Thursday, October 05, 2006

Introduction and Glossary of Terms

The concept of possession-based analysis will serve as the backbone for all statistics discussed in this forum. By using possession-based (or tempo-free/tempo-adjusted) stats, the effect of pace can be normalized. That is to say, the numbers put up by Paul Westhead's run-and-gun Loyola Marymount teams of the late 80's can be directly compared to the numbers of Pete Carril's methodical Princeton teams by using a common denominator (the possession).

I am certainly not the first to use possession-based stats-- they have been slowly gathering mainstream momentum over the past decade. In basketball circles, Dean Smith (and other coaching staffs across the country) have been using these concepts since at least the 1960's (see Smith's seminal book Basketball: Multiple Offense and Defense). More recently, Dean Oliver's book Basketball on Paper delves into some possession-based analysis (and is a must-read for anyone with even a passing interest in basketball statistics). John Hollinger's Pro Basketball Prospectus series also has a lot of great possession-based analysis (he's now providing Insider content at For possession-based NBA analysis, there's nothing better than, created by Roland Beech. Roland's site includes +/- data and possession-based stats for the entire NBA. The charting efforts at are also the most advanced and organized that I've seen, providing breakthrough insights on individual defense and passing, among other things. Another important contributor to the tempo-free movement in basketball stats is Ken Pomeroy. Ken's site ( provides possession-based stats for all 334 NCAA Division I teams, as well as great insights and commentaries. If you're a college basketball fan, add his site to your bookmarks (if it's not already there). While Ken's site has a national flavor, I'm hoping mine can develop into its ACC counterpart (while adding features such as individual defensive boxscores and +/- statistics for individuals and line-up combinations).

As for some of the terms and statistics that will be commonly-used on this blog, here's a glossary (yes, I realize that these aren't alphabetized-- I was attempting to start with the basics of possession-based stats and move forward from there):

Possession: the period of time that a team has control of the ball before losing control to the other team; possessions can be estimated as FGA + (0.44*FTA) + TO - OR

Play: a play is defined by Dean Oliver as "the period between when one team gains control of the ball and when they lose control of the ball, either when the opposing team gains control or when a shot goes up"; Dean Smith's definition of a possession was synonymous with this definition of a play; the critical distinction between a play and a possession involves offensive rebounding-- a team that misses a shot, gets the offensive rebound, then makes the follow-up has used two plays but only one possession

Pace: the number of possessions per 40 minutes used by a team; the league average for the ACC in 2006 was 68.0, ranging from 63.6 (Boston College) to 74.2 (Maryland)

Offensive Efficiency: points scored per 100 offensive possessions; the league average in 2006 was 107.7, ranging from 101.4 (Georgia Tech) to 114.6 (Boston College)

Defensive Efficiency: points allowed per 100 defensive possessions; the league average in 2006 was 99.6, ranging from 94.6 (Clemson) to 104.6 (Wake Forest)

Net Efficiency or Efficiency Margin: offensive efficiency minus defensive efficiency; the league average in 2006 was 8.1, ranging from -0.3 (Georgia Tech) to 18.3 (Duke)

Floor Percentage: the percentage of an individual's (or team's) possessions in which a score occurs (from Basketball on Paper)

Points Produced: the number of points generated by an individual player through field goals, free throws, assists, and offensive rebounds (see Basketball on Paper for a detailed formula)

Offensive Rating: points produced per 100 offensive possessions (from Basketball on Paper)

Defensive Rating: points allowed by an individual per 100 defensive possessions; defensive boxscores, compiled from charting games, are used to calculate defensive stops (forced missed shots, turnovers forced, and defensive rebounds) and stop percentages (defensive stops / individual defensive possessions) in order to calculate defensive ratings (see Basketball on Paper for a detailed formula)

Percentage of Team Possessions: the fraction of team offensive or defensive possessions used by an individual player; with 5 players on the court per team, the average value for this stat is 20%; percentage of defensive possessions is factored into the formula that calculates defensive rating; percentage of offensive possessions can be used to differentiate between role players and primary options and to rank players with similar offensive ratings (assuming similar above-average offensive ratings, a high usage player is more valuable than a lower usage player; conversely, assuming similar below-average offensive ratings, a high usage player is more detrimental to his team's offense than a low usage player)

PER (Player Efficiency Rating): created by John Hollinger, PER is a formula for rating players that incorporates linearly-weighted boxscore statistics into a single number; statistics are pace-adjusted and the formula includes team-dependent factors (e.g., percentage of assisted FG's and offensive rebounding percentage) which makes PER the best of the playing rating formulas that use linear weights; see Hollinger's Pro Basketball Prospectus series for details on how the linear weights are calculated/assigned and for the complete PER formula

"the four factors": Dean Oliver's four factors have been singled out as the most crucial statistics in determining wins and losses; the factors are:

1.) Effective field goal percentage (eFG%): eFG% incorporates made three-pointers into a standard FG%-- eFG% = (FG + 0.5*3Pt.FG) / FGA

2.) Offensive rebounding percentage: OR% = OR / (OR + Opponent's DR)

3.) Turnover percentage: TO% = TO / Offensive Possessions

4.) FTA / FGA: this pace-independent statistic demonstrates a team's ability to earn trips to the free throw line

The four factors be viewed from either an offensive or defensive perspective. Defensively, the corresponding stats are, of course, eFG% allowed, defensive rebounding percentage (DR/{DR + opponent's OR}), turnovers forced percentage (turnovers forced / defensive possessions), and opponent's FTA / FGA.

