THE THEORY BEHIND IT ALL
My goal was to create a measurement that summarizes a player's contributions to his team. The way I decided to go about this was to use SportVu data to look at how many points a player created above what an average player would have created. One of the main dilemmas I faced was whether to use the league average (shooting percentage, rebound rate, whatever) or to use the average of all the player's rates. I decided to use the average of all the player's rates, as using the league average would value more players who took more shots, rebounding more, etc. True to my hypothesis, I found the average of the player's rates was a slight bit lower in every single case than the league average. I used this rather than the league average because I am trying to find how many points a player created above what an average NBA player would have created.
One important thing to keep in mind is that these will depend heavily on usage and on position. For example, if Ty Lawson has a higher points added above average on passes on LeBron, does that mean he's a better passer? No, it just means he has had more chances, and therefor added more to his team by passing that LeBron has. Also, if Brook Lopez has added less points by rebounding than Eric Bledsoe, does that mean that Bledsoe is a better rebounder than the seven foot tall Lopez? No, but since Lopez goes against centers for his rebounds, and Bledsoe goes against shorter point guards, it is easier for Bledsoe to grab a rebound. That is why is useful to compare individual categories across position only, but ideally the total sum will be comparable across all players.
Now onto how I calculated the various categories:
SHOOTING
The SportVu data on NBA.com has information for four (really six) different types of shots: drives, close shots, pull up shots, and catch and shoot shots. For both pull up and catch and shoot shots there is separate data for both two pointers and three pointers. For pull up and catch and shoot shots I use the player's shots attempted and shots made information to calculate their shooting averages for each type of shot. Then, using the average of the players shooting averages, I calculated how many shots each player made above what an average player would have made, and from there I got their points above average. For drives and close shots I used roughly the same technique except I found the average points per shot, instead of shooting percentage, to account for free throws drawn which occur much often on drives and close shots than on the other two types of shots. I have already written two posts on this technique (one on drives, one on other shots).
Ways to improve: Ideally I would like to look at each shot considering how open or how guarded the shooter was. Obviously the expected shooting percentages would change as the player got more or less open, and it would interesting to see which players are having to take the most contested shots.
REBOUNDING
Ideally, I would like to work only with contested rebounds above average, since it doesn't add any value to one's team to grab uncontested rebounds, since anyone could have grabbed it. Unfortunately, NBA.com does not provide us with contested rebound percentage, so I was forced to use regular rebound percentage. An idea I am toying with though is to use the same technique as found here, and get a rough a approximation of contested rebound chances by subtracting uncontested rebounds from total rebound chances, the idea being that a player grabs all the uncontested rebounding chances he has. This, of course, is not true however, as two or more players on the same team could be in the vicinity of an 'uncontested rebound', but only one can grab it. For the most part though the two techniques yield fairly similar results, with a few noticeable differences though. To turn rebounds grabbed above average into a point value, I multiplied the rebounds above average by 1, since an extra rebound is essentially an extra possession, and the average points per possetion is around one.
EDIT: as of 12/29 I will be using the rough approximation of contested rebounds above average.
Ways to improve: Use a contested rebound rate which only involved opportunities with an opponent in the vicinity.
PASSING
Again, the ideal stats are not up on NBA.com. Ideally, I would like to work with total frontcourt passes and calculate the percent of which are turned into assist opportunities. I chose to work with assist opportunities and not assists so that passers surrounded by bad shooters are not hurt. I don't want to use total passes because the results are then greatly skewed by big men who grab rebounds and just hand it off to a point guard - it doesn't seem fair to count that as pass that they could have gotten an assist on since they weren't in a position to do so. So in its place I am debating between using total passes minus defensive rebounds, or total frontcourt touches minus shots. For both cases, the results are basically the same. After calculating assist opportunities above average, we now need to turn it into points added above average. Since roughly half of all assist opportunities become assists, and an assist is worth around .67 points, I multiplied each assist opportunity by .33 to find a player's points above average on assists.
Ways to improve: Use front court passes plus outlet passes that lead to a fast break.
DEFENSE
The SportVu stats on defense are greatly lacking, as are defensive stats in general for the NBA. The only thing they have available is opponent's shot percentage at the rim. Using this, I was able to calculate what an average player lets opponents shoot at the rim, and then from there calculate how many shots, and then points, a defensive player saved.
Ways to improve: Use all opponent shooting percentage, not just rim defense.
IN THE WORKS
I would love to do something will perimeter defense, ideally using opponents shooting percentage against to calculate points saved. I would also love to do something with turnovers and steals, so those are very important and they either lose or gain one's team a whole percentage. Although the SportVu data on NBA.com doesn’t track these stats, they are fairly easy stats to get ahold of. Maybe turnovers per minute of possession? Maybe steals per minute of possession defended? NBA.com offers players time of possession, but they don't offer time of possession in which they are defending the ball handler. An idea I had though was use assume that if you handled the ball a lot you would also be guarded players who handled the ball a lot, so you could, for simplicity and because there is no other data to use. This of course isn't exact by any means, but it's a good rough approximation (top five in steals above average are Tony Allen, Trevor Ariza, Andre Drummond, Kawhi Leonard, and Corey Brewer). This however is biased against player like LeBron, who run a lot of their team's offense but guard a position that typically doesn't handle the ball much. To remedy this, I considered calculating time of possession per minute played by position and using that. Finally, I'm hoping to introduce a dribbling aspect, since driving and shooting is way more efficient than pulling up and shooting. I'm still looking for ways to measure this.
None of these techniques are perfect by any means. If you have any comments or questions, either leave them below in the comments or send me an email and I'll try to answer them as best as possible. If you have additional data that you would want to share or collaborate on, also let me know.