Point projection: Obama’s percent of the nationwide two-party vote:

52.47%

See here. It’s going to be even more quiet around here than usual. Thanks to everyone for reading and contributing your ideas.

Borrowing from the extremely useful DougStats, and making use of Google Docs, I present a (more-or-less) daily-updated list of the 100 most valuable WNBA players, using the BoxScores methodology.

WNBA Top 100 BoxScores

easy URL: http://bit.ly/wboxscores

As I said, this ought to be updated more-or-less daily, and should serve as an easy, quick reference to see the state of the WNBA. For the uninitiated, BoxScores attempt to estimate the value of each individual player in terms of contributions to team success, and the unit being estimated is wins. Thus, as of this posting, we can see that rookie Candace Parker leads the league with a 3.76 BoxScore/wins created, followed by Lindsay Whalen with 3.34… odd that Whalen failed to make the Olympic team, being that she is the second most valuable WNBA player in the league right now.

Note: Since the regression coeffeicients employed in Model-Estimated Value (MEV) were fitted for the NBA, it is unclear whether or not their values translate identically to WNBA play–that is, a steal in the WNBA may be worth more than in the NBA, or less, etc. However, based on the work of others, I’m assuming there is relatively little difference between the leagues on this front, and since the formula is applied evenly across all WNBA players, I will assume that the differnces even out on average. Let me know if you find this list useful, and whether or not the ranking seems to mesh with your own subjective perceptions.

Many conversations about sports revolve around comparisons of quality — team A is better than team B, player X is the best of all time, this draftee will help his team more than that one, etc. For this type of discussion, many metrics exist, both qualitative and quantitative, one of which is BoxScores, developed here at the Arbitrarian. Other conversations center around similarity–team C plays like team D did in the 1980s, player Y is a taller, faster player Z, etc. The Arbitrarian has spent substantial time investigating this type of comparison as well, using statistical proximity and network diagrams. Yet another characterization, somewhat more general than direct similarity comparisons, is that of type, or style. While playing style has been discussed here, and style markers can be seen everywhere in my work in the form of various colorations, I would like to develop the idea a little more fully, and present a novel graphical visualization of the concept applied to NBA players.

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 accross 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 triplet of (0.8, 0.2, 0.7) is an interior scorer, without much perimeter production. A player with this triplet (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 paired 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.

The advantage of a conversion from RGB to HSV is that, by combining the S and V, we can represent the entire playing style spectrum in a format resembling a color wheel. This is the most straightforward and useful format for presentation, and this graphic is the big payoff:

Click to view in a Google Maps format. Also available at the easy-to-remember http://bit.ly/spi

As you can see, each of these NBA greats is aligned at a certain angle and distance from the center (I used polar coordinates as a basis for this plot), and this allows us to identify relatively similar players, player’s “opposites,” clusters, and other interesting observations. In this graphic, players with greater MEV (Model Estimated Value) are larger, and this allows comparisons along radii, as in X plays in a similar manner to Y, but is more valuable/productive.

Vocabulary

There are several ways our statistical vocabulary can be expanded via the SPI Style Trichotomy. The first is that we can characterize the degree to which a given player is Scoring/Interior/Perimeter-focused by reporting their index value. The second is that we can describe the player’s color–”He’s a deep blue defensive center,” or “Shane Battier is not chucker! He’s a cyan-colored scorer’s opposite type.” Finally, we can approximate a vector–I suggest the convention of overlaying the hours of a clock over the spectrum diagram (to indicate vector direction), with 12 o’clock at the very top, 1:00 at the interior’s opposite position, 3:00 at the scorer’s position, 4 o’clock bisecting the scorer and perimeter’s opposite position, etc. Distance from the center of the diagram (the length of the vector) indicates the degree to which a player fits exactly into their playing style–those players whose games are more balanced are closer to the center, players whose games are more specialized or narrow are further from the center. So, one could say, for example, “Dikembe Mutombo is a pure 7 o’clock,” or, “Michael Jordan was between about a two and three for most of his career, but in 88-89, he shifted closer to a pure 11.” And so forth.

Feedback

I would be very interested to hear any and all comments–does the trichotomy make sense? Is it useful? Are the S/P/I typologies a reasonable first division? Is it helpful to have a more continuous, yet still quantifiable, tool to describe player type than just position labels? Do you like the idea of equating, for example, a shoot-first point guard with a yellow-green 12 o’clock player? Does the graphic offer any new insight, confirm your subjective observations, or conflict with your opinions? I will be following this post up with many more using this methodology and this type of display, I hope you will come back often, or possibly subscribe.

