Expanded Glossary of Basketball Stats

Below is an expanded glossary of advanced basketball statistics. For most stats, there is a brief explanation of what it is and how to calculate it, historical examples, and a pro/con analysis of the stat. You can also click on any stat whose heading is linked to find the most up-to-date leaders in the category.

Click on a stat here in the table of contents to jump to its description and explanation.

  1. Single-number” Box-score Metrics
    1. Player Efficiency Rating (PER) and Estimated Wins Added (EWA)
    2. Win Shares (WS) and WS/48
    3. Wins Above Replacement Player (WARP)
    4. Box Plus Minus (BPM) and Value Over Replacement Player (VORP)
  2. Plus-minus stats
    1. Basic Plus-Minus
    2. Real Plus-Minus (RPM)
  3. Advanced shooting stats
    1. Effective Field Goal Percentage (eFG%)
    2. True Shooting Percentage (TS%)
  4. Pace and minute-adjusted box-score stats (“Rate” stats)
    1. Total Rebounding Percentage (TRB%)
    2. Assist Percentage (Ast%)
    3. Turnover Percentage (TOV%)
    4. Steal Percentage (Stl%)
    5. Block Percentage (Blk%)
    6. Usage Percentage (Usg%)
    7. Offensive Rating (ORtg)
    8. Defensive Rating (ORtg)
  5. Advanced Team Stats
    1. Point differential, Pythagorean Wins, and Simple Rating System (SRS)
    2. Four Factors
    3. Pace Factor
  6. Player Tracking Stats

“Single-number” box-score metrics combine traditional box-score stats to estimate a player’s total value in a single number. Most stats listed below are controlled for pace and offer both opportunity-controlled (e.g., per-minute, per-game) and gross measures of productivity. While these metrics do a good job separating a player from his team, they have difficulty approximating a player’s defensive impact because the defensive stats tracked in the box-score are limited; similarly they fail to capture other aspects of basketball beyond the box score.

Player Efficiency Rating (PER) and Estimated Wins Added (EWA)Each year, the league average PER is adjusted to be exactly 15.0. PER adjusts for both pace and minutes, while EWA uses minutes to estimate how many wins a player adds to an average team. Read about how PER is calculated here in detail. Creator: John Hollinger.

Example: Here are the top 8 in PER from the 2010-11: LeBron James (27.3), Dwight Howard (26.1), Dwyane Wade (25.6), Kevin Love, (24.3), Kobe Bryant (23.9), Chris Paul (23.7), Kevin Durant (23.6), Russell Westbrook (23.6).

Here are some players’ career PER. Michel Jordan: (27.9), Yao Ming (23.0), Michael Redd (19.5), Derrick Coleman (18.0) Tom Chambers (16.5), Ricky Davis (14.7), Dennis Rodman (14.6), Ron Mercer (12.5), Mark Eaton (10.9). Bruce Bowen has the 24th worst-ever PER at 8.2.

Pros and Cons: PER rankings often align more with normative perceptions of players’ abilities. PER doesn’t statistically explain previous wins/losses or predict future wins/losses as well as other advanced stats. PER also rewards inefficient volume shooting, theoretically to account for the value of shot creation. David Berri noted  that players “break even” by hitting 30.4% on 2PT FGA (other analysts claim a higher break-even point for PER). If PER has a bias, it’s an emphasis on volume shooting. For a detailed explanation of PER’s origins, read Hollinger’s Pro Basketball Prospectus. A detailed criticism of PER can be found here.

Win Shares (WS) and WS/48: Estimates how many wins a player is responsible for on his team. A team’s win total should roughly equal the sum of each its individual player’s Win Share totals. Calculating Win Shares is complicated; it requires a player’s Offensive RatingDefensive Ratingtotal possessions used. These stats are used to calculate Offensive and Defensive Win Shares, which combine for total WS. WS/48 is a player’s Win Shares per 48 minutes. The league average WS/48 is always .100. Creators: Bill James (baseball) and Justin Kubatko (basketball)

Example: Here are the top 8 in Win Shares from 2010-11: LeBron James (15.6 WS, .244 WS/48), Paul Gasol (14.7, .232), Dwight Howard (14.4, .235), Chris Paul (13.9, .232), Derrick Rose (13.1, .208), Dwyade (12.8, .218), Kevin Durant (12.0, .189), Paul Pierce 11.6 .201).

