I've constructed this site to serve as a portal for the use of statistics in the NBA and particularly as a reference for those just beginning to learn about the field. If you have any questions this page fails to answer, feel free to contact me at kpelton@hoopsworld.com.
- Kevin Pelton (Updated November 2007)
RESOURCES
APBRmetrics Forum
The premier location for discussion of advanced basketball statistics, featuring many of the big names of the field.
82games.com
Using various online resources and independent scorers, 82games generates extremely detailed statistics for every NBA player. The key draw is plus/minus ratings, but here is much more to this site, including breakdowns of inside and outside shots, defense by position, breakdowns of turnovers, own shots blocked, so much more. One could literally get lost on 82games for hours. 82games has become message boards' version of American Express -- don't argue without it.
Basketball-Reference.com
Basketball-Reference.com has established itself as the best source for historical statistics - and, equally notably, the most friendly to APBRmetrics. B-R.com includes John Hollinger's stats, Dean Oliver's stats, similarity scores and much, much more.
BasketballProspectus.com In the fall of 2007, Baseball Prospectus came to basketball. This site features advance analysis of both college and NBA ball.
KnickerBlogger.net Stats Pages
While B-R.com provides advanced stats for years gone by, for current statistics, KB.net's stats page is the place to go. The available stats include Oliver's Four Factors for teams and Hollinger-style statistics, as well as per-40-minute statistics, for individuals.
dougstats.com
Thank you, Doug Steele. To many people, this is the most valuable site out there. Why? Because Doug updates statistics on a daily basis and provides them in a format that is easily transferable to Excel (there are instructions on the site). Paste these numbers into Excel, and you're ready to have fun with whatever kind of statistics you feel like calculating. Doug also provides some defensive stats by position, as part of his own take on TENDEX. The statistics go all the way back to 1988-89, and it's not a coincidence most team-based analysis cuts off then. Do note that the team turnovers Doug reports are the sum of individual turnovers and do not include turnovers assessed only to the team, as the official NBA stats do.
Popcorn Machine Game Flows
Mike Lawler provides a complimentary service to 82games.com, offering minute-by-minute analyses of games with the lineups on the court (and their plus-minus) and player stats in given times on the court. Great for looking at teams' rotation patterns.
APBR.org
Baseball statistical analysis is called sabermetrics after SABR, the Society for American Baseball Research. The APBR plays the same role in basketball (and the term APBRmetrics is catching on). Founded by Robert Bradley and run by Ray LeBov, the APBR features discussion at its message board, but the site itself is a fine historical resource
DatabaseBasketball.com
Another source for historical stats. The main thing DB.com has to offer that B-R.com does not is a downloadable file with complete stats.
ANALYSTS
Roland Beech
Since bursting on the scene in 2003 with his innovative Web site 82games.com, Beech has become quite a force in the world of NBA statistics. Beech himself says on the site that its general principle is to let the numbers speak for themselves, but his analysis is also a key part of the site. Beech has been described as having, "a very basic curiosity about the game," and it's a complement; he asks questions some would find too obvious, and regularly comes up with answers that are anything but.
Bob Bellotti
Bellotti wrote five books during the late 1980s and early 90s, most of them under the name The Points Created Basketball Book. As our more intelligent readers might guess, these were based on Bellotti's rating, which was called, say it with me, "Points Created". Bellotti recently helped collaborate on Total Basketball and continues to serve as a consultant to NBA teams. You can find out more at his website, BellottiBasketball.com. Bellotti was also partially behind (I think) a site that, through the 2000-01 season, was the only place to find detailed statistics for every player on the internet,
NBA Stats Site: The Hidden Game.
Dave Berri
Berri is an economics professor at Cal State-Bakersfield. His search for a method to evaluate basketball players -- a very valuable thing for economists, who can use it to study issues like biases in salaries or All-Star voting -- culminated in a rating system, Wins Produced, that is featured prominently in the book The Wages of Wins, co-written with Martin Schmidt and Stacey Brook and published in May 2006. Berri and his co-authors have also started a blog. Years ago, Berri managed to get his work into an AP article disavowing Allen Iverson's selection as the MVP in 2000-01.
