One point I'll start with is that people have been doing this for years, even before regression and camera-tracking were common tools within the NBA. If someone wants to argue that Bill Russell is the greatest of all-time, he says that Bill has 11 championships; if someone argues for Michael Jordan, it's six titles and the highest points per game in NBA history; and if someone wants to argue that it's Wilt, then his hallowed season of 50 points per game will soon be presented, along with a bevy of other unbelievable stats. Those are all stats themselves, and it's the same form of an argument as someone saying LeBron is the greatest since Jordan because of his career PER number.
But there's a context missing for these stats. There's no real analysis or even thought. Russell won with a league fundamentally different than our own, still in its infancy with teams not understanding basics about defense and with an entire league in the early 60's with as many teams, or less, as two of our modern divisions have. Jordan has the highest points per game average, yes, but the game is obviously more than scoring, even if some statisticians assume it is. (In compiling a list of the best athletes ever, a British statistician used such enlightening stats as points per game for basketball and batting average for baseball.) Wilt played in an entirely different league where there were more opportunities to score and rebound, allowing for eye-dropping stats, and he played huge minutes -- focusing on his accomplishments, however, there are definitely instances where he played for numbers and not wins, and even when he was hooked into a team concept it was still an era where, again, one could argue the competition was lacking.
I'll note that the above paragraph is an example of arguments, and not exactly what I believe; but it's important so showcase how people lead from numbers into substantial claims. With the internet, there a millions of arguments strewn about cyberspace, and many are picked about because they lack an important structure: context.
For an example, I'll take one of my favorite advanced stats, true-shooting percentage, and compare two players. It's common for people to claim someone is a better scorer simply with whoever has the greater TS%, but there's a lot of subtlety lost by blindly posting stats.
Chris Paul has a TS% of 60.4 right now, while Chris Anderson, midseason acquisition for the Heat, has one of 62.3 (via hoopdata on Sunday April 14th.)
True-shooting percentage is like field-goal percentage but adjusted for three-pointers and free throws. The formula is simply Points / (2*( field goal attempts + 0.44*free throw attempts) ) where the 2 is to convert points into field-goal percentage (since FG% is not points per shot) and the 0.44 coefficient to convert free throws into field-goal attempts. Since a free throw is worth half a normal field goal, you need to multiply by 0.5, and then you reduce it down to 0.44 to account for and-1's, technical free throws, etc. A TS% of 60 is stellar, and around 54 to 53 is generally the league average. Out of players with at least 30 games and 15 minutes a night, Anderson is 9th in the league and Paul is 22nd.
Since Anderson has a higher TS%, one may be pressed to say he's a more efficient scorer/shooter, or even a better scorer/shooter. If a person is against TS% as a stat, he or she will probably use the example of Anderson and Paul to say the stat is broken. However, that argument is simplistic, uninteresting and fails to reveal the most fascinating story behind the numbers, which reveals the intrigue and complexity of the game.
The first point is obvious. Chris Anderson is a low volume shooter, while Paul is a larger part of his offense. Anderson has a usage% of 13.55 and Paul 22.43. (Usage is number of possessions used per 100 possessions, and this includes FGA, FTA and TOs.) The league average is always near 20 because there are five guys on the court (100 divided by 5), and it's always lower than 20 because some possessions are lost; right now the league average is 18.8. It's harder to maintain high efficiency shooting when you shoot more, and the difference between these two is dramatic. You're also adding more value when you shoot more often at a slightly lower efficiency. For an extreme example, you can't compare Michael Jordan's efficiency with Biedrins in 2012, who developed some sort of allergy to shooting and only shot the ball when all the planets were in alignment.
At the next level of analysis, you have the location of shots. The top of the TS% list is littered with guys who only shoot when they're next to the rim, and if you don't see how it's easier to be more efficient that way try feeding yourself by flinging spoonfuls of food across the room into your mouth. In the modern NBA, you generally can only have one player near the rim, sometimes two, so it's unfair to compare the efficiency of guys who camp out under the basket versus ones on the perimeter. If you put everyone near the rim you will be ridiculously easy to defend; and those guys on the wings allow for post players to set up without being swarmed. This is something that Wages of Wins and Professor Berri miss: those guys who put up freakishly high field-goal percentages are lucky to be in the paint.
Out of Chris Anderson's 78 shots, 81% have come at the rim, and he has just 8 jump shots total. Chris Paul, however, takes over 8 jumpers past 16 feet per 40 minutes (Anderson's at 0.8 per 40 minutes.) Even though midrange jumpers are the death knell of efficient possessions, at some points you have no other options, and Paul's so reliable at 51% from 16 to 23 feet that it's actually not a bad option. Paul, basically, can kill you anywhere on the floor, spacing the floor for Griffin underneath, while Anderson lives on cheap baskets under the rim while occasionally chucking an awkward jumper.
Moving on from shot location, there's shot creation. As I've said, Chris Anderson gets cheap buckets camped out under the rim, while Paul is a focal point. Anderson has little ability to create his own shot, relying on others to do it for him. A possible exception is crashing the boards for put-backs, but that also is an action dependent on others. Anderson has 83% of his field goals assisted, while Paul is at a paltry 22%. Obviously, Paul is assisted less because he can't pass for himself and he's the point guard, but he doesn't get the advantage of coming off picks for open shots or roaming to the basket for an easy lay-up off a pass. The league average right now is near 58% on assisted shots, while some of the top non-point guard scorers range from 30 percent (Kobe and Harden) to 40 percent (Carmelo and LeBron) and up to 50% for guys who use a lot of screens (Durant.) Top scorers with high assist percentages are usually big men with jumpers from Brook Lopez (60 percent) to Bosh and Horford (near 75%.)
You can also combine the categories of shot volume, shot creation and assisted shots. Anderson is assisted on 83% of his at the rim attempts, while Paul is amazingly low at 17%. Paul also is assisted on only 45% of his three-pointers -- the league average is 82% because of how much more difficult off the dribble three-pointers are, and with the notable exception of Stephen Curry percentages usually plummet when they're not assisted.
The last note is that turnovers are often ignored even a loss of possession can kill a team. Chris Paul is an all-time great in this regard: his turnover rate (turnovers per possessions where a possession is defined by a FGA, FTA or a turnover) is at a minuscule 8.9. Even though he's a point guard second in the league in assists per game, his turnover rate is below the league average of 11.3. Chris Anderson, however, is near 11.9, which isn't terrible but this is someone who rarely holds onto the ball for long. This is another reality check in why you can't just pack the paint on offense and expect good results, or rely on players like Anderson for "offense": if you give them the ball too much, your turnovers will spike. A midrange jumper is better than Omer Asik losing the ball within one second of catching it.
Chris Paul is an efficient scorer who creates other opportunities for others at a high rate while rarely turning the ball over and defenses have to account for him everywhere on the court due to his superior jump shot, not to mention the instances where he has to bail his team on offense and create a shot before the 24 second block expires -- and Anderson is assisted on four out of every five shots, most of which occur within three feet of the basket. So, yes, Chris Anderson is a better shooter than Chris Paul because his TS% is larger ... only when you ignore shot volume, shot creation, assisted shots and turnovers.