Here are some players’ career WS/48. Michel Jordan: (.250), Yao Ming (.200), Michael Redd (.134), Derrick Coleman (.119), Tom Chambers (.111), Ricky Davis (.061), Dennis Rodman (.150), Ron Mercer (.034), Mark Eaton (.085), Bruce Bowen, (.086).

Pros and cons: Win Shares, like PER, is pace-adjusted and has a per-minute and gross measure of productivity. Defensive WS can sometimes be misleading because a) it relies on the box-score, favoring stat-stuffing defenders over “no-stats” defenders, and b) it has a strong team-adjustment, meaning poor defenders on good defensive teams can wind up with good DWS, and vice-versa. Lastly, WS has a higher threshold for efficient scoring than PER. Some say WS underrates distributors and overrates players whose scoring is frequently assisted (e.g., Amare on the Suns). To learn about Win Shares (and many other important topics), I suggest reading Dean Oliver’s Basketball on Paper.

Wins Above Replacement Player (WARP): In creator Kevin Pelton’s words: “Conceptually, the WARP system seeks to evaluate players in the context of a team made up of them and four completely average players. The performance of this team is then compared to that of a team made up of four average players and one replacement-level player.” A replacement level is said to perform at 83% of an “average player,” and a team full of replacement level players would win 10 games over an 82 game season. Read how WARP is calculated here. Creator: Kevin Pelton

Example: Here are the top 8 in WARP from 2010-11: LeBron James (21.2 WARP, .748 WS%), Dwight Howard (20.5, .751,), Dwyane Wade (17.1, .705), Derrick Rose (16.6, .679), Chris Paul (16.3, .687), Kevin Love (16.3, .715), Pau Gasol (15.4, .658), Kevin Durant (14.1, .637)

Pros and cons: Pelton has this to say about WARP: “By eschewing the traditional linear weights method so common in basketball analysis, I believe WARP does a better job of incorporating defensive value…It requires a number of assumptions–the value of assists, the tradeoff between usage and efficiency, and replacement level.” WARP also accounts for the floor-spacing value that 3-point shooting provides and weights assisted and unassisted field goals differently.

Box Plus-Minus and VORP: Estimates a player’s contribution to his team’s point differential (on offense and defense, separately), relative to an average player whose BPM is zero. BPM uses box-score rate-statistics as inputs, whose weights are derived from a regression onto 14 years of Regularized Advanced Plus-Minus. VORP (Value Over Replacement Player) is a minutes-weighted counterpart to BPM. Read about them more here. Creator: Daniel Myers.

Example: Here are the top 8 in ASPM from 2010-11: LeBron James (8.2), Chris Paul (5.8), Derrick Rose (5.8), Dwyane Wade (5.6), Manu Ginobili (5.2), Russell Westbrook (5.0), Pau Gasol (4.8), Joakim Noah (4.7).

Pros and cons: BPM is neat parallel to measure of actual plus-minus. BPM is limited by the box-score on defense (and incorporates a team-adjustment). Most important, BPM is the best box-score metric for predicting out of sample results and isn’t prone to the colineairty that plagues measures of actual plus-minus.

Plus-minus statsA family of metrics that attempt capture a player’s direct impact on winning/losing by measuring how his team performs with/without the player. Some favor plus-minus stats because they can capture a player’s impact beyond traditional stats, especially on defense where the box-score stats are limited.

Basic Plus-Minus is the net score for a player’s team (points scored minus points allowed) while the player is in the game. This is what we see in modern box scores. This stat can also be made to be per-minute or per-possession.

