Offensive and Defensive Efficiency
Offensive Efficiency and Defensive Efficiency (also called Offensive and Defensive Rating) are pretty straightforward. You divide points scored or points allowed by possessions, multiply by 100 (for ease of comprehension) and what you have left is a team's OE or DE for a given game.
This allows you to compare teams on even ground. When you compare teams using points-per-game, you don't take into account the differing paces at which they play. Teams that play at a slower tempo aren't going to score as many raw points as teams that love to run, but that doesn't necessarily mean the slower teams are less effective at the offensive end.
Dean Oliver is the creator of this metric, and you can find more discussion on the topic here.
Dean Oliver calculates possessions this way:
Possessions = FGA - OReb + Turnovers + (0.4 x FTA)
When you're deriving possessions from a box score, you'll want to calculate possessions for both teams and average them, then use that average to calculate the efficiencies for both teams. Let's go through an example. We're going to use 0.475 as the multiplier for free throws, as Ken Pomeroy has found that that number better fits the college game.
Here's the box score from NC State's 75-63 win over Charlotte in the 2005 NCAA Tournament. In the link, we've got all the numbers we need.
NCSU Poss = 59 FGA - 11 ORebs + 16 TOV + (0.475 x 22 FTA)
NCSU Poss = 64 + (10.5)
NCSU Poss = 74.5
UNCC Poss = 58 FGA - 12 ORebs + 20 TOV + (0.475 x 14 FTA)
UNCC Poss = 66 + (6.7)
UNCC Poss = 72.7
Average = (74.5 + 72.7) / 2
Average = 73.6 (round to 74.0)
Thus, each team had approximately 74 possessions in the game. Now, to calculate efficiencies, we simply take points scored/allowed and divide by 74. That number is points scored/allowed per possession, but we'll multiply it by 100 just to make it easier to absorb and compare.
NCSU Off Eff: 75/74 x 100
NCSU Def Eff: 63/74 x 100
NCSU Off Eff: 101.4 (101.4 pts scored per 100 possessions)
NCSU Def Eff: 85.1 (85.1 pts allowed per 100 possessions)
UNCC Off Eff: 63/74 x 100
UNCC Def Eff: 75/74 x 100
UNCC Off Eff: 85.1
UNCC Def Eff: 101.4
If you take a quick visit to Ken Pomeroy's stats page, you can get a feel for what's good and what's bad when it comes to OE and DE. In our example, neither team was very impressive at the offensive end. NC State's offensive efficiency was mediocre at best (you can see from the Pomeroy link that Hawaii ranked 110th in the country with an OE of 101.4 for the season). Charlotte was simply awful (not many teams score fewer than even 95 pts/100 poss).
As always, you should compare these numbers to others in the box score, and you should see things that make sense. For instance, Charlotte shot 39.7% for the game and committed 20 turnovers, so you'd expect that they weren't very efficient with their possessions.
Now that I am more comfortable with these numbers, I much prefer them to PPG and Pts Allowed Per Game. Consider:
Over the course of a season, Team A averages 85 points (85 PPG) on 79 possessions (OE = 107.6).
Over the course of a season, Team B averages 75 points (75 PPG) on 65 possessions (OE = 115.4).
Which has done a better job at the offensive end?