Don't forget the other plus to Kidd getting an MVP: Steve Nash's MVPs suddenly get placed in context. Scorers dominated the MVP voting during our lifetimes, and then Nash won two, so should Kidd win the award, we might not have to explain to future young 'uns the weirdness of Nash's awards when so many great points before him hadn't won any.

If you're using different averages for different positions, it seems like it would be more accurate to use the ratio of win score to average position win score, because points above the position average would still have the same skew towards more productive positions, or at least that's how it seems to me

I played around with a lot of different ways to apply the positional averages, and I'm certainly not convinced that the way I settled on is the best.

One approach I considered was to calculate Win Score/48 minutes (unadjusted for position) and subtracting from that the average Win Score/48 minutes that you'd expect from that position. But using that formula gives basically the same results.

The reason I included WSAA was that I wanted to reward guys who were on the court more: guys who have missed time due to injury, or who just don't play as many minutes, don't contribute to their team in the same way as guys who log long minutes.

I agree that people who log more minutes should be rewarded, and I think that total win score would be more valuable than win score per 48 minutes which would eliminate the difference in time and games.

My argument is, if you are trying to eliminate the fact that some positions are naturally more productive than others, a simple points above average for the position does not adequately accomplish this. For example, is the avg WS for a guard is 300 and the avg for a center is 400, then a guard being 100 points above the average would be more significant than a center being 100 points above the average. The guard would be 33% above the average guard while the center would only be 25% above. That's why I feel a ratio of total WS over the average position WS would be more descriptive, as the guard would have a score of 1.33 and the center 1.25, with the average being 1 for each given position. This would show how valuable each player is compared to an average player at the position in terms that take into account the natural variance in productivity between positions.

I apologize for the length and argument, it's a slow day at work.

I think I understand what you're getting at, and I like your idea: here's the same ten players as the Top Ten in WSAA/48 but with their Win Score Rating (as I'll call it)

10. Emeka Okafor - 1.59
10. Dwight Howard - 1.59
9. Dwyane Wade - 1.96
8. Amare Stoudemire - 1.59
7. Tim Duncan - 1.62
6. Dirk Nowitzki - 1.70
5. Steve Nash - 2.20
4. Carlos Boozer - 1.76
3. Kevin Garnett - 1.78
2. Jason Kidd - 2.36
1. Shawn Marion - 2.36 (1.96)

The number in parentheses for Marion is his rating if you consider him a 3/4 as opposed to a pure small forward (which is probably his natural position but the Suns play him at the 4 quite a bit). Kidd and Marion are essentially even, but considering the records of the two teams I couldn't blame anyone for voting for Marion over Kidd (or even Nash over Kidd). For perspective's sake, Kobe Bryant has a Win Score Rating of 1.70, and LeBron James checks in at 1.49.

MVP assessments are not only about stats. Without Kidd, the Nets would stink, but then, they also stink with him, so how valuable can he be? His enterprise is ultimately worthless. Despite his greatness, he has failed to create something of "true value", a championship-caliber team. Which is more valuable, a diamond on a crackerjack ring, or a virtually identical diamond on a 24-kt gold ring? Neither diamond can be separated from its surroundings, just as Kidd can't wander off and play for the Knicks (or play by himself, 1 on 5). Evaluating MVPs should be a non-linear process; there is tremendous value in being the most valuable component of something that is, of itself, also valuable, i.e. being the "marginal difference" in team goodness vs. team greatness. For that reason, Marion cannot be the MVP because he isn't the most important component on his team. If it had been Marion out for three games instead of Nash, would PHX have lost three in a row? Same argument for DWade -- is he really the most important component on his team, or do the Heat really become elite only when Shaq is playing? I am not arguing that the undisputed best player on the league's best team is the automatic MVP, but they should definitely rank above a great player on a bad team. I believe the true MVPs have a "reserve stat capacity", a supply of additional greatness that is only tapped when needed. How many stats does Dirk NOT get because his team is cruising, up 20 in the 4th, and he doesn't need to take over the game or pad his stats, even if he's on the floor (and thus, diluting his "per 48" stats)? How many extra stats does Nash get merely because of the pace and thin rotation that PHX uses? Simple rules for MVPs:
1. Must be on a "top 5" team.
2. Must be the undisputed most important component of that team.
3. Must have stats that are very significantly above average.
4. Must demonstrate the ability to take over and win close, critical games.
Answer: 1) Dirk, 2) Nash, 3)Duncan

Jim:

Obviously, when it comes to things like naming the "most valuable player," no one set of criteria will satisfy everyone. I wouldn't argue that your points are wrong, though I may not agree with the order in which you present them.

But assigning value to players is a difficult business. It's hard enough to do in baseball when each player functions, more or less, as an autonomous unit on the field. In basketball, the interchange between teammates is much greater and more constant, and thus players can never be truly removed from the team context (this is also the case in football, and probably other sports like soccer and hockey as well).

But when you start inventing scenarios (like stats that Dirk doesn't get), you enter an even murkier realm, one in which a reasonable case for a host of players can be made, because the reasons called upon are no longer based in actual statistical fact but in far more subjective judgment.

It's up to you to decide where you want to put the most weight statistically. Perhaps you feel that the raw amount contributed to a team makes an MVP, and positional/minutes played adjustments be damned. That's your prerogative, but I'd simply say that you're not using the most precise tool for the job.

NBA fans enjoy the MVP debate precisely because there's a subjective component. If it were otherwise, we'd just do the calculation and see who's "ahead" at any point in the season. It would be no different than a BCS calculation or the NFL QB rating system (remember how that was considered a joke when it first came out, and now it's routinely cited as if it's some sort of fundamental law of nature?) It may be that the subjective component of the MVP race is really a manifestation of the lack of a deeper mathematical analysis of what constitutes an MVP in the collective eyes of those who actually vote. The debate here over the best statistical model is really a discussion about who OUGHT to be the MVP, but a much more challenging assignment would be to develop a predictive model of who WILL be the MVP. In addition to traditional stats and the various formulae derived from them, I believe such a model would need to incorporate elements of non-parametric data (i.e. ranking instead of value). For example, suppose the model incorporated some sort of periodic poll to rank the importance of each player on his own team. I'd guess that this would filter the pool of potential MVP winners quite effectively just by eliminating any player who is not ranked first on his team by 80% (or 90 or 95%?) of the respondents. How can a league MVP not be the undisputed MVP of his own team? I think Nash would meet this threshold (meaning that Marion and Amare would not). I don't think that DWade would as long as Shaq is around. In the list of Top Ten WSAA/48, Marion, Amare, DWade and possibly Boozer would all drop off the list for this reason. And since team ranking/record is clearly a predictive factor, Okafor, Kidd, Howard and Garnett drop off. I also think "trend" is an element, i.e. Duncan won't win it this year because the Spurs "trend" is downward compared to last year (and the MVP is selected before the playoffs). That leaves Dirk, Nash and possibly Boozer. Obviously, Boozer won't win it -- perhaps there's a "dues paying" component as well?