Example: If Michael Ruffin’s team scores 25 points and allows 22 points while he is in the game, he is +3. If he played 12 minutes and 20 possessions on each side of the ball, he’d be +12 per 48 min and +15 per 100 possessions.

Pros and cons: A player’s plus-minus in a given game, or even across an entire season, is largely beyond his control. A poor player can have a good plus-minus if he plays alongside good teammates and vice-versa. Because certain players almost always play with other players, plus-minus often cannot separate the impact of two players who always share the floor. Plus-minus stats vary from season to season and thus is not a reliable measure of a player’s impact.

Real Plus-Minus (RPM) and Wins Above Replacement (WAR): Captures how many points per 100 possessions a player adds to / subtracts from his team’s scoring margin. WAR is a minutes-weighted version of the statistic, approximating how many wins a player is responsible for above replacement. RPM is broken down into offensive and defensive parts, as well. RPM is the ESPN.com product of the evolution of variants RAPM and xRAPM; its calculation can be read more, here. Creators: Jeremias “Jerry” Engelmann and Stephen Ilardi

Example: Here are the top 8 in xRAPM from 2010-11: Dwight Howard (9.7), LeBron James (8.1), Chris Paul (7.5), Dirk Nowitzki (6.9), Manu Ginobili (6.9), Tim Duncan (6.1), Dwyane Wade (5.9), Kevin Durant (5.7).

Pros and cons: RPM controls for many thing: It uses play-by-play data to account for teammate and opponent quality, it reduces error by using previous years to help inform the current year (i.e., a ridge regression), and it also uses box-score input to help reduce error. It still suffers from collinearity, but it is the best plus-minus statistic there is.

Advanced shooting stats go beyond traditional shooting statistics (FG%, 3pt%, FT%) to paint a more accurate picture of a player’s shooting efficiency. They can be used for players and teams.

Effective Field Goal Percentage (eFG%) is a modified FG%, taking into account the increased value of made three pointers. On the team level, team eFG% and opponent eFG% are a part of Dean Oliver’s Four Factors. The formula is: eFG% = 100 * (FG + 0.5*3PT) / FGA.

Example: If Darius Miles shoots 5 for 10 with all his makes being 2-pointers, he has a eFG of 50.0%. If Ricky Davis shoots 4-10, making one 2-pointer and three 3-pointers, his eFG of 55.0% bests Miles’, even though Davis’ FG% is worse than than that of Miles.

True Shooting Percentage (TS%) takes into account field goals, 3-point field goals, and free throws. TS% = 100 * PTS / (2*(FGA + 0.44*FTA)).

Example: Here are the top 8 in TS% from 2010-11:  Tyson Chandler (69.1%), Nene (65.6%), Arron Afflalo (62.0%), Paul Pierce (62.0%), Chauncy Billups (61.7%), Dwight Howard (61.6%), Ray Allen (61.5%), Richard Jefferson (61.2%)..

Pace and minute adjusted box-score stats (“Rate” stats) take traditional box-score stats (rebounds, assists, turnovers, steals, blocks) and adjust for the pace and volume, i.e., the number of opportunities that each player gets to record these stats. These stats can be calculated for both players and teams (although listed below will be the player-versions).

Total Rebounding Percentage (TRB%) is the percentage of available rebounds a player grabbed while he was on the floor. TRB% = 100 * (TRB * (Team MP / 5)) / (MP * (Team TRB + Opp TRB)). In addition, this stat can be calculated separately for offensive and defensive rebounding. On the team level, ORB% and DRB% are part of Dean Oliver’s Four Factors.

Example: Here are the top 8 in TRB% from 2010-11: Kevin Love (23.6), Kris Humphries (22.1), Dwight Howard (21.8), Zach Randolph (20.1), Tyson Chandler (19.7), Blake Griffin (18.6), Tim Duncan (18.3), Andrew Bogut (18.3)

Assist Percentage (Ast%)  is the percentage of teammate field goals a player assisted while he was on the floor. AST% = 100 * AST / (((MP / (Team MP / 5)) * Tm FG) – FG).