Kevin Broom
An old colleague of mine from his days at Hoopsworld.com, Broom has moved on to a role as a senior writer for RealGM.com. Unfortunately, Broom doesn't have the time for regular columns, but does fine work when he does get the chance under the "Goaltending" column title. My favorite Broom invention is his "Diamond" rating, which seeks to formalize the process of identifying players underrated by their per-game stats because they play limited minutes. I've used this rating to a casual fanbase a couple of times. A more recent project for Broom has been collecting defensive stats from Washington Wizards games, which he turned into a column for SI.com during the 2005 Playoffs.
Bob Chaikin
Chaikin has used his simulation program, Bball, for NBA teams. With remarkable attention to detail, Chaikin's simulation can simulate hundreds of games in minutes to assess the impact of various lineup and rotation changes. It is valuable both as a coaching tool and for front offices, and several teams have used it. Chaikin has also been a leader in the use of "touches" in evaluating players and has contributed occasional columns to HoopsAnalyst.com.
Mike Goodman
Goodman has worked extensively on player ratings, culminating in his eWins metric. Goodman regularly posts his ratings at the APBRmetrics Forum. He has also posted some of his work at HoopsAnalyst.com. Goodman's use of playoff statistics is relatively unique, and he specializes in historical ratings.
Dave Heeren
Heeren was probably the most famous NBA statistical analyst following in the wake of James. Also a columnist for USA Today, Heeren wrote a series of books under the Basketball Abstract name. These were based on what is generally considered the first linear-weights player rating system, TENDEX. Heeren also wrote some columns for CBSSportsline.com a few years ago. Since then, Heeren has written about preps for the South Florida Sun-Sentinel and peddled his TENDEX ratings for teams looking to evaluate NCAA players. He used to do that through the website TendexHoops.com,
but the site is no longer up.
John Hollinger
The most visible APBRmetrician, Hollinger parlayed the success of his website, AlleyOop.com into a gig with SI.com. In February 2005, Hollinger was hired by ESPN Insider to write weekly columns, increasing his profile. (Hollinger also writes three times a week during the regular season for the New York Sun.) Equally important has been Hollinger's book series, formerly the Pro Basketball Prospectus for both 2002-03 and 2003-04. His 2004-05 offering was re-titled Pro Basketball Forecast, as was the 2005-06 edition. Since then, Hollinger has moved his annual player and team analysis online as part of his Insider offerings. Hollinger is the best-known statistical analysis amongst casual NBA fans, and has helped bring concepts like offensive and defensive efficiency to a wide audience. His books include a number of enlightening studies, and he has done ground-breaking work on evaluating defense by the performance of opposing players at a given position.
Martin Manley
Manley followed in the wake of Heeren, writing a similar series of books (these were both basically aping James' Baseball Abstracts). They were titled Basketball Heaven, for reasons I can't comprehend. Manley used a simplified version of TENDEX called "Manley Credits", which have outlived his own work. Manley recently resurfaced using his analysis for the Kansas City Star.
Dean Oliver
Oliver is generally recognized as the Bill James of basketball and the leader of the APBRmetrics movement. Most of Oliver's work has been published on his website, The Journal of Basketball Statistics (JoBS). While the vast majority of articles on that site date back to the late 90s, if not earlier, Oliver has kept busy. In 2003, he published his first book, Basketball on Paper. Oliver spent two seasons with the Seattle SuperSonics in a pioneering role as a consultant before becoming director of quantitative analysis for the Denver Nuggets in 2006. His work has focused largely on how to eliminate -- or at least consider -- situational elements when evaluating players and teams.
Kevin Pelton
Quality aside, I do write analytical columns, for what it's worth. Currently, that work is published at BasketballProspectus.com. I wrote for a year and a half at Hoopsworld.com, under the "Page 23" label. I also wrote commentary for 82games.com and SI.com. By day, I write for SUPERSONICS.COM and storm.wnba.com, where I've tried to introduce these concepts to a general audience.
Dan Rosenbaum
Better known as the foremost expert on the NBA's luxury tax, Rosenbaum, an economist at UNC-Greensboro, turned to statistical analysis, using his economics background with fascinating results. Most notably, Rosenbaum has replicated WINVAL (see below) and improved upon it by considering traditional statistics alongside "impact" statistics. The resulting "DanVAL" is one of the more interesting rating systems ever created and has some revolutionary implications about what traditional statistics are important. Dan's work is collected on his NBA research page, but he cut back his work after joining the Cleveland Cavaliers as a consultant at the start of the 2005-06 season.
