Advanced NBA Stats for Dummies: How to Understand the New Hoops Math

Ehran Khan@@ekhansworldContributor IIIOctober 18, 2013

Advanced NBA Stats for Dummies: How to Understand the New Hoops Math

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    In a heated debate over who is the best shooting guard in the league? Advanced stats will win you that argument.
    In a heated debate over who is the best shooting guard in the league? Advanced stats will win you that argument.USA TODAY Sports

    The NBA's analytics revolution (insert Revenge of the Nerds joke here) has changed the way we think and talk about basketball.

    These days, you can't have an intelligent conversation about hoops without relevant statistics to back up your thoughts and lend credence to your opinions.

    Read any respectable basketball columnist (as well as those striving to reach that level, like yours truly), and you'll come across a plethora of advanced metrics which support their claims and provide astonishing insight into the game.

    Don't be blinded by the raw numbers though; it's how you interpret the numbers that really matters, as these are what truly enhance your basketball sophistication.

    Use this primer as a guide for which metrics to study when taking an in-depth look at players and teams. Looking at these statistics will paint a more complete portrait of a player's or team's profile while also revealing hidden traits which can support your opinion—or change it entirely.

    And don't sweat the calculations. I'll give you tips for where to find all the relevant numbers (Tip No. 1: just have open in your browser at all times).

    Follow along, and you'll discover effective ways to augment your NBA analysis.

Player Efficiency Rating (PER)

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    Nathaniel S. Butler/Getty Images


    Popularized by former ESPN analytics guru John Hollinger, PER has become perhaps the most commonly used advanced metric.

    A common misconception, though, is that it's a catch-all stat that determines a player's ranking in the NBA hierarchy—much like WAR in baseball—but even Hollinger concedes that this is simply not the case.

    What it's supposed to do is measure a player's per-minute productivity. It adds up all the positive contributions a player makes to his team, while subtracting the negative ones in a statistical point value system. It also adjusts for both pace and playing time to make it easier to compare players to one another (click here for the specific calculation).

    What holds it back is that there aren't many reliable defensive stats to input into the formula. We would all agree that steals and blocks don't necessarily correlate to good defense. So defensive specialists are at a disadvantage in this metric, and great two-way players may rank lower than offense-only guys (i.e. Paul George had a lower PER than Jamal Crawford and J.R. Smith in 2013).

    Top players can generally be found at the top of the list, so it's a nice snapshot of where players stand in relation to one another. Just remember, it's not the be-all, end-all stat.


    According to ESPN's PER ranks from 2013, the top-five players in this metric were (in order) LeBron James, Kevin Durant, Chris Paul, Carmelo Anthony and...Brook Lopez.

    Does that mean Lopez is the fifth-best player in the NBA? Of course not.

    But it does tell you that perhaps Lopez is better than you think, especially on offense (which is heavily weighted in PER's calculation). 

    You might have dismissed Lopez from the conversation of the best center in the NBA, but the fact that he outshines all other 5's in PER means that you should do a little more digging before arriving at that conclusion.

    Where to Find It

    The exact PER number can vary slightly depending on where you look. The discrepancies are usually negligible so the cause may just be rounding error. The order of the players should remain the same though.

    If you're an ESPN Insider, you can see their PER ranks here.

    Basketball-Reference has a PER for every player on each respective player's personal page (just search for the player). You can find league leaders in PER for every season as well.

    HoopData has PER (as well as "alternate PER," but don't worry about that) on their advanced stats page, as well as on each player's personal page (just search for the player).

Win Shares

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    Noah Graham/Getty Images


    Win shares estimate an individual player's contribution to their team's win total.

    Through a complex formula it credits offensive win shares by calculating a player's marginal points from his points produced and offensive possessions and dividing it by the marginal points per win.

    Defensive win shares are credited by computing a player's marginal defense from his defensive rating and dividing it by the marginal points per win.

    Simply add offensive and defensive win shares together to get total win shares. You can find the entire mathematical process laid out in painstaking detail here.

    Essentially, win shares measure a player's value based on wins. Splitting them into offensive and defensive win shares is important because it values both halves of the game equally.

    I like looking at win shares more than PER because the number is translated into a value for you. With PER, you get a player's per-minute productivity, but the value placed on that is at your discretion.

    Another thing I like about win shares is that it values playing time. Andray Blatche had a higher PER than Stephen Curry last season, but Curry had more than twice as many win shares as Blatche did.

    There's a reason Curry played twice as many minutes as Blatche, and win shares reflect that.

    The downside of that is players who miss time due to injury get downgraded. But win shares are also broken down into a per-48 minute number in order to account for those who play less minutes overall but still make a big contribution when on the court.