+/- Statistics: like the commonly-used hockey stat (for all you Hurricanes fans and Canadians), basketball's +/- stat captures the score during the minutes (or, more accurately, possessions) that an individual player, line-up combination, or player pair/trio is on the court; the +/- data is useful for determining a team's most effective offensive and defensive line-ups and frontcourt/backcourt combinations

On-Court/Off-Court: this stat is based on +/- data and shows the difference in net efficiencies during the possessions when a player is on the court versus the possessions that player is on the bench

For example, assume Reyshawn Terry plays 42 offensive and defensive possessions and UNC leads 51-36 during that time. Terry is on the bench for 34 offensive and defensive possessions, during which time UNC leads 37-33.

Terry's On-Court/Off-Court for this game would be: (Off.Eff. On - Def.Eff. On) - (Off.Eff. Off - Def. Eff. Off) = {((51/42)-(36/42)) - ((37/34)-(33/34))} * 100 = +24.0

A positive On-Court/Off-Court means that the team was better with that player on the court. A negative On-Court/Off-Court means that the team was better with that player on the bench.

Defensive Boxscore: defensive boxscores (compiled while charting games) show the contributions made by individual defensive players during the course of a game; they can be interpreted as the antithesis of a traditional boxscore-- while high FG%'s and low turnover totals are good in the traditional boxscore, low FG%'s and high turnover totals represent a strong defensive boxscore; FG's and FGA's (as well as FT's and FTA's) are pretty straightforward in the defensive boxscore-- they just represent shots made and attempted against an individual defender (half credit can also be awarded at the charter's discretion for good or poor help defense); turnovers forced include steals, charges/offensive fouls drawn, forced 5-second calls, and all other turnovers that can be directly attributed to an individual defender

Some FG's and FGA's cannot be assigned to any individual defender (e.g., a fast break dunk after a steal in the open court or a wide-open three after a failed trap at midcourt). These attempts fall into the 'team' category when charting. Some forced turnovers can also fall into the team category. In general, though, 90+% of defensive possessions can be attributed to an individual defender (or pair of defenders).

WORP (Wins Over Replacement Player): this is a stat used primarily in baseball circles and pioneered by the folks at Baseball Prospectus; basically, this stat represents the number of wins that a player is responsible for, as determined by substituting that player's minutes for those of a "replacement-level" player at his position; in baseball, a replacement-level player is generally viewed as the type of player that is constantly shuttling between AAA and the majors-- the college basketball equivalent would be a walk-on who's earned some spot minutes (e.g., Will Johnson or Patrick Johnson) or a lightly-recruited player who is just filling out a roster spot (e.g., Jonathan Holmes); replacement-level varies by position, with point guards and centers being the most difficult to replace

In my version of WORP, I use Hollinger's PER and make adjustments for team defense, relative pace of the league (relative to the years 1982-2006), and relative strength of the league (relative to the years 1982-2006). After making these adjustments, a player's PER can be compared to that of a replacement-level player at his position. Using a linear regression to estimate the highly-correlated relationship between defense-adjusted PER and winning percentage, a player's adjusted PER (over replacement player) can be converted to wins (over replacement player.

WORP / 35: this stat represents WORP per 35 games; this adjustment is necessary because the college season (unlike the NBA season) is not a fixed number of games (it can range anywhere from the high 20's to the low 40's depending on post-season success, pre-season exempt tournaments, etc.); by using the 35-game denominator (along with pace and strength of conference adjustments), apples-to-apples comparisons can be made across all players from 1982-2006

The top 5 individual seasons in the ACC from 1982-2006 based on WORP / 35 were:

1. Tim Duncan (1997) 8.55
2. Tim Duncan (1996) 6.58
3. Kenny Anderson (1991) 6.40
4. Ralph Sampson (1982) 6.30
5. Tim Duncan (1995) 6.30

Duncan's WORP / 35 in 1997 can be interpreted as turning a 17-18 team into a 26-9 team by replacing the minutes of a replacement-level center (say, Ralph Kitley as a freshman) with Tim Duncan as a senior. Duncan's 1997 season is 30% better than the next best ACC season of the past 25 years. Any WORP / 35 over 5 is rarefied air-- only 26 such seasons have been recorded since 1982.

I will have a follow-up post that talks a little more about the mechanics of the WORP formula and walks through an example. That, unfortunately, will probably be just as dry as this post. Once all the terms are defined and described, though, I promise that subsequent posts will a lot more exciting and enjoyable and a lot less like your garden-variety root canal.


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