# Stats Analysis: Offensive Efficiency - Center

The Bootleg's Basketball Stats Analyst Cameron Tana checks in with the fourth in his fascinating series of columns, this time focusing on the historic individual "offensive efficiency" of Stanford centers. Cameron has broadcasted Stanford MBB games, both as Dave Flemming's color man in 1996-97 & as play-by-play announcer in 1997-98. He has also done NBA game charting for www.82games.com

The last column introduced the concept of individual player offensive efficiency ratings and focused on Stanford point guards over the last decade or so. The parts incorporating offensive rebounds were not discussed in detail because offensive rebounding is not typically a big part of the point guard role. Incorporating offensive rebounds is critical for post player offensive efficiency ratings so this column will discuss the offensive rebound parts with the goal of evaluating star sophomore Brook Lopez's offensive efficiency.

The last column introduced a formula structure for calculating points produced and scoring possessions as:

Points Produced = (Field Goal Part + Free Throw Part + Assist Part) x (1-Team Offensive Rebound Part) + Offensive Rebound Part

This reflects the fact that a team can score by field goals (including three pointers) and free throws, but there are two other offensive statistics: assists and offensive rebounds. Assists directly lead to field goals, while offensive rebounds extend possessions and sometimes lead to points.

The "Team Offensive Rebound Part" is subtracted from the scoring parts to distribute credit away from the scorer and assister and to teammates whose offensive rebounds gave the team another chance to score. The "Offensive Rebound Part" adds back in the credit for the individual's offensive rebounds that give the team another chance to score. "The Offensive Rebound Part" has the following formula:

Offensive Rebound Part ~ Offensive Rebounds x Team Offensive Rebound Weight x Team Play Percentage

The "Team Play Percentage" is basically the probability that the offensive rebound will lead to points on the next play started by the offensive rebound. A "play" is the extra chance to score and is technically defined by the period when a team obtains the ball until they shoot a field goal or free throw or turn the ball over.

The "Team Offensive Rebound Part" distributes credit between the offensive rebounder and the scorer/assister duo. It estimates the difficulty of an offensive rebound (the "Team Offensive Rebound Percentage") relative to scoring on a play (the "Team Play Percentage" again). Dean Oliver set this calculation up by using the log5 method (http://www.diamond-mind.com/articles/playoff2002.htm) introduced by Bill James to calculate how difficult it is for team B to beat team A, except Oliver's team B is the rebounder and his team A is the scorer/assister duo. The team offensive rebound weight is thus

Team Play % - Team Offensive Rebound % x Team Play % divided by Team Play% + Team Offensive Rebound % - 2 x Team Play % x Team Offensive Rebound %

This year, Stanford's offensive rebound percentage is 39%, ranked by kenpom.com as 20th-best in the country. The Cardinal's play percentage is 45% so it's slightly more difficult to offensive rebound and the "Team Offensive Rebound" weight is 0.56, which is relatively low. Stanford is a good offensive rebounding team, so an individual's offensive rebounding is less important than on other teams.

Offensive rebounders are generally very efficient scorers as they often obtain the ball near the basket with the defender out of position to defend, but this efficiency is already included in the scoring parts of the equation. The scoring parts reflect put-backs, while the offensive rebound part reflects credit for starting a new play.

In 2006-2007, Brook Lopez was credited with 21 points from the offensive rebound part out of his total points produced of 290 points. Robin Lopez was credited with 37 points for the offensive rebound part out of his total points produced of 240 points. Brook Lopez's low offensive rebound rate (offensive rebounds divided by offensive rebounding opportunities) of 8% in 2007 is one of the reasons why his offensive efficiency rating his freshman year was an unimpressive 99.9.

Here is a comparison of Brook Lopez's freshman year to Robin's as well as two other centers in their class who were NBA lottery picks, Greg Oden and Spencer Hawes.

Freshman Centers in the 2007 Season

 Player Pct POSS OFF Rtg EFG OR Rate TO Rate FT Rate AST Rate Lopez B 26.7% 99.9 50.2% 8.1% 18.6% 15.5 7.6% Lopez R 19.6% 99.1 48.0% 12.4% 19.0% 17.4 8.0% Oden 28.9% 117.4 61.6% 15.0% 16.0% 30.7 5.0% Hawes 24.9% 109.6 53.3% 8.2% 19.9% 18.9 14.0%

Brook Lopez was nowhere near as efficient as the lottery picks. His effective field goal percentage and free throw rate was not as good as Oden's or Hawes'. Lopez's low shooting percentage and free throw rate were caused by a tendency to shoot fading way from the basket. His skill level that allows him to make difficult shots is enticing, but too many of his shots had a degree of difficulty. His low offensive rebound rate also limited easy shots for him.

Robin Lopez was nearly as efficient as Brook Lopez during their freshman season. This is mostly due to the lower percentage of possessions used by Robin. If he used as many possessions as Brook, his efficiency would have been lower. Likewise, Brook's efficiency would have been higher if he passed up some of those difficult shots and lowered his possession usage. Brook's high possession usage did allow his teammates to operate at a more efficient level. Stanford's offensive efficiency (adjusted by kenpom.com  for opponents defense) improved from 105 to 111 when Brook returned from injury.

This year, in the four games since his return from academic suspension, Brook Lopez has shown improvement in his efficiency even though his field goal percentage has not been good. His main improvement is in his ability to get to the free throw line. It did look like he was doing a better job of moving towards the basket before he reverted to old habits in the UCLA game. He has also lowered his turnover rate and improved his assist rate. Here are his efficiency stats along with Robin's and three freshman centers who are getting publicity, DeAndre Jordan of Texas A&M, Kosta Koufos of Ohio St., and Kevin Love of UCLA.

Lopez Twins and Freshman Centers in 2008 Season

 Player Pct POSS OFF Rtg EFG OR Rate TO Rate FT Rate AST Rate Lopez B 33.2% 107.5 46.3% 10.9% 14.4% 33.7 11.6% Lopez R 23.1% 110.0 57.1% 15.1% 22.7% 23.6 6.9% Jordan 23.6% 111.7 78.0% 15.4% 20.9% 16.5 2.1% Koufos 27.8% 113.1 52.1% 13.4% 9.7% 15.5 4.4% Love 27.7% 128.1 59.3% 16.5% 16.0% 46.9 13.9%

Kevin Love stands out here and it is especially impressive how good is numbers are in all aspects. Brook Lopez's high possession usage and low field goal percentage point to poor shot selection. Unfortunately, Thursday's game demonstrated this quite well as Love had a game offensive rating of 125 and Lopez a game offensive rating of 107, very near their season averages. Still, 107 is an improvement over last year and if Brook can up his field goal percentage with a combination of better finishing and shot selection, his production will more likely lead to better team production.

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