    This is a very easy metric to interpret. No stat is perfect, though, so again, it isn't the catch-all stat to rank players by.

    However, it is a powerful tool to judge the impact players have on their team's offense, defense and overall success.

    Marc Gasol ranked sixth among all players in win shares in 2013 with 11.5. Mike Conley was 11th with 9.9. That doesn't mean they're the sixth and 11th best players in the league, respectively, but it does tell you that even though they don't put up eye-popping numbers, they do things to win basketball games.

    It also shows you why the Memphis Grizzlies trading away Rudy Gay (their perceived best player, who mustered just 4.0 total win shares last year) wasn't a straight salary dump; it made actual basketball sense as well.

    It also hints that a Zach Randolph (7.9 win shares) trade would not be a death blow to the Grizzlies, especially if they get a decent return.

    Where to Find It

    Basketball-Reference is the place to look up win shares. Win shares are located on each player's personal page (just search for the player). League leaders for every season can be found as well.

Offensive/Defensive Efficiency

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    Nathaniel S. Butler/Getty Images


    Basketball is all about efficiency. Maximizing points scored and minimizing points allowed on each possession is more important than overall totals.

    Totals are influenced by variables like pace—or the number of possessions a team gets in a game—which can differ depending on coaching philosophies (i.e. the Houston Rockets averaged nearly eight more possessions per game than the Memphis Grizzlies last season).

    Offensive and defensive efficiency are adjusted for pace, calculating points scored and allowed on a per-possession basis. To make the numbers easy to digest, they are reported per 100 possessions so they look similar to points-per-game figures.

    Calculating an individual's offensive and defensive rating (described here) is a bit more complicated, as it's harder to suss out an individual player's possessions, especially on defense.


    Last year, the New York Knicks averaged exactly 100.0 points per game, good for 11th in the NBA and just above the league average.

    Most people would say that the Knicks had the 11th best offense in the league. You hear such interpretations on NBA broadcasts all the time. However, New York was third in the league in offensive efficiency, meaning they actually had the third best offense on a per-possession basis.

    Their offensive prowess was masked because they played at the fifth-slowest pace in the league.

    Where to Find It

    Offensive and defensive efficiency numbers can vary by site due to different definitions of what exactly constitutes a possession. The overall rankings are usually about the same, though.

    ESPN and HoopData's numbers match up, though you need to be an Insider to get access to ESPN's advanced team statistics. HoopData's numbers are publicly available. You can find team efficiency data on their team stats page.

    Basketball-Reference has their own efficiency numbers listed on their team pages (just search for the team) and also calculates individual offensive and defensive ratings for every player on each player's personal page (just search for the player).'s stats tool also provides the metric with plenty of options for filtering the data.

Points Per Possession (PPP)

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    Noah Graham/Getty Images


    This might sound similar to offensive and defensive efficiency, but I wanted to highlight one particular iteration of PPP stats.

    Data from statistical service Synergy Sports Technology has become more prevalent in NBA analysis.

    What it does is break down points per possession for teams and individuals based on the specific play type.

    For example, you can see how many points per possession the Los Angeles Lakers give up to pick-and-roll ball-handlers, or how many points per possession Tim Duncan scores on post-ups.


    These numbers are extremely specific, but they are a powerful tool when drilling down to a player's or team's scoring tendencies.

    It makes it easier to support your claim for, say, who the best post player in the league is, or debates of that nature.

    When you think of post players, you think of big men. But did you know that Kobe Bryant was fifth in the entire league in points per possession on post-ups last season? He shot better than 55 percent on those plays and also drew a shooting foul nearly 13 percent of the time.

    Where to Find It

    Unfortunately, Synergy is a professional service that caters to actual teams. Their full database is not available to the public.

    However, there is a sample available for free at You can look up individual players or teams and get a small selection of PPP breakdowns there.

True Shooting Percentage (TS%)

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    Layne Murdoch/Getty Images


    When evaluating shooting efficiency, it's not enough to just look at traditional field goal percentage. 

    Field goal percentage treats two-pointers and three-pointers equally, even though threes get you a crucial extra point. It also doesn't take free throws into account.

    We know that two of the most efficient ways to score in basketball are via three-pointers and free throws. True shooting percentage takes them both into account, weighting free-throw attempts and using total points scored instead of total field goals made in the formula (found here).

    True shooting percentage can be applied to teams as well. But when looking at teams, it is customary to separate free throws from field goals. Instead, one should look at effective field goal percentage, which measures a team's shooting efficiency strictly from the field.


