Player Evaluation Metrics
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Term Definition

What Adjusted Plus-Minus (APM) in brief is:
Over a given time period, the basic plus-minus results are getting adjusted to account for both the teammates and the opponents on the court.

It reflects the impact of each player on his team's scoring margin after controlling for the strength of every teammate and every opponent during each minute he's on the court.

Every time segment a player is in a game, adjusted plus-minus tracks:
(1) The other nine players on the floor,
(2) The length of the segment,
(3) The score at the start and at the end of the segment.

How to interpret Adjusted Plus-Minus numbers:
Adjusted +/- ratings indicate how many additional points are contributed to a team’s scoring margin by a given player in comparison to the league-average player whose adjusted +/- value is zero over the span of a typical game. It is assumpted that in a typical game a team has 100 offensive and 100 defensive possessions. For example, if a +6.5 "adjusted +/-" player is on the floor with 4 average teammates, his team will average about 6.5 points better per 100 possessions than 5 average players would.

How are the estimates for Adjusted Plus-Minus calculated?
It's a matter of finding out the estimates of player variables which produces the smallest difference between expected margin and the actual margin in the matchups. This is how a regression model works, basically.

What are the PROs and CONs for Adjusted Plus-Minus?
PROS:
The biggest advantage of adjusted plus/minus ratings are that they are one of the the closest we can come to an unbiased measure of a player's effectiveness.
CONS:
(1) Adjusted plus/minus ratings are have a high variance. The regression tries to find a constant value for a player, but this value can change pretty dramatically with a different role, a different coaching scheme, different teammates, or different match-ups.
(2) There is noise in the data. For some players, especially when only looking at data over just 1 year, there are some strange results, but that is to be expected. An examination of 239 players revealed that only 7% of the variation in a player’s adjusted plus–minus value in 2008-09 was explained by what he did in 2007-08. Although more data does increase the level of statistical significance, it’s still the case that most players even when five years of data is employed are not found by this method to have a statistically significant impact.
(3) Another issue which adjusted plus-minus technique struggles to address is the multicollinearity issue. Coaches prefer to use some player duos/trios frequenly or rarely since all players could not be on the court with every other teammate at the same time.

Adjusted plus/minus technique is first developed by Wayne Winston and Jeff Sagarin in the form of their WINVAL system in 2002. For each player, it starts with the team’s average point differential for each possession when they are on the court. This gives a number showing how effective the player’s team was when they were in the game. The problem with using this to evaluate individual players is that it is biased in favor of players who play alongside great teammates and players who play against weak opponents.
Dan Rosenbaum initially outlined his approach in an influential article that analyzed the 2002-2003 and 2003-2004 seasons as a combined dataset.
David Lewin then published both 2004-2005 and 2005-2006 ratings.
Likewise, Steve Ilardi determined adjusted +/- ratings for the 2006-2007 season using a similar approach. While the previous analyses were conducted at the conclusion of a season, he presented the first in-season computation of adjusted +/-.
From 2007-08 season to 2011-12 season, daily updates of the APM calculations are available on Aaron Barzilai's BasketballValue website.

Approximate Value

#### The metric which is an estimate of a player's value, making no fine distinctions, but, rather, distinguishing easily between very good seasons, average seasons, and poor seasons. There are two ways to calculate approximate value:

Credits=(Points)+(Rebounds)+(Assists)+(Steal)+(Blocks)-(Field Goals Missed)-(Free Throws Missed)-(Turnovers)
AV= (Credits(3/4) )/21

Alternative method shall be assigned according to the following rules shown here

Comments: Before the '73-74 season, steals, blocks, and turnovers weren't kept as official stats. In the credits formula, those stats are just omitted as they tend to cancel each other out to some degree when included anyway

Assist Percentage

#### Assist percentage is an estimated percentage of teammate field goals a player assisted while the player is on the court.

Assist Percentage=100*Assists/(((Minutes Played /(Team Minutes/5)) * Team Field Goals Made) - Field Goals Made)

Box Plus Minus

#### Daniel Myers has created box plus minus (BPM), which is a box score-based metric for evaluating basketball players' quality and contribution to the team from play-by-play regression.BPM takes box score stats from an individual and team level and tries estimate player performance relative to NBA average. Since BPM is a per-100-possession stat where 0.0 is league average, +5 means the player is 5 points better than an average player over 100 possessions (which is about All-NBA level), -2 is replacement level, and -5 is really bad.

