I think Mr Berri's done us all a great favor by crunching the appropriate marginal value of wins out of each statistical category the NBA compiles. As others (Dean) have pointed out, Berri's linear method is better than TENDEX because it converts offensive and defensive stats into wins instead of some dimensionless and meaningless production number. Points for and points surrendered determine wins. Baal James uses Win Shares, so should we.
I'm no statistician, but I'm sure it's hardly a settled matter in his profession if one can use quasi-R-squared tests to decide which model (each using equations estimated via differing functional forms) offers the greatest explanatory power. But who cares? His marginal values work well enough for teams, Berri's Table 11 is good enough proof for me. So let's figure out what can be done to better convert them to individuals.
Berri adjusts his per minute production numbers for team tempo, team defense, position and another one to add in the league average of minutes per win (0.0052).
I think Berri's position adjustment tries to do what all you guys want, but doesn't go far enough. It's the nature of basketball that the taller, stronger players (Centers, Power Forwards) operate closer to the basket and are more likely to get more rebounds than the guards. Berri says why over-reward the big tall guys for getting more rebounds than guards? That's why the coach has big guys close to the basket and his guards getting back on defense or leaking out for the outlet pass. Similarly, the nature of basketball is that SOMEBODY has to advance the ball up the court---usually that somebody is a guard, with the occasional exception of a Pippen or Pressey. Berri says why punish the advancer? Advancing and handling the ball is a dangerous job, a guard has more opportunities to turn it over, whereas Rodman runs down the court and leaves the guards to their fate and doesn't blemish his own turnover ratio. Because he sees guards, forwards and centers as complementary rather than substitutes, Berri thereby tries to factor ROLE into the model. The position adjustment, while a good start, might be improved upon.
I think (rightly or wrongly) that the most valuable skill in basketball is the ability to get, and make, a shot even if a player is guarded closely by one guy, or guarded by two or three guys. This ability CUTS ACROSS POSITIONS. A coach sees that ability in a player and puts the ball in that players hand's much more often than a Rodman, Outlaw or Jayson Williams. SOMEBODY has to score, SOMEBODY has to take the chance of missing a shot. Therefore, Karl Malone or Michael Jordan should not not be penalized compared to Rodman because his coach relies on him to be the focal point of the offense. They are penalized in Berri's model because they miss more shots in the aggregate than DRodman and have a correspondingly greater negative marginal value from those missed shots.
What adjustments might Mr. Berri make to the model so it won't over-penalize the offensive players? One suggestion I have is that he could adjust for how much a player handles the ball. For example, in 1998 Rodman had 360 FGA's, 111 FTA's, 1201 rebs, 230 asts, 47 steals and 147 TO's. He touched the ball in a statistically measured way roughly 2040 times. Karl Malone had 1472 FGA's, 825 FTA's, 834 rebs, 316 asts, 96 steals, 247 TO's. That's roughly 3377 touches. The rate of turnover per touch is about the same for Malone and Rodman, yet because Malone had 100 more aggregated TO's he is overly penalized in Mr Berri's model. Perhaps a rate of TO's to total touches should be used to evaluate individual players instead of just the gross amount of TO's; or maybe Berri could add an average production number for groups of players with certain ranges of touches per minute to the individual players Win totals.
Another way might be to take an average production number for players that shoot 0-5 times a game, for those that shoot 6-10 times a game, and so on---and add that to a players win total.
This was just a thought experiment.