    I find it much more worthwhile to look at TS% for perimeter players, because big men typically don't shoot a lot of threes, eliminating the need to take that particular shot into account.

    Last season, Andre Iguodala shot 45.1 percent from the field, while James Harden shot 43.8 percent. Without thinking, you might say that Iggy is the more efficient offensive player.

    But Iguodala shot just 31.7 percent from three (on 3.6 attempts per game) and an abysmal 57.4 percent from the line (on 3.4 attempts). Harden, meanwhile, shot 36.8 percent from deep (on 6.2 attempts) and 85.1 percent at the line (on an otherworldly 10.2 attempts).

    Consequently, it was Harden with the much better true shooting percentage (59.8 percent) than Iggy (52.0 percent). Due to the nature of Harden's point distribution, he is a much more efficient scorer than Iguodala.

    Remember to factor in player roles in your evaluation as well. True shooting percentage favors catch-and-shoot three-point specialists who knock down a high percentage of their (mostly wide open) treys without doing much else on offense.

    The fact that guys like Harden, Kevin Durant and LeBron James have true shooting percentages that rank up there with the Kyle Korvers and Steve Novaks of the league is a testament to how efficient they are given their higher volume and degree of difficulty on offense.

    Where to Find It

    True shooting percentage is widely available. You can find it on ESPN's Hollinger stats page (Insider only).

    Basketball-Reference provides TS% for each player on their personal page (just search for the player) as well as league leaders in the category by year.

    HoopData's advanced stats page also lists true shooting percentage, with the added bonus of filters available to sort the list by team or position, as well as to introduce games played and minutes played thresholds. They also have them for each player on their player pages (just search for the player).'s new and improved stats tool also includes true shooting percentage with more customizable filtering options.

Free-Throw Rate

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    This one is so elementary, I'll give you the calculation for it.

    Free-throw rate is simply free-throw attempts divided by field goal attempts.

    It's one of the "Four Factors of Basketball Success," according to basketball analytics legend Dean Oliver.

    Free-throw rate an indicator of offensive efficiency. Free throws are one of the most efficient ways to score, along with three-pointers and shots at the rim. The more free throws you attempt per field goal try, the more effective your offense will be.

    This metric can be calculated for both players and teams (where it can be calculated for both offense and defense) and is a useful measure for analysis in either case.


    From a player perspective, John Wall shot just 44 percent from the field and took less than one three-pointer per game in 2013, but he would have finished as the 15th-best scorer in the league if he met the leaderboard qualifications.

    Why is that? Because he posted the third best free-throw rate among point guards (and the seventh best among all perimeter players, ahead of guys like LeBron James and Kobe Bryant).

    Even though Wall's effective field goal percentage is one of the lowest at his position, he remains a semi-efficient offensive player because he gets to the line so often.

    From a team perspective, the Atlanta Hawks posted the league's sixth highest effective field-goal percentage (another of the "Four Factors"), yet finished just 18th in offensive efficiency, per Basketball-Reference.

    You might be hard pressed to put your finger on the cause of the discrepancy unless you also look at their free-throw rate, which ranked 25th in the NBA.

    Atlanta is very effective at producing good shots and converting them, but unless they get to the line more frequently, they will remain a below-average offensive squad.

    Where to Find It

    Basketball-Reference provides team free-throw rates on their team pages in the miscellaneous section of team stats and recently began listing individual free-throw rates on their player pages (just search for the player).

    HoopData has individual free-throw rates on their scoring page, as well as for each player on their player pages (just search for the player). They also have team free-throw rates on their team stats page.

Usage Percentage (USG%)

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    Usage percentage estimates the percentage of a team's possessions used by a player when he was on the courtwith a possession normally being defined as a field goal attempt, shooting foul drawn, or turnover.

    The exact formula can be found in Basketball-Reference's glossary (just scroll down to find it).

    Ball-dominating perimeter players tend to lead the league in this category (Brook Lopez was the only big man in the top-10 last year, and he finished 10th), and the top of the leaderboard is typically littered with the best players in the game.


    In general, efficiency decreases as usage increases. One of the defining characteristics of a superstar is that he can use a large number of possessions with a minimal drop-off in efficiency.

    A team can optimize their offensive output by constructing lineups that balance out usage percentage. It's an interesting stat to look at when projecting new lineups after a team's roster changes.

    For instance, I'm very interested to see how the Brooklyn Nets' new core group will function as a unit. If you add up the usage percentages from last season for their projected starters, it adds up to 126.6 percent. 

    There will be significantly fewer touches to go around, and it will be fascinating to see how new coach Jason Kidd manages that with all the egos and star power on the roster.

