I've added some pages relating to NBA Player rankings; the All-Star break seems like a good time to introduce this player rating system, which I'll explain here.
The ratings are based on a "Total Performance" concept that Lute Olsen has used throughout his coaching career to capture a player's stats beyond simple "points per game" or "points plus rebounds." I don't know what his formula was, but there are many ways to do it, with the caveat that you A) have to have the stats available to calculate it and B) it has to be fairly easy to get these stats into a spreadsheet or computer.
Yahoo! Sports to the rescue. Their NBA stats pages aren't as good as they used to be—they lists stats as per-game averages, which dilutes their quality—but they can be cut and pasted into Excel.
The formula
Total Performance =
Points scored - shots missed (FG or FT) + rebounds + assists - turnovers + steals + blocks - fouls
Pretty basic; you get credit for all points you score, 2 for a FG, 3 for a 3-pointer, 1 for a free throw, but lose a point for any shot you miss. It's pretty lenient, in that shooting over 50% on free throws, 33% on FGs, and 25% on 3-pointers puts you in positive ground. But the negatives do their job to dilute the efforts of high-scorers who just shoot a lot, and reward those who help their teams with good shooting.
Rebounds are self-explanatory; some people think offensive rebounds should be worth more, and the Yahoo stats break them into offensive and defensive rebounds, but I don't make that distinction. This keep the system simple: everything good you do gets you a point, whether that good thing is scoring a point or getting a rebound.
Likewise, an assist is worth 1 point, not two; after all, you didn't score the bucket yourself. A steal gives the opportunity to score but doesn't guarantee it, and it does deprive the opponent a scoring opportunity, so a case could be made for valuing it more. Again, I keep it simple, giving 1 point. A block is also worth one. Turnovers and fouls subtract from the total.
The stats are necessarily offense-oriented. Steals and blocks are the only truly defensive stats here, though fouling is somewhat related to poor defense (but not always). There just isn't a way to incorporate more given what's available. A good stat to have would be "charges taken", and especially, "shots successfully defended" but I don't see them, especially the latter, being tracked and widely available any time soon.
Once we have the basic score that a player has achieved, we can do a few things to it. The first two tables I'm keeping are the basics: Total Performance per game, and Season Total Performance. The first is a good replacement for just looking at the NBA leading scorers chart; the latter shows how much each player has contributed over the course of the season. This is good for tracking potential MVP candidates, since one has to consider injuries when awarding the MVP. A great player who misses half the season probably isn't an MVP candidate, and this will show up in his total cumulative output.
An issue with Total Performance systems that I had early on is that naturally, players who play a lot will have higher scores. Sometimes, though, you want to see who is making the most of his time on the court. So long ago I decided that Total Performance should be divided by number of minutes played, and this is reflected in the Total Performance Per Minute chart. In the past several years this type of Player Efficiency calculation has become a lot more popular, with several high-profile sites adjusting stats per minute played. So why isn't Total Performance Per Minute the one chart needed to grade a player's performance?
Looking at the list, you'll notice something right away: several of the top players are those who have very few minutes. Rather than arbitrarily screen them out, I leave them there as it's not hard to scan past them, and it keeps all the charts in synch in terms of number of players included. A good rating system has to include some aspect of Efficiency, but should also realize that, as playing time increases, high efficiency is more difficult to maintain. Players get tired, they get double-teamed, they play more often in the heart of the game than just at the end when the outcome is settled. There are many reasons.
To encompass both Total Performance and Per-Minute Performance, I multiply the two values together, yielding the Total Score chart. A player gets credit for his output at a percentage defined by his per-minute performance. Essentially, this Total Score is his Total Output multiplied by itself and divided by minutes played, since
Total Score = Total Output x Efficiency,
and
Efficiency = Total Output / Total Minutes;
therefore
Total Score = (Total Output x Total Output) / Total Minutes
but as originally envisioned, it allows a player to "keep" that percentage of his output that is regarded as "efficient" output.
Now the MVP issue. Clearly those with a great Total Score should be leaders in the MVP hunt. But what if their team is not doing very well? Can they really be said to be great players if they aren't elevating their team sufficiently?
The way the MVP award is handed out, in practice, suggests the success of the team is very important in voters' minds. Sometimes this is unfair, as in the case of a player who has no quality supporting cast to work with; other times it's right on the money, as a superstar hogs the ball to pad his stats and diminishes his team in doing so. In practice, there's no way to tell which is which just based on the stats, but it's easy to reward players whose teams are doing well, and that's by multiplying their Total Score by their team's winning percentage (which in the NBA as opposed to College ball is an accurate proxy for team quality), and this yields my final chart, the MVP Rating.
Back-tested for 2007, Dirk Nowitsky indeed finished first last year; I'll be testing a few more years back just for kicks, to see how many of Steve Nash's awards the system thinks he deserved. There were a few interesting, close years there. As of the mid-way point of the 2008 season, Amare Stoudemire has just overtaken Kevin Garnett at #1. He's played several more games, which helps his total, but if Garnett stays healthy in the second half and Boston keeps doing what they're doing he'll be hard to beat.
Overall, the list seems to reflect consensus fairly well, and has the benefit of being totally objective. Tweaking the values here and there could improve it, and with more data a superior system could be designed. Taken together, I think these charts provide a good insight into a player's total performance and efficiency that's hard to gather by leaderboard stats alone.