Stat Central: Rethinking Basketball Statistics — Intro

Over the next few months I will be diving into a new way to look at NBA basketball statistics. My weekly articles will mostly exist as parts to an extended essay that intends to push basketball statistics in a new direction — with the creation of new advanced statistics and slight tweaks to existing ones — with ultimate goal of creating a genuinely effective, all encompassing player rating system, as well as providing a different perspective on team statistics. In general, I am not trying to reinvent the wheel here, but more so hope to take the tools the statistics community has developed so far and continue the evolution of basketball’s advanced metrics.

A New Definition of Possession

The main source of this evolution is a new definition of possession, what that definition implies, and what new statistics can be developed because of this new definition. Possession as it exists now, is simply a trip up the basketball court. boasts ‘true’ possession numbers while Basketball-Reference uses an in depth formula to calculate an estimate of possessions in a game (Pace). Every basketball game has roughly the same number of possessions — the only differing variable being which team gets the last possession of every quarter and overtime period — as any particular possession does not end until the ball actually switches possession between teams.

For this Rethinking of Basketball Statistics (RBS) a possession is not only ended by a switching of possession, but can also be ended by any shot attempt — either a field goal attempt or shot that draws a foul. So formally, the definition of possession will go as follows:

A possession is any segment of play that begins with a change of possession — either via a turnover, defensive rebound, loose ball foul that switches possession, offensive foul, or made shot — or begins with an offensive rebound and ends with another change of possession, a field goal attempt, or foul that leads to free throws.

The main difference from the typical definition of possession, then, is that an offensive rebound starts a new possession instead of continuing the previous one. So, if Deron Williams takes a shot, that possession for the Brooklyn Nets is finished, and a new possession begins if Reggie Evans grabs an offensive rebound; where as with the traditional definition, that first possession would continue even after Williams missed and Evans grabbed the board. With this definition of possession, calculating possessions becomes quite easy. You can calculate a team’s number of ‘RBS possessions’ using this formula:


Where Two Shot Fouls Drawn (2SFD) is the number of fouls drawn that lead to a a player taking two free throws and Three Shot Fouls Drawn (3SFD) is the number of  fouls drawn that lead to a player taking three free throws (and one’s are accounted for in field goal attempts).

What’s The Difference?

Fortunately, already keeps statistics using this definition, or at least one that is very similar. In addition to providing those handy per 100 possession stats, they also provide per 100 plays statistics. By the looks of it,’s definition of a play is very similar to the definition of a RBS possession. So, using their per play statistics should be good source to explain the difference between the traditional view of possession and the this new definition.

That difference is per play numbers show how efficient a team is offensively or defensively on a single play while per possession numbers can be boosted or reduced by offensive rebounds. We can use this year’s Miami Heat and Los Angeles Clippers as an example. The Miami Heat are currently scoring 111.8 points per 100 possessions this season — ranked first in the NBA — and the Los Angeles Clippers are right behind them with 109.4 points per 100 possessions. Per 100 plays both teams still lead the NBA in scoring but the margin between number one and number two grows, with Miami scoring 104.7 points and the Clippers scoring 97.7 points per 100 plays. So even though Miami only scores a couple of more point per 100 possessions than the Clippers, they score seven more points per 100 plays.

This is because Miami runs significantly less plays, mostly because they do not grab as many offensive rebounds. Miami averages 95.79 possessions per game (via Pace statistic) and runs 102.01 plays per game.1 This makes sense, since Miami averages 6.4 offensive rebounds per game. The Clippers grab 12 offensive rebounds per game and as a result run 112.59 plays per game, about 12 more plays over their 100.41 possessions per game. So, the Clippers run an extra 12.13 plays per 100 possessions while the Miami Heat only run an extra 6.49 plays per 100 possession.2

Analytically speaking these number indicate a couple of things. 1) Miami is much more efficient scoring the ball on any individual play than the Clippers (and any NBA team for that matter) and 2) the Clippers can match Miami offensively still because they grab much more offensive rebounds.

Why Change It?

Based on scoring per play numbers alone, though, that is the most that can really be drawn from the numbers. That is, the only information the points per play numbers are revealing is which teams are more efficient in executing on particular plays instead of possessions that can last multiple plays via offensive rebounds. That information is valuable — for instance it could reveal how Memphis and Indiana’s half court offense may be even more below par because so much of their offense comes via offensive rebounds — and as a complement to per possession numbers they can help us better understand how offensive rebounds are affecting the game. But just on those laurels alone there is not necessarily enough there to justify scrapping the old definition of possession in place of this new one.