    Where to Find It

    With the definition of a possession being somewhat variable, usage percentage numbers can be slightly different on different sites.

    Basketball-Reference has USG% numbers for every player on their player pages (just search for the player).

    HoopData also lists the stat on their advanced stats page and's stats tool displays it as well.

    ESPN offers usage rate, which differs from usage percentage, in that it tabulates the total number of possessions a player uses per 40 minutes. As usual, it's available to Insiders only.

Rebound Rate

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    Scott Cunningham/Getty Images


    Instead of total rebounding numbers, rebound rate calculates the percentage of available rebounds that a team, or player, grabs.

    This adjusts for variables like pace (teams who have more possessions will have more shots, which produce more rebounding opportunities that drive up raw totals) and, for individual players, it adjusts for minutes played.

    Rebound rate can be further compartmentalized into offensive and defensive rebound rates.


    For team rebounding, rebound rate shows you the percent difference between the rebounds one team gets compared to their opponents. It's in line with standard rebounding margins, but it provides a little more context with the conversion to percentages.

    For players, it's a more enlightening stat.

    Guys who don't play very much (which keeps their rebounding totals down) can be overlooked when it comes to evaluating their ability to clean the glass.

    For instance, Milwaukee Bucks rookie forward John Henson averaged an underwhelming 4.7 rebounds per game last year, but that was mostly due to him playing just 13 minutes a night.

    In fact, Henson finished tied for ninth in the league in rebound rate, grabbing nearly a fifth of all available misses—more than Dwight Howard and Tyson Chandler.

    Where to Find It

    Rebound rate is a common stat found on any advanced stats site.

    Basketball-Reference, HoopData, and ESPN (Insider only) all carry offensive, defensive and total rebound rates on their sites for both players and teams.

    The links provided earlier in the piece will get you to the correct pages.

Assist/Turnover/Steal/Block Rate

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    Danny Bollinger/Getty Images


    All of these metrics convey information in a similar manner, so I'm lumping them all together.

    Again, these are rate statistics which adjust for pace and playing time, and they can be computed for individuals and teams alike. 

    Different sources crunch the numbers in slightly different ways, but the essence of each stat is evident.

    Assist rate estimates the percentage of teammate field goals a player assisted on while on the floor. Steal rate estimates the percentage of opponent possessions that end with a steal by a player. Block rate estimates the percentage of opponent field goals that a player blocks. Turnover rate estimates the percentage of a player's possessions that end in a turnover.

    Calculations for all of these stats can be found in Basketball-Reference's glossary.

    It's easy to take those definitions and extrapolate them to the team setting.


    I particularly like to look at assist rate for teams. Understanding the proportion of baskets which are assisted shows which teams are good at moving the ball and creating open looks.

    Much like with rebound rate, you can see which players excel in these categories, even if their playing time keeps their raw numbers low.

    Turnover rates for star players can illuminate a talent that's not always obvious. Players who use a lot of possessions always lead the league in turnovers. That makes it seem like they're hurting their team, but in reality, they may be providing an extra benefit because a low percentage of their possessions end in turnovers.

    Take Dirk Nowitzki, who is the only player in the last 20 years besides Michael Jordan to post a turnover rate under eight percent while using more than 30 percent of his team's possessions.

    Where to Find It

    These metrics are common, and you can find them through Basketball-Reference, HoopData,, or ESPN (Insider only). The links provided earlier in the piece will guide you to the right pages.

Shot Locations/Shot Charts

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    Issac Baldizon/Getty Images


    There are now powerful tools available that break down shooting stats into compartmentalized shot locations.

    You can easily see how players and teams shot from different areas of the court, as shot location data is segmented by range or zone. 

    Ranges start at the rim and move out five to eight feet at a time until you get to three-point range.

    Zones begin in the restricted area, move to the rest of the paint, then go to mid-range and eventually threes.

    In addition, shot charts for single games or entire seasons are available, as are heat maps which show the frequency at which a player gets his points from specific areas of the floor.


    Attaining this data furnishes you with greater context for shooting percentages. 

    You can see that Chris Bosh's deadly mid-range shot—he led the NBA in field goal percentage on shots from 16-24 feet—fueled the Miami Heat's top-ranked offense, because he was able to make defenses pay for helping off him when LeBron James and Dwyane Wade drove to the basket.

    Or you can learn that Ricky Rubio's struggles to score don't all stem from his inaccurate outside shot. He also had the worst field goal percentage in the restricted area out of any guard in the NBA.

    Where to Find It

    Basketball-Reference has shot location data for every player under the "Shooting" tab in their player pages (just search for the player). There, you will also find a season shot chart that provides the details of every shot a player took during a given season along with a heat map.

