Been a while since the last of this stats series, but back at it. Up next is a super fundamental concept that I'm sure many of you are familiar with already- possessions. I'll toss it up here for two reasons: (a) completeness' sake and (b) to wrap up all the different per-possession statistics before we move on to more all-encompassing stats

The concept of a possession was alluded to in both Stats 101 and Stats 102. This post will probably be like 5 sentences long, but if you understand this, you understand a ton of "advanced" stats by default.

In Stats 102, the concept of a "possession" was defined- a possession ends or begins when the ball switches teams. So a possession can only end in a defensive rebound, a turnover, or made free throw. A missed shot does not inherently end a possession, because the other team still needs to get the defensive rebound.

Put mathematically: Possessions = FGA - Off. Rebounds + Turnovers + 0.4 * FTA.

The overall goal is that we stop referring to "per game" statistics, and replace them with "per possession" statistics.

There are many different ways to explain why this replacement is important. Here's the way I understand it best: all games are not created equal. One game you might have 100 opportunities to score (ie, a 100 possession game), and another game, you might have 60 opportunities to score. Per game stats treat these two games exactly the same. By definition, possessions are an "equal" stat. They may not all last the same amount of time (ie, the Suns' 7 seconds or less offense vs. the Spurs half-court), but teams choose how long they want their possessions to last. A team's coach may decide to rifle through his given possessions while his opponent may try to slow down his possessions in the same game. At the end, they will have played the same amount of possessions, even though they played them in their respective desired styles.

It's really straightforward, but it's at the basis of most rate stats. Turnover rate is turnovers per 100 possessions. Assist rate is assists per 100 possessions. Offensive Efficiency is simply points scored per 100 possessions. Defensive Efficiency is points allowed per 100 possessions. And so on.

At this point, it'd probably be a good idea to offer a roadmap of where this series is headed. Most of the so-called small advanced stats have been covered. We've gone over eFG%, offensive and defensive rebounding %, game pace, and the various different rate stats. On the horizon is a discussion of statistics which take all these small stats and combine them into a single big one. Whether it's PER, Wins Produced, Win Shares, WARP, Adjusted +/-, etc., each of the all-in-one stats is essentially an attempt to uncover what relationship the smaller stats have with one another- a macroscopic quantization of various microscopic phenomena.

Once the bigger stats are discussed in some depth, there should be some interviews with statisticians, a few stories on where defensive metrics are and where they're headed, and a lot more original stats work similar to Stats 103.

The next story will be about Usage Rate (USG%); USG% is not only one of the primary bridges between the small stats and the big stats, but will also be at the center of many more articles in the future, dealing with aspects like team construction, styles of play, and teamwork.