Who are the most consistent scorers in the NBA? This is a question of some interest for those who participate in fantasy leagues, as consistency might be a virtue in determining the value of a player on your roster. For various reasons, a player might be worth more to you if they score 20 points every game, rather than alternate between 10 and 30 every other game. Further, some measure of consistency may highlight a player’s ability to impose their will on a game: a player able to get his scoring in, regardless of the opposition, could be said to be more of a game-defining player.

I’ve managed to estimate, for players since the 86-87 season, each individual’s mean points per 48 minutes, as well as the standard deviation of said statistic, and thus the coefficient of variation (sd/mean) and 95% confidence interval. Here’s a spreadsheet of the top (634) players in the league, by mean pts/48, sorted by coefficient of variation. Thus, the players at top could be said, in some way, to be more consistent scorers than those at the bottom.

Most consistent scorers, 1986-2008

Below is another way to view the same question. Using each player’s mean and standard deviation pts/48, along with the sample size, we can construct a 95% confidence interval for our estimate of their true mean. In the graphic linked below, each player is ranked by their mean pts/48, and the x-axis indicates how they fare under this measure of scoring. Each mean is surrounded by a line indicating the 95% confidence interval. This means, essentially, that we can be 95% sure that the player is within the span of their colored line. For players with smaller samples or greater variance, the error bars will be wider.

NBA Pts/48 min means with error bars

As you can see, some players have no error bars at all–this means that they only have one observation. Others’ error bars go down past zero. This means that we can be 95% sure that their mean pts/48 is in a range that includes zero, which doesn’t tell us very much. Anyway, here is the same graphic, for the 2007-08 season only:

Note that Carl Landry (#73) has a greater variance than most players around him, but he ranks as a better per-48 scorer than Shaquille O’Neal.

Finally, here’s a regular-season 2007-08 graphic for players’ MEV (or model-estimated value, using regression-derived regression weights like those seen here). Landry does even better here (18th), in terms of his mean, but his confidence interval is very large. This estimate suggests, though, that at worst, he’s about as good as Odom, Andre Miller, and Kirilenko; while at best, he is in rarified air. Keep in mind that this is still just a 95% confidence interval, so statistically, there’s still a 1 in 20 chance the true mean isn’t even in this interval. All should be taken with a grain of salt. One of the things I like most about this presentation is that it’s a per-minute stat, which controls for playing time (although not pace), but still reminds us that estimates for those players with little playing time should be taken with large grains of salt, and might not really mean much of anything. Josh McRoberts, for example, is probably not the 406th, much less the 6th, most valuable player in the NBA, even though his simple arithmetic mean indicates as much–his confidence interval reminds us of this, while maintaining the simple ordering.

I suppose this is also the public debut of any sort of official MEV ordering for 2007-08. I’d be interested to hear what people thought about this… this is something similar to Berri’s estimates, but I think the weightings are a little more appropriate. Let me know in the comments if they seem, at least, per-minute, to be reasonable estimates and orderings of player value.

All Johnsons, all Phoenix Suns players. In fact, some of the greatest Johnsons to ever play the game played some of their best seasons for the Suns. Looking at Winshares, over the history of professional basketball, approximately 2.4 percent of all wins can be attributed to players with the Johnson surname. For the Suns franchise, however, that number jumps to 7.8 percent. A look at the Suns’ Winshare franchise history gives a sense of just how pivotal these Johnsons have been:

Barkley had the all-time most valuable season for a Sun in 1992-93, but it certainly looks like Stoudemire has the potential to take that title away. Amare had a huge rookie year in terms of Winshares, and was duly recognized for the Rookie of the Year award. Since then, he has essentially doubled his win production, and his best years are likely still ahead of him.

Another pattern of interest in this visualization is the recent history of all-star quality point guards. Kevin Johnson, Jason Kidd, Stephon Marbury (when he was a productive player), and Steve Nash, all played large roles in their teams’ success. However, it’s equally interesting to note that they played very different types of games. Just looking at their playing type spectrum coloration (see this post for more detail), it is possible to see that KJ and Nash are much purer perimeter players, while Kidd, as evidence by his slightly bluish tinge, was more of a rebounder, and mustard-colored Marbury shows evidence of a proclivity toward scoring along with his perimeter play–at least moreso than the other three.

What other trends do you notice in this history? Is it possible that Nash hasn’t ever been the Suns’ most valuable player, even in his MVP years? Can any of you basketball historians comment on the Westphal, Davis and Nance years?

