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The Basketball Notebook

Monday, December 12, 2005

Basketball Notebook Stats Primer

New to The Basketball Notebook? Read this explanation of the nontraditional numbers and terminology often used on this blog.

In baseball, each team is allowed 27 outs to record as many runs as possible. Basketball's equivalent to the out is the possession. Each team has roughly the same number of possessions as its opponent, so the team that better converts its possessions into points wins the game.

Since the possession is the fundamental unit for analyzing basketball performance, it's important to know exactly what it means. A possession is simply the events that occur from the time one team gains control of the ball until the the time at which the other team takes control. By definition, then, both teams in any given game will have the same number of possessions (give or take one or two, since the team that starts a half with the ball might also end with it).

Example - Connecticut's Marcus Williams steals the ball from Illinois's Dee Brown, then fires a pass to Rashad Anderson in the corner. He doesn't get the shot to go, but Josh Boone corrals the rebound and throws down a two-handed stuff over Brian Randle. UConn's possession begins when Williams steals the ball but does not end until after Boone makes the shot, because that is the point at which Illinois regains control of the ball.

There are several ways for a team's possession to end - it can make a field goal or free throw, it can miss a field goal or free throw that the other team rebounds, or it can just simply turn the ball over. These events are represented by the following formula -

Possessions = FGA - Oreb + 0.475*FTA + TO

Field goal attempts minus offensive rebounds represents all the shots a team either makes or allows its opponent to rebound, and turnovers are self-explanatory. The free throw term can be a little confusing. Not all free throw attempts can end a possession, since some are the first of a pair and some are part of three point plays (where the possession is already counted by the made FG). Reasearch by Ken Pomeroy indicates that about 47.5% of free throws end possessions.

The unit commonly used to measure a team's offensive and defensive performance is points per game. This can be very misleading. What if a slow, walk-it-up team shoots 60% but only scores 60 points because of their deliberate style - would they be a poorer offensive team than one that runs and guns its way to 70 points on 40% shooting? The first team is making better use of its possessions, and its opponent will need a great offense to win, because it only has the same number of possessions with which to score.

To make it easier to compare teams with varying paces, performance is measured as points per possession (PPP). The formula is as simple as it sounds (except that we multiply by 100 to leave ourselves with friendlier numbers) -

(Points / Possessions) x 100

Thus a team's offensive efficiency is expressed as the points it scores per 100 possessions, and its defensive efficiency is the points it allows per 100 possessions. You might think that it would make sense to measure the spread between a team's offensive and defensive efficiencies. One step ahead of you.

Note - I use the terms PPP, offensive efficiency, and offensive rating interchangeably.

Leading basketball analyst Dean Oliver breaks offensive performance into four categories, which he calls his Four Factors - shooting efficiency, turnover rate, offensive rebounding, and free throw conversion. They are listed in the order of their importance.

Shooting Efficiency
Shooting efficiency is measured by a stat called effective shooting percentage (eFG%) or adjusted field goal percentage (adjFG%). Traditional field goal percentage just measures the ratio of made field goals to field goals attempted. This doesn't take into account the added points from three point field goals. To illustrate the point - if J.J. Redick makes 4 out of 10 threes, he scores 12 points. If Shelden Williams makes 5 out of 10 two-point shots, he only scores 10 points, but has a higher FG%. Effective FG% eliminates that bias. The formula -

eFG% = (FG + 0.5 x 3FG) / FGA

Turnover Rate
As you already know, a turnover is a loss of a possession, which lowers offensive efficiency. A team can't score when it gives the ball away before it can shoot. Turnover rate is a simple ratio -

TO% = Turnovers / Possessions

Offensive Rebounding
In the event that a team does miss a shot, it can prolong its possession and give itself an additional chance to score by rebounding its own misses. Please don't perpetuate the myth that team rebounds per game, team offensive rebounds per game, etc, are a worthwhile stat. Use this instead -

Oreb% = Offensive Rebounds / (Offensive Rebounds + Opponent's Defensive Rebounds)

This way, you only measure how many rebounds a team grabs based on what's available. For example, if you use "team offensive rebounds per game," a team that shoots 30% is probably going to grab a lot of offensive rebounds, whether they're a good rebounding team or not. If you use Oreb%, you're looking at a ratio of how many rebounds a team grabbed compared to how many were available.

Free Throw Conversion
The final component of offensive performance has two parts - the ability to get to the free throw line, and the ability to make free throws. However, we want to express this factor with just one number. If you're more concerned with measuring how often a team shoots free throws, use -


If you want to see how well a team shoots at the line in addition to how often they get there, use -


Dean Oliver created a stat he calls "Offensive Rating" to measure an individual player's efficiency at producing points for the offense. The end formula is simple -

Offensive Rating = (Points Produced / Individual Possessions) x 100

However, its components are rather complicated. Points can be produced through field goals, free throws, assists, and offensive rebounds. Individual possessions are the sum of a player's scoring possessions (field goals, free throws, plus partial credit for assists), missed field goals and free throws that the defense rebounds, and turnovers. For details on the calculations, consult Dean's book.

Much like Dean's Four Factors for team offensive production, I like to look at how well a player performs in each area of the offense - shooting, passing, rebounding, and turnovers.

One simple measure of shooting effectiveness is eFG%, which is calculated the same way as described above. I usually prefer to use a variation of John Hollinger's True Shot Percentage (TS%), because it takes free throws into account.

TS% = Points / [ 2 x (FGA + 0.475 x FTA) ]

The fewer the field goal and free throw attempts a player uses to score points, the higher his true shot percentage. Simple enough.

Individual rebound percentage (Reb%) is similar to the team Reb% formula above, except that you must account for playing time. Since all missed shots must be rebounded by the offense or defense (or at least they're credited to one of the teams), we can measure how effective a player is at rebounding by comparing his rebound total to the number of shots missed while he's on the court.

Reb% = Rebounds / [ (Team's rebounds + Opponent's Rebounds) x (Minutes / Team Minutes)]

You mulitply the number of rebounds in the game times the percentage of the game that the player was on the court to arrive at an estimate of how many missed shots were available to a player to rebound. The percentage of those available rebounds that he actually grabs is his rebound percentage.

This is another simple one.

TO% = Turnovers / Individual Possessions

Individual possessions, as noted earlier, are the sum of scoring possessions, missed shots and free throws not rebounded by the player's teammates, and turnovers.

Want More?
I first learned most of this stuff by reading books written by Dean Oliver and John Hollinger, so click on their names if you're interested in further reading.