A0007: Envisioning the Olympics

Admittedly, it's a little late for Olympic basketball coverage, given that the competition ended sometime around 4:00 am EST on Sunday morning, but Thursday is Arbitrarian day, and so today I'm going to try to tell the story of the US Men's Olympic basketball team retrospectively, in statistics and graphics.

Predecessors

This most recent iteration of the US men's basketball team was slated to "redeem" the American program in international competition. After several successive failures to dominate their competition, much was made about the degree to which the rest of the world had caught up to the level of American basketball and/or how the American players, because of [insert arbitrary reason here] would no longer be able to dominate in international competition. Several of the more recent US squads were derided as selfish, non-fundamentally sound, failing to take international competition seriously--the narrative was one of how hubris could lead even the mightiest to fall.

It has been said that during those dark years, the US was "just fielding all-star teams," and that part of Jerry Colangelo's plan for a return to dominance was to field carefully constructed teams, with role players and specialists--not just 12 guys who could score. To what extent is this true? How much credit does Colangelo's craftsmanship deserve? As we like to do here, let's take this subjective claim, and apply a little bit of rigor to see if it holds up without the patriotic feelings and stirring redemption narrative clouding our judgment. For answers, let us look to an application of the SPI style trichotomy:

(Note: If you turn captions on (second button from left on bottom), each diagram is labeled with its year. Also, hit pause and use the arrows to review each image at your own pace.)

Above is a series of graphics depicting the SPI styles (based on their NBA statistics) of each team fielded by the US in major international competition, from the Dream Team in 1992, to this year's "Redeem" Team, with the exception of the 1998 World Championship team, which was largely composed of non-NBA players.

What differences can we identify in each team's composition? Did Colangelo really put together a thoughtfully composed team? It appears to me that this was at least some part of the difference between this year's team and those of the recent failures. The main thing I notice, in comparing the 2002, '04, and '06 teams (although especially the first two) to each of the others, is a relative dearth in the pure perimeter region.

Each of these teams has an eclectic smattering of interior types--some years they appear more offensively-minded than others, and the 2008 Olympic team, interestingly has only three players classified as such in the SPI scheme. But look first at the 1992 team, which is stacked to the gills with players in the 10 o'clock to 12 o'clock range, meaning that their statistics indicate a focus on perimeter play, or an absence of focus on scoring, relative to the league. Such is the case, to a slightly lesser extent, with each of the other teams up through 2000.

In 2002, the perimeter appears to have become less of a priority, stocked with
Andre Miller, Davis, and young Jay Williams--good players, but not the "pure point" types which manned some of the other teams. Further, that team was full of Perimeter Scorer types, three of which (Reggie Miller, Finley, and Allen), are known more for their shooting than their all-around game.

2004 may have been an even more poorly-constructed team, with essentially no Pure Perimeter players. James and Wade are capable of facilitating, but this is not typically their primary role, and James played relatively few minutes anyway. Instead, that role was left mainly to Marbury and Iverson, who are known to look for their own shot as often as they pass--and this subjective reputation is backed up by the SPI analysis.

The 2006 team was much better--it is obvious that effort was made to compose a team of players of many different types--this is the only year in which there is at least one player from each sextant of the SPI plot. This is not necessarily a good thing for winning, but it indicates that thought was put into how each player would fit together into a whole. Further, two actual perimeter players were included, Paul and Hinrich, and this team performed substantially better than their Marbury- and Iverson-lead predecessors.

This year's team sees a return to past glory, likely in no small part to a fully-stocked trio of Pure Perimeter players, able to push the ball up court and facilitate any of the able scorers on the team. Interior play was de-emphasized, as the team's focus would be on a disruptive defensive style aimed at generating turnovers and leading to fast breaks--for this, speed, not size, was key.

In sum, it appears as though part of the credit for the USA's Olympic success really might belong to Mr. Colangelo. Though it is the players on the floor who do the actual winning and losing, a large part of the results likely stemmed from what happened way before the opening tip.

Now that we have covered the pre-Olympic preparation phase, let us turn our attention to what actually happened in Beijing.

Assessing productivity in these Games

Due to limitations on the ease with which game-by-game data can be collected for the Olympic tournament, I will be discussing productivity (as measured by MEV) rather than value (as measured by MVP)--but here, the story is pretty clear. Below is a list of each athlete, with their SPI factors, points- and MEV-per game numbers, and Valuable Contributions Ratio. I've also included what I call Points Per Points Possible (p4), which divides points scored by the number of points possible on each of their shot attempts (2 for all field goal attempts, plus an extra one on three attempts, plus one for each free throw).


Many of the most productive individuals play professionally in the NBA. These numbers indicate that LeBron James was the most valuable to Team USA, but note that Wade was almost as productive in substantially fewer minutes (his VCR is the highest on the US team). As such, I have to name James the MVP (for the team and the whole tournament), but Wade is the US's Most Efficient Player, which is exactly what the team needed from its first man off the bench.

How did contributions break down for each team? Below is a series of charts that plot the sources of production for each team, based on tournament-cumulative MEV. Each player is colored according to their SPI type, and players with negative MEV are zeroed out (because it's hard to depict the area of a negative number):



Among the best teams in the competition, Argentina was more highly dependent on their top-tier players than were Spain and the US. The two teams most reliant on a single player were China, anchored by Yao Ming, and Iran, lead by Ehadadi. Croatia appears to have had the most balanced contributions, although this is often a trait of weaker teams, because it is easier to field a team of equally poor players than one of equally excellent players.

What did each player produce individually? The table above gives the summary report of the points-value of each player's production, in the form of MEV. Below, however, I have the complete breakdown of each player's counting statistics for the Olympic tournament, as a percentage of the simple sum of these stats for that player. I have tried to arrange the graphs such that adjacent areas make for easy comparison of paired statistics--missed field goals is next to points, assists next to turnovers, offensive and defensive rebounds together, followed by the defensive statistics, etc. Players are sorted by MEV/gp. Coloration is of course derived from SPI type based on Olympic statistics.


Click here if you want a whole window full of these little pie graphs.

Seeing these pie charts all together as small multiples allows us to easily compare two or more players. Note, for example, that Dwight Howard and Chris Bosh were almost perfect substitutes for one another: they have almost identical per-game MEVs, and their stat distributions look very similar--the only exception seems to be that Bosh seems to have grabbed relatively more defensive rebounds and turned the ball over slightly more, while Howard did a lot more fouling.

