Understanding the NBA: Explaining Advanced Comprehensive Stats and Metrics

Adam Fromal@fromal09National NBA Featured ColumnistFebruary 4, 2012

Understanding the NBA: Explaining Advanced Comprehensive Stats and Metrics

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    This is the third part of my three-part series about understanding the complexities of NBA statistics. The next few slides deal with advanced overall statistics.

    While there's no such thing as a perfect statistic, there is such a thing as the perfect application of a statistic. 

    While some people believe too fully that there is nothing more to basketball than the "human aspect," others realize that numbers can explain a whole lot about the action on the court. Those that embrace the numbers generally tend to see their knowledge of the game increase, but only if they know how to use the stats.

    I do understand that some of the advanced stats and metrics can be a bit intimidating because they're unfamiliar and, in some cases, complicated. It doesn't help that we're force-fed traditional, sometimes useless stats by the media.

    Every time I see someone immediately dismiss an advanced statistic because it's "useless," it kills a little part of me. No stat is worthless if you know how to use it. 

    The following nine slides explain the most common of the advanced overall stats and metrics. Click here for my explanation of the offensive statistics or here for my explanation of the defensive ones.

    And as always, feel free to leave any comments or questions in the appropriate section.   

    You can find all of these stats and more at Basketball-Reference.com82Games.com and HoopData.com.

Total Rebounding Percentage (TRB%)

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    Where TRB=Total Rebounds, TMP=Team Minutes Played, MP=Minutes Played, TTRB=Team Total Rebounds, OTRB=Opponent Total Rebounds


    Essentially, total rebounding percentage is a weighted average of defensive rebounding percentage and offensive rebounding percentage because it takes into account all available opportunities to crash the boards. 

    I have previously explained DRB% as the following:

    Whenever a shot clanks off the rim, there are four possible outcomes: The ball could go out of bounds and be counted as a defensive team rebound; the ball could bounce off a defensive player and go out of bounds to be counted as an offensive team rebound; the ball could be pulled down by a defensive player and counted as a defensive rebound; or the ball could be pulled down by an offensive player and counted as an offensive rebound.

    If you add up all four of those results, you account for all of the potential rebounds in a game.

    Defensive rebound percentage calculates the percentage of available defensive rebounds that a player grabs while he's on the court.

    This is the last of the commonly-used defensive tempo-free rate stats and much like the previous two, it doesn't account for pace or volume.   

    Replace all instances of the word "defensive" in the final two paragraphs with "offensive" and you have the explanation for ORB%. 

    These are two very distinct skills, but put together they form TRB%.


    The stat fails to differentiate between offensive rebounding and defensive rebounding, which, as indicated above, are two very different skills. 


    Example Usage

    "Dwight Howard has the best TRB% in the NBA with a mark of 23.7 percent."

    How I interpret that sentence: Dwight Howard pulls down the highest percentage of rebounds when he's on the court, thanks to his dominance on the defensive glass. 

Plus/Minus (+/-)

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    Where TPOC=Team Points While On Court, OPOC=Opponent Points While On Court


    This one is as simple as the calculation makes it sound. 

    Generally used in reference to a single game (although it is possible to look at plus/minus throughout a season), this statistic tries to show how valuable a player was during a single game by looking at the score differential while the player was on the court. 

    That's really all there is to it. 


    This stat should always be taken with a grain of salt. It's a handy reference point, but it's not as though a player is always solely responsible for the points scored and points allowed by their team while they're on the court. 

    Take the following example.

    Let's put me in at point guard for the Miami Heat and let me play all 48 minutes during the game against the Washington Wizards. I'm literally just going to stand at the top of the key on defense and off behind half court on offense so I can stay out of the way.

    My final stat line will read: 48 minutes played, no points (on 0-for-0 shooting), no rebounds, no assists, no steals and no blocks. But the Heat are so much better than the Wizards that they're still going to win by 20 points even while playing four-on-five.

    That means my plus/minus for the game was plus-20 because I was on the court for the entire game.

    Meanwhile, LeBron James put up a triple-double while scoring 30 points. But he was on the floor during a few of the Wizards' offensive runs so his plus-minus for the game was only plus-15.

