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# Advanced Stats For Babblers

A Daily Babble Production

In yesterday's philosophical musing about statistical analysis in basketball, I pledged to provide a guide to the measures used in this space that leave the realm of the traditional box score. This is that document.  Since I used about a week's worth of your allotted Babble reading time with yesterday's ruminations, let's get right to it with our glossary of stats currently in common use at Babble Central.

Team Stats

Possessions: FGA - OREB + TOV + 0.44 x FTA

A possession is one team's turn with the ball for a chance to score.  Possessions end with a made field goal, a made free throw, a defensive rebound or a turnover.  As we discussed yesterday, possessions are valuable statistical tools because in any given game, both teams receive very close to an equal number of possessions, thus allowing us to predict how well one team will do against another by looking at which uses its possessions more effectively.

That formula above is a slightly modified version of the approximation presented in Dean Oliver's Basketball On Paper, with FGA representing field goal attempts, OREB as offensive rebounds, TOV as turnovers and FTA as free throw attempts. Oliver references a more technically nuanced version of the formula in the book, but the one above allows for relatively accurate calculation.  The coefficient slightly lower than one-half for the free-throw attempt multiplier is used to account for situations such as conventional three-point plays and technical fouls.

There are some who choose not to subtract offensive rebounds in the formula, counting each chance offered by offensive boards as another possession.  I don't espouse that method because, as will be evident with some of the per possession measures discussed below, that seems to punish teams for offensive rebounding, which is an important skill that should if anything be rewarded rather than penalized.

Pace: possessions per game

Measures how quickly a team plays.  Not surprisingly, the Warriors and Knicks, two teams whose coaches advocate pushing the ball and getting shots up quickly, top the league in pace in 2008-09.

Offensive efficiency: points scored per 100 possessions

Measures how well teams use the possessions that they have.  Per game stats don't account for pace differences, which makes comparing teams who play at different rates difficult.  Again, since two opposing teams will have the same number of possessions in a game, who uses those possessions best will determine the outcome of the game.  Offensive efficiency normalizes for pace.  Remember, offensive efficiency is really a measure of points per possession.  But like many others, I find it easier to conceptualize the bigger numbers with fewer digits to the right of the decimal point.  Therefore, you see points per 100 possessions here.

Defensive efficiency: points allowed per 100 possessions

The same rationale used for offensive efficiency works at the other end of the floor as well.

Rebound rate: the percentage of missed shots that a team rebounds

Another stat that normalizes for pace.  Teams that play at faster paces should grab more rebounds simply because more shots go up each game.  That doesn't necessarily make them better rebounding teams.  A good rebounding team cleans the glass and keeps the opponents off it as much as possible.  Rebound rate can also be split into offensive (team offensive rebounds divided by the sum of team offensive rebounds and opponent defensive rebounds) and defensive (team defensive rebounds divided by the sum of team defensive rebounds and opponent offensive rebounds) rates to explore how teams perform on the glass at each end of the floor.

Turnover rate: turnovers per 100 possessions

Again controlling for pace.  For example, the 2008-09 Warriors turn the ball over 14.8 times per game, tying them for 20th in the league, which looks more alarming than it really is.  They play the NBA's fastest pace and actually only give the ball away on 14.9 percent of their possessions, good for 12th in the league.

Effective field-goal percentage: (FGM + 0.5 x 3PM) / FGA

This adjusts field-goal percentage to account for the value of the three-pointer.  While the shot is more difficult to make and thus shot at a lower raw percentage, it is also worth 150 percent of a two-pointer.  The common example is comparing a center who shoots 3-for-5 from the block to a guard who shoots 2-for-5 from the three-point line.  The center's raw field-goal percentage is 20 percent higher, but the two players have been equally effective, each scoring six points.  Thus, effective field goal percentage, or eFG, counts each three-point basket as one and a half makes.  As suggested by the example, eFG is viable as an individual stat as well.

True shooting percentage: total points / [2 (FGA + 0.44 x FTA)]

True shooting builds on eFG by incorporating not only three-pointers but how often teams and players get to the foul line and how well they shoot from there.  Like eFG, true shooting is also usable as an individual evaluator.