Example: Here are the top 8 in Ast% from 2010-11: Steve Nash (53.1), Rajon Rondo (47.1), Deron Williams (45.9), Chris Paul (45.8), Jose Calderon (43.0), Russell Westbrook (42.7), Derrick Rose (38.7), Devin Harris (38.2)

Turnover Percentage (TOV%) estimates a players turnovers per 100 possessions used. TOV% = 100 * TOV / (FGA + 0.44 * FTA + TOV). The lower the number, the better your TOV%

Example: Here are the best 8 in TOV% from 2010-11: Al Jefferson (6.8), Tayshaun Prince (7.1), Channing Frye (7.7), Jason Richardson (7.8), Nick Young (8.0), Travis Outlaw (8.1), Elton Brand (8.5), Glen Davis (8.5)

Steal Percentage (Stl%) estimates the percentage of opponent possessions that end with a steal by the player while he was on the floor. STL% = 100 * (STL * (Team MP / 5)) / (MP * Opp Poss).

Example: Here are the top 8 in Stl% from 2010-11: Tony Allen (4.5), Chris Paul (3.5), Rondo (3.2), Russell Westbrook (2.8), Metta World Peace (2.7), Jason Kidd (2.7), Manu Ginobili (2.6), Monta Ellis (2.6)

Block Percentage (Blk%) is the percentage of blocks a player makes on opponent two-point field goal attempts while he was on the floor. BLK% = 100 * (BLK * (Team MP / 5)) / (MP * (Opp FGA – Opp 3PA)).

Example: Here are the top 8 in Blk% from 2010-11: JaVale McGee (6.7), Serge Ibaka (6.5), Darko Milicic (6.3), Bogut (5.8), DeAndre Jordan (5.4), Andrew Bynum (5.4), Dwight Howard (4.9), Tim Duncan (4.8)

Usage Percentage (Usg%) estimates the percentage of team plays “used” by a player while he is on the floor. Usg% = 100 * ((FGA + 0.44 * FTA + TOV) * (Team MP / 5)) / (MP * (Team FGA + 0.44 * Team FTA + Team TOV)). Usage is one way of measuring how much offensive load a player takes on.

Example:Here are the top 8 in Usg% from 2007-08: LeBron James (33.5), Kobe Bryant (31.4), Tracy McGrady (30.4), Carmelo Anthony (30.2), Dirk Nowitzki (28.8), Manu Ginobili (28.7), Amare Stoudemire (28.2), Tim Duncan (28.2)

Offensive Rating (ORtg) is a measure of offensive efficiency. For players it is an estimate of points produced per 100 possessions used, while for teams it is points scored per 100 possessions. This rating was developed by Dean Oliver, author of Basketball on Paper. For teams, ORtg is synonymous to a team’s “offensive efficiency” and the best way to evaluate a team’s offense.

Example: Here are the top players 8 in ORtg from 2010-11: Tyson Chandler (131.0), Amir Johnson (123.7), Nene (123.4), Pau Gasol (123.3), Kevin Love (123.1), Arron Afflalo (122.8), Chris Paul (122.2), Greg Monroe (120.2)

Here are the top 8 teams in ORtg from 2010-2011: Nuggets (112.3), Spurs (111.8), Heat (111.7), Rockets (111.3), Thunder (111.2), Lakers (111.0), Knicks (110.9), Mavericks (109.7)

Pros and Cons: For teams, ORtg is the best measure of offense. For players, ORtg is a useful stat, although it is better looked at alongside USG% for context.

Defensive Rating (DRtg) is a measure of defensive efficiency. For players and teams it is points allowed per 100 possessions. To measure points allowed for players, you must look at a player’s defensive stops. For teams, DRtg is synonymous to a team’s “defensive efficiency” and is the best way to evaluate a team’s defense.