    Wooooooo I was better than LeBron!

    See why this is flawed? 

    Example Usage

    "During the Memphis Grizzlies' 96-77 win over the Atlanta Hawks, Marc Gasol had a plus/minus of plus-40."

    How I interpret that sentence: Marc Gasol played well and was on the court at the right times. 

Net Plus/Minus (NPM)

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    Where OnC+/-48=On-court plus/minus per 48 Minutes, OffC+/-48=Off-court plus/minus per 48 Minutes


    Developed by Roland Beech, the founder of 82games.com, this statistic is also known as, creatively enough, the Roland Rating.

    Taking the original plus/minus system one step further, Roland wanted to discover what a player's value to his team was in terms of his plus/minus.

    The stat finds a player's plus/minus and translates it to a per-48-minute basis and then also finds the team's plus/minus while the player is not on the court.

    So let's say that a player was on the court for 36 minutes during a 10-point win and had a plus-15. It logically follows that the team was minus-5 during the 12 minutes he was on the bench.

    Extrapolating these numbers to find per 48-minute values, we get an on-court value of plus-20 and an off-court value of minus-20. Subtracting the latter from the former, we find that the player had an NPM of plus-40 for the game.

    Generally, this statistic isn't applied to single games, though. Rather, it is used to look at cumulative data over the course of a season.  


    The statistic is intended to do only what I explained above. The following quote about the statistic's limitation is taken directly from Roland himself:

    These ratings represent a player's value to a particular team and are not intended to be an accurate gauge of the ability and talent of the player away from the specific team.

    Another limitation is that you will get very skewed numbers if there are limited sample sizes. For example, right now Joe Johnson's NPM is plus-10.5 and Donald Sloan, who plays just two percent of the Atlanta Hawks' minutes, is blowing Johnson out of the water with an NPM of plus-38.8. 

    Example Usage

    "Dwyane Wade actually has an NPM of minus-5.4 right now because he has a net on-court plus/minus of 4.1 and off-court plus/minus of 9.5." 

    How I interpret that sentence: This shows that the stat is flawed because Dwyane Wade is unequivocally valuable to his team, although the Miami Heat have performed quite well in his absence.

Efficiency (EFF)

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    Where P=Points, R=Rebounds, A=Assists, S=Steals, B=Blocks, FGM=Field Goals Missed, FTM= Free Throws Missed, T=Turnovers


    This statistic can be applied to either single games or seasonal per-game averages, although it's more telling with the larger sample size of the season than the smaller one of the single game.

    All that efficiency does is add up all positive box score contributions a player can make and subtracts the negative ones—free throws and field goals missed, as well as turnovers.

    About the only positives here are that you can very easily calculate it and it does generally put the best players in the league near the top of the leaderboard.  


    You would be hard-pressed to find a single statistical mind in the basketball community that places a lot of value on this statistic. 

    Although it's convenient, the stats aren't weighted at all and it overlooks quite a bit of the game by only looking at box score data. 

    Simplicity is the name of the game here. 

    Example Usage

    "The top 10 players in the NBA in terms of Eff right now are LeBron James, Kevin Love, Kevin Durant, Dwight Howard, Kobe Bryant, Chris Paul, LaMarcus Aldridge, Blake Griffin, Marc Gasol and Derrick Rose."

    How I interpret that sentence: Okay. So what?

Game Score (GmSc)

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    Where P=Points, FGM=Field Goals Made, FGA=Field-Goal Attempts, FTA=Free-Throw Attempts, FTM=Free Throws Made, ORB=Offensive Rebounds, DRB=Defensive Rebounds, S=Steals, A=Assists, B=Blocks, F=Fouls, T=Turnovers


    This stat is the brainchild of ESPN's John Hollinger, intended to calculate just how well a player performed during a single game while looking only at box score measures. 

    As you can tell from the calculation section, all stats are weighted differently and according to the frequency with which they occur. Positive contributions receive positive coefficients and negative ones receive corresponding negative coefficients. 

    Just because of the fact that the box score stats are weighted, game score is light years ahead of efficiency in terms of usefulness. 