Defensive Plus-Minus

#### A metric that measures the difference per 100 possessions in points allowed with a player on the court versus off the court. The accuracy of this measure varies dependent upon how often the player is on the floor and whom the player share it with. In most cases it provides a good indication of a player’s overall defensive value to his team.

Defensive Rating
Author: Dean Oliver

#### A metric which is invented by Dean Oliver. The premise of individual defense is that players force "defensive stops", preventing the other team from scoring.

An individual can do that by forcing a missed shot that then gets rebounded by his team, by getting a defensive rebound, by forcing a turnover, or by fouling a player who misses both foul shots, the second of which is then rebounded by the defense.

Defensive Stop

#### A defensive stop occurs when a player or team defense regains the ball without allowing the opponent a scoring possession.

Ways to get the "defensive stops" done:
1. Forcing a missed shot that then gets rebounded by his team,
2. Getting a defensive rebound,
3. Forcing a turnover,
4. Fouling a player who misses both foul shots, the second of which is then rebounded by the defense.

Diamond Rating
Author: Kevin Broom

#### A metric which is invented by Kevin Broom who devised a simple general formula that works with any per-minute statistics. Fomula subtracts the player's rating per game from his rating per 40 minutes to figure out how much his per game stats undervalue his potential contributions. He then subtracts league average from the player's per-40 minute rating and adds this amount to ensure the player is actually playing well in the minutes he does get.

Diamond Rating Formula=(Per Minute Rating)*40-(Per Minute Rating)*(Minutes Per Game)+[(Per Minute Rating)-(League's Per Minute Rating)]*40

Comments: The fewer minutes a player plays per game, and the better he does in those minutes, the better his Diamond Rating.Diamond Rating makes sense to eliminate players from consideration who are over 27, have more than five years experience, play more than 30 minutes per game or played less than 250 minutes total.

Game Score
Author: John Hollinger

#### A metric which is John Hollinger’s simple and linear version of the Player Efficiency Rating.

Game Score Formula =(Points)+0.4*(Field Goals Made)+0.7*(Offensive Rebounds)+0.3*(Defensive rebounds)+(Steals)+0.7*(Assists)+0.7*(Blocked Shots)- 0.7*(Field Goal Attempts)-0.4*(Free Throws Missed) - 0.4*(Personal Fouls)-(Turnovers)

Comments: Game Score does not make any adjustments like PER does for team pace. It simply adds and subtracts the box score statistics, according to the various weights Hollinger has chosen.

Individual Floor Percentage
Author: Dean Oliver

#### When a player ends his team's possession, it would be a possession charged to him. This is player's total possessions. When a player scored or assisted on a score, a scoring possession would be charged to him.

Individual Floor Percentage Formula=100*(Player's Scoring Possessions)/(Player's Total Possessions)

NBA Efficiency

#### A linear and basic metric which indicates players' efficiency.

NBA Efficiency Formula = (Points)+(Rebounds)+(Steals)+(Assists)+(Blocked Shots)-(Turnovers)-(Missed Shots)

Comments: NBA Efficiency does a nice job of explaining free agent salary. NBA Efficiency tells us about perceptions of performance. It just has some problems if our objective is to measure the impact a player has on wins.

NBA.com Plus-Minus

NBA.com Plus-Minus is a plus/minus tool to find out best player combinations. It looks at the point differential when players are both in and out of the game, to see how the team performs with various combinations.

#### A variety of combinations including the best two player, three player and even five player combinations for each game can be provided with this tool.

Net Plus-Minus
Author: Roland Beech

Net plus-minus, a.k.a. unadjusted plus-minus, is invented by Roland Beech and measure the plus-minus statistics for a given player when the player is in the game relative to the plus-minus statistics when the player is NOT in the game. Net plus-minus combines offensive and defensive plus-minus.