Note: Since this post was published, the Winshares formula has undergone some revisions of some substantive import. To see the most current iteration and accurate tables and graphs, please see the Winshares page.

Here’s the game two estimate of who deserves credit for the win:

I’ve added a column since last time, G/B, which stands for “Good over Bad,” meaning I divide the linear-weighted sum of good things the player did over the linear-weighted sum of the bad things he did. It’s a playing-time-independent measure, and it highlights especially those players who were a “spark” off the bench, like Posey and Powe (who sounded on the radio like he had an incredible game), and Turiaf.

Two things to worry about if you’re a Boston fan and be happy about if you’re a Lakers fan: Kobe Bryant almost did enough to get the win for his team–he finally had a quarter and a half-ish in which he really took over and made his team compete. Kevin Garnett had a pretty poor game last night–missing as many shots (with a worse percentage) as did Kobe, and turning it over four times. He rebounded well, but the Celtics as a team out-rebounded the Lakers by only one. Put it this way for Garnett: Leon Powe, in just over a third of Garnett’s playing time, outplayed Garnett (in terms of Credit for the win) by half. We’ll see how things pan out in LA.

I also thought I’d also look into home-away free throw and personal foul disparities. Over the 1986-97 to 2007-08 period, in regular season games, home teams were called for an average of 22.17 personal fouls, compared to 23.04 on the visitors. Home teams shot 27.08 free throws to away teams’ 25.71. Difference of means tests for both of these were significant. Interestingly, free throw percentages are also significantly different: 0.752 for the home team, 0.750 away.

Note: Since this post was published, the Winshares formula has undergone some revisions of some substantive import, as well as a renaming. To see the most current iteration and accurate tables and graphs, please see the BoxScores page.

This post is a lengthy discussion of the theory and methodology behind the Winshares player value metric. If you are already familiar enough with Winshares, or are impatient, read the “In brief” section just below, and then you might want to skip ahead to the payoff graphics at the very end of this post. As always, comments and criticisms are encouraged!

In brief

Winshares are a statistic developed to estimate a player’s value in terms of wins. Combining individual statistics with team performance, Winshares allocate credit for team wins according to each team member’s contributions to team total production. As of the end of the 2007-08 regular season, Winshares are calculated as follows:

winshr = (val / team val) * team wins

val = pts – fgx*0.5603802 – ftx*0.9345311 + as*0.7697530 + or*0.8709732 + dr*0.7111727 + st*0.9190908 + bk*0.9495596 – to*0.8473544 – pf*0.7729732

Motivation

Why create yet another statistic that attempts to reduce all of player value to one number? Especially when there are so many other good and widely accepted measures already in use? Because the theory is sound, the operationalization is elegant, and the results appear valid.

Why use boxscore stats, ignoring plus/minus and everything that modern science now knows about possessions and efficiency, especially since defense is so poorly captured and other statistics, like assists, are arbitrary? Because boxscore stats go back to the beginning of professional basketball. Plus/minus is extremely data-intensive to calculate, and we have no way of getting that kind of data for most historical games. I’m ignoring possessions, and not emphasizing defense, because it is my belief that comparing one player’s boxscore stats to those of his team gives a reasonable estimate of player contributions–sometimes overestimating, other times underestimating, but on average, getting it approximately right. Mostly, though, calculating Winshares is possible as long as the same stats are tracked for all players on a team, and we know how many times the team won–meaning it can be applied very generally.

Why even try to use statistics to measure player value? You can’t capture that with a number! There is much to be said on both sides of this issue. I am of the opinion that statistics ought to be considered within a larger context of other data, qualitative and quantitative. However, I do feel strongly that numbers have a lot to tell us–they allow us the hope of greater objectivity, and therefore possibly less subjective, more accurate assessments. When applied identically to all players, Winshares will adjudicate “fairly,” paying no attention to max contracts, shoe endorsements, nicknames, or “intangibles.” Intangibles are tricky–they may indeed be part of player value, but they are also, by definition immeasurable, and may therefore expand to fill the role required of them? Was your favorite player not voted league MVP? Certainly they failed to consider his intangibles, which would have easily put him over the top…

Why are Winshares measured in that specific way? Don’t you know that linear weights are no good, or that assists are worth much more than you give them credit for? Read on…

Theory

Imagine a cooperative grocery store, owned by those who work there. At the end of one year, the store’s revenues exceed its expenditures by a large margin, and the workers are to be paid out of this surplus. One concept of fairness might dictate that a worker who worked p% of the total man-hours for that year ought to receive p% of the surplus. Arguably, he contributed p% of whatever effort determined whether or not the store would succeed, and should be rewarded accordingly. A worker working a large number of hours could be said to have contributed more to the store’s success or failure than another who only worked one shift a month–if the store profits by a large margin, that employee should receive a larger share of the windfall, just as if the store loses money, that employee should be held culpable for a larger share of the deficit.