    It is also set up so that the scale is relatively similar to how we would interpret points per game. 40 is absolutely incredible, 20 is good and so on. 


    While it can work this way, this statistic isn't meant to do anything other than look at individual games, so don't try to apply it to season stats or anything like that. 

    Also, it's interesting to note that you need to shoot 57 percent from the field to break even in the shooting categories.

    The stat focuses on efficiency, but you can be helped by playing more minutes. 

    Example Usage

    "Michael Jordan has 14 of the 27 highest game scores in NBA history, including the best ever (since 1978 when all stats were recorded) with a 64.6 GmSc on March 28, 1990."

    How I interpret that sentence: Michael Jordan was really good. 

Player Efficiency Rating (PER)

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    Step One: Calculate uPER

    uPER=(1/M)*(TP+(2/3)*A+(2-factor*(TA/TFG)*FG)+FT*0.5*(1+1-(TA/TFG)+(2/3)*(TA/TFG))-VOP*T-VOP*DRB%*(FGA-FG)-VOP*0.44*(0.44+(0.56*DRB%))*(FTA-FT)+VOP*(1-DRB%)*(TRB -ORB)+VOP*DRB%*ORB+VOP*S+VOP*DRB%*B-PF*((LFT/LPF)-0.44*(LFTA/LPF)*VOP))

    Where M=Minutes, TP=Three-Pointers, A=Assists, TA=Team Assists, TFG=Team Field Goals, FG=Field Goals, FT=Free Throws, T=Turnovers, DRB%=Defensive Rebound Percentage, FGA=Field-Goal Attempts, FTA=Free-Throw Attempts, TRB=Total Rebounds, ORB=Offensive Rebounds, S=Steals, B=Blocks, PF=Personal Fouls, LFT=League Free Throw, LPF=League Personal Fouls, LFTA=League Free-Throw Attempts

    Step Two: Calculate factor and VOP


    Where LA=League Assists, LFG=League Field Goals, LFT=League Free Throws


    Where LP=League Points, LFGA=League Field-Goal Attempts, LORB=League Offensive Rebounds, LT=League Turnovers, LFTA=League Free-Throw Attempts

    Step Three: Adjust for pace and league to calculate PER


    Where LPace=League Pace, TPace=Team Pace, LuPER=League uPER 


    As loyal readers of my articles may have noted, I'm a fan of using PER as a baseline measurement of a player's performance because it's a metric that is both easily accessible and whose output is easy to understand. 

    In John Hollinger's words, "The PER sums up all a player's positive accomplishments, subtracts the negative accomplishments, and returns a per-minute rating of a player's performance."

    To be perfectly honest, there is no way that I can possibly sum up the calculation of Hollinger's most famous statistic. If you really want to understand where he got each number from, I would highly recommend reading his books. 

    The basic idea though is that PER spits out one number to represent a player's performance. It accounts for per-minute performance and how a team's pace of play compares to the league average. 

    Hollinger set up the system so that a PER of 15 is the league average number.

    As you'll soon see in the limitations section, although this is the single best measure to use when describing a player's overall performance because of it's scaled appearance, it does lack in some areas. 


    As much as PER takes into account, it still has its flaws, as does any stat. 

    Hollinger himself won't deny that the system he has set up doesn't take into account anything on the defensive side of the ball other than blocks and steals. Although both are important measures of defensive play, they are by no means an all-encompassing way of valuing a player's defensive contributions. 

    A second major flaw is the rewarding of inefficient shooting. Dave Berri, in The Wages of Wins, writes the following: 

    Hollinger argues that each two-point field goal made is worth about 1.65 points. A three-point field goal made is worth 2.65 points. A missed field goal, though, costs a team 0.72 points. Given these values, with a bit of math we can show that a player will break even on his two-point field-goal attempts if he hits on 30.4% of these shots. On three-pointers the break-even point is 21.4%. If a player exceeds these thresholds, and virtually every NBA player does so with respect to two-point shots, the more he shoots the higher his value in PERs. So a player can be an inefficient scorer and simply inflate his value by taking a large number of shots.

    A third and final major flaw is that you can routinely find players who have astronomical PERs due to the fact that they have played extremely limited minutes. Hasheem Thabeet's PER is 19.1 right now, for example. While that's not an astronomical figure, it is for Thabeet.