For example, if a team scores 115 points (per 100 possessions) while a given player is on the court and 98 points (per 100 possessions) while he is off the court, his net offensive plus-minus is +17 (115-98=17).
If the team allows 110 points (per 100 possessions) while given player is on the court and 105 points (per 100 possessions) while he is off the court, his net defensive plus-minus is +5 (110-105=+5).
So, net plus-minus for the given player is +17-(+5)=+12

Comments: It’s better to have a positive net offensive plus-minus and a negative net defensive plus-minus.
Find out the top players sorted by 2010-11 net plus-minus ratings.

Net Points
Author: Dean Oliver

#### Net Points is one way to burn indivudual Offensive and Defensive ratings into one metric.

Net Points=(Points Produced)-(Points Allowed)
Where "Points Allowed" can be calculated by using the following formula:
Points Allowed=[(DefensiveRating/100)*(.2*{(MinutesPlayed/(TeamMinutes/5)}*TeamPossession))]

Non-Scoring Player Possessions

#### A player's non-scoring possessions would be his missed field goals, plus free throws that weren't rebounded by his team, plus his turnovers.

Non-Scoring Possessions Formula=(Player's Field Goal Attempts)-Player's Field Goal Made)+0.4*(Free Throw Attempts)+(Player's Turnovers)

Offensive Conversion Rate

#### Offensive Conversion Rate measures the percentage of a player's steals that result in a made basket or free throw attempts within 5 seconds. The reason for taking 5 seconds is to measure a player's transition defense in terms of how frequently his steals lead to offensive production.

Offensive Rating
Author: Dean Oliver

• #### Individual points produced, which represents the credit an individual gets for the points that his/her team generates on the offensive end.

Per Minute Ratings

#### The common notation for per-minute ratings is using per 40 minute stats.

Per minutes ratings are calculated by taking the player's total in any category (points, rebounds, assists, etc.) divided by total minutes played.

Personal Foul Efficiency
Author: D. Nelson, D. Walker

#### Personal Foul Efficiency measures ratio of steals plus blocks to personal fouls. Indicates how efficiently a player forces turnovers, removing the bias of jump-happy or slaptastic players who accumulate deceptive block or steal totals.

Comments: Andris Biedrins’ block total seems comparable to Ben Wallace’s, until you realize that Wallace has more blocks with half the fouls. This statistic can be deceiving, since fouls may increase with defensive effort, but it is still a useful measure for comparative analysis.

Player Efficiency Rating (PER)
Author: John Hollinger

#### The metric that which boils down all of a player's contributions into one number. John Hollinger's formula adds positive stats and subtracts negative ones through a statistical point value system.

Comments: PER largely measures offensive performance. Hollinger freely admits that two of the defensive statistics it incorporates -- blocks and steals can produce a distorted picture of a player's value and that PER is not a reliable measure of a player's defensive acumen.

Player Tracking Plus Minus (PT-PM)
Author: Andrew Johnson

#### Andrew Johnson's Player Tracking Plus Minus (PT-PM) is a player evaluation metric based on a combination of: Real Plus Minus (RPM), Box score data, SportVu data PT-PM is split into offense and defense in terms of estimates of a player's impact on the floor. Offensive PT-PM (OPT-PM), per 100 possessions equals=-4.123 + .594xPoints + -.559xFGA + Passing Efficiencyx21.809 + -.587xTOV per 100 touches + 4.241xContested Rebound Pct + .043xMinutes per Game + -.247xFTA + .138xRebsx3P RateWhere; Passing Efficiency: points created per pass attempts TOV per 100 touches (TOVtouch100): the number of turnovers committed per 100 touches. Contested Rebound Pct: % of rebounds a player gets that are up for grabs with the opposing team Defensive PT-PM (DPT-PM) equals to 1.605+ -5.627xOpponent FG%Rim + .953xSteal100 + .145xOppFGARim -0.159xPF100Where; OpponentFG%Rim is % a players opponent shot at the basket when they were in position to contest the shot. OppFGARim, is the number of times per 100 possessions the player was in position to contest a shot at the rim.

Plus-Minus

The plus-minus, a.k.a. +/-, simply keeps track of the net changes in score when a given player is either on or off the court.