Carlos Delfino's SPI color identifies him as a very tournament-representative player; that is, his relative distribution of scoring, perimeter, and interior statistics reflect that of all players collectively. The gray color indicates this league-relative neutrality, and he serves as a useful benchmark against which to compare others.

As is evidenced by his orange color and large segment devoted to pts and fgx, a large portion of Bryant's statistical contributions came from scoring. However, these statistics likely do not give the full picture for Bryant, as his role for most of the duration of the tournament was to shut down the opposition's best players, not unlike a "Doberman."

Jason Kidd (very pale blue, about halfway down) is one of few players for whom pts is not the largest segment. Rather his defensive rebounds and assists took priority, although so too, unfortunately, did his turnovers and personal fouls.

Michael Redd (rusty color, much closer to the bottom of the list) offers an interesting example of the usefulness of such a visualization. The first thing one notices is that his pts sector is matched in size by his fgx sector--he missed almost as many baskets as he scored points. Tip for the uninitiated: this is not a productive way to play basketball.

Another way to look at the data is through parallel coordinate plots, which are useful for depicting the rank of an individual across multiple categories. Below, I present PC plots for each member of team USA, where the vertical axis indicates that individual's rank in each of 9 metrics, relative to the entire pool of Olympic players. On each plot, for ease of comparison, I draw gray lines for the remainder of the US team, but highlight each player individually in their SPI color.


Click here if you want a whole window full of these parallel coordinate plots.

p4 is Points Per Points Possible, described above, AS:TO is the assist-to-turnover ratio, TR/min is total rebounds per minute, DEF:PF is (BK+ST)/PF, which is just an amateurish way of measuring defensive skill.

Looking at these plots, we can see that Wade performed very well. He is in the top for on the US team in each stat, and it is apparent that he is in the top half across the board among all Olympians. Redd, although he was called upon to provide a shooting spark off the bench, was mostly a dud, with a p4 among the lowest in the competition. Bryant was second lowest on the team, but his shooting efficiency looks to have been better than about a third of the Olympic players, and thus much better than Redd's. Note that due to a small sample size, some of these ranks will appear odd, namely Redd's high ranking on the DEF:PF statistic and Kidd's high p4 rating. Neither of high rankings are what we would expect from these players, but Redd played relatively few minutes, and Kidd only took shots he couldn't refuse to take, resulting in good ratings for in these areas over a small number of observations.

I would be very interested to hear any more insights you glean from the above displays--feel free to copy any of the charts for your own use, just also please provide a link back to HP.

Olympic style

We've seen the NBA styles of the players that make up Team USA, we've seen their SPI factors and even their specific statistical breakdown. Now, we turn to a full SPI Spectrum graphic depicting each Olympic competitor, and their type, based solely on their production in the Olympics. Player names are scaled according to their MEV totals, so that the most productive players are the easiest to spot.


Fullscreen Version

Several things stand out to me. First, I am impressed by the degree to which this Olympics-based diagram matches up with the NBA-based diagram, for players who appear in both. Redd, Bryant, Williams, Kirilenko, Howard, Yao and Boozer all played similar styles in these Olympic games as they did in the 07-08 NBA.

Even more enlightening are the differences: Louis Scola played much more of a scoring role for Argentina than he does for the Rockets (understandably so). Dwyane Wade and Chris Paul shifted their focus away from scoring, relative to their NBA style, likely because they were not required on this team to carry their team's point production. Anthony's purported focus on rebounding is reflected in his shift from a somewhat perimeter-biased Scorer to an Interior Scoring type. Jason Kidd became an even more extreme Scorer's Opposite, eschewing shooting opportunities whenever possible.

The most significant shift, however, might be seen in the play of LeBron James. Last season in the NBA, James lined up at about 12 o'clock on the diagram; the style with which he most closely aligned was Perimeter Scorer. In these Olympics, however, James' style reflects his commitment to doing whatever was needed by the team. His minty-green color and placement at a little before 11 o'clock reflect his Pure Perimeter style, though his relative proximity to the center of the diagram indicates that his fit here is not perfect. Rather than being the primary scorer for this team, as he is accustomed to being in Cleveland, James stepped up the defensive intensity, leading his team in blocks (with eight), and finishing second in the tournament in steals (with 19!), not to mention leading the tournament, by a landslide, in menacing scowls. Further, he was second on the US team in assists (30; Paul had 33), his assist-to-turnover ratio was a respectable 1.76, and he finished in the tournament top ten in total rebounds. To put it in perspective, the role James filled for this US team was similar to that played by Magic Johnson on the showtime Lakers, which is quite a niche, indeed.

Conclusion

In sum, we can see that at least some of the hype is true. There has been some well-placed cynicism regarding the extent to which the "Redeem Team," and our collective impression thereof, is a product of marketing. I have no doubt that at least some of what we believe about this team and its players is fabricated for the purpose of generating a positive image, and greater sales. However, at least two claims made about this team can be empirically verified, and I have tried to do that here.

The first claim is that this team is different from the failures which came before. Using NBA statistics and the SPI Typology, I am inclined to believe that in construction, this team is different than its three previous iterations, and more similar in design to the Dream Teams of the 1990s.

The second claim is that the players on this team changed their styles to accomodate each other, to better fit together as a team. Comparing SPI positions in the Olympics to SPI positions in the NBA, we can see which players had similar statistical distributions, and those which modified their style. Each player on the US team was either accustomed to or able to lead their NBA teams in scoring on any given night, and in Olympic competition, this ability to rely on others to score allows (at least theoretically) unselfish play. The question was always whether or not this team of able shooters would be able to "put aside their egos" and fill a specific role for this team, which may or may not include a substantial amount of offensive production. By and large, it appears as though the players asked to do so have responded positively. Though several US team members played with styles similar to their NBA styles, this reflected the reported desire of the coaching staff and management of the team (i.e. Michael Redd is supposed to be a shooter). Other players saw drastic shifts in their style of play, especially movement away from a focus on scoring, as a universally capable offense permitted each individual to do less of the shooting than may be required on their NBA squads. Based on this graphical evidence, I am willing to advance a tentative rejection of the null hypothesis that the players did not fill the roles they were asked to. Rather, it appears as though they played as a cohesive unit, maximizing their strengths and possibly sacrificing for the team.

I hope this late coverage was worth waiting for. I would be very interested in hearing your reactions to any of the ideas I've put forward, and I would especially like to know if you see any interesting relationships jump out in any of the SPI diagrams. I haven't even begun here to discuss the interesting similarities between several of the international players and those from our own NBA in the Olympics, I suppose I will leave that to you. As usual, I'd love to hear from you in the comments, and in the survey, and please Buzz this up!