Now imagine another similar store competing in the same market. Its surplus at the end of the year is twice that of the first store. Is it possible to compare the value, in terms of surplus, of employees from the two different stores? I would argue that it is possible: if pay is allocated in the same manner in both stores, with worker i in store j receiving payment in proportion to his labor contribution, the worker who receives the highest paycheck is the most valuable. That is, if pay is equal to worker man-hours over store total man-hours times store surplus, we can compare employees across any two firms in the same market.

But wait–what if some employees are more efficient workers than others? What if Alice can generate three times the revenue that Bob can generate in the same number of hours? Doesn’t our payment formula then overpay Bob and under-reward Alice, and doesn’t this complicate yet again the comparison across firms? Yes it does, and so we might try to find better measures of worker contributions to the surplus. Perhaps we could keep statistics on the number of cans shelved, or the number of transactions tendered, or the number of smiles flashed–if we could figure out even just the relative value of each of these things (that is, not necessarily how they each translate into surplus, but whether one smile is worth two cans shelved, etc.), then we are back on track. It doesn’t matter whether or not we can measure exactly how much revenue is brought in by each additional shelve stocked (although this would be interesting and useful), but if we know that it’s worth more (by some scalar factor) to clean the bathroom than it is to check receipts at the door, we can still estimate each workers contribution to the total amount of valuable work being done at the store.

This analogy carries over very well to sports, and specifically here, to basketball. A player who plays fully 1/5th of total team minutes played (that is 48 minutes per game for 82 games) ought to be credited with approximately 1/5th of his team’s success or failure–both of which can be measured in terms of wins. Using minutes to assess contributions runs into the same problem as in the stores above–they say nothing about efficiency–and as such, it is useful to find other statistics that more accurately estimate contributions to team success. The statistics employed in Winshares are boxscore stats, such as points, rebounds, assists, missed shots, etc. These are imperfect measures, but to the extent their relative value can be assessed, they may be useful in estimating each player’s contribution.

Calculation

Unfortunately, this relative evaluation is very difficult. It is often claimed by more “sophisticated” observers of the game that most fans fail to look past point-per-game numbers, giving infinitely more weight to scoring than to any other contributions. Yet, it is exceedingly difficult to identify just what the appropriate weights might be. Multiple regression analysis yields somewhat unsatisfactory results when applied in a straightforward manner–typically finding, for example, that offensive rebounds are actually detrimental to team success. Other work, including that done by Berri and Hollinger, is much more thorough, but leaves something to be desired (a topic which has been covered better elsewhere than can be possibly done by this author in this exposition).

As for Winshares, it would be disingenuous to claim that the ideal and true set of values has been found, but it is my belief that the reasoning is sound, and the results pass the “laugh test,” that is, given a subjective assessment of the sport, the relative importance of each boxscore statistic seems to be, at the very least, in the right order.

To identify the weights used, we may begin with a simple but strong assumption: the most valuable “good things” are those that opponents are most resistant to allowing, and thus are relatively rare, while the most detrimental “bad things” are those that a player is most trying to avoid, and thus are similarly relatively rare. With this in mind, I present counting sums for each of 8? boxscore counting stats from 1979-80 through 2007-08 (which I call the Modern era, characterized by the introduction of the three point shot to NBA play):

* field goals missed and free throws missed

Dividing each of these totals by the sum of the totals (17,008,507), we arrive at the following frequencies:

Normalizing these frequencies to that of points, we get:

Then, subtract each of the above from 1, so we are placing more weight on the rarer occurances, and set the points coefficient to 1, because the ultimate aim of all defense is to prevent scoring, and the ultimate aim of all offense is to score:

Assign positivity and negativity according to whether each is helpful or deleterious to team success, and we arrive at a set of scalars for estimating valuable contributions (often abbreviated val):

val = pts – fgx*0.5603802 – ftx*0.9345311 + as*0.7697530 + or*0.8709732 + dr*0.7111727 + st*0.9190908 + bk*0.9495596 – to*0.8473544 – pf*0.7729732

Any player’s val less than zero is then set to zero, but val is rarely a large negative number. Compared to the difficulty of valuable contribution assessment, the final steps in Winshare calculation are extremely simple: merely find each player’s percent contribution to his team’s total sum of valuable contributions from all players, and multiply this by team wins:

winshr = (val / team val) * team wins

We are left with an estimate of individual player value that combines individual contributions and team success, and allocates the most credit to those players who did the most to win the most. There is just one adjustment made to allow comparisons across all NBA seasons: for seasons prior to the official distinction between offensive and defensive rebounds, the formula is adjusted to incorporate total rebounds in their stead.

