Envisioning the NBA

Statistics

This glossary describes and details each of the original statistical measures I have developed for the analyisis of NBA players and teams.

dist is a measure of per-game statistical "distance" from the "origin." See this explanation for more details.
ds if you can't decide whether you prefer dist or side, just multiply them together. No geometric analogy, just for the sake of interest.
flex, or position flexibility, is a herfindahl-like index of the degree to which a player's statistics characterize him as fitting perfectly into his p0s (higher) or as being fairly close to more than one p0s (lower, to a minimum of 0.2). See also p0s.
herf, or Herfindahl Index, is a measure of concentration used in the social sciences. Here, I use it to measure the degree of concentration of production by team. To derive herf, one sums the squares of each player's percent contribution to the team total. The higher the Herfindahl Index, the greater the concentration -- a herf of 1 indicates perfect monopoly.
metric is a team-success-independent measure of player performance, based entirely on individual-level statistics. This measure weighs each counting statistic equally and takes into account both absolute productivity and versatility. metric = wilt * oscar, and as such the maximum possible metric approaches 1.
o, when preceding a statistic such as pts --> opts or owpct (opposing teams' winning percentage), indicates that the statistic measures opposing teams' performance.
oscar, named for Oscar Robinson, is a measure of statistical production that emphasizes versatility. Derived from the geometric mean, the formula is: oscar = pts*tr*as*st*bk/to/(gp^4), and then the percentile of this number relative to all other players is taken, to normalize.
other is a simple unweighted sum of several individual level statistics, to give an idea of non-scoring contributions:
(tr+as+st+bk-to)
p0s or proximity-based position estimate is a guess at player positions. The dataset I've been using doesn't have player position data, so I have attempted to estimate it. By choosing one "prototypical" player at each position, I use an algorithm that finds the euclidian distance from a player to each of the five "ideals". The position of the closest "ideal" is then assigned to the player. The tricky part is picking the right ideal types. See also flex.
side is a measure analogous to the volume of a rectangular prism formed by a player's per-game statistics. See this explanation for more details.
t, when preceding a statistic such as pts --> tpts or val --> tval, indicates that the statistic measures a team's performance.
val, or "valuable contributions," began as a straightforward, unweighted sum of player and team statistics: (pts+tr+as+st+bk-to). However, it has since been modified to weigh assists and blocks somewhat differently:
(pts+as/(tfgm-fgm)/(tfga-fga)+tr+st+bk/(tdr/(tdr+oor))-to)
Similarly for teams.
valpct for each player is that player's val divided by his team's total tval.
wilt, named for Wilt Chamberlain, is a measure of statistical production that emphasizes absolute statistical accumulation. Derived from the arithmetic mean, the formula is: wilt = (pts+tr+as+st+bk-to)/gp, and then the percentile of this number relative to all other players is taken, to normalize.
winshr, or win share, is a measure of productivity. Essentially, it credits each player for their contribution to team performance, allocating team wins to each player according to their valpct: (valpct*tw) The idea is that each player is responsible for some of his team's production, and that team's production results in some number of wins -- if a bad player is responsible for a large valpct, team wins will be lower than if a good player was in his place, this difference is reflected in winshr. This measure is useful in attempting to determine value, as it is a more flexible way of determining the "best player on the best team", leveling the playing field for good players on great teams and great players on good teams, for example. See also this background.
wtdwn, or weighted winshares, is used as a career measure of winshares, rather than the per-year average. wtdwn adjusts for an 82-game season, which de-emphasizes the toll of injury. This concession makes this less of a value measure than the original winshr.

Tables

Winshr MVPs player with highest winshr, by year. This is how I would pick the MVP.
Winshr Top 1000 Seasons highest winshr seasons, modern era.
Winshr Top 1000 Careers players with most total career winshr, summed since the 1979-80 season.
Wtdwn Top 1000 Careers players with greatest weighted winshr averages for their career (since 1979-80). Adjusts for injury- and strike-shortened seasons.
Proximity P0sitions 100 players, with proximity-based position estimates and flexibility scores. Mostly a novelty, but the algorithm does a pretty good job of guessing positions correctly.
Dist Top 1000 Seasons listed with side, for comparison.
Side Top 1000 Seasons listed with dist, for comparison.
Dist Top 1000 Careers listed with side, for comparison.
Side Top 1000 Careers listed with dist, for comparison.
DS Top 100 Careers doesn't really mean anything, but I think the rankings look good.
Metric ROYs rookies with highest metric, by year. Seems to be a better predictor of actual ROY awards than winshr. Listed along with the top draft pick for that season and their performance, for comparison.
Metric Top 1000 Seasons highest metric seasons, modern era.
Metric Top 1000 Careers players with highest career metric, since the 1979-80 season. Other than ranking Elton Brand above Magic Johnson, this statistic seems to sort everyone pretty well.

Graphics

Here is a collection of graphs derived from and illustrating relationships in the data. For some of the larger graphs, I recommend using the center-mouse-button scroller to slide around. Made with Stata and Adobe Illustrator.

Scatter of points and "other" (as+tr+st+bk-to) per game, with labels color-coded according to playing styles. The composition of each player's statistics were scaled relative to the rest of the league, and RGB color values were assigned according to this relative tendency. For example, a player who rebounds and blocks shots an inordinate amount relative to his shots taken, assists and steals, (and relative to the league) will appear a very pure blue color. Players with very league-typical distributions of statistics are gray, etc. For the 2006-07 season. view
Click here first! Similar to the previous scatter, except that this covers the entire modern era (1979-2007), and is much, much larger. view
new Table-like scatter of teams over time, displaying per-game point differential, and indicating success with a value scale. Teams listed in descending order of winning percentage over the course of the modern era. Useful for noting trends in team success over the years. view
new Scatter of weighted winshares over draft pick number, to give an idea of the relative value potential of a given draft position. Weighted winshares are used to indicate per-season value over each player's career, and minutes per season (another indicator of success, if not production) is indicated by a value scale. Expected values (empirical means) for each pick are indicated in light pink, as are the points one standard deviation above and below that mean. view
new Scatter of winshares by years in league, for players whose careers have spanned at least ten years (the median career length). The general shape of the scatter, augmented with a median spline plot, give and indication of an NBA-typical career arc. I eliminated players with shorter careers based on the observation that those who have shorter careers typically do so because of lack of production or injury. My interest was to focus on those players who "made it" -- the best players in the league, and their career arcs. It is also interesting to note the players at each experience level who outproduce their peers. view
new Scatter of team winning percentage by team herfindahl index of val. Contrary to my initial expectation that the best teams would be those with the best balance of good players, it appears that teams for which valuable contributions are highly concentrated see the most success. The worst teams are those with more uniformly bad players. Recalculating the herfindahl index for only the top five players, or using minutes played instead of val, results in similar findings. A value scale indicates approximate pace of play for each team; there does not seem to be a causal relationship between pace and success. view
new Display of player winshr over time, for the careers of the top 28 players of the modern era, by wtdwn. Players listed in order of the median year of their career. Each season's winshr are totals noted, reinforced by a value scale, to make trends more noticable. view
new Graphic detailing two ways to measure statistical performance, dist and side. view