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Plus/Minus for Basketball

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PLUS/MINUS FOR BASKETBALL

In America the mathematics of sport is much more than a tool to determine the winner and the loser of an athletic contest. Many spectators regard statistics as an indispensable aid to their enjoyment. They cheer for a team, but also for the individual members of a team. Knowing the score is not enough for these fans, who crave statistics, which can help them to understand and appreciate the performance of the individual athletes in whom they are interested.

Most basketball fans, like the majority of fans of any sport, prefer to watch offense. Counting the points scored by each player continues to be the foremost postgame preoccupation of fans who like basketball statistics. For a player, scoring points is the fastest and surest route to stardom. Nobody noticed tiny Rio Grande College until freshman Clarence "Bevo" Francis burned Hillsdale College for 113 points in a 1954 contest. Time has not diminished the public's fascination with the 1962 NBA game in which Wilt Chamberlain scored an even 100 points. Chamberlain's scoring spree, impressive even by his standards, made headlines then, and now it has assumed legendary status.

The desire of basketball fans to evaluate individual performance more thoroughly has inspired the current practice of tallying rebounds, assists, blocked shots, steals, turnovers, personal fouls, and minutes played as well as points. When the insights that could be derived from simple addition did not entirely satisfy, the calculation of shooting percentage brought division to the quest to measure player productivity. Knowledge of individual minutes played now enables fans to answer other questions by calculating simple ratios. For instance, which Los Angeles Laker was a greater force on the boards in the fourth game of the 1980 NBA playoffs: Kareem Abdul-Jabbar, who pulled down 11 rebounds in 39 minutes, or Mark Landsberger, who earned his 10 rebounds in 17 minutes?

It is likely that statistics which add up will always be most important to basketball fans, and of these, points scored still reigns supreme. A newspaper account of a basketball game invariably begins with a sentence like "Kenny Pine scored 18 points to lead the Dordt College Defenders to a 71-70 win over the visiting Gorillas of Pittsburg State." But quantifying achievement over the course of a season may mislead. The player who scores the most points does not always lead his or her team to the most victories (ask Wilt Chamberlain). Similarly, the team that scores the most points does not always win the most games. The 1980 San Antonio Spurs led the NBA with 9788 points scored in 82 games. But their points allowed, 9819, also led the league. The offense-minded Spurs were outscored for the season and won only 41 of their games.

As in a game, so also in a season: points scored is less important than point differential, the numerical gap between the points a team scores and the points it allows its opponents to score. Point differential usually correlates with won-lost percentage, but not necessarily. A blowout or two can skew such assessments. If the Dordt College Defenders lose their opening game 90-45, then win each of their next 25 games by 1 point, their season point differential would be minus-20 despite their 25-1 won-lost record. Point differential, then, must yield in its turn to the ultimate basketball yardstick, the team won-lost record.

Jamaal Magloire did not score a point in Kentucky's game at Florida on January 29, 1997. He fouled out after playing just 19 minutes. When the Gator faithful taunted Magloire by chanting "No points," the Kentucky center silenced them by pointing to the scoreboard, which displayed a double-digit Wildcat lead. However undistinguished Magloire's individual box score line, his afternoon must ultimately be regarded as successful because he was on the floor while Kentucky was outscoring Florida. He must have been doing something right.

Magloire appeared to understand the principle that in playing a team sport, a player's primary goal is to help his or her team outscore its opponent. Individual offensive and/or defensive accomplishments are only important insofar as they contribute to the winning of the game.

Plus/minus statistics may help illuminate a player's value to the team effort in basketball, where, unlike baseball and football, offensive and defensive responsibilities are fluid. Hockey, which resembles basketball in this regard, already records plus/minus statistics.

An individual player's "plus" or "minus" is the difference in points between the teams while that player is on the floor. To tally plus/minus, it is necessary only to know who the starters are, when a substitution is made, which players are involved, and the score at the time of the substitution.

Plus/minus is the simplest and most basic of all statistical attempts to place individual achievement in the context of team success. Plus/minus assumes that every player on the floor is contributing to the team's success or failure, as it is measured by the ultimate arbiter, the scoreboard. It further assumes that each player is contributing equally. This is of course an oversimplification.

Imagine that all five of Dordt College's starters played the entire 20 minutes of the first half of their home game against Pittsburg State. Dordt leads at the half, 37-31, so each of the five Dordt players has earned a plus-6 (the difference in points between Dordt and Pittsburg State) for their 20 minutes of work. All the plus-6s are equal, but a spectator may feel certain that Kenny Pine is playing better (or worse) than his teammates and is doing more (or less) to help the team. This subjective assessment may be a true one. By the logic of plus/minus, however, its truth or falsity is less important than the recognition that each player is one member of a five-person team. Whether Pine stole the ball 10 times or turned it over 10 times in the 20 minutes he played, his team is still 6 points better than its opponent, and the spectator would probably prefer to see a Dordt College victory than any of the individual heroics of which Kenny Pine might be capable.

