For many who watch NBA basketball and partake in fantasy leagues, player box score statistics are the most important key to seeing who should be chosen and who has the best chance of taking your (real or fantasy) team to the top.

Given the overwhelming popularity of basketball over the decades, sports analysts have tried to optimize the use of player statistics to extrapolate and predict how a team is affected by each player. That is the plus-minus in NBA basketball.

In simple terms, basketball’s box plus-minus (BPM) method determines how many points a player would make on the court versus how many points the team would have off the court. Coaches and commentators use this statistic to predict possible outcomes of a game if a player is hurt, sick, or ejected from the game.

First introduced in the 2007-2008 season, the plus-minus statistic has become a powerful tool to see how likely a team is to win.

The plus-minus statistic is calculated using the player’s total box score statistics per 100 possessions, the team’s adjusted efficiency per 100 possessions, and the player’s position. The player position is used to see how frequently they are on the court during the game and what role they play in scoring.

With the predicted impact of the player on the court, a sports analyst would be able to measure how many points a player would contribute and allow in a game.

For example, throughout his career with the Cleveland Cavaliers, Lebron James was a vital player and component in how far the Cavaliers would go during their season. As a top scorer, known statistically as a pure contributor, and a relatively consistent defensive player, James consistently had a high BPM, with a lifetime BPM of 8.86.

This high BPM means that, theoretically, without Lebron James on the court, a team would have to put up an average of additional 8.86 points to make up for the loss.

However, Lebron’s extremely high BPM is a statistical outlier similar to Michael Jordan’s statistics. Every player starts at 0.0 for their BPM at the start of each season and game. This BPM is the league average.

Having just a 2.0 BPM would make a player a good starter, and a 4.0 would put the player in all-star consideration. Oppositely, a 0.0 BPM is just average, whereas anything under a negative 2.0 is an end-of-bench player.

## Why Calculate the Plus-Minus in Basketball?

Calculating the box plus-minus (BPM) marked the beginning of a new era of basketball analytics. From the beginning of the NBA league, only minimal statistics were tracked during basketball games. From 1955 to 1971, only basic statistics like points put up (Pts), rebounds (Reb), Assists (Ast), and total field goals and free throws were made in a game (FG/FT).

In 1974, the framework of the BPM was laid, with NBA statisticians also tracking the number of offensive rebounds (OREB), the number of steals (Stls) and blocks (Blks), and the team turnover rate (Tm TOV).

These numbers determined a player’s plus-minus score by seeing how their offensive statistics aided or hurt a team. From there, individual statistics were taken. By 1978, the modern box score was implemented.

These statistics became vital in predicting the winners of championships, which had been a staple of the NBA since its beginning season. The BPM looked at how likely a team was to win based on the team’s assets.

Yet, the box plus-minus score only tracked season-value levels. So, players like Kareem Abdul-Jabar and Bob McAdoo dominated the NBA in the 1970s but did not have personal game-by-game BPM measures. They only had seasonal ones.

Individual statistics would come about in 1983 when complete game logs were kept during each game. These numbers allowed statisticians to calculate the contributions made by each player to a team. Therefore, by the 1980s and 1990s, players like Magic Johnson, Shaquille O’Neal, and the legendary Michael Jordan had record-breaking BPMs and consistently took their teams to the top.

Today, players’ statistics flash on the screen at an NBA game. These statistics appear before, during, and after each game. In the current era of “Data Ball,” which began in 1997, players are not only tracked by their statistics but also by individual plays and optical tracking.

These additions take the old plus-minus scale to the next level by not only looking at career and game stats but also the individual’s athleticism and skill which can be compared to other players in record time.

## Mathematical Mishaps of the Plus-Minus Statistic

However, the box plus-minus has always had issues. Historically speaking, the first plus-minus scale was taken from baseball, which had been used to rate players given their many contributions during a game.

However, baseball has many discrete variables, like catches, hits, and outs, which do not change value during a game. If New York Yankee Alex Rodriguez hits three home runs, each person that makes it home is one point, no matter what.

Oppositely, basketball is extremely fluid with the variables constantly changing. If Steph Curry successfully makes three baskets in a row for Golden State, this can range from three to nine points, depending on the type of shot and the location he shoots from.

This fluidity has created a problem in NBA statistics since many coefficients and variables have to be added to a player’s statistics. But the equation used has to be consistent across the game.

The initial player evaluation metrics that predated the plus-minus box score had to combat these issues by incorporating more complex mathematical terms to balance the scores. For example, nonlinear terms like outliers would throw off the data, so all data added into the system was converted to a linear term.

The regression of the data, or the statistical explanation of how the inputs define the outputs, was widened to have a wider data spread and account for outliers.

Also, the inclusion of each player’s Minutes per Game (MPG) was initially used to determine how important a player was to a team. However, many things factor into a player’s MPG, and some are already represented in the box score.

While using each player’s MPG helped with season-level accuracy for players that excel at defense rather than offense, eliminating the statistic aided the system’s accuracy and data interpretability.

## A Generally Biased System?

Aside from equational issues, one of the biggest complaints of the system is that it takes a long time for the statistics to accurately represent the player. For example, in his first season with Seattle, Kevin Durant put up 20.3 points on average, 4.4 rebounds, and 2.4 assists, leading to him receiving the Rookie of the Year award. However, his average BPM for the total season was -651 or around -7.9.

Largely contributing defensively and having such a low average for the number of minutes he played, Kevin Durant’s plus-minus score makes him look like a terrible player. However, in his worst scoring season in 2014-15, Kevin Durant scored just 686 points in 82 games or 8.3 points on average.

Yet, his average BPM for that season was around +168 or +2.04. This average is because once he was an established player, his defensive contributions made him a more valuable player.

The plus-minus in NBA basketball is highly variable and often does not accurately represent the box score statistics. This lack of representation is because the statistics depend on more offensive statistics. Like Kevin Durant, rookies who mainly contribute defensively have extremely negative BPM numbers. These negative BPM numbers are due to the minutes they are on the court, defensive players have few possessions and fewer baskets.

Eliminating the MPG makes time played weigh less in the equation but does not remove it from the equation.

During overtime, these BPM numbers stabilize, but when averaged with the rest of a season, these numbers still weigh down a player’s average contributions. It also cannot take a team’s strength or their opponent’s skill into account. To combat the conflict, a new statistic was implemented to improve the accuracy of the BPM.

Borrowed from baseball, Value Over Replacement Player (VORP) uses a player’s statistical contributions and places it in a gameplay situation. This process is done by lowering the player average from 0.0 to -2.0 and multiplying the calculated BPM by the new average.

This adjusted BPM is then multiplied by the percentage of possessions and the percentage of games played out of 82 games in a season. The total is the player’s overall value to a team.

However, the VORP still relies on the box plus-minus score, which means it cannot completely replace the old system. For this reason, it is important to look at the complete picture when looking at NBA statistics. Even though the plus-minus in NBA basketball seems like a simple statistic for a player’s contributions, there is no simple way to see how much a player contributes to their team.