An Intro to Gotbuckets and a Brief Primer on Adjusted Plus / Minus

Plus Minus Pic

So, provides 2-year Adjusted Plus-Minus (APM) data Why, you ask?  A little intro…

Let’s start by acknowledging that lacks groundbreaking new statistics.  APM and Regularized Adjusted Plus Minus (RAPM) have been in the public conscience for over a decade.  A number of sources played a part in developing the methods we use here, including: Wayne Winston, Jeff Sagarin, Dan Rosenbaum, Aaron Barzilai, Jeremias Engelmann, and Eli Witus.  They are all smarter than we are.

The creators of this blog are writers at other team-centric basketball blogs though and wanted to have a place to write about the NBA at-large.  APM and RAPM data somewhat dried up, with Mr. Barzalai’s site not being updated, and Mr. Engelmann’s  only refreshing periodically.  Combining these two factors, we calculated and provide APM, with short-term ambitions of an RAPM variation, and intend to supplement it with NBA writing; sometimes APM / RAPM-centric, other times, not so much.

So what benefits can APM provide?

Every game ends with one team scoring more points than the other; being that team is the goal of every contest.  A myriad of useful box-score derived stats succinctly measure player performance in wins: Extra Wins Added, Win Shares, Wins Above Replacement Player, Wins Produced, etc.  But ultimately, none originates directly from scoreboard impact.

Plus-minus derivations help in that regard, and inform a well-rounded understanding of contributions to a team’s bottom line.  Everyone understands raw Plus/Minus.   It simply determines how much a player’s team won or lost by while they played; a guy played 30 minutes and his team outscored the opponent 62 to 58 during that time, then he finishes +4.  Easy stuff, but unfortunately it doesn’t account for a player’s teammates or opponents.  Prone to all sorts of randomness, bad calls from referees, an opponent blazing through a hot stretch, excellent teammates, etc, can all impact a player’s Plus/Minus.

As an evolution, along came Adjusted Plus Minus.  Derived from work originally performed by Winston and Sagarin , APM assesses the plus-minus outcome of tens of thousands of annual lineup matchups via a regression model.  Every line-up matchup is an equation and each player a variable.  Home court advantage is accounted for, and the regression calculates a per possession value for every player in the NBA.  Every line-up matchup / equation contains two known values and ten variables.  The ten variables are the players on the court.  The known values are the average per possession home court advantage in the NBA and the scoring differential between the two line-ups (extrapolated to 100 possessions; if Lineup X bested Lineup Y by three points during their ten possessions on court together, then the Margin equals 30).  If the home lineup beat the away lineup by an extrapolated 30 points per 100 possessions, and the average home-court advantage is three points per 100 possessions, and X represents a home player; and Y an away player, then the equation is:

30 = 3 + X1 + X2 + X3 + X4 + X5 – Y1 – Y2 – Y3 – Y4 – Y5

Utilizing tens of thousands of these equations and statistical computation software “R”, a regression is run that calculates a value for each variable (player) surpassing a specified minimum playing time threshold.  The regression weights each equation by number of possessions, and  the value derived is the player’s approximate worth to his team per 100 possessions, compared to an average player.

The idea is explained in some detail here, by Rosenbaum , however diverges from his method in some regards.

  • The calculation that we provide is “pure” 2-year APM.  Anything after Section II.1 of the Rosenbaum article doesn’t apply to gotbuckets.  So, no “Statistical Plus-Minus” or “Overall Plus Minus”.
  • All of the APM regressions are two year regressions, but no weighting is applying to make the most recent season more valuable than the prior.
  • No adjustments have been made for “garbage time” or “clutch time”.  Home-court advantage serves as the only number in each equation that isn’t a direct outcome of the actual line-up match-up.
  • Reference Players constitute players in the approximate bottom 25th percentile for minutes played during the two seasons (750 total minutes).  This group is lumped together as one.  This prevents extremely erratic results caused by small sample size.
  • Playoff results are included, though also not weighted.
  • The calculation is split into offensive and defensive components, using a method described in an article by Eli Witus.
  • In addition to those sub-numbers, plus their total summed 2-year APM, each APM Page includes the number of minutes each player played during those two seasons, as well of the standard deviation associated with the APM.

So, that is the “cliff’s notes” version of APM and some specifics of the data currently at gotbuckets.  The primary allure of APM is that it provides an unbiased look at player performance, and the intent of the process described above is to limit any biases.  Scoreboard result in; APM out…no coefficients correlating the value of assists, rebounds, steals, etc to a number of wins.

Weaknesses include a lack consistency from season to season; some players vary wildly over a few years, hence some issues as a poor predictive model.  The stat is “noisy”, caused to some extent by collinearity.  Some players see almost all their on-court time with another player, and the model cannot differentiate who deserves credit for the team’s performance.  The small sample of possessions available of when those players do not share the court dominate their results. As is typical, gotbuckets provides standard deviations with the APM.  With relatively large standard deviations, many players overlap within one standard deviation.  Particularly in small sample sizes, this makes differentiating similarly ranked players somewhat foolhardy. Gotbuckets attempts to account for this by providing two-year regressions.

Long story short: APM is imperfect, but proves informative as a counter-balance to the box-score based stats, particularly for players making their impact at the defensive end.  For additional insights into APM’s usefulness, check out this handy analysis.

So, there is a brief description of what we’re doing.  As part of a balanced player evaluation process, we look at box-score derived stats and scoreboard derived stats.  Come back frequently for writing that is analytics based, or not, and focused on APM / RAPM, or not.  Ideally in the coming weeks, we continue to fine tune the site and soon provide an RAPM version that improves on season to season consistency and out-of-sample prediction ability.

Hopefully this site forms a useful new component of your basketball fandom. If you like what we’ve started, need a hobby, and are interested in contributing with number-crunching / programming or writing, please contact me at


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2 Comments on “An Intro to Gotbuckets and a Brief Primer on Adjusted Plus / Minus
  1. Pingback: GotBuckets | Testing the Predictive Power of APM, PER, and WS/48

  2. Pingback: Links to the Present, “Daniel LaRusso’s going to fight!” (maybe) edition « Cavs: The Blog

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