NBA.com has been publishing plus-minus values in official box scores since 2007-2008 season.

#### Since the invention of basic plus minus, the plus-minus technique has been developed in order to get more accurate results. There have been some stat heads who have developed different types of plus minus metrics. Here's a collection: Net Plus-Minus (NPM) Adjusted Plus-Minus (APM) Statistical Plus-Minus (SPM) Regularized Adjusted Plus-Minus (RAPM) Real Plus-Minus (RPM) Box Plus-Minus (BPM) Player Tracking Plus-Minus (PT-PM)

Points Created
Author: Bob Bellotti

#### Points created is a metric that evaluates overall player performance.It comprises all current primary and secondary statistical categories: points, rebounds, assists, steals, blocked shots, missed shots (both field goals and free throws), turnovers, and personal fouls.

Points Created= PTS + AST * (2-VBP) + (REB + STL + BLK) * VBP -(FGMiss + FTMiss + TOV) * VBP – 0.5 * VBP * PF
VBP = the value of ball possession is league’s average points per 100 possessions.

#### It measures overall performance rather than a single skill (such as shooting) or set of skills (such as shooting, rebounding, and shot-blocking). Therefore, the result is a clear composite of a team or player's total performance.

Comments: Points Created is valuable in many ways. It is comprehensive, and can be used to evaluate players and teams on any level of basketball, in any league where statistics are kept. You can use it to study one game, many games, a season, and a career.

Points Produced
Author: Dean Oliver

Points Produced is a measure of player's offensive contribution. "Points produced" metric has been considered more important than the "points scored".

#### A player produces points through made shots, assists, and offensive rebounds. The number of points produced by the various methods depends on the actual number of points scored and the importance of the player's contribution.

Comments: The sum of all teammates' individual points produced should be very close to the number of points actually scored by the team.

Author: David Berri

#### The "Win Score" metric that takes player's "primary position played" into account.

PAWS48 =PAWS per 48 minutes=[WS48 – Average WS48 at primary position played]

WS48 =Win Score per 48 minutes

Real Plus Minus (RPM)
Author: Jeremias Engelmann

A metric provided by former Phoenix Suns consultants Steve Ilardi and Jeremias Engelmann, based on Engelmann's version (xRAPM) of Regularized Adjusted Plus-Minus

#### Real Plus Minus is the player's average impact in terms of "net point differential" per 100 offensive and defensive possessions. RPM can be broken down to offensive and defensive metrics: Offensive Real Plus Minus: (ORPM) Player's average impact on his team's offensive performance, by the points scored per 100 offensive possessions Defensive Real Plus Minus: (DRPM: Player's average impact on his team's defensive performance, by the points allowed per 100 offensive possessions.

Access the RPM stats at ESPN.

Rebound Percentage

#### Total rebound percentage is estimated percentage of available rebounds grabbed by the player while the player is on the court.

Total Rebound Percentage=100*(Total Rebounds*(Team Minutes Played/5))/(Minutes Played*(Team Total Rebounds + Opponent Team's Total Rebounds))

Author: Joe Sill

In "Regularized Adjusted Plus-Minus" (RAPM), the goal is to provide more accurate results by employing a special technique called "ridge regression" (a.k.a. regularization). It significantly reduces standard errors in Adjusted Plus-Minus (APM).

#### Conventional adjusted plus-minus is shown to do a poor job of predicting the outcome of future games, particularly when fit on less than one season of data. Adding regularization greatly improves accuracy, and some player ratings change dramatically. The enhancement with the RAPM is a Bayesian technique in which the data is combined with a priori beliefs regarding reasonable ranges for the parameters in order to produce more accurate models. That is what ridge regression (a.k.a. regularization) does.

Comments: RAPM is about twice as accurate as an APM using standard regression and using 3 years of data, where the weighting of past years of data and the reference player minutes cutoff has also been carefully optimized.

Roland Rating

#### The Roland Rating is a basic, quick look at the player that 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. It represents how successful a player is with a given team.

The on court +/- number represents the team's net points with the player on the floor per 48 minutes, while the off court number is the team's net with the player off the floor per 48 minutes. The Roland Rating is the difference between the two, with a positive number indicating the team has played better with the player than without.