A0006: Assigning Credit for Game Outcomes

Two weeks ago, we explored a statistical estimator of value, BoxScores, which estimates player contributions to team success at the season level. Aside from the time-honored complaint that it doesn't account for defense, there are at least two other improvements that I might wish to make to improve the accuracy of this value estimator.

First is the problem of trades, and more generally, varying team success across the duration of the season. As it stands now, if player A is traded from team X to team Y in the middle of the season, his BoxScores are calculated by finding his PVC to team X's entire season's worth of MEV and multiplying that by X's entire season's worth of wins; then adding to that the same calculation for team Y to find the player's season-cumulative BoxScores figure. This is good enough, for an estimate.

However, imagine if both teams are made significantly better by player A. Team X might be on pace for a very successful season up until the trade, and might begin to tank once he leaves. Team Y may have had an inauspicious start, but with the addition of player A, they might turn the season around. If this is the case, player A might be responsible for more success than his BoxScores indicate. Alternatively, similar situations can be envisioned in which much-injured players' contributions are over- or under-estimated, since BoxScores (using season-level counting statistics) cannot account for game-level success and variations thereof.

Another problem is with comparability, especially comparisons of good players on bad teams to good players on good teams. According to BoxScores, Al Jefferson was less valuable in 2007-08 than was Andris Biedrins. This could be true, but it could be that while Al Jefferson did more every game to help his team win, he could not, (essentially) alone, carry his team enough to get very many wins. The point was made by a commenter on a previous post that a team of Michal Jordan and eleven pre-schoolers would never win an NBA game, though Jordan could be incredibly productive. BoxScores, multiplying productivity by success, would assign Jordan and his eleven weaker teammates the same value: 0. This is certainly an extreme example, but it highlights a possible shortcoming in the BoxScores methodology--wins are discrete, binary events. Either a team wins a game, or it does not. Regardless of whether the score was 101-100, or 130-70, a win counts the same.

The solution, in the form of a more specific metric

The appeal of BoxScores has been (among other things) that it can be applied to every professional basketball player, because season-level box score stats are very widely available. The downside to a more specific, game-level estimator is that the increased accuracy comes at the cost of universality: Game-by-game box score statistics are only available going back to the 1986-87 season. Nevertheless, here I will develop a value estimator that works at the game level, to give us an even more accurate picture of just how much each player contributes.

For each game, we first must calculate each player's MEV. (See this post for a very detailed description of how this is done.) Then we calculate each player's Marginal Victories Produced (MVP):

MVP = Player MEV / total MEV sum for both teams

As you can see, in each game, there is a total of 1.00 MVP to be allocated. Each individual's contribution to the total production in the game is considered their Marginal Victory Production. This way, players on losing teams can be seen as producing valuable contributions--they might be valuable enough to get their team right to the cusp of victory--and this value shows up in MVP (but not in BoxScores).

Here is an example of MVP calculated for a game on April 11, 2008, between the LA Lakers and New Orleans Hornets:



The Lakers won, 107-104. Total MEV for the Lakers was 110.7, and for the Hornets, it was 106.0, so the Lakers' total MVP allocation was 0.511, versus the Hornets' 0.489. If we were focusing on wins and losses alone, the Lakers would get 100% of the credit for this game. Arguably, though, the Hornets produced something of value here--they got within four points of winning, and thus MVP is a much more accurate estimator of value.

One interesting way to think of MVP numbers is to note that a team needs a total of at least 0.5 MVP to win a game.¹ Thus, in the game detailed above, Bryant got his team almost a third of the way to the win (0.165 MVP), Paul/Chandler/Stojakovic together got their team 2/3 of the way to a win (0.335 MVP), etc.

MVP value at the season level

To estimate a player's value for the duration of a season or career, we need only sum their game-level MVP. One nice property of MVP is that the sum total of MVP is equal to the total number of games played--the "value of each game" is divided among each participant, so that all games are accounted for in their entirety. Further, team season-total MVP can be translated to wins and losses by a method similar to the Pythagorean win projection (more on this sometime in the future). How many marginal victories did your favorite players produce? See below...



The first tab ("07-08 MVP") lists the total number of MVP for each player last season. I would argue that this is a valid way of identifying the league Most Valuable Player. Just as in the BoxScores rankings, Chris Paul comes out on top, followed by LeBron James and Kobe Bryant. However, the differences in the two estimators can be instructive. According to BoxScores, Al Jefferson is the 74th most valuable player--by MVP, Jefferson is 11th, just behind the player for whom he was traded, Kevin Garnett. Dwyane Wade moves from 188th most valuable (BXS) to 67th (MVP) for his his injury-shortened season. Good players on bad teams are not "punished" for having low-quality teammates. Rather, everyone is rewarded based on their contributions to competitiveness, even if that competitiveness doesn't result in winning every time.

The "86-08 MVP Seasons" tab lists just that--the most valuable seasons from my limited dataset according to MVP. Unsurprisingly, Jordan dominates this list, along with other modern luminaries. Keep in mind that the MVP number is not a number of wins--it's "Marginal Victories"--but also keep in mind that teams need only 0.5 total MVP in a game to win it. One way, thus, to look at season-total MVP numbers is to say that, for example, Jordan in 87-88 contributed enough MVP to help his team win the equivalent of about 27 (13.52 / 0.5) games. Bear in mind, though, that this is just an interesting shorthand, because summing this figure for each team will not come close to matching that team's win total. If Jordan had accumulated 0.5 MVP in each of 27 games, and sat out the rest of the season, his team would have won each of those games, and he'd be credited with 13.5 MVP. However, Jordan played for a whole season, and accumulated MVP in pieces (never as many as 0.5 at a time--no player won any game "single-handedly"), so the 27 win estimate is interesting, but not literal.

The final tab, "86-08 MVP Careers," lists the most valuable players during the period covered by the data set. Thus, many of Larry Bird's and Magic Johnson's best years are excluded, as are the first years of Jordan, Olajuwon, Stockton, etc. since they came prior to the 86-87 season. This is important to keep in mind when viewing game-average MVP numbers. Larry Bird falls relatively low on the list in no small part because we're comparing his later years to the primes of LeBron James, Chris Paul, and Dwyane Wade.

