Differential Production Defined

Basic Concept

Two popular team statistics in the NBA today are Offensive Rating and Defensive Rating, defined as points scored and allowed per 100 possessions.  For the past 2+ years, NBA teams on the whole have averaged somewhere between 103 and 105 for these statistics, which is actually very close to 1 point per possession (PPP).

Differential Production (DP) attempts to identify individual contributions to a team's Offensive and Defensive Ratings.  The term "differential" refers to the fact that each possession is scored relative to 1 PPP:  a 3-point possession is +2, a 2-point possession is +1, 1 1-point possession is 0, and a 0-point possession is -1.  The interesting part is breaking down a team's DP for a given possession into individual contributions.  To do this, the scorer needs to watch every possession in a game and assign individual credit or blame.  How this is done is detailed below.  One by-product of determining the DP statistic is that one gets a sense for the holy grail of NBA statistics (not directly available through boxscores or even play-by-play recaps): individual defense.

Scoring: Offense

On offense, DP points are assigned as follows:

  • A made 2-point basket is +1 and might be divided between the shooter and passer depending on how responsible the pass was for the shot.  If the shooter did most of the work, he gets the full +1 or +0.75 (with +0.25 to the passer).  A good pass resulting in an open shot is usually +0.5 for both the shooter and passer.  In rare cases where a great pass leads to a lay-up or dunk, it's +0.25 for the shooter and +0.75 for the passer. [Theoretically, the divisions can be finer than a quarter of a point, but my smallest divisions are a quarter for relative simplicity.
  • A made 3-point basket is +2 and can be divided between shooter and passer as above.  Most often, I assign +1.5 to the shooter and +0.5 to the passer.  If a pass results in a wide-open 3-point attempt, I will assign a +1 for the shooter and +1 for the passer.  I never assign more than +1 for the passer on a made 3-pointer, because even open 3-pointers have some degree of difficulty.
  •  The positive points for made field goals go under the categories "Positive Shots" and "Assists" in the final Offensive DP (ODP) breakdown
  • A missed field goal attempt resulting in (an opponent) defensive rebound is -1 for the shooter.  A missed field goal attempt resulting in an offensive rebound is -0.5 for the shooter and +0.5 for the offensive rebounder.  A commonly asked question is why missed shots count differently depending on who gets the rebound.  The answer to this requires understanding both the offensive and defensive side of the DP statistic and thus will be given below after both have been explained.  The negative points from missed field goals go under the category "Negative Shots" in the final ODP.
  • Free throws are handled differently than field goals, so that the net ODP works out correctly for all cases.  When a player goes to the line, he immediately gets credit for the points he would obtain if he made all the free throws (+2 for three free throws, +1 for two free throws, +1 for an and-one free throw or a technical foul).  He then gets a -1 for every missed free throw before the last, with a miss on the last free throw being treated in the same way as a missed field goal (-1 if the defense rebounds, -0.5 if there is an offensive rebound.
  • Example #1:  a player draws a 2-shot foul, misses the first makes the second.  He gets +1 under Positive Shots for getting the foul shots, then -1 under Negative Shots for the missed free throw.  The net is 0 (as it should be for a 1-point possession).
  • Example #2:  a player draws a 2-shot foul, makes the first, and misses the second, but the free throw results in an offensive rebound.  The foul shooter gets +1 under Positive Shots for getting the foul shots, then -0.5 under Negative Shots for the missed free throw.  The offensive rebounder gets +0.5 for the rebound.  The possession proceeds as any normal possession (except that one point has already been scored).
  • Example #3:  a player makes a basket and draws a foul.  Besides the +1 for the made basket, the player also gets +1 under Positive Shots for the free throw attempt.  If he misses the free throw, it's a -1 under Negative Shots.
  • Example #4:  a player shoots a technical foul shot.  The player gets a +1 (under Positive Shots) for the free throw attempt and a -1 (under Negative Shots) if he misses the free throw.
  • As noted above, offensive rebounds are +0.5 for the offensive rebounder.
  • Turnovers are -1 for the perpetrator.  In some cases, the negative points for turnovers can be divided if responsibility is shared.  A common example is when someone receives a good pass but fumbles it out of bounds (almost always, the passer is officially charged the turnover, but in truth responsibility is shared for the turnover).  If a team has the ball at the end of a quarter but doesn't get off a shot, "Team" is given -1 under Turnovers.
  • The five categories for Offensive Differential Production (ODP) are thus: Positive Shots, Negative Shots, Offensive Rebounds, Assists, and Turnovers.


Scoring: Defense:

