statistics

How Efficient are You? The NBA's "Best Basketball Player" Calculation

How efficient are you? Let's take your job. Add up all the number of tasks you did well today at work. Subtract the amount of mistakes you made. Divide that number by the amount of days you have worked. Such a hypothetical number might give you an estimate of how efficient you were at your job. If you had an army of statisticians observing your every move, you might be able calculate this number. And if you could accurately calculate that number for every employee in your organization, it would be very hard to argue with the boss's selection of "Employee of the Month."

Lebron jamesLeBron James currently has the highest PER in the NBA, and at this rate, he might have the highest PER in a season ever, besting even Michael Jordan's highest.

There actually are a few jobs out there that have armies of statisticians monitoring the performance of every employee, and NBA basketball is one of them. And much like your current job, basketball is a group activity in which an individual player can affect the performance of others in the group. Moneyball author Michael Lewis recently wrote, "there is a tension, peculiar to basketball, between the interests of the team and the interests of the individual." Unlike baseball, where games usually play out as a network of individual player situations, or football, where plays are painstakingly scripted, the players on a basketball team have the freedom to make individual decisions about what they do at every moment. For example, a player who makes a tough shot, instead of making a pass for an easy score, increases his own scoring average at the expense of the stats of another player.

However, players don't all make the same amount of money. Some players are clearly more talented than others. But in a sport where one player's stats can be so dependent on other members of the team, how does one attempt to quantify a player's value? One way is to try to calculate efficiency: How well does a player do things, without making mistakes, while in the game?

John Hollinger of ESPN attempts to answer the question of "Which player is the most efficient?" with his Personal Efficiency Rating, or PER. BasketballReference.com describes Hollinger's PER as a number that "sums up all a player's positive accomplishments, subtracts the negative accomplishments, and returns a per-minute rating of a player's performance." The complete method of calculating a PER (along with many necessary normalizations) is here, but the quicker, dirtier, and similar NBA Efficiency Rating can be calculated using this formula:

NBA Eff. =[(Pts + Reb + Ast + Blk + Stl) - (Missed FG + Missed FT + TO)] / Games Played

So, who has the highest PER rating of all time? Well, it's hard to compare players of past generations to current ones, because rules and scoring opportunities haved changed over the years. For example, there was no three-point line in the NBA before 1979. However, many people have attempted to find ways to normalize efficiency data across each of season of not only the NBA, but the ABA as well. BasketballReference.com, for example, claims that the players with the highest career PER ratings, in descending order are: Michael Jordan, Shaquille O'Neal, David Robinson, Wilt Chamberlain, and LeBron James. Does that sound like a list of five of the best players of all time? I would say that it's not too far off. Where's "the Logo," Jerry West? #20. How about Magic Johnson? #11. Dr. J? #24.

Is it possible that a player is valuable even if they don't put up big offensive numbers? What if the player contributes to a game without contributing many of the stats featured in PER rating? I recently blogged about a great article by Michael Lewis which describes the game of Shane Battier, the "no-stats All-Star." Lewis claims that Battier's contribution to the game - for example, striving to defer to a teammate in a more efficient scoring position - is not easily measured by formulas like the PER. Instead, Battier contributes a great deal to a different stat known as the "plus-minus," which basically measures how many more points the team scores when Battier is in the game. Apparently, Battier's "plus-minus" is similar to the ratings of other All-Star players such as Carmelo Anthony.

All this being said, I think there is an even more interesting individual performance stat, and the only possible values are "Yes" or "No": Can a basketball player in the NBA score 16 points in 2 minutes? If that player is LeBron James, the answer is Yes. And the video is here.

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