Bearing this in mind, the list is still highly instructive. Since it takes a total of 0.5 MVP to win the game, players from Jordan down to Garnett are generating at least a quarter of the value their teams need to win (0.125 / 0.5= 0.25). Players with MVP over 0.1 are doing more than a fifth of the work needed to get a win, and since no player plays over a fifth of his team's minutes, these are obviously some of the most valuable players--overrepresented in value relative to playing time. The rankings on this list are unsurprising, and read like a roll-call of the best players of the last 20 years. These are the guys around which you'd want to build a team.

Greatest single-game performances

What's the point of having a game-by-game data set if you don't look at game-by-game value? Below is a list of the 100 most valuable performances of the 07-08 season, and the 500 most valuable performances from 1986-2008. These are the herculean efforts from which legends are made. Here we can see how MVP automatically adjusts for pace, and assigns value above and beyond MEV's measure of productivity. Since MVP is a percent of total production, it makes no difference how fast the game is played, how long the game is, or how much is produced in total, contributions to winning are measured against the other players in the game. Also, since as opponents' MEV decreases, a player's MVP increases, the better the player contributes defensively (i.e. outside of his box score stats, but visible in the other team's production), the better will be his MVP. The margin column, incidentally, indicates the final point spread in favor of a given player's team. If it is negative, that player's team lost the game.



Both lists are topped by players you might expect to be there, but interspersed are some surprises: John Salmons? Willie Burton? It goes to show that on any night, any player can be a hero, and that a single sample can be very misleading. Nevertheless, there is a lot of data to be gleaned here. Note that the best games played see players generating over a third of the total production, which gets their team 2/3 of the way to a win. Not even the greatest can win completely on their own.

I'd like to digress here briefly, on the subject of Kobe's 81 point game. Note that he produced about 1/3 of the total valuable contributions in that game, but look at his MEV: 68.96. That means that by missing 18 field goals, and doing very little other than shooting, he cost his team about 12 points in the final margin. The Lakers still won by 18 points, but to me the 81 point achievement is somewhat underwhelming, because of what it took to get there. Edit: Apparently, you put it one little paragraph about Kobe Bryant, and it makes your whole post about Kobe Bryant... All I'm trying to say here is that Kobe, by missing 18 shots (and turning the ball over, while not doing a lot of rebounding or box score defending) cost his team a few points. Most players couldn't dream of generating 69 points, and this is an impressive feat, but also, most other players don't even take 18 shots (doing so would put them in the 94th percentile of all games in the data set). All I'm saying is that it might be somewhat less impressive than some of the others on the list, like, for example, Jordan's incredible performance against Cleveland.

The future

In the future, I plan on developing an approximation of MVP based on season-level statistics, for those seasons in which game-by-game data is unavailable. Next week, I am planning on applying some of the methods discussed here to the performance of the US Men's Olympic basketball team. Today, I have three requests for you: First, please leave insights or any questions you might have in this post's comments. Second, please take a moment to fill out the survey below with your thoughts, ideas, and criticisms. Third, if you found this post interesting, click the little "Buzz up!" button below, to express your approval.





¹ Game-total MEV margins correlate with game-level point margins at 0.947, and looking at MEV winners correctly classifies actual point winners 92% of the time.

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A0005: A generalized continuous typology of playing styles

What does it mean to be a Point Guard? Typically, point guards are expected to carry the ball up the court, set up the offense, make passes, and take few shots, at least relative to other players on the court. But how much can the term "point guard" actually mean if it applies to both Jason Kidd and Baron Davis? Further, what does it mean to be a "small forward" if Dominique Wilkins, LeBron James and Shane Battier all fall into that category? What do Vlade Divac and Amare Stoudemire have in common, aside from both being called "centers"?

The obvious point is that traditional position classifications, while they mean something, still convey relatively little information about a player's function on the court. As observers of the game, we attempt to compensate for this by adding any number of modifiers to these position descriptions: combo guard, pure point guard, defensive center, swingman, etc. Each of these is used to more accurately specify a player's style or role on the team, yet each is still somewhat definitionally ambiguous and subjective by design. One Tom Ziller has done some work in attempting to statistically classify guards on a continuum between "small two-guards" and "pure points," but this is only a small first step in the right direction. I present here a generalized methodology for structuring a playing style spectrum, and identifying each player's position within the continuum. By looking at actual statistics produced, we may eschew fuzzy descriptors of position and style in favor of a very specific, yet still highly flexible system of style identification--which provides us with an improved vocabulary with which to describe, among many other things, player types and team styles.

Very rudimentary factor and cluster analysis I performed a long time ago indicated that there are distinctions in the data between players who tend to try to score a lot, those who play a “smaller” game, and those who play like “big men.” In terms of the NBA’s tracked counting statistics, this translates to a differentiation between those who specialize in points and field goal attempts, rebounds and blocks, and steals and assists. I have chosen to call each of these three tendencies Scorer, Perimeter, and Interior, and collectively they form the SPI Style Trichotomy.

Calculation

To identify each player’s style is conceptually simple, but computationally somewhat more complex. Essentially, one sums each player’s fga + tr + bk + as + st, and determines what percentage of the total each SPI factor constitutes:

• Scorer percentage = fga / (fga + tr + bk + as + st)
• Perimeter percentage = (as + st) / (fga + tr + bk + as + st)
• Interior percentage = (tr + bk) / (fga + tr + bk + as + st)

These numbers are interesting on their own, but for the calculation of an index of style, they require further manipulation. In the league as a whole, the Scorer percentage is around 50%, the Perimeter percentage around 20%, and Interior 30%. Thus, if using these percentages, the vast majority of players would appear to be very scoring-centered. My concern here, in constructing a useful index, is to identify player propensities relative to other players, and for that, I calculate the percentile of each player’s percentages.

• Scorer index = percentile(Scorer percentage)
• Perimeter index = percentile(Perimeter percentage)
• Interior index = percentile(Interior percentage)

Thus, even though the maximum Scorer percentage in a season might be close to 75% while the maximum Perimeter percentage is closer to 25%, the players with the highest percentages in the sample under consideration will be assigned an index value of 1. Players with median values on a percentage will have an index value of 0.5, and so on. The percentilization normalizes across style tendencies and player subpopulations, and has the added virtue of scaling from 0 to 1.

Interpretation

Thus we have a set of three numbers for each player which can be used to characterize his playing style. The numbers easily translate to more qualitative descriptions. A player with a SPI triple of (0.8, 0.2, 0.7) is an interior scorer, without much perimeter production. A player with this triple (0.1, 0.7, 0.75) is anything but a scorer, sometimes called a “glue” guy. Someone at (0.5, 0.5, 0.5) produces the league median of each type, which is different from a player whose percentages are 33%, 33% and 33%. Such a player would have a relatively lower Scoring index, for example.