  • A made basket is either a -1 (for a 2-pointer) or a -2 (for a 3-pointer), with blame assigned according to who is responsible.  Made baskets are filed under the "Scored On" category.  Sometimes (as in an isolation), the responsible defender is clear, but other times it is not.  The follow type of plays require subjective judgment on the part of the scorekeeper:
      •  On a pick and roll, sometimes the other defender doesn't show hard enough or a switch occurs.  In this case, both defenders share the blame, with the relative blame assigned according to the relative responsibility for the breakdown.
      • On a switch, if the "new" defender after the switch has a chance at defending, he usually bears responsibility for what happens after the switch.  But if a defender simply loses his man and another defender switches at the last moment, most of the responsibility goes to the original defender.
      • If an offensive turnover causes a breakaway, the player who caused the turnover bears all of the responsibility for the basket.  If there is a defender back on a fastbreak after a turnover, some blame can be assigned to the defender depending on how realistic a shot he has at stopping the basket.
      • On a double team, if the player left open cuts and scores a basket, responsibility is shared between the double-teaming player and the defender who should have switched to cover the open shooter.
  • A missed field goal attempt is +0.5 for the defender and gets filed under the "Stops" category.  The positive points can be divided in half if two defenders are involved in causing the miss.  Sometimes, no one is near the shooter who misses (i.e., the shot is wide open), in which case "Team" gets credit for the +0.5 under "Stops.
  • A defensive rebound is +0.5.  The positive points can be divided in half if two defenders are involved in the rebounds, for example if one player taps it to another.  Team rebounds (e.g., if the ball goes out of bounds) are credited to "Team" unless a defender is specifically responsible for the team rebound (e.g., a defender intentionally bounces it off an offensive player's leg), in which case the defender still gets the +0.5 under Defensive Rebounds.  A player who draws a loose ball foul in rebounding action also gets credit for +0.5 under Defensive Rebounds.
  • An offensive rebound allowed is -0.5 for the player responsible, most often the defender of the offensive rebounder but sometimes the nearest player.
  • Free throws are handled in a way that mirrors what happens on offense.  When an opposing player goes to the line, the defender responsible for the free throws immediately gets blame (under "Score On") for the points that would be allowed if the opposing player makes all his free throws (-1 for 2 free throws, -2 for 3 free throws, -1 for an and-one free throw or technical foul).  The blame can be divided as with made field goals, depending on who is responsible for giving up the foul shots.  On any missed foul shots, "Team" gets credited +0.5 for a "Stop" (because no defender caused the miss).  On missed foul shots before the last, "Team" gets credited +0.5 for a Defensive Rebound.  A miss on the last foul shot is +0.5 for the defensive rebounder or -0.5 for the offensive rebound allowed.
  • A forced turnover is +1 for the defender who caused it.  Sometimes credit can be shared, e.g., if one player tips the ball to another player.  Unforced turnovers are +1 for "Team."
  • If the other team has the ball at the end of the quarter but doesn't get a shot off, "Team" is credited +1 under "Stops."
  •  The five categories for Defensive Differential Production (DDP) are: Scored On, Stops, Defensive Rebounds, Offensive Rebounds Allowed, and Turnovers Forced.

DP Interpretation

The following relationships hold once all DP categories are tallied:

  • DP = ODP + DDP.  Total DP is the sum of Offensive DP and Defensive DP.
  • DP = (Point Spread) + (Possession Differential).  For example, if a team wins by 10 and had 2 fewer possessions than the other team, the net DP should be 8.
  • (Team ODP+Team Possessions)*100/(Team Possessions) = Team Offensive Rating
  • (Team DDP+Opponent Possessions)*100/(Opponent Possessions) = Team Defensive Rating
  • Some of the DP categories (like rebounds, assists, and turnovers) will be close to what is in the boxscore.  Keep in mind, though, that standard boxscores do not include team statistics such as team rebounds and team turnovers (e.g., 24 sec. violations).  In DP, everything is accounted for in some way.
There are some potentially confusing aspects in interpreting DP.  Here are some of them, along with some further explanations:
  • On offense, credit for made baskets is often divided between shooter and passer, especially if the pass led to a good shot.  However, blame for a missed basket goes entirely to the shooter (one cannot blame the passer for a missed shot).  Thus, it should be kept in mind that it is easier to accumulate (negative) points under "Negative Shots" than under "Positive Shots."
  • Similarly on defense, credit under "Stops" for a missed field goal followed by a defensive rebound is divided between the defender and the rebounder (usually half-and-half).  However, blame under "Scored On" for a made field goal goes entirely to the defender.  Thus, it is harder to accumulate points under "Stops" than (negative) points under "Score On."  A positive (Stops - Scored On) total for a given game shows exceptional defense; even a net of zero for (Stops - Score On) shows good defense.
  • On offense, a missed field goal is counted differently depending on whether there is an offensive rebound.  This is to ensure symmetry of Offensive DP with Defensive DP.  On defense, there are two components to every successful possession [that includes a shot]: the defensive stop (by the player defending the shooter) and the defensive rebound.  Each of these is credited with +0.5.  On offense, for symmetry, a -0.5 is given to the shooter for a missed shot (since his defender receives a +0.5 for the stop) and another -0.5 is given to the shooter if there is a defensive rebound (since the defensive rebounder receives a +0.5).  If there is an offensive rebound, the offensive rebounder is given the +0.5, the net is zero (as it should be), and the possession proceeds from there.
  • Free throws are accounted differently than field goals for Positive and Negative Shots.  This is because each free throw (worth 1 point) has an effect on the total score and needs to be accounted for (make or miss) in some way.  The system described above (for both offense and defense) ensures that the math works out.  But as a result, a missed free throw counts as -1 under Negative Shots, the same as a missed field goal.  To make the math work out, the shooter of the foul shots is given "theoretical credit" once he earns the free throw attempts and then greater blame for any missed foul shots.  One by-product of this scoring is that a player who shoots well from the field but poorly from the line will have a higher than expected total under Negative Shots.  The important thing is that the team (Positive Shots - Negative Shots + Assists) should reflect its shooting fairly well.
  • Finally, some statisticians have pointed out that defensive stops are harder to accomplish than defensive rebounds.  This would argue for weighting them differently on a successful defensive possession (say, +0.7 for the stop, +0.3 for the defensive rebound).  Currently, DP divides the credit equally in most cases (+0.5/+0.5), and the reason again is symmetry.  If, say, the +0.7/+0.3 division is used, then on offense it would make sense that the shooter is penalized -0.7 for a missed shot and an offensive rebounder would obtain +0.7 for an offensive rebound.  This would result in giving offensive rebounds more than twice the value of defensive rebounds.  Now some might argue that offensive rebounds are truly more valuable than defensive rebounds, but the rebuttal is that a defensive rebound prevents an offensive rebound and is thus equally important.  The latter is viewpoint behind current DP scoring.