Scoring Player Possessions
Author: Dean Oliver

#### A player's scoring possessions would be his field goals that weren't assisted on, plus a certain percentage of his field goals that were assisted on, plus a certain percentage of his assists, plus his free throws made.

where;

Q=5*(Player Minutes)*(Team Assist Total)/(Team Total Minutes)-(Player Assists)
R=5*(Player Minutes)*(Team Field Goals Made)/(Team Minutes)-(Player Assists)

Seasons Left
Author: Dean Oliver

#### The estimate of how many seasons the player has left to play.

Seasons Left Formula=27-0.75*(Age of The Player)

Simple Projection System
Author: Tom Tango

#### It's been developed to account for aging when calculating player efficiency. SPS uses 3 years of data, with the most recent data weighted heavier. It regresses towards the mean. So the model has an age factor and the numbers are adjusted to account for age.

An example of how the SPS is calculated for Dwight Howard's rebounding in 2008-09 season by using data of previous three seasons.

Statistical Plus-Minus
Author: Dan Rosenbaum

Statistical Plus/Minus (SPM) is an estimate of the player's contribution to the team's point differential per 100 possessions, using his box score stats as inputs. In another words, SPM can be considered as a way of estimating adjusted plus-minus from box score stats. Statistical plus minus puts a weight to basic box score stats like, points, steals, blocks etc., in a effort to solve the lowest mean residuals (average errors).

The goal with the SPM technique is adding a more stable component to player's basic stats as a counterbalance to the basic plus-minus. As a well known fact, basic plus-minus can be wildly inconsistent for individual players from season to season or under different coaches in a season.

Dan Rosenbaum has outlined different ways of addressing adjusted plus-minus' accuracy issues, by employing additional analyses based on box score stata.

#### In a lot of cases the statistical plus/minus ratings might be a more accurate predictor of future defensive performance. To characterize past defensive performance, adjusted plus-minus does a good job. A combination of the adjusted and statistical plus-minus will do a better job when we want to find out which players are going to be good or bad defenders in the future.

Comments: Statistical Plus/Minus is an "organic" way of deriving a linear-weights-style box score based formula from actual, real-life data.

Steal Percentage

#### Steal Percentage is the percentage of estimated opponent possessions that end with a steal by the player while the player is on the court.

Steal Percentage=100*(Steals*(Team Minuted Played/5))/(Minuted Played*Opponent's Possessions)

TENDEX
Author: Dave Heeren

#### Dave Heeren's player evaluation metric which is generally considered the first player rating system with linear weights.

The Tendex Formula=[(Points)+(Rebounds)+(Assists)+(Steals)+(Blocks)- (Missed Field Goal Attempts)-0.5*(Missed Free Throws)-(Turnovers)-(Fouls)]/(Player's Minutes)

Total Player Possessions
Author: Dean Oliver

#### The metric that represents a player's total possessions in the game. In other words,a player's total possessions is the total number of how many times he ends his team's possession.

Player's Total Possessions Formula=(Player's Scoring Possessions)+(Player's Non-Scoring Possessions)=(Player Field Goal Attempts)-(Player Missed Shots)*(Team Offensive Rebounding Percentage)+0.37*(Player Assists)-0.37*(Field Goals Made)*Q/R+(Player Turnovers)+0.4*(Player Free Throw Attempts)

Where;

Q=5*(Player Minutes)*(Team Assist Total)/(Team Total Minutes)-(Player Assists)
R=5*(Player Minutes)*(Team Field Goals Made)/(Team Minutes)-(Player Assists)

Touches
Author: Bob Chaikin

Touches estimate the number of times a player touched the ball in an attacking position on the floor. The theory behind the formula is that once a player gets the ball, he can only do one of four things (aside from dribbling, of course): pass, shoot, draw a foul, or commit a turnover.

Touches=Field Goal Attempts + Turnovers + (Free Throw Attempts / (Team's Free Throw Attempts/Opponents Personal Fouls)) + (Assists/0.17)

#### The estimate using a player's age and his approximate value to determine how much value a player has left in his career.

