Friday, April 21, 2006

Homecourt Advantage?

Question: Which NBA statistics are responsible for the homecourt advantage?

Answer: See my article at


Thursday, December 29, 2005

To Assist or not to Assist

………………..that is the question. The NBA is plagued by talented players that are overzealous and shoot, shoot, shoot all game long. Lebron James recently declared jokingly that he hopes to never have another 50 point game because he has lost both games in which he scored 50 or more points. And then, there is Kobe who attempts 30 plus shots per game and makes approximately 44% of those shots. With the exception of Cleveland, the top five scorers in the game (Iverson, Kobe, Lebron, Arenas, and Paul Pierce) play for teams that are ranked lower than number five in their conference.

So, how important are assists. Looking at the top and bottom six teams in the league in winning percentage indicates that assists are very important. Differential team APG (DTAPG) was computed by taking the difference between the Team Avg APG and the Team Avg Opponent APG. The top six teams in the league (Detroit, San Antonio, Dallas, Cleveland, Phoenix, and Memphis) have an average DTAPG of +2.8. All of the top 6 averaged more assists than their opponents and had positive DTAPG with the exception of Cleveland (deja-vu) whose DTAPG was -2.5. Phoenix, thanks to the great Steve Nash, had the highest DTAPG (10.4). In contrast, the bottom six teams in the league (Toronto, Atlanta, New York, Charlotte, Portland, and Houston) have a -2.8 average DTAPG, and all averaged less APG than their opponents.

DETROIT .885, 24.0, 19.4, 4.6
SAN ANTONIO .759, 19.9, 16.6, 3.3
DALLAS .750, 17.4, 17.0, 0.4
CLEVELAND .630, 18.9, 21.4, -2.5
PHOENIX .630, 26.3, 15.9, 10.4
MEMPHIS .630, 19.3, 19.0, 0.3
TORONTO .241, 19.7, 23.3, -3.6
ATLANTA .259, 18.0, 19.6, -1.6
NEW YORK .259, 17.4, 20.7, -3.3
CHARLOTTE .345, 19.9, 22.1, -2.2
PORTLAND .357, 17.1, 19.2, -2.1
HOUSTON .370, 17.4, 21.1, -3.7

To Assist or not to Assist is the question and the answer appears to be……… To Assist.

Thursday, December 08, 2005

Not All Divisions are Created Equal: Goodness of Team Factor (Part 2)

Philadelphia is currently number one in the Atlantic Division; however, their record is a mediocre 8-10 (0.444). Lucky for the 76ers they are in a division that is averaging only 0.36 wins. The Central division is led by the Pistons who currently have the best record in the league (0.867). This division is one of the most competitive in the league with all teams coming out on top more than 50% of the time thus far this season. Team schedules are weighted more heavily be teams in their division and conference; thus, the quality of opponents is not equivalent in the NBA.

The number of wins is macroscopically a function of points and points allowed which are functions of most statistics i.e. FG%, TO, RB, 3PT%, BLK, STL, FT%, and PF. Wins are positively influenced by increases in FG%, RB, 3PT%, BLK, STL, and FT%, and increases in TO and PF negatively win percentage. A team win is a result of superior stats and/or a suppression of an opponent’s stat or stats.

Any statistical comparison made in the NBA between players or teams requires some factor to account for the quality of opponent to mitigate error and add validity.
The individual game statistics for a team that has won only 20% of their games against an opponent that has won 90% of their games (and vice versa) must be analyzed appropriately. The Goodness of Team Factor (GTF) provides one method of accounting for opponent quality in statistical comparisons. The GTF can be used to account for single game statistics (discrete GTF) or season average statistics (continuous GTF).

Equation 1:

GTFx (discrete) = 1 + (y-x)/f

GTFy (discrete) = 1 + (x-y)/f

Where x = # wins/ total number of games played for team A

y = #wins/total number of games played for team B

1/f = stat factor (1/4 is an approximation)

The stat factor is the contribution of the statistic in question to win percentage. The GTFx (discrete) or GTFy (discrete) may be used to multiply the following individual game team or player statistics for Team A or Team B: FG%, PPG, RB, or 3PT%.

Equation 2 depicts the continuous GTF which can be used to determine the quality of opponent effect on the following season averaged team or player statistics: FG%, PPG, RB, or 3PT%.

Equation 2:

GTFx (continuous) = 1+ SUM (y-x)/ fN

Where N = total number of games played


The 76ers play the Pistons. The Pistons have won 87% of their games compared to the 76ers who have a 44% winning percentage. Both teams shoot 50% from the field. How would you rate their performance? Adjusting the FG% for opponent quality, results in a FG%gtf of 55% and 45%, respectively, for the 76ers and Pistons. The GTF provides a method of quantifying the fact that although both teams had the same FG%, the 76ers’ 0.50 FG% against a team with a much higher win percentage was more impressive.

76ers, Pistons
win% 0.444, 0.867
GTF 1.106, 0.894
actualFG% 0.500, 0.500
FG%gtf 0.553, 0.447

Sources of Error in the GTF:

1. The GTF is more accurate as the number of games played increases.

2. The stat factor is just an approximation. I will perform a rigorous determination of this factor based on historical NBA data.