    HoopData has shot location numbers for players and teams under their shot location tab (or you can search for a specific player). provides shot location data by range and zone for players and teams (check the Bosh and Rubio links). As an added bonus they separate three-pointers into corner threes and above-the-break threes. They also have fully customizable shot charts which can be filtered just about any way you like.

On/Off Splits

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    Mike McGinnis/Getty Images


    On-court/off-court splits are a simple concept to understand. They just record a team's performance (offensive and defensive efficiency, rebound rate, effective field goal percentage, turnover rate, etc.) when a certain player is on or off the court.

    One player's performance in relation to another player being on or off the court can also be tracked, though that data is much harder to find.


    On/off splits help demonstrate an individual's impact on different aspects of a team. Mind you, it's not a perfect measuring stick for value because it doesn't account for teammates or opponents, so use your common sense when evaluating these metrics.

    For instance, Thabo Sefolosha's on/off splits look incredible, but remember, he gets to play with Kevin Durant, Russell Westbrook and Serge Ibaka for nearly all of his minutes. Obviously, those guys will drive the team's performance, not Sefolosha.

    There are still plenty of interesting nuggets to mine for in the on/off data though.

    Consider this: when Brandon Jennings was on the court last season, the Milwaukee Bucks were outscored by 4.4 points per 100 possessions. When Jennings (generally considered Milwaukee's best player) was off the court, the Bucks not only improved upon that margin, but actually outscored their opponents by 6.9 points per 100 possessions.

    Is it any wonder they were so determined to dump Jennings this past offseason?

    Where to Find It

    Basketball-Reference has on/off splits on both their player and team pages (just search the player or team), though I'd like to see them expand upon the data they provide there.

    Another site with a little wider array of stats in their on/off section is Just navigate to a specific player's page and scroll to the bottom.

Lineup Data

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    Ron Hoskins/Getty Images


    Similar to on/off splits, the performance of specific lineups can also be tracked and is now publicly available.

    Lineup data can be sorted into five-man, four-man, three-man and two-man groups.


    Determining how various lineups perform illustrates which personnel groupings function best on a team. You can use the data to evaluate the rotations employed by coaches.

    You can also use it to project future performance.

    For instance, you may have predicted the Indiana Pacers' playoff success if you knew that their starting lineup outscored their opponents by 12.1 points per 100 possessions, the third-best mark of any five-man group in the NBA that played at least 500 minutes together lat year.

    Knowing that starters log more minutes in the postseason, you could have envisioned a scenario where the Pacers knocked off the Miami Heat and made it to the NBA finals, as the Heat didn't have a lineup which performed as well as that Pacers crew.

    Indeed, that almost came to pass, as the Pacers starting five did outscore the Heat when they were on the floor, but their bench could not sustain the advantage.

    Where to Find It's stats tool has the best lineup data out there. It's fully customizable so you can extract pretty much any information you want from there.

    Basketball-Reference has the top-10 five-, four-, three- and two-man lineup combinations for each player on their player pages (just search for the player and check the "Lineups" tab) and the top-20 units for each team on their team pages.

    The top-20 five-man groups for each player are also available on's player pages.

Adjusted Plus/Minus (APM)

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    Mike Ehrmann/Getty Images


    The final advanced metric I leave you with is adjusted plus/minus.

    Adjusted plus/minus is not as widely used as other advanced stats, but many people swear by it as the ultimate indicator of a player's direct impact on the scoring margin.

    What it tries to do is reflect the impact of each player on his team's scoring margin after controlling for the strength of every player (teammate and opponent) on the court for every minute he's out there.

    Don't bother with the exact formula unless you're super into regression models (in which case click here).


    The number itself represents how many additional points are contributed to a team's scoring margin by a player (per 100 possessions) in comparison to a league-average player whose adjusted plus/minus rating is plus-0.0.

    So if a player whose APM rating is plus-5.0 is on the floor with four average teammates, his team's net rating would be five points per 100 possessions better than a lineup of five average players.

    There are some issues with APM, though.

    First, there is a high variance because a player's role, teammates, matchups, or coaching scheme can change their value in the regression model.

    Second, there is a lot of noise in the data. It's always best to draw conclusions from APM ratings over multiple seasons in order to cancel out some of that noise.

    There is also a regularized version of adjusted plus/minus (RAPM) which attempts to filter out more noise.

    Where to Find It

    These numbers are not commonly published. One site that does provide it is BasketballValue, though it's not currently up to date.

    The blog Shut Up and Jam has published RAPM data from the past 12 seasons.


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