Plus/minus will please the fan who believes that a basketball player whose team outscores its opponent has succeeded, irrespective of his individual numbers. Plus/minus yields insights into single games or segments of games, into series of games or entire seasons. Plus/minus is not a magic formula, nor is it a substitute for basketball's traditional bulk statistics. It simply offers an interesting and revealing supplement to the information in a newspaper box score.

Plus/minus is a way to gauge whether a player's efforts are paying off in team performance, and to what degree. Almost every basketball player would rather own a championship ring than a scoring trophy. The team's accomplishments ultimately loom larger than those of its individual players.

Plus/minus is not a rating system. If during the 35 minutes Kenny Pine played for Dordt College against Pittsburg State his team was outscored by 7 points, that is as much a matter of fact as his personal total of 18 points scored. Plus/minus reveals the degree to which the Dordt College team prospers with Kenny Pine on the floor, or on the bench. But if the meaning of plus/minus is clear, its significance can be variously interpreted.

Plus/minus can illuminate the often dramatic effect on a game, for good or ill, of a substitution. Should Pine relinquish his starting job to his backup, Benny Klein, who played 5 minutes in which Dordt outscored Pittsburg State by 8 points? Such a conclusion is tempting, but plus/minus is no more or less prescriptive than traditional statistics. A player who shines in a limited role might not have the stamina to play effectively for longer periods. Moreover, who plays when is often a matter of game tactics. The coach spots a mismatch, decides how best to exploit it, and instructs his or her players accordingly. But not every player is equally adept in every defensive or offensive deployment. Kenny Pine might score at will against certain types of zone defense, but turn the ball over when guarded closely in man-to-man coverage.

Unfortunately, there is no existing statistical system (plus/minus included) which can calibrate the quality of the opposition during the minutes a player is in the game. For example, a player who enters the game only in the last minutes of a blowout may have an impressive plus/minus rate, but the accomplishment could be less significant than it appears if the opposing coach is also employing substitutes.

Neither plus/minus nor the newspaper box score will reveal which Pittsburg State player(s) guarded Kenny Pine (or vice versa), when, or for how long. Authors Robert Bellotti, Dave Heeren, and Martin Manley (to name but three) offer sophisticated analysis of basketball statistics, but even they have not been able to surmount the barrier of situational measurement.

Statistics are fun and provide food for thought and argument, but it is not accurate to describe basketball (or any sport) as a "game of statistics." None of them tell the whole story. The basketball coach, it is probably safe to say, pays far less attention to statistics than fans do.

To state the obvious: a good team is a team with a good coach and good players. A good coach assigns roles to his or her players which are based on a wise understanding of their individual capabilities. A good player is smart enough to understand his role, disciplined enough to accept it, and talented enough to execute it. He or she is willing and able to do whatever will help the team win, as scorer, playmaker, and defender.

Plus/minus supports this concept of team play. It gives equal weight to efforts at both ends of the floor by measuring player success (plus) or failure (minus), and the degree of success or failure, by the difference in points between the two competing teams.

Incidentally, you can’t do this scoring at home. Plus/minus can only be recorded by watching a game in person. Media accounts (newspaper, television, radio) do not supply substitutions, times, and scores.

June 1997

Addendum: During the last decade the plus-minus concept has crept its way into the consciousness of professional NBA watchers like Steve Hirdt and Harvey Pollack. As yet, however, the NBA has not officially embraced plus-minus.

Somebody seems to be keeping these stats, but I never see them published. Here's a quote from an ESPN.com article by Marc Stein, dated July 12, 2003, entitled "What's next in free agency for Spurs, Mavs?"

“The Spurs still have to re-sign Stephen Jackson, and never far from their thoughts looms the Manu Ginobili situation. Burning all their cap room this offseason means that Ginobili will essentially be the league's next Gilbert Arenas next season. Cap restrictions on second-round picks completing the second year on their contracts will leave San Antonio unable to match offers higher than the mid-level exception to keep Ginobili, arguably the Spurs' second most valuable player as a rookie, judging by plus-minus statistics in the playoffs.”

Mike Berheide comments:

“Plus-minus is one of the best pure measures of "MVP" status, as it is improved by everything that is good in the game. Got the hot hand? It goes up. Putting the glove on a guy? It goes up. Finding the open man? It goes up. Carrying on like this for an extended period of time? It goes up. Et cetera.

“Of course, like all stats, it has its limitations, and people have to know how to use them. I've heard some people say they would start the top five plus-minus guys on the team, which is idiotic. I also find it more valuable as a season summary and as a measure of "who works against this particular team" than as a guide to who's doing well in the middle of a season, as it seems to me to be dramatically affected by playing conditions (read: who's the opponent?). And, like Donald Terman and Steve Hirdt, I'd also like to see it reported as a [per 40- or per-48 minute] ratio -- but I would still look at the total, too, as that is a measure of long-term contribution (just like we look at batting average AND total hits).”

A tip of the hat to Gorm Munksgaard and Enrico Edagiata.

July 2007

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