Individual stats

Per-minute stats

In order to compare production of players receiving varying degrees of playing time, one can divide a player's total volume stats by his minutes played.  As with points per 100 possessions, we often then multiply these stats back out to create more easily understandable, "game-like" figures.  Because I'm a Basketball-Reference aficionado, I often use player stats per 36 minutes, but one may also occasionally come across stats in per-40 or per-48 form here.

Effective field goal and true shooting percentage: see team stats section for details

Rebound rate: percentage of total rebounds a player acquires in his time on the floor

Rather than total rebound volume, this takes into account the varying opportunities players have to get rebounds, another issue created by pace.  As with team rebound rate, this can be split into offensive and defensive rate as well.

For a clearer idea of the scale for rebound rate, I consulted Sactown Royalty's Tom Ziller, who offered the following via email:

It's rather positional -- 20 is elite, 15 is good for bigs. [Less than] 15 is mediocre, 12 or so gets real bad (Blount/Mikki territory).  For small forwards, there's quite a range -- 8 or less is bad, you can see it up to 12 (quite good) or even 15 (Marion).

Non-Kidd/Rondo point guards generally top out at 6 or so; two-guards can get up to 10, but 8+ is strong and 7 is average.

That's all based on the last couple years, and it's total rebound rate. The offensive/defensive splits have wider ranges.

Usage: FGA + TOV + 0.44 x FTA + 0.33 x AST

Usage provides an indication of how much a player dominates the ball in his team's offense, or how many possessions he "uses" over a certain period of time (with assists adjusted for given that any assist comes on a possession also used by someone else - the guy who took the shot).  I like usage percentage, which is how many possessions a player uses per 100 plays, though it should be noted that Basketball-Reference uses a somewhat different formula to calculate usage.  Also viable is John Hollinger's usage rate, which calculates a player's usage per 40 minutes.

Turnover percentage: how often a player turns the ball over per 100 plays

Courtesy of the folks at Basketball-Reference, this estimates how regularly a player is giving the ball away.

On/off-court efficiency stats

This comes courtesy of 82games.com, which tracks each team's offensive and defensive efficiencies with and without each player on the court.  Not an end-all by any means - especially because the difference in a team's performance with and without a player depends on who his teammates and replacement players are - but it does provide another angle on the relative worth of a player to his team.

Opponent counterpart eFG percentage

One more stat brought to us by 82games, this one comes with the disclaimer that it is clearly flawed.  So far as I understand, this does not take into account team defensive schemes such as trapping, doubling and using zones or individual play nuances such as switching on screens or even cross-matching.  Counterpart eFG numbers are by no means a definitive mark of a player's defense, but they do provide a measure of how the opponent at the corresponding position performed while a given player was on the court.  Occasionally worth looking into, but perhaps it would be fairest to phrase this as "circumstantial evidence."

Shot selection

82games breaks down each player's shots into four categories: jump, close, dunk and tip.  The last three categories combine to form "inside" shots.  While the dimensions for what constitutes a jump shot as opposed to an inside shot aren't explicit, this provides a step toward differentiating between a player's shooting performance near and away from the bucket.  Further, NBA.com's hotspots charts offer a more exacting shot distribution for each player.

That about does it for now as far as the out-of-the-box stats currently used here at the Daily Babble are concerned.  As I mentioned yesterday, there are plenty of metrics that aren't listed here, not because I dislike them but because I'm still reading up on them and don't understand them well enough yet to make a judgment on using them here.  That list includes but is certainly not limited to Player Efficiency Rating (PER), Value Added, Wins Produced, Win Shares, Composite Score and Wins Above Replacement Player (WARP).  Those statistics will be added to this glossary over time as I see fit.

For now, I leave those of you interested in reading further on your own on these topics with the following list of resources and mini-blogroll, as compiled through my own research as well as discussions with Ziller and Third Quarter Collapse's Eddy Rivera:

Basketball On Paper by Dean Oliver

APBRmetrics forum

Basketball-Reference and its blog

John Hollinger's player and team stats at ESPN.com

Basketball-Statistics

Basketball Prospectus, especially Kevin Pelton's work

Basketball Value

Basketball Geek

The Wages of Wins by David Berri, Martin Schmidt and Stacey Brooknow, as well as the Wages of Wins Journal

Doug's Stats

82games

NBA.com hotspots

Thanks to each and every one of you for bearing with me through this two-day statistics extravaganza.  As always, please feel free to put forth in the comments section any questions or comments you have as well as any pertinent links omitted above.

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