Trade Value Formula=[(Approximate Value- 27-0.75*Age )^2( 27-0.75*Age +1)*Approximate Value]/190+(Approximate Value)*2/13

#### The mathematical relationship between usage rate and efficiency.

Trade off between usage and efficiency explains the player's gain of offensive rating (points per 100 possessions) for drop of each percent of usage.

True Shooting Percentage

#### The metric that factors a player's performance at the free-throw line and considers their efficiency on all types of shots.

True Shooting Percentage Formula=(Player's Total Points)/[(2*(Player's Field Goal Attempts+ 0.44*Player's Free Throw Attempts)]

Usage Percentage

#### Usage percentage is an estimate of the percentage of team plays used by a player while he was on the floor.

Usage Percentage Formula=100*[(Team Minutes)/(5*(Player Minutes))]*[(Field Goal Attempts)+0.44*(Free Throw Attempts)+(Turnovers)/[(Team Field Goal Attempts)+0.44*(Team Free Throw Attempts)+Team Turnovers)]

By balancing usage rates and the varying offensive ratings of the five players on the court, a team can achieve optimal offensive output for the personnel.

Comments: The stats show that, for all players, as the player uses more possessions, his efficiency decreases. What defines a superstar, in Dean Oliver's statistical analysis, is that he can shoulder a larger proportion of a team's possessions with only a relatively small drop in efficiency. Meanwhile, the opposite is also true: players perform more efficiently when they are asked to use fewer of their team's possessions. As a result, the greater burden on the superstar means that supporting players maintain low usage rates, allowing them to operate closer to their peak efficiency.

Versatility Index
Author: John Hollinger

Calculate versatility index and many other metrics with accessing to our NBA player historical data sets

#### The Versatility Index, which was designed by John Hollinger, is a metric that measures a player's ability to produce in more than one statistic. The metric uses points, assists, and rebounds. The average player will score around a five on the index, while top players score above 10. and more information can be found in this article.

Versatility Index Formula=[(PPG)*(RPG)*APG)]^(0.333)

WINVAL
Author: J.Sagarin, W.Winston

#### A program which measures team chemisty and analyzes a player's impact on his team's ability to produce points. WINVAL is the labor of Jeff Sagarin and Wayne Winston, who are both graduates of MIT. WINVAL's most unique characteristic is that it measures individual and team performance after every lineup change in every game. WINVAL's ratings also factor in who each individual is playing with and against at all times. The WINVAL scouting reports also include data on referees.

Win Score
Author: David Berri

#### The metric that indicates the relative value of a player's point, rebound, steal, turnover, and field goal attempt.

Win Score Formula=(Points)+(Rebounds)+(Steals)+(½Assists)+(½Blocked Shots)-(Field Goal Attempts)-(Turnovers)-½(Free Throw Attempts)-½Personal Fouls

Comments: Win Score is sufficient to give you a quick snapshot of a player?s performance. And it is especially useful if you wish to know if a player is playing better or worse than he did before.

Win Share
Author: Justin Kubatko

#### A Win Share is worth one-third of a team win. Win Shares are assigned to players based on their offense, defense, and playing time. If a team wins 60 games, there are 180 Win Shares to distribute among the players. This is always true; if a team wins n games, then there are 3n Win Shares to allocate to the players.

Wins Above Replacement Player (WARP)
Author: Kevin Pelton

#### Using replacement level shows the value of players who can play heavy minutes and avoid injury while continuing to perform above replacement level. Using wins gives a measure of value that is easy to understand and constant over time. Lastly, by eschewing the traditional linear weights method so common in basketball analysis, WARP does a better job of incorporating defensive value. Learn more about WARP calculation.

Comments: Like all rating systems based on box-score data, WARP cannot account for contributions that are not tracked in the box score, most notably on defense. It does no better than linear weights methods at evaluating players like Bruce Bowen. Also, it requires a number of assumptions - the value of assists, the trade-off between usage and efficiency, and replacement level. But, this rating system is very flexible. Players can be rated on a per-minute basis (using the theoretical "winning percentage" of the team with four average players), in terms of their offense and defense and in terms of their overall value.

Wins Produced
Author: David Berri