Since each individual is characterized by three variables, their SPI type can be plotted in three dimensions. Unfortunately, three dimensions are difficult to convey on a computer screen, so here is a plot which depicts Perimeter indices along the X-axis, Interior indices on the vertical axis, and Scoring indices as the size of the point.

(Click to enlarge)

Historical application note: Since steals and blocks have not been kept for the entirety of the history of professional basketball, players from earlier eras may have slightly skewed SPI values. While percentages and indices can still be calculated based only on fga, tr, and as, it is not difficult to see that leaving out blocks and steals, in comparison to eras in which those defensive statistics are included, will tend to skew players from an earlier era more toward the Scoring type. Unfortunately, without substantial era-specific correction, this effect is unavoidable. However, the sorting still manages to work well, especially if this detail is kept in mind when making certain cross-temporal comparisons.

Presentation

One of the advantages of using three sub-indices to construct the overall SPI Trichotomy is the convenient translation of index values to color. The three primary colors of light are Red, Green and Blue, and when combined in certain proportions, it is possible to generate infinite gradations of color (see Wikipedia). This means that each SPI triplet for each player can be represented as a single color. This aids understanding and comparison, as it is much easier to keep in mind that a certain player is a deep red than that his SPI triplet is (0.9, 0.1, 0.2), or that a player is a medium grey than that his triplet is (0.45, 0.53, 0.55). Further, a greenish-blue player is easily identified with another greenish-blue player, without having to specifically compare each of the players’ three index values. The human eye is capable of extremely high-resolution discernment, and using a single color to represent three numerical values takes advantage of this.

Here is the above plot, with color added according to RGB values derived from each player’s SPI indices, as you can see, “blueness” increases from bottom to top, “greenness” from left to right, and “redness” varies with the size of the point. The top-right corner is aqua or cyan, while the bottom left is mostly reddish, due to an absence of green and blue.

(Click to enlarge)

Unfortunately, this presentational format leaves a lot to be desired. Since each player can be represented by just one color, can we do better than a pseudo-3-dimensional plot? The answer is yes and no: No, because to ensure that the hue, saturation, and value of each color are captured, we still require three variables (see Wikipedia); yes, because most of what we are interested in here is hue–the underlying color for each player, red, yellow, green, aquamarine, vivid tangerine, indigo, etc. The other two components of HSV color space, saturation and value, allow us to see how “pure” the hue is, which in our basketball application, translates to how “pure” an individual’s playing style is.

Playing style as a continuous spectrum

Using polar coordinates, we can plot each player's position in a continuous spectrum of playing styles. Each individual may be represented as a vector, with Hue translating to direction/angle and Saturation+Value translating to magnitude/distance. The angle of the vector indicates the player's style, and the magnitude of the vector indicates the "fit" of that player to that style--that is, since it is unlikely any given player's statistical profile will assign him perfectly to a given category, there is a level of fitness that captures the extent to which they do. Very rarely will a player have some assists and steals, but no blocks, rebounds or field goal attempts, which would give them a P index of 1, but S and I indices of 0. Because of this, rarely will any player be a pure green, or pure blue or red. The degree to which they are a mixture of styles/colors is captured somewhat by their fit.

We can describe a player's style by their SPI indices, or by their color, but we can also describe them according to their angle, which is most easily communicated by referring to positions on a clock. In the graphic below, the top of the circle can be thought of as 12 o'clock, the far right translates to 3:00, the bottom is 6 o'clock, etc. This is yet another way to describe style more easily than by referring to the player's SPI triple, but more accurately and consistently than by descibing color. Finally, I have assigned arbitrary descriptive names to each of six major "spokes" on the diagram, which should help the uninitiated translate commonly-used adjectives into positions on the clock. Here is a listing of SPI indices, fit, clock positions, and shorthand labels for each player in the 07-08 season, as well as 500 all-time greats.


Graphical Display

Below is a graphical depiction of the SPI Playing Style Spectrum, with the positions of 250 of the NBA's all-time best.


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As you can see, the SPI typology encompasses Mr. Ziller's point guard continuum, and much more. "Small two-guards" (exemplified by Barbosa, Ellis, Terry and Iverson) line up at about 1 o'clock; "Combo guards" mostly fall between 11:30 and 12:30; "Pass-first points" even more to the left; "Pure point guards" are seen at about 11 o'clock. The spectrum continues, however, to more defensive/bigger guards, more well-rounded perimeter players, point-forwards, glue guys, defensive stoppers, big men, widebodies, power forwards, pure scorers, and back to shooting guards.

One interesting use of the spectrum graphic is to make comparisons. Unsurprisingly, Kevin Johnson and Steve Nash have similar styles; Kobe Bryant and Michael Jordan are in close proximity; and Tim Duncan and David Robinson filled almost exactly the same role for the same team. It's also interesting to make comparisons across eras: Dennis Rodman/Bill Russell, Vince Carter/Rick Barry, Michael Jordan/Jerry West, Magic Johnson/Jason Kidd, etc. It's also possible to identify stylistic opposites: Chris Paul-David West, Shaquille O'Neal-Kobe Bryant, Allen Iverson-Marcus Camby, etc.

Here is a SPI plot for just the 2007-08 Season:


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Thus far, the SPI typology is useful mostly as a classification system, but if you're interested, I've spent some time looking into the relative value of certain types, as well as their interactions. There's much more to be done in this vein, but some of the initial findings have been interesting. (APBRmetrics discussion)

Conclusions

Evidently, it's possible to develop a comprehensive classification system of playing styles using statistics alone. Now that the SPI color scheme has been introduced, you might find it interesting to refer back to the graphics I presented last week, in which I've applied the scheme. It adds a dimension of information to the season and team history graphics. I'd be very interested in hearing your thoughts in the comments, as well as in the obligatory survey below.

NEW! I've just created desktop wallpaper-sized All-Time Great SPI Graphics. Download them and enjoy! [1024 x 768] [1280 x 1024]

A0004: Individual contributions to team success

Last week, we looked at player productivity, as based on box score output. Today, we're going to look at value, which, as you will see, is somewhat different than productivity.