    You'll find one more way that PER can be improved on the next slide.  

    Example Usage

    "LeBron James has a PER of 33.33 this season, a mark that would beat Wilt Chamberlain's all-time record of 31.84 if it was maintained throughout the rest of the 2011-2012 campaign."

    How I interpret this sentence: LeBron James is really good. 

Adjusted Player Efficiency Rating (APER)

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    The calculation for APER is basically the same as the PER formula, but with two major differences:

    1. Field goals are broken down further to include both unassisted and assisted field goals. 

    2. Charges taken are incorporated. 

    Unfortunately, I do not have access to the formula that includes these two elements. 


    APER does essentially the same thing as PER but it includes the two elements listed above, thereby giving it a more comprehensive feel. 

    That's really the only difference. 


    The same flaws apply to APER that applied to PER. 

    Example Usage

    "Derrick Rose is seventh in the league in PER and fourth in the NBA in APER."

    How I interpret that sentence: Derrick Rose is tremendous when it comes to creating his own shot, which provides him that boost. 

Win Shares (WS)

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    Where PP=Points Produced, LPPP=League Points Per Possession, FGA=Field-Goal Attempts, FTA=Free-Throw Attempts, TO=Turnovers, LPPG=League Points Per Game, TP=Team Pace, LP=League Pace, MP=Minutes Played, TMP=Team Minutes Played, TDP=Team Defensive Possessions, LPPP=League Points Per Possession, DRtg=Defensive Rating, LPPG=League Points Per Game


    Win shares are simply the summation of offensive win shares and defensive win shares. 

    I have previously described OWS:

    As explained by Basketball-Reference, this is really a five-part calculation, the details of which can be found in the page hyperlinked to. 

    Win Shares are easily the best metric for evaluating the offensive play of a single player because it accounts for almost everything and scales the result so that one OWS is actually equal to one win added to the team's cause. 

    Points Produced takes all facets of the offensive game into account: points scored, assists and offensive rebounds. Moreover, the metric is tempo-free.

    Similarly, I have described DWS as:

    If this calculation seems intimidating right now, imagine how intimidating it would be if Dean Oliver's couple formula for Defensive Rating was included in it. 

    The formula's numerator is essentially a calculation of a player's marginal defensive value, or the quantifiable amount that the team's defensive ability increases while the player is on the court.

    As for the denominator, it's simply the marginal points per win. In a less jargon-y sentence, the denominator uses a team's pace of play to adjust the player's contributions to a more standard rate. 

    Defensive Win Shares takes all facets of the defensive game into account and is tempo-free. 

    The metric is scaled so that one DWS is equal in value to one win added to the player's team's record. 



    The only true flaw for WS is that while it accounts for pace of play, it's still a counting stat.

    Although different from counting stats like total blocks, there is still a clear benefit to players who are on the court for a lot of minutes. 

    Moreover, we have to rely on databases to calculate the stat for us as DRtg helps to make up the formula. 

    Example Usage

    "Kyrie Irving has produced 2.0 WS so far this season, far more than anyone else in his draft class."

    How I interpret this sentence: Kyrie Irving has been a great player on both ends of the ball and the gap between his WS and MarShon Brooks's 1.1 indicates that he's clearly been the best player taken in the last draft. 

Win Shares Per 48 Minutes (WS/48)

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    Where WS=Win Shares, MP=Minutes Played


    I wrote on the Win Shares slide that one of the limitations was that it was a counting stat, giving the advantage to players who spend a considerable amount of time on the court.

    Making this a per 48-minute stat completely takes that out of the equation, pun intended.  


    The biggest flaw with WS/48 is that the output is extraordinarily small. Michael Jordan, as is probably expected, is the career leader at 0.2505. 

    But because the numbers are all decimals and you commonly have to go to the second or third digit after the decimal, it's tough to easily differentiate between players. 

    Example Usage

    "When you look at WS/48 instead of WS, Chris Paul jumps up from 17th to second in the NBA."

    How I interpret that sentence: Chris Paul is both very good and very efficient on a per-minute basis. 

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