The reason for using this new definition instead comes from the other potentials of a system based on this definition of possession. Specifically, I believe there are two big advantages that can come from using this definition of possession.

First, I believe this new definition can open the door up for much better player evaluation statistics. It sounds weird to say, but as basketball metrics have advanced we have not developed many great ways to evaluate a players effectiveness on the court. PER is the best player evaluation statistic we have to this point, but John Hollinger himself has confessed the shortcomings of the metric. In general it seems like our current advanced statistics do a great job of evaluating team efficiency, but falls short when it comes evaluating an individuals players effectiveness. A new category of statistics based on this new idea of possession may also fall short — instead in terms of team evaluation — but it also has the potential to evaluate players much more effectively.

Even looking at a particular statistic like scoring, we can find major shortcomings in our current evaluating tools. Field Goal Percentage, Effective Field Goal Percentage, and True Shooting percentage all attempt to calculate scoring efficiency — and the latter two do a relatively good job — but all tend to undervalue the fact that three pointers are worth more than 2s and the way each statistic accounts for free throws is more or less arbitrary. You cannot use a points per (traditional) possession type metric in this case because a player can easily go one for three on a possession (a poor percentage) and still be rewarded with as many as four points for that possession. With a new definition of possession, though, we may be able to develop a very specific and simple way to calculate how efficient a player is scoring per play — and we will definitely be getting into this concept going further. That kind of thinking can expand to many statistical categories, and the per play format may prove to be a better way to develop advanced statistics for players.

Breaking Down The Game Into Three Parts

The biggest advantage of this new definition, though, is that it allows us to break up the game into three easily identifiable parts. Those three parts are offense — the ability score the basketball on a particular play; defense — the ability to stop your opponent on a particular play; and possession — the ability to gain extra scoring opportunities for your team. Offense and defense are simplified into your literal ability to score (as well as facilitate scoring) and stop opponents from scoring on any particular play — again, this is not a great method for calculating team efficiency but could be a great way to calculate player effectiveness. And while the first two parts evaluate the ability to take advantage of scoring opportunities, the possession aspect of the game monitors the ability to gain extra scoring opportunities over the opponent. This is an extremely important part of the game that often gets marginalized for the other two parts. However, it was the crux of Miami’s pivot to smaller lineups and was also the reason Indiana was able to push Miami to seven games last year despite inferior offense. With this new definition of possession, we will be forced to take that aspect of the game into account.

The Layout

As we go on we will be breaking down these three aspects of the game into even smaller categories. Specifically we will be breaking offense down into two categories: scoring and facilitating; defense into three categories: individual defense, help defense, and team defense; and possession into two categories: defensive rebounding and no shot possession (that term will be explained down the line). Within each category there will be one to as many as five or six statistics that we will use to evaluate a player or team’s effectiveness or efficiency in that category and the end goal will be to combine all of these statistics to come up with ratings for each category and then an ultimate player or team rating. Here is a quick outline of all the categories:

Offense — The ability to score on a particular possession

  • Scoring — the ability to score on a particular possession
  • Facilitating Scoring — the ability to facilitate (assist) a scoring play

Defense — The ability to defend against a score on a particular possession

  • Individual Defense — an individual player’s ability to stop his match up from scoring on a particular possession
  • Help Defense — an individual player’s ability to stop a player that is not you particular match up from scoring
  • Team Defense — a team’s ability to stop their opponent from scoring on a particular possession.

Possession — The ability to win extra possession and scoring opportunity

  • Defensive Rebounds — the ability to win possession by securing the basketball after an opponents miss
  • No Shot Possession — the ability to win a possession that takes away the opponents scoring opportunity

We’ll begin to delve in next week. It should be fun.


1. For anybody that might do some extra research here: does not actually provide a plays per game statistic. Instead I calculated the Heat and Clippers plays per game by taking their points per game and dividing it by their points per play (which you can obviously get by taking points per 100 plays and dividing by 100. So the formula is: (PTS/GM)/(PTS/PLAY) which math nerds may notice becomes (PTS/GM)*(PLAY/PTS). And since the points would cancel each other out we would be left with PLAY/GM. Math is fun.

2. The same type of magic used in the first footnote is used to calculate extra plays per 100 possessions here. In general whenever you want to calculate a team statistic (let’s call it ‘x’) per possession all you have is take the per game average of statistic x and divide it by the average number of possession per game for that team (which is the Pace statistic). So the formula is: (x/GM)/(POSS/GM) or (x/GM)/(PACE). The same type of math from endnote one plays out and we would be left with (x/POSS). See ya next week.

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