The MVP is not necessarily the best player in the league, nor the most efficient. Many times, the MVP award goes to the player widely considered to be the best player on one of the better teams, but when it comes to arbitrating between comparing the best players on several of the best teams, there appears to be no hard-and-fast rule, and subjectivity enters into play. Today, I will propose that value ought to be quantified in terms of individual contributions to team success, where success is measured in wins.

If we can estimate the number of wins for which each player is responsible, we can do away with the arbitrary focus on only the best few teams. It is theoretically possible, for example, for the most valuable player to be an absolutely dominant but lonely contributor on a middling team, while the better teams each have enough decent players that no single one can be credited with a large portion of their success. We are still, however, left with the problem of objectively measuring each player's contribution to team wins. To do this, I'd first like to explore...

A non-basketball thought experiment

Imagine a lemonade stand owned and staffed by Xavier, Yvette, and Zach. They make money by selling home-brewed lemonade at the end of their cul-de-sac, and only one of them staffs the stand at any given time. After their first month in business, they look at their lemonade sales revenue, and try to figure out which salesperson deserves what part of the income. One option would be to split the revenue into thirds--three employees, three parts. Zach claims that such a distribution is unfair because he worked over half of the total number of hours, while Yvette and Xavier worked about a quarter of the hours each. He claims that the distribution should thus be more like (1/4, 1/4, 1/2).

Xavier points out, however, that if they are trying to assess each employee's value, they should try to find a more specific measure of actual revenue generated by each seller. He suggests that, since revenue is generated by lemonade sales, revenue generation should be measured in terms of the number of lemonades sold by each employee. Since they kept detailed records of such numbers, this is easy to calculate: Xavier sold 2/5 of all glasses, Yvette 1/2, and Zach just 1/10. Zach is disappointed that his pay-per-hour gambit was foiled, but must concede that this arrangement is more just--Yvette and Xavier are much better salespersons, and did more to help the company make money, while Zach mostly daydreamed during his hours on the job.

Back to basketball

What I have in mind is the application of a similar methodology to basketball. We have an excellent estimator of aggregate value--team wins; and credit for these wins can be apportioned to the players who work for those wins. There are a plethora of ways this could be done--we could arbitrarily estimate credit for each player on each team: The superstar might get 50% of the credit, the rest of the starters get 10% of the credit each, while the remainder is split amongst the bench players. Perhaps we could look at minutes played--after all, ceteris paribus, removing a mediocre player, and replacing him with a better player for the same number of minutes, should result in a greater number of team wins. Similarly, increasing the number of minutes played by a good player (to a point) should increase wins, while increasing minutes played by a bad player should lead to fewer wins.

This method isn't foolproof, however: certain high-minute players might be daydreamer-types like Zach in the example above, while others might be feverishly productive. Consider, for example, Matt Carroll versus Yao Ming in 2007-08. Both played roughly the same number of minutes (2016 and 2044), but Yao was substantially more productive (by almost any measure) than was Carroll in that amount of time. Estimates of their value should reflect this difference.

Instead of minutes, I have chosen to use Model-Estimated Value (or MEV, discussed here) as an estimate of player productivity. There are several advantages to this choice, but two stand out. First, as discussed previously, MEV is a good estimator of per-game productivity, and so is more helpful to us than looking at, say, games played, minutes played, or points scored alone.

The second advantage comes from the fact that MEV does not perfectly capture player value. If it did, then team-level MEV would correlate perfectly with team wins, and we would not need separate measures for productivity and value. Rather, since some aspects of player value are omitted from the box score--things like defense, effort, intensity, etc--we may scale our MEV productivity estimates by team success, which does implicitly measure all of each player's contributions.

Bruce Bowen, for example, had a 07-08 per-game MEV of 5.60, which put him below, among others, Wally Szczerbiak. Many would cite this as an example of the failings of MEV--its inability to fully measure defense (not to mention a lack of adjustment for playing time and pace) leads to an undervaluation of players like Bowen. However, Bowen's defense does show up in the Spurs' success--no small part of their winning can be attributed to his contributions. Similarly for Szczerbiak--his contributions are reflected in the success had by Cleveland and Seattle--that is, relatively little success. Thus, by crediting players for team success, using MEV as our measure of productivity, we may get closer to measuring each players' actual value.

This method is still not perfect. We might still be undervaluing Bowen's relative contribution to the Spurs, and overvaluing Szczerbiak's contribution to his teams. However, given two players with idential MEV numbers on teams with otherwise identical rosters, the player whose MEV is "worth more" will help his team win more games.

Calculation and results

The measurement of each player's value to their team is straightforward. Merely take each player's season total MEV for a given team, and divide it by that team's season total MEV. This gives us a metric I call Percent Valuable Contributions, or PVC. For Kevin Garnett in 07-08, this calculation takes his season total MEV (1,534.19) and divides it by that of the Celtics as a whole (8,282.62), resulting in a percentage (expressed as a decimal): 0.185. This means that Garnett is responsible for 18.5% of the Celtics' success, which is a rather large portion, indeed. From here, estimation of value is very easy. Simply take this PVC number, and multiply it by team wins. This gives you each player's BoxScores (BXS), their individual contribution to team success. The first tab on the table below depicts the numbers that go into the BoxScores calculation for each player in the 2007-08 season.

I've sorted each player by their PVC for the sake of comparison. In terms of value to their team, the top three players are James, Paul, and Jefferson. All three are good players, but certainly Jefferson is a step below the other two. Since BoxScores accounts for team success, we can clearly see Jefferson's actual value is much less than that of James and Paul--he might be the most valuable player on the Timberwolves roster, but such is not a high distinction.

For more insight, note the series of players whose PVC comes it at around 0.185: Steve Nash, Joe Johnson, Kevin Garnett, Richard Jefferson, and Carlos Boozer. Even the casual fan knows that these players are not all equally valuable, though they may be equally valuable to their respective teams. Note that Nash and Boozer generated a much higher MEV total than the other three--this is largely because, as the table also shows, Phoenix and Utah had much greater team MEV totals, thanks to a faster-paced playing style. Team wins complete the picture--Richard Jefferson was responsible for 18.5% of his team's 34 wins. His value is thus estimated at 6.29 BXS. Kevin Garnett was responsible for 18.5% of his team's 66 wins. His value is thus 12.23 BXS. As you can see, by accurately measuring productivity (MEV), and accounting for team success (wins), we are able to objectively assess each player's value (BXS).