Jeff Sagarin/Wayne Winston
The Indiana University professor and NCAA ratings expert have made as much impact in NBA front offices and the traditional media as anyone with their WinVAL system. At IU, Winston teaches a statistics class once attended by an undergrad named Mark Cuban. When the two met up again with Cuban owner of the Dallas Mavericks (and a proponent of statistical analysis, even if he doesn't always agree with the leaders in the field), he charged Winston to create a better way to rate players. Winston enlisted the help of Sagarin, who is better known for his NCAA basketball and football rating systems. Using Cuban's access, they were able to get complete NBA play-by-play data and use this to create a modified plus-minus system which adjusts for the quality of teammates and opponents. In theory, this is the least biased and most accurate rating system possible, but the high variance produces inconsistent results year-to-year and often means the ratings don't pass the "laugh test" (for example, San Antonio swingman Hidayet Turkoglu was rated the NBA's top player in 2003-04).
Harlan Schreiber
I previously mentioned HoopsAnalyst.com, and Schreiber is the man
behind it. The site is probably the closest NBA statistical analysis comes to a BaseballProspectus.com,
at least in terms of a site with various different authors providing analysis. I particularly enjoy Schreiber's Transaction Analyses, which break down the excruciating minutiae of NBA transactions. Schreiber also does a terrific job of keeping his finger on the pulse of international basketball.
THE FOURTH ESTATE
There are some excellent examples of reaction to what NBA teams and independent analysts have been doing. These are some of the most relevant of these articles.
Wired to win Mark Monteith, Indianapolis Star, July 3, 2002
The article that first introduced WINVAL to the world, with the angle being that W&S are from Indiana University and the Pacers have used WinVAL some. This is reprinted at the APBR discussion group, so you can follow the thread to see the amazement with which we all read about WINVAL at first.
This Just In Aaron Schatz, Boston Phoenix, November 21-28, 2002
A review of Hollinger's first Pro Basketball Prospectus
effort, lauding Hollinger for being the first to extend the Bill James revolution to another sport. Schatz is now quite famous in his own right as the proprietor of the incomparable FootballOutsiders.com, which bills itself as "Football stats for the Moneyball era."
Positive news for Sonics Danny O'Neil, Seattle Post-Intelligencer, December 16, 2003
Based on the impressive rating of then-Sonics forward Richie Frahm, O'Neil looks at how plus/minus ratings are gaining in importance in NBA circles. Quotes from Oliver and Cuban, along with then-Sonics assistant Dwane Casey, help lend an inside perspective to this article.
He stats! He scores! Tommy Craggs, SF Weekly, February 11, 2004
Craggs has an excellent profile of Beech's background and his mission. A nice touch to this article was that Craggs was able to take Beech and Oliver to a Warriors game (both live in the Bay Area) where, he reports, they discussed "the most effective way to razz a free-throw shooter".
Numbers game Patrick Hruby, Washington Times, April 13, 2004
A fawning, but informative, description of WINVAL.
Reserve guard Butler rates well with Wizards Patrick Hruby, Washington Times, April 13, 2004
The companion WINVAL piece notes that journeyman Mitchell Butler is the best-rated Washington player. Very much worth a read.
Aptos basketball junkie takes NBA stats to new heights Bob Linneman, Santa Cruz Sentinel, April 21, 2004
Linneman fawns a bit over the work at 82games.com while giving us more background on Beech and how he got where he is today.
NBA free agent madness King Kaufman, Salon.com, July 22, 2004
Kaufman gets to the heart of the matter I've maintained basketball teams should really be learning from Moneyball -- spending money efficiently. Oliver and Rosenbaum are quoted on what NBA teams did wrong during a summer that saw money get thrown around with little regard to actual value.
Getting serious about stats Rich Evans, Deseret Morning News, November 7, 2004
Stat geeks love Andrei Kirilenko. So realizes Evans in this piece, authored shortly after Kirilenko signed a six-year, $86 million extension with the Jazz. Evans talked to Beech about why Kirilenko is so valuable without being a high scorer. Evans continued to use 82games numbers throughout the year.
Scientist signs on with Sonics Danny O'Neil, Seattle Post-Intelligencer, December 30, 2004
O'Neil profiles Oliver with regards to his current role with the Sonics. O'Neil does a good job of simplifying Oliver's complex work for a general audience, but I think he tends to make Oliver come off more geek than stats -- the guy did play some basketball in college.
Keeping Score: N.B.A.'s New Math Finds Willing Students David Leonhardt, New York Times, January 9, 2005
(Registration required.) The Gray Lady takes a broad overview of Oliver and his role with the Sonics, noting the role of Wally Walker and Rich Cho in the Sonics' statistical development.
