Sunday, December 26, 2010

Core Statistic: Successful Possession Rate (SPR), the Basketball Version of OBP

I happened upon a new basketball statistic, the Successful Possession Rate, because I was trying to come up with the basketball equivalent of baseball's On-Base Percentage (OBP).  In baseball, the OBP is the sum of hits and walks, divided by plate appearances. In general, it is a measure of an offensive player's ability to not surrender an offensive opportunity and allow the other team to get a crack at his own defense:  If you never get out, the other team can never win.

But basketball works a little differently, since possession constantly changes hands, even after you succeed (i.e., score a basket) -- and because of the shot clock, you cannot simply hold on to the ball.  Whereas in baseball, all you need to do to achieve a successful offensive opportunity is not get out ("a walk is as good as a hit"), in basketball you have to score.  And so the basketball equivalent of an OBP would be defined as any offensive possession in which a player contributes a field goal, a free throw, or an assist. 

Admittedly, this is an incomplete measure: a player can make a pass that leads to the pass that is credited as an assist, for example, and not get any credit for the success of that particular possession.  Likewise, a player can gather an offensive rebound and then kick the ball back out to the point guard, who starts a new possession that leads to a bucket, and also get left out in the cold, at least statistically.  But as a general metric, field goals, free throws and assists are the most easily measured statistics in evaluating the success of a possession.

With this in mind, the numerator of the SPR is the sum of two-point field goals made (2PFGM), three-point field goals made (3PFGM), free throws made (FTM), and assists (AST).  Since the standard of a successful possession is a two-point bucket, however, these values need to be weighted: 3PFGM are multiplied by 1.5, since they are worth 50% more than a standard basket, and FTM get divided by two, since they are worth only half; 2PFGM and AST, both of which lead to two points, are left alone.  And the so the numerator of SPR is:

[2PFGM + 1.5(3PFGM) + (FTM/2) + AST].

The denominator, of course, would be the sum of all offensive actions intended to produce a successful possession: field goal attempts (FGA), free throw attempts (FTA), assists (AST), and turnovers (TOV).  The denominator of SPR, too, is an imperfect measure: bad passes that lead to somebody else's TOV are not debited against the player, for example, and FTAs that are part of an "and-one" or technical foul situation still count as half of an opportunity, even though it is really an "extra-credit" bonus -- but it appears to be a close approximation of offensive opportunity, good and bad.  The denominator of SPR also needs to have weighted values -- not for field goal attempts, since a missed three-pointer still only costs you two points worth of opportunity, but for FTA, which is worth only half as much as a FGA.  And so the denominator of SPR is:

[FGA + (FTA/2) + AST + TOV].

Taken together, the entire formula of SPR is:

SPR = [2PFGM + 1.5(FGM) + (FTM/2) + AST]/[FGA + (FTA/2) + AST + TOV]

Having developed this formula, I wanted to try it out on a group of players of varied career accomplishments, to see if there was any validity to the stat.  The first player I tried it out on was Magic Johnson, who has a career SPR of .666 -- or, in other words, his contribution to any possession he participated in led to success two-thirds of the time!  It was no wonder that a player like this, with such a high SPR, would play on five world champions, an NCAA national champion, and win an Olympic gold medal.  I next tried the formula out on two more members of basketball's pantheon: Michael Jordan has a career SPR of .581, and Larry Bird comes in with a career SPR of .591.  It seemed to me that greatness hovers at around a 60% success rate -- a fact that rang true when I calculated the SPR of Steve Nash, to the tune of .644.

The next validity check on the SPR involved trying it out on marginal professional players.  Adam Morrison, for instance, came in with a paltry SPR of .450.  Current D-League player Rashad McCants has registered a career SPR of .484 during his NBA days.  End-of-bench legends Chuck Nevitt and Ken (The Animal) Bannister barely eclipse .400.

And so the SPR appears to be a valid measure of a basketball player's "on-base percentage," with limitations that I have already acknowledged.  But in running through the SPR of a number of different players of various levels of achievement, it became apparent to me that, as a comparative statistic, it is not fair to compare the SPR of players at different positions.  Many Hall of Fame centers have an SPR very close to .550, for instance, whereas some good point guards who will nevertheless never qualify for an All-Star team have an SPR in the range of .580.  Hall of Fame point guards, such as Magic and Nash, have an SPR that exceeds .600, but swingmen such as Jordan and Bird -- players who were every bit as good, and perhaps even better -- have an SPR in the .580 to .590 range.  There appears to be a different standard for defining an excellent SPR, depending upon what your role is on the court.

The issue, of course, is how the stat is calculated:  SPR gives an awful lot of credit to assists.  Assists are in both the numerator and the denominator, and though they are offset by turnovers (players who make a lot of assists tend to make a lot of turnovers, too), good point guards routinely have assist-to-turnover ratios that exceed 2:1.  If you measured assists alone, the very good point guards would have SPRs in the range of .667 or higher.  Meanwhile, the best of shooters can only be expected to hit their shots at a 55% clip (if they are low-post), and in the 48-50% range if they are perimeter players -- and because they are good scorers, they get less assists, and are comparatively "punished" in this way.  The other thing to note is that, as beautiful as an assist may be, the harder thing to do is still score a basket, and the SPR does not draw a distinction between making the pass and finishing the play.

This is an issue that I will address in a future post: the evaluation of SPR by position.  Players in the NBA can be divided into quintiles (five different "positions," or position tendencies), based on their likelihood of passing the ball.  This can be estimated with a very simple statistic, one that I will get to in the near future, and it will become apparent that the difference in SPR between a great like Jordan and another like Magic is that one was more often the finisher (Jordan) while the other received a tremendous amount of statistical credit for being the distributor (Magic).  Without stealing the thunder of a future post, let me just say that Magic was 3.49 times as likely as Jordan to pass up a shot for an assist -- which undoubtedly helps your statistical SPR.  This is not to say that Jordan was a selfish player -- he, in fact, was not at all -- it is just an acknowledgement that he took on a larger scoring burden than the typical point guard, and his slightly lower SPR is reflective of that fact.  Steve Nash, for instance, was 5.63 as likely to pass the ball as Shaq, and his higher career SPR reflects this (O'Neal comes in at .551) -- but I think that this is more a reflection of their different roles on the court (as well as Shaq's inability to hit a free throw).  Again, the different SPR standards by position will be discussed in future posts.

And so I conclude this inaugural post with the proposition of a new statistic, the SPR -- basketball's version of the on-base percentage.