Example: Here are the top 8 players in DRtg from 2010-2011: Dwight Howard (94.0), Kevin Garnett (95.0), Joakim Noah (96.8), Andrew Bogut (97.3), Taj Gibson (97.7), Ronnie Brewer (98.4), Carlos Boozer (98.7), Marcus Camby (99.8)

Here are the top 8 teams in DRtg from 2010-2011: Celtics (100.3), Bulls (100.3), Magic (101.8), Bucks (102.5), Heat (103.5), Lakers (104.3), Sixers (105.0), Mavericks (105.0)

Pros and cons: For teams, DRtg is the best measure of defense. For players, DRtg can sometimes be misleading because a) it relies on the box-score, meaning stat-stuffing defenders are overrated and lock-down “no-stats” defenders are underrated and b) it has a strong team-adjustment, meaning poor defenders on good defensive teams can wind up with good DWS, and vice-versa.

Advanced Team Stats help us understand a team’s quality beyond a simple win-loss record.

Point differential, Pythagorean Wins, and Simple Rating System (SRS) are three related measures of team performance. Point differential is a team’s offensive efficiency (points scored per 100 possessions, i.e., ORtg) minus its defensive efficiency (points allowed per 100 possession, i.e., DRtg). SRS is point differential with adjustments for strength of schedule. Read more about SRS here. Both of these stats are better predictors of future performance than traditional W-L record. Pythagorean wins is an expected W-L record based on point differential or SRS.

Example: Here are the top 8 teams of all time in SRS: 1970-71 Bucks (12.22), 1995-96 Bulls (12.10), 1971-72 Lakers (11.24), 1971-72 Bucks (10.69), 1996-97 Bulls (10.49), 1991-92 Bulls (9.86), 1985-86 Celtics (9.55), 1990-91 Bulls (9.26).

Pros and cons: Historically, point differential and SRS do better predicting future victories than does traditional W-L record. One small problem, however, is that teams that rest their starters in blow outs will have a lower SRS than they “deserve” while teams that run up the score might have a higher SRS than they “deserve.”

Four Factors are the four most important variables in evaluating, explaining, and predicting team performance, as calculated by Dean OliverAccording to EvanZ, the Four Factors explain 96% of point differential.  Here are the The Four Factors with their relative importance indicated by the shown percentage:  Shooting (40%; as defined by eFG% and opponent eFG%), Turnovers (25%; as defined by TOV% and opponent TOV%), Rebounding (20%; as defined by ORB% and DRB%), and Free Throws (15%; as defined by FT/FGA and opponent FT/FGA). Sometimes, people (such as NBA.com) use FTA/FGA for their measure of free throws, instead.

Pros and cons: The Four Factors are an interesting way to break down the sport on the team level. One factor to think about is to what extent the factors are independent of one another. For instance, do teams that opt to crash the offensive glass leave themselves vulnerable on defense? Also, I find it interesting that Oliver doesn’t incorporate the floor-spreading value of 3-pointers.

Pace Factor is the estimated of possessions a team uses per 48 minutes. It’s calculated with the following formula: 48 * ((Tm Poss + Opp Poss) / (2 * (Tm MP / 5))). A possession is with this formula:  0.5 * ((Tm FGA + 0.4 *Tm FTA – 1.07 * (Tm ORB / (Tm ORB + Opp DRB)) * (Tm FGA – Tm FG) + Tm TOV) + (Opp FGA + 0.4 * OppFTA – 1.07 * (Opp ORB / (Opp ORB + Tm DRB)) * (Opp FGA – Opp FG) + Opp TOV)).

Player Tracking StatsSportVU cameras (six cameras in each arena that record player movement 25 times a second) provide a new wealth of NBA stats. Most of these data are not available to the public, but NBA.com provides various stats for each of the following categories: Catch and shoot, Defense, Drives, Passing, Possessions, Pull-up Shooting, Rebounding Efficiency, and Speed.

2 Responses to Expanded Glossary of Basketball Stats

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