Keeping Score: A Statistical Holy Grail: The Search For the Winner Within Dan Rosenbaum, New York Times, April 10, 2005
(Abstract only.) Rosenbaum has guested a pair of "Keeping Score" columns, one on luxury tax issues and this on his DanVAL system and the lessons provided by looking at adjusted plus-minus statistics as compared to traditional statistics.
Statistics gurus work their way into NBA offices Michael Cunningham, South Florida Sun-Sentinel, April 17, 2005
(Abstract only.) Cunningham offers one of the most in-depth looks at the statistics community and its progress into NBA front offices. This is the main article; others looked at the occasionally contentious relationship between Winston and Sagarin and other stat geeks and looked at leaders in various rating systems.
Basketball's new math Chris Ballard, SI.com, October 21, 2005
In conjunction with a feature for the Sports Illustrated preview edition, Ballard discusses the advances made by the APBRmetrics community, particularly focusing on how teams have made use of statistics. In particular, Ballard gives credit to adjusted plus-minus ratings for capturing things that can't be quantified through traditional statistics.
Rockets' GM Dawson will groom Morey as successor Jonathan Feigen, Houston Chronicle, March 30, 2006
In March 2006, the Rockets made headlines by naming Celtics Vice President of Operations and Information Daryl Morey as assistant GM and the eventual replacement as of the 2007-08 season for GM Carroll Dawson. Morey, who worked at STATS, Inc. while in college (famously, he transferred Bill James' Pythagorean Winning Percentage formula to other sports, including the NBA), had provided statistical analysis to the Celtics front office but also played a key role in the team's business operations. A James devotee, Morey could reasonably be called the first APBRmetric GM.
GLOSSARY
Assisted field goal - Simply, a field goal on which a player received an assist. This matters because credit must be split between the assisting player and the scoring player. Play-by-play data like that used by 82games.com can be used to find each player's exact percentage of assisted field goals, but it is usually estimated.
Defensive Rating - Points allowed per 100 possessions (see Offensive Rating).
Effective Field-Goal Percentage - An adjusted form of field-goal percentage that takes into account the added value of three-pointers by weighting them as 1.5 times as valuable as two-pointers. This is a popular statistic with the general public that is available at ESPN.com. It was popularized by Rick Barry's Pro Basketball Bible in the 90s, which was where I first saw it as a kid (see True Shooting Percentage). Statistically: (FGM + .5*3PM)/FGA
Floor Percentage - The percentage of a team's possessions that end in scoring possessions.
Four Factors - Oliver evaluates teams and players with four factors on offense and defense -- shooting (effective field goal percentage); getting to the free-throw line (FTM/FGA); turnover percentage (per possession); and offensive or defensive rebounding percentage.
Free-throw modifier - Because basketball analysts usually express statistics in terms of possessions, an adjustment needs to be made for the fact that two free throws do not always constitute a possession. Three-point plays, three-shot fouls, and technicals all increase the number of free throws per possession. Thus, we need to use something less than 0.5 when multiplying by free throws to calculate possessions. Analysis has revealed that the appropriate multiplier is 0.44 (see Possessions).
Linear weights formulas - Rating systems that assign a value to each major statistical event on the court (PTS, FGA, FTA, OR, DR, AST, STL, BLK, TO, PF) and sum these. The most common form of rating system; TENDEX and Manley Credits (in both cases, all weights are 1 or -1) are both examples.
Offensive Rating - Points scored per 100 possessions (see Defensive Rating).
Plays - See Possessions.
Play Percentage - The percentage of a team's plays that end in a score.
Points per shot - This is something you'll see those who are not statistical analysts use to evaluate scoring efficiency. Usually, it simply means points per field goal attempt, which means that tight ends are essentially free points for the player. Players like Shaquille O'Neal, who attempt a high number of free throws, are overrated by this method. (See True shooting percentage.) Statistically: Pts/FGA
Possessions - Here is one place where defining a term becomes tricky, because there are two different definitions of possessions used by various analysts. (Baseball analysts, alas, are lucky enough not to have this problem. An out is an out is an out.) The most commonly-held view is that a possession is all the time a team holds the ball before the other team gets it. The defining characteristic of this definition is that an offensive rebound does not start a new possession. There are also those who view the offensive rebound as starting a new offensive possession. These people define possessions as time before an attempt to score is made or a turnover is recorded. Analysts operating on the first definition call these plays instead of possessions. Statistically: .96 * (FGA + 0.44*FTA + TO - OR) or
FGA + 0.4 * FTA - 1.07 * (OReb/(OReb + OppDReb)) + TO
Plays: FGA + 0.44*FTA + TO
Possession usage - The percentage of a team's possessions used by an individual player, also known as simply usage. On average, naturally, a player uses 20% of his team's possessions.