An aside into rated productivity

Another useful measure, especially for comparing players on poor teams, or those who played limited minutes, is what I call the Valuable Contributions Ratio (VCR). This is a pace- and playing time- adjusted metric of productivity assessed at the per-minute level. As above, this calculation is straightforward and intuitive. Merely take each player's PVC (MEV/team MEV) and divide it by each player's percent of team minutes played (min/team min). Thus, we are dividing a percentage by another percentage (which is why I call it a ratio--units are somewhat meaningless). This statistic controls for team pace and playing time, and is independent of team quality--it captures productivity relative to the time allowed for production.

This is useful for comparing bench players, players who miss a substantial number of games, and rookies. Bench players get a "fair shake" by this statistic, because they often have less time on the floor in which to accumulate MEV toward a larger cumulative share of team success. Same for injured players--Andrew Bynum did not play very many games for the Lakers in 07-08, and as such was less valuable in terms of team wins. However, when he did play, he produced very efficiently, with a VCR of 1.36. (This means that he was responsible for 1.36% of his team's production for every 1% of team minutes played--which is very efficient.) VCR is useful for comparing rookies, as well, since they often play relatively few minutes, and since their teams often win very few games. Rookies with high BXS are the most impressive, but more often than not, rookies don't produce many wins. Rather, they may produce MEV efficiently, and we can see this in VCR. Among rookies with substantial playing time in 07-08, Carl Landry produced the most efficiently, with a very respectable VCR of 1.39. (The Arbitrary Rookie of the Year, Kevin Durant, was 7th among rookies by VCR, and 5th on the rookie BXS list after Scola, Horford, Moon, and Thaddeus Young. He did, however, lead all rookies in points per game. WoW Club!)

BXS MVPs and all-time greats

Look again at the table above, but this time, select the second sheet, titled "07-08 BXS." This lists each player from the 07-08 season, on each team for which he played, and includes measures of productivity (PPG, and MEV/gp), efficiency (VCR), and value in terms of BXS. As you can see, the obvious most valuable player in 2007-08 was Chris Paul, who was responsible for over a quarter of his team's 56 wins, for a BXS of 15.41. Kobe Bryant, this year's Arbitrary MVP, had a good showing as well, but was responsible for almost three fewer wins than was Paul. Kevin Garnett, who was thought to be a more subjective favorite for MVP, acquitted himself nicely in objective terms, by generating 12.23 wins even while missing eleven games.

For a more historical perspective, see the third tab, "BXS Seasons." This lists the same information, but for the 500 most valuable seasons from the population of every professional basketball season since the beginning of the NBA, even including the ABA. Unsurprisingly, Chamberlain tops the list, although his most valuable season was not his most productive in MEV terms. Shaquille O'Neal's dominating performance for the incredible 67-win 99-00 Lakers is the most valuable season in recent memory, followed closely by Jordan's post-first-retirement 72-win season in Chicago. Perhaps surprising, but perhaps not to those who have always appreciated the Big Ticket, is Kevin Garnett's extremely high value in 03-04. Always a valuable player to his team, Garnett and the Timberwolves finally put it together for one great year, and Garnett's relative value (PVC) translated to absolute value (BXS).

The final tab, "BXS Careers," accumulates the performance of 500 NBA greats. The table is sorted by BXS82, which is the number of wins each player would be expected to produce in 82 games played, given his career performance. There may be a few surprises, but they are instructive: The first is Alex Groza, who was a great player in the early years of professional basketball, but whose career was cut short. The second surprise might be the ordering of Michael Jordan, relative to Magic Johnson and Tim Duncan. Many fans and observers would identify Jordan one of the most, if not the most, valuable player ever, and here he ranks sixth at a per-game level. The first thing to note is that Duncan has always been more valuable than his box score statistics might indicate, and this is reflected in his BXS measure. Secondly, Duncan has not yet seen his productivity or value decline substantially due to aging. For the most part, Duncan's 13.73 BXS/82 average comes from the peak of his career. Johnson retired after a relatively short career, and his comeback in 1996 was brief. Jordan, by comparison, had a second comeback for Washington during which he played 142 games of much less valuable basketball. If you exclude Jordan's Washington years, his career BXS82 becomes 14.62, which puts him solidly above the other two.

Visualizing value

Now for the first graphical visualizations in the life of this young column. Since BXS is derived by multiplying player contributions (PVC) by team success (team wins), we can envision BXS itself as the area of a rectangle with sides of PVC and Wins. This lends itself to graphical expression, with the league as a rectangle, 41*30= 1230 wins wide, and 100% high. Partitions may be made on the horizontal axis for each team, scaling each section by that team's number of victories. Within each team's segment, further divisions can be made for each player, according to their contribution to team success. The best explanation is an example, displayed below:


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You may use the controls at the top left to zoom in and pan across the graphic to see more detail, or an expanded overview, as you wish. The "Fullscreen Version" link directs you to a much larger version of the same display, which may be easier to grok. The graphic above displays BXS for the 2007-08 season, with team success increasing from left to right, and player contributions increasing from bottom to top. Colors are derived from statistically-derived playing style, where red indicates a propensity for scoring, green denotes perimeter play, and blue highlights interior-play tendencies. Much more will be said about this classification scheme next week.

Several things I'd like to point out in the graphic above to get you started: First, note how tall the rectangles of Chris Paul, LeBron James and Al Jefferson are--this is because height is scaled according to PVC, and these three players were the most responsible for their teams' success.

Looking across the top row of the graphic, we can identify each team's Most Valuable Player. For the lowly Heat, Dwyane Wade was most valuable, despite injury. Calderon was most valuable in Toronto (7.1 BXS), though Bosh was a very close second (7.0 BXS). The most valuable player on the best team was Kevin Garnett, but since he had a very supportive team behind him, his individual value was somewhat less than that of Chris Paul, whose supporting cast drops off substantially in terms of contributions after Stojakovic.

One useful perspective granted by displaying contributions in this manner, is that it is easy to compare units across teams. For example, Boston was famed for the Big Three of Garnett, Pierce and Allen. Using the scale on the right of the graphic, we can see that together, these three accounted for almost half of Boston success. Looking across the graphic from the lowest part of Allen's rectangle, however, we can see that the big three that was most valuable to their team can actually be found in New Orleans, where Paul, West and Chandler can be credited with almost 60% of the Hornets' success. On the other side of the coin, Detroit, Houston, and Chicago all got a fairly balanced set of contributions, as their subjective reputations might have suggested. I would be very interested to hear about your own observations, as well as your opinions as to how well this graphic meshes with your subjective opinions, in the comments.