Discussion

The first thing to note is that as we apply the formula increasingly further back in time, we might become somewhat less certain of its absolute accuracy as the boxscore statistics on which it is based drop from the official record. Thus, for the very earliest years of the BAA, we might not be as confident in our estimate as for most years since, but the results are still very compelling, and seem to hold up to scrutiny despite the relative dearth of data. One of the merits of Winshares as a measure is that it is relatively flexible across a variety of situations, relying as it does on player percent contributions, which can almost always be measured in some manner.

Another caveat is to bear in mind that Winshares is a season-cumulative statistic, and so the ceiling varies by the number of games played in a season. Winshares for the strike-shortened season of 1998-99 are much lower than other contemporary seasons, due to the fact that all teams won fewer games than they normally would have. Adjustments can easily be made, however, by finding per-game or per-minute Winshare rates, and making comparisons at that level. This helps, too, in determining the impact of an injured player, given that he has played fewer games. However, the initial impetus for constructing Winshares was to estimate player value in terms of wins, and this is best done on a season-cumulative scale.

One thing done relatively poorly by Winshares in its current iteration is measurement of the value of players traded during the season. To do this completely accurately, it would be useful to isolate only the games the player appeared in for each of his several teams, looking at individual statistics and team wins within those sub-season units. However, this sort of analysis requires data not generally available in convenient form, and truly, the logical extension of this idea is fairly well captured by the plus/minus statistic. As it stands, Winshares still does a relatively good job (subjectively assessed) in measuring traded players’ value, but it is something worth noting.

Winshares in application

Often understanding is best achieved through application, and so I present

The Top 1,000 Winshare Seasons

covering the NBA, ABA, and BAA from 1946-2008. Keep in mind the above caveats about data availability, especially for seasons prior to 1951-52. In a similar vein, here is a list of

The Top 100 Winshare Careers

again, this is cumulative across the entirety of each player’s career, and so players with longevity are advantaged. I have included games played in this listing, to allow the reader to make his or her own adjustments.

Finally, every player, every team played for, 2007-08 season.

Geometric representation

One of the more useful ways to conceptualize Winshares is as player percent valuable contributions * team success. This has a particularly interesting expression in geometric terms, where Winshares can be thought of as the area of the rectangle created by multiplying valpct by team wins. The following series of visualizations depicts Winshares as a geometric comparison of player value. The color scheme is based on playing style–more detail on this classification may be found here.

2007-08 NBA: Chris Paul edges out Kobe Bryant as most valuable player according to Winshares, Kevin Garnett and Paul Pierce turn in stellar seasons for the Celtics, and LeBron James carries a huge load for his team, and is rewarded in terms of Winshares, if not in post-season success.

1986-87 NBA: A season featuring more all-time greats than perhaps any other (as noted here), we see Larry Bird and Magic Johnson at the height of their rivalry, Michael Jordan and Hakeem Olajuwon coming into their own, and too many other star players to even mention.

1971-72 NBA & ABA (combined): Classic Lakers and Celtics teams, a young Dr. J, Kareem’s greatest year, an almost-as-great year from Artis Gilmore, and countless other NBA past greats.

Sacramento Kings Franchise History: This storied franchise didn’t quite make the playoffs in a very competitive 2007-08 Western Conference, but its history is littered with greats such as Oscar Robertson and Chris Webber.

Thought I’d point you to the People’s Statistic Project: http://peoplesstatistic.googlepages.com. Go and make your voice heard, I’ll have some analysis of the project up later.

I wasn’t invited to the TrueHoop Stat Geek Smackdown (see also), but I figure I’m just as capable of making wild, semi-empirically based predictions as anyone else, so I have done so. I’ll try to keep this up, round-by-round, and we’ll see how I do against more well-known Stat Geeks. Perhaps if I do well, someday I will be a TrueHoop-acknowledged geek…

Using just True Winning Percentages and bernoulli probabilities, I’ve calculated the probabilities of each possible series outcome, and then normalized to sum to one. (See my spreadsheet) For the first round, I have:

BOS in 4
CLE in 7
ORL in 6
DET in 5
LAL in 6
HOU in 7
SAN in 7
NOR in 6

Probabilities, as sparklines: