots and getting rebounds, but also for racking up more fouls than points. Scoring Paint Protector. These players stand out on offense and defense, scoring, rebounding and blocking shots at a very high rate. Examples include Kevin Love and Blake Griffin. NBA 1st-Team. This is 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. Kevin Durant and LeBron James fall in this category. NBA 2nd-Team. Not quite as good, but still really, really good. Rudy Gay and Caron Butler are examples. Role Player. Slightly less skilled than the 2nd-team guys, and they don't play many minutes. Guys like Shane Battier and Ronnie Brewer fall under this position. One-of-a-Kind. These guys are so good they are off the charts — literally. The software could not connect them to any other player. Derrick Rose and Dwight Howard are examples, but you already knew that.

The 13 positions are based on how players compare to the league average in seven statistical categories: Points, rebounds, assists, steals, blocked shots, turnovers and fouls. The stats were normalized on a per-minute basis to adjust for playing time, so starters got the same consideration as backups.

That said, the names of some of these new positions could use a bit of work. For example, Rondo, the Celtics' floor leader, is classified as a "role player," which is commonly used in basketball to describe a so-so player with a specific, if unremarkable, set of skills.

Even if no one is going to refer to Dirk Nowitzki of the Dallas Mavericks as one the league's best "scoring rebounders" any time soon, Alagappan's prize-winning analysis could change how coaches and general managers think about the roles their players fill. Alagappan proved the title-winning Mavs had a solid diversity of "ball handlers" and "paint protectors," giving them the ability to put a balanced lineup on the floor with few weak spots. The Western Conference cellar dwellers the Minnesota Timberwolves, on the other hand, had too many players with similar styles and a dearth of "scoring rebounders" and "paint protectors," leaving them vulnerable along the front line.

Alagappan's findings won the award for best Evolution of Sport this spring at the annual MIT Sloan Sports Analytics Conference.

Whenever sports and numbers meet, the Moneyball question inevitably arises: Is it possible to use big data sets to find undervalued players? Alagappan believes it is.

He isolated the 40 players in the "scoring rebounder" section who best epitomized that group. At the top were the stars you might expect: Carmelo Anthony and Amare Stoudemire of the New York Knicks, along with Nowitzki and the Los Angeles Lakers' Paul Gasol. But lesser-known players like Marreese Speights of the Memphis Grizzlies and the Lakers' Devin Ebanks produced statistically similar per-minute results. Even better, where Anthony's salary averages around $18.5 million per year, the Lakers are paying Ebanks about $740,000.

Another inevitable question: Could Ayasdi's software have predicted the success of Knicks rookie Jeremy Lin? Alagappan concedes Lin's college stats wouldn't have suggested or predicted Linsanity, but he did create a similarity network to identify those players most similar to Lin in college. Three names emerged from the 3,400 analyzed: DeMarcus Cousins, who the Sacramento Kings picked fifth overall in the 2010 NBA draft; Alec Burks, picked 12th in 2011 by the Utah Jazz; and Nik Raivio, a University of Portland guard currently playing ball in Kaposvar, Hungary.

The lesson? For teams who buy into this new classification of players, the next Jeremy Lin might be in Hungary, awaiting your call.

Photo: Dallas Mavericks' Dirk Nowitzki (41) and Jason Terry (31) defend Miami Heat's Dwyane Wade during the second half of Game 2 of the 2011 NBA Finals. Photo: David J. Phillip/Associated Press