Putting it all together
So, I've now determined valuations for points, rebounds, assists, blocks, steals, and turnovers. Defense I'm going to leave aside for now, until and unless I figure out a good way to measure it. (However, I think for most players defensive differences are not that big of a factor. Defense is a learned skill rather than an innate one. Certainly, some players are better at it than others, but the overall FG% allowed by a team is first and foremost determined by the team defense that is taught and implemented by the coaches. Individual effects are, I think, secondary. The example of Dan Majerele is an example. For most of his career, he was a gunner on offense who never paid much attention to defense. Then, we he went to Miami and had Riley coaching him, he suddenly became an excellent defender.)
The only remaining factor is fouls, which will also be a small effect. Their biggest impact is in limiting the number of minutes a guy can play, and that will show up in his other averages. A secondary effect is getting the other team into the bonus more, but my gut feeling is that, on average, this will be a small effect. Similarly, drawing lots of fouls will show up primarilly in the number of FTA you get, and hence in the points scored numbers. Getting more FTA for the team via the bonus will be a second order effect and so can be ignored for now.
The only other wrinkle is normalization factors. As mentioned earlier, if your team gets more possessions, you're naturally going to score more, get more steals, etc. Similarly, if the opponents miss more shots, you will get more defensive rebounds. If your team misses more shots, you'll get more offensive rebounds. So, for all these stats, we want to normalize numbers to the average team. We'll normalize steals and turnovers to the number of possessions the team averages. We'll normalize blocks to the number of FGA the opponents had. Points will be normalized to the (number of shots taken + FGA/1.9), the number of offensive attempts. Similarly, for the calculation of the adjusted point value, we'll normalize each player's FGA and FTA to the league averages. Assists will be normalized to the number of made FG's the team has.
So, let's take a look at some players in the NBA this year. The usual debate is who the MVP should be. The main candidates are Shaq, Kobe, Tracy McGradee, Kevin Garnett, Tim Duncan, Jason Kidd, and Allen Iverson. Let's see how they come out. I'm just going to quote the bottom line numbers, with some comments.
McGrady: (30.7 PPG, 6.7 RPG, 5 Assists): 43.9
McGrady grades out as the best all around player in the NBA. He does everything well, and scores in bunches for a team that actually averages fewer possessions than is the norm.
Duncan: (23.7 PPG, 12.9 RPG, 2.9 BPG) : 40.4
Duncan squeeks into second place here. Despite his relatively low scoring average, he scores very efficiently which makes up ground. His excellent rebound and block numbers finish closing the gap, while his very respectable 4 assists per game also keeps him among the elite.
Kobe: (29.6, 7.1 RPG, 6.5 Assists): 40.3
Kobe's all around game adds up here. His rebounding numbers are excellent and he gets plenty of assists, too, to go along with his scoring. Basically the entire difference between he and McGrady is due to Tracy's higher scoring. And while he gets more assists and slightly more rebounds than McGrady, he also averages 1.2 more turnovers per game.
Shaq (25.9, 10.6 RPG, 2.3 Blk): 40.2
Despite shooting 10% better than most of the other candidates, Shaq's efficiency-adjusted scoring does not increase much more than the other players under consideration, because of his poor FT percentage. That keeps him out of the top despite, despite excellent offensive rebounding and block numbers.
Those four are clearly the class of the group, with a significant drop off to the next bunch.
Garnett (22.2, 12.8 RPG, 5.7 assists): 36.2
The difference between Garnett and the players above him is entirely attributed to his lower scoring. If he averaged 25 points per game, he would also be in the low 40's. He suffers in comparison to Duncan because he isn't as efficient a scorer and because Duncan blocks more shots.
Nowitzki (23.5, 10 RPG): 35.3
I was surprised Dirk was this high up. Although his rebounding numbers are good, of those 10 rebounds only 1 per game is an offensive rebound, which means those rebounds aren't as valuable as they look. But he picks up points here and there, with 1.5 steals per game, 1.2 blocks, and obviously his scoring. He also only turns it over 1.7 times per game.
Chris Webber (23 ppg, 10.5 RPG, 5.5 APG) 35.3
Webber isn't higher because his offensive efficienct is terrible for an elite player. He barely averages any more points per offensive attempt than the league average (even Iverson beats the league average by a fair amount), largely because he only gets to the line 6 times per game.The top tier players get there 8-10 times per game.
Iverson (26.8, 4.8 Assists, 2.53 steals) 31.2
Iverson, despite only shooting 40% from the field, is still more efficient than the league average, in large part because he gets to the line 8+ times per game and shoots well from there. His stelas help his bottom line score as well, making a case for him to be among the elite despite not averaging a lot of assists or rebounds. But his relatively low offensive efficiency compared to the others on the list, combined with his not piling up big numbers elsewhere, keeps him well below the very best in the league.
Kidd (19.6, 8.4 assists, 5.8 RPG) 28.7
I was surprised Kidd was so far down the list, but his lack of scoring killed him, compounded by a low shooting percentage. And although his other numbers are good, 8 assists and 6 rebounds don't stack up against the rest of the list. His 3.5 turnovers per game also hurt him.