As I mentioned in my first post, I am no expert in advanced basketball analysis. It appears, however, that much of the analysis is based off one important concept: estimating possessions.
Estimating possessions is important because it is a way to put teams on equal footing, so to speak. Let's just take a random example with numbers for illustration only. One offense gets about 67 possessions a game and they score 63 points a game. Another team gets 77 possessions a game and scores 72 points per game. Now, if you're looking at the basic stats, it looks like the second offense (the one that scores 72 a game) is clearly better. However, once you realize that they receive more possessions, i.e., more opportunities to score per game, you see that they really aren't the better offense. The first team scored .94 points per possession, while the second one scores .935 points per possession. In the end, they're of course very similar, but the first team is probably a little better offensively (at least they're more efficient). It's the style of the second team (more fast paced) that allows it to score more point per game.
On Ken Pomeroy's site, this is the definition he gives for estimating possessions for teams: field goal attempts - off. rebounds + turnovers + .475*free throw attempts. Doing this with Cincinnati in 2007 -- they had about 1,977 possessions in 30 games, or about 66 a game. That's right around the the ncaa average of 67. (For some reason, he gets 65 possessions per game for Cincy, while I get 66. I believe it may have something to do with adjusting for overtime games, but I'm not sure. Anyway, it's not a huge deal, but I may look into it in the future.) That put Cincy at about 98 points per 100 possessions, which ranks them 236 out of 336 division I teams. However, after Pomeroy adjusts that number (Im guessing for competition, i.e., playing in the big east), they end up ranking 138th in offensive efficiency. That's another story, though.
And, of course, it doesn't stop with points. You can look at blocks, rebounds, turnovers, etc. per possession and adjust for a team's style of play. Is Air Force really great at not turning the ball over year in and year out (I don't even know if they are -- I'm assuming their TO numbers are relatively low), or is it just because they get 10-15 less possessions per game than the average team? Once you look past the regular numbers and adjust for a team's context, you can get a better feel for how they play the game. A lot of the analysis on this blog will be based on per possession stats.