I've also developed an interactive presentation of the graphic above, with even more detailed statistics. Just follow the link below to the Interactive BoxScores Explorer page. The league-wide graphic has been scaled to fit in your browser window, and players' statistical details pop up on mousover. Try it--it's somewhat addictive.

Make sure to click around a little bit--I've created "player cards" for each individual, which display even more detailed statistical information, including their playing style, most and least similar players, the mean and standard deviation of their "counting" statistics, and a season-long sparkline of their productivity. Feel free to use them in any application you wish.

The player cards are a quick and easy way to quickly assess any player. For fantasy purposes, for example, if you're comparing two players with similar averages in assists, you might want to pick the player with the smaller standard deviation about that mean, as indicated by the error bars in the middle section of the card. Alternatively, if you are interested in whether a certain player tends to produce more as the season goes on, the seasonal trends should give some insight into this, as well as how long it takes the player to recover fully from injury, or how much they produce when their minutes go up. Also, I've included each player's most- and least- similar match, based on the 07-08 season, which can help give you an idea of the niche they fill on their team.

Historical BXS franchise timelines

Another excellent use of this BXS area diagramming visualization is to display franchise histories. Better years are represented by wider segments, and the best players rise to the top with tall rectangles. Eras can by identified by patterns in color. Here are two examples, the first depicting the LA Lakers franchise, and the second, Boston Celtics history:


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Several eras stand out in the graphic above. The Mikan era was eventually replaced by the Baylor/West dynasty which became the Chamberlain/West years. Notice, incidentally, how West becomes "greener" over the course of his career, indicating a shift away from focusing on scoring, and toward a concentration on other perimeter contributions. A Kareem era follows, though his best years are at this point behind him, and massive team success comes only with the addition of Magic Johnson. Johnson leads the Lakers for ten consecutive years and his retirement marks the end of an era of dominance. LA returns to form in the late 1990s in the hands of O'Neal and Bryant, who turn in some incredible performances--interestingly, there is an obvious breakpoint between 2001 and 2002 on the graphic indicating the switch from the Lakers being "Shaq's team" to being "Kobe's team." The 2006 version of Bryant was forced to carry the scoring load to a massive degree, but the 2008 version (as is evidenced by a much less red color), has been freed up to focus less on point production, and more on doing other things to help his team win. Perhaps the 08-09 season will see Gasol and Bynum float to the top of the column, turning in full, healthy seasons for a very successful LA team.


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Boston history is marked even more clearly by the careers of its greatest players. The Celtics of the 1960s are consistently topped by Bill Russell's defensive-interior blue, and bolstered by some great scorers, like Havlicek and Jones. The 1980s saw a parallel to the Lakers above, in which a perimeter player (here Bird) lead a team supported by strong interior scorers. The 1986 and 1987 Celtics offer an interesting starting lineup of all greens and blues--no single player was responsible for most of the scoring, while other types of contributions were made by all. After years of seasons with little success and narrow columns, the Celtics finally turned it around last season with the addition of Garnett and Allen, almost tripling 06-07's win total.

The final graphic below offers an alternative take on presenting BoxScores, by tracing the careers of each of 50 NBA greats. Following the peaks and valleys of each player's tenure, we can also see the years in which many stars were shining brightly. 1972 was a great year for the sport, as was 1990--many of the NBA's greatest players had good seasons in these years, and the league may be seen to peak at these points. The graphic makes it possible to see the beginning of new eras--witness the start of Bird's and Johnson's careers, followed shortly by the rookie seasons of Thomas, Drexler, Jordan, Olajuwon, Stockton, and Barkley. We can see a big dip in strike-shortened 1999, and then another in 2004. This second dip may be troubling--has the quality of the league declined so sharply? Worry not--many modern greats retired in the years just before 2004, meaning that their layers drop out of the picture, setting the stage for the new era of NBA stars we are witnessing today.


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Conclusion

As always, I'd very much like to hear your opinions of BoxScores as a measure of value, as well as whether or not you think it gets things right. Was Magic really at his peak in 1987? Were Garnett and Pierce in 2008 in the same league as Bird and McHale in their prime? Should Chris Paul have been the MVP this past season? Were the Rockets really the most balanced of the good teams last year, and will the addition of Ron Artest make them that much more indomitable? Please feel free to leave a comment and take part in the now-customary brief survey below. Next week, I'll go into much more detail on a new way to describe players, without having to use all those pesky words.

PostScript: Discussion of the "50-Win Standard"
I hope you took the time to read Josh Tucker's excellent discussion on the established precedent of giving the MVP award only to players on teams with fifty or more wins. I have a few thoughts on how the 50-win minimum precedent fits in with the BoxScores methodology I've established here.

The first is that I essentially agree with the implied criteria of such a cutoff (or the implementation of the "Bryant-Nash Rule"). That is, I think that value should determine the MVP, and value is measured in wins, not strictly in individual statistics.

However, as an Arbitrarian, I would tend to shy away from establishing an arbitrary (though precedented) line of demarcation between those who should and should not be under consideration. I think that if you put Wilt Chamberlain on a team with 11 kindergartners, and that team won 41 games, I'd want to consider Chamberlain for MVP. That is, there should be a sliding scale, in the sense that each of the Detroit Pistons individually are less valuable than a single LeBron James, though the Pistons collectively tend to do better than do the Cavaliers collectively.

This is built right into the estimation of BoxScores: A player contributes X% of the production for a team with Y wins, and so he is credited with X•Y of those wins. Fortunately, from the standpoint of the 50-win precedent, as team wins decrease, it gets harder and harder for any player to outproduce a player on a 50+ win team.

For example, imagine a season in which player A contributes 20% of the production for a 50-win team. (20% is on the low end for MVP-candidate PVC, and 50 wins is at the low end for a contender as well, so this is a conservative estimate for an MVP frontrunner.) Such a player accumulated 0.2*50 = 10 BXS. Player B, let's say, is on a 41-win team. In order to be more valuable than A, B would have to be responsible for 10/41 = 24.4% of his team's production, which is very high, indeed. In 07-08, only two players had more than a quarter of their team's valuable contributions, and one of those was the BoxScores MVP, Chris Paul (whose team had 56 wins). LeBron James was the other, and despite contributing more than 2/7 of his team's production, Cleveland's win total of 45 reflected James' second-most-valuable status.

In sum, even if we use BoxScores as our measure of value, it is highly unlikely (although not impossible) that the MVP will come from a sub-50-win team. The precedent will likely remain intact.