Pythagorean winning percentage - A Bill James invention in baseball, Pythagorean records are based on the knowledge that team winning percentages are generally closely related to points scored and points allowed (and, in cases where they differ, the reason is usually temporary luck). This relationship can be approximated by PF^x/((PF^x) + (PA^x), where x depends on the total points scored. In baseball, over the course of a season, x is close enough to be approximated by two. In basketball, x is a little more difficult to calculate. When Oliver did it a decade and a half ago, it was about 16.5. Now, because point totals are lower, the exponent is believed to be closer to 13 or 14. It is also possible to calculate Pythagorean percentages in different ways, like a multiplier (2.7) by the team's point differential (for an 82-game season). This is slightly less accurate, but much easier. A third, more complicated method is employed by Oliver, which takes into account the variability in a team's points scored or points allowed and is thus more accurate. Statistically: PF^13.5/((PF^13.5)+(PA^13.5))
Expected wins = 2.7*(PF/G-PA/G) + 41
Rate - This is usually used to denote that a statistic is being calculated on a per-minute basis. "Rebound rate", for example, generally means rebounds per 48 minutes (it may be expressed in per-minute form as well).
Rebound percentage - The percentage of all available rebounds that a player or team grabs, often broken down into offensive rebound percentage and defensive rebound percentage. This is a better measure of rebounding prowess than rebound rate because it adjusts for game pace, although total rebound percentage is skewed by the ratio of offensive and defensive rebound opportunities. (In other words, a team with a really great defense will have its total rebound rate artificially inflated because defensive rebounds are much easier to grab.) Usually, rebound opportunities are estimated for players based on the team's rebound opportunities per minute, but play-by-play data -- like that used by 82games.com -- can identify a player's exact opportunities. Statistically: for teams, Reb/(Reb+OPPReb)
for players, (Reb*Min)/((TMReb+OPPReb)/(TMMin/5))
Replacement level - A valuable concept borrowed by some NBA analysts from their baseball counterparts, replacement level estimates numerically the performance of players who can be aquired at little or no cost to the team. This generally means either players signed as free agents during the season or those who make teams as training-camp invitees. I studied replacement level for Hoopsworld.com. (See Value Over Replacement Player.
Scoring possession - Any possession on which the offense scores at least one point. (See possessions.)
Similarity scores - A measure of how statistically similar two players are. There are several such ratings floating around. Oliver and BR.com use methods that are rather literally trying to compare statistics -- on a pure stat basis (i.e. 350 rebounds vs. 400). Hollinger, B-R.com and I have ratings that are skill-based, looking at the differences in secondary statistics like shooting percentages, rate stats, and our overall ratings. (Actually, Oliver uses something more like this, but it's proprietary.) These are generally complicated formulas.
Two-point percentage - The percentage of a player's two-point attempts he makes. Though field-goal percentage and three-point percentage are often used together to determine approximately how effective players are inside the arc, this is a more accurate measure. Statistically: (FGM - 3PM)/(FGA - 3PA)
True shooting percentage - One of the trickiest things about creating a glossary for NBA statistics is that so many terms are used differently by different people. Even I use at least two different terms for what I've chosen to call true shooting percentage. Other terms used are scoring efficiency, adjusted shooting percentage, effective percentage, and points per shot attempted (Hollinger used to use this term and did not express the concept as a percentage, but has since converted). What these all are getting at is that this is the truest measure of a player's efficiency in terms of shooting, how many points he scores divided by how many shooting possessions he uses. (True shooting percentage can also be used to mean effective field-goal percentage.) Statistically: Pts/(2 * (FGA + (0.44 * FTA)))
Value Over Replacement Player (VORP) - This is another baseball concept, which is based on the premise that players have value to their teams by being better than replacement level. A player's VORP is calculated by their per-minute rating (any will work) minus replacement level times minutes. (See Replacement level.)
Wins Above Replacement Player (WARP) - A similar concept, but using some calculated winning percentage as a rating.