3. The GTF does not account for different dependences of stats on winning percentage. In theory, each statistical measure of basketball should have a unique GTF.

Monday, November 28, 2005

Not All Divisions are Created Equal: Goodness of Team Factor

The Goodness of Team Factor (GTF) provides a method of accounting for opponent quality in statistical comparisons. For example, the Washington Wizards were 3-0 against Toronto, New York, and Orlando. On the other hand, Cleveland began their season facing a tougher line-up and were 1-2 against New Orleans, San Antonio, and Memphis. Comparing the individual player or team averaged statistics for these two teams during this period of time may result in improper conclusions. The GTF can be used to account for opponent difficulty in single game statistics (discrete GTF) or season average statistics (continuous GTF).

Stay tuned.................


Sunday, November 13, 2005

Red Hot in DC

Last night the Wizards shocked the Spurs. This was definitely a break out game for the Wizards. The Spurs came into this game 5-1, while holding their opponents to an average of 88.8points. But, the Wizards rained on their parade beating the Spurs 110 to 95while shooting 55%. Gilbert was again spectacular and scored 43 points while shooting 75% from the field against the reigning NBA champions (wow).
The Wizards' bench scored over 20 points which is a vast improvement from
last years' team. Another key to this win was the Wizards' defense (Haywood,
Ruffin, and Jeffries) who were able to shut down Tim Duncan. Tim
scored only 11 points (3/18 from the field), and remained scoreless in the
second and third quarters. The Wizards' only weakness was their free throw
shooting percentage. Their defense, bench scoring, field gold
percentage, assists, and rebounds were exceptional, and led to an exciting defeat of
the Spurs.


Tuesday, November 08, 2005

Wizards’ Report Card-Week 1: How much better are they?

The Wizards have defeated Toronto, New York, and Orlando to begin the season 3-0 (hooray). But, wins are not the only important numbers. A comparison of average player stats last season to the first week averages of PPG, TO, MPG, FG%, OFF REB, DEF REB, APG, SPG, and BPG was used to grade each starter. One point was accessed for each stat that was higher than last season’s average (with the exception of TO). One point was granted when TO was less than last years’ average. For all stats that remained the same as last year, 1/2 point was given.

Gilbert Arenas: Grade = B (4/9)
Biggest jump: +14% in BPG; Biggest bump: -43% in SPG

Antonio Daniels: Grade = C (2.5/9)
Biggest jump: +15% in APG; Biggest bump: -47% in PPG (MPG were +4%)

Brendan Haywood: Grade = A- (5.5/9)
Biggest jump: +79% in BPG; Biggest bump: -67% in APG

Antawn Jamison: Grade = A (7/9)
Biggest jump: +179% in BPG; Biggest bump: -17% in OFF REB

Jared Jeffries: Grade = C- (2/9)
Biggest jump: +196% in BPG; Biggest bump: -65% in OFF REB

1. Haywood was the only starter up in OFF REB.
2. The only starter down in TO was Jamison.
3. Largest overall increases were in BPG.
4. 3PT% and FT% were not included because of lack of data.


Saturday, November 05, 2005

What is the NBA’s most valuable position?
Vol 1.

Last season point guard Steve Nash was named the league’s regular season MVP. But, how does his position rank? We know that all men are created equal, but how do NBA front offices think of court positions?

Depth Chart Data obtained from was used to determine the position distribution for the upcoming NBA season. Data shows that the NBA is position weighted almost evenly with a slight surplus of point guards. Thus, the Supply of positions is nearly even and not a factor. (I know what you are thinking. Player quality is another story and is not addressed in this observation.)

Point Guards = 23% of NBA

Shooting Guards = 21% of NBA

Small Forwards = 20% of NBA

Centers = 18% of NBA

Power Forwards = 18% of NBA

Statistics from last season were analyzed for position bias. The top 15 players in PPG, APG, 3PT%, TOPG, FT%, SPG, BPG, ORPG, and DRPG for 04’-05’ were assessed to determine which positions performed the best. Point guards and power forwards performed the best while small forwards accounted for the smallest number of stat leaders last year.

Point Guards = 27% of the stat leaders

Power Forwards = 26% of the stat leaders

Centers = 18% of the stat leaders

Shooting Guards = 15% of the stat leaders

Small Forwards = 13% of the stat leaders

John Hollinger’s PER ratings indicated that power forwards had the highest PER ratings. The average PER ratings per position were computed for last season.

Power Forwards = 15.36

Point Guards = 14.55

Small Forwards = 13.71

Centers = 13.64

Shooting Guards = 13.41

The NBA efficiency (2004-2005) rating for the top 50 efficient players was analyzed, and the position breakdown is given below. Similar to the PER ratings, the NBA efficiency was highest for power forwards.

Power Forwards = 38% of the 50 most efficient players

Shooting Guards = 24% of the 50 most efficient players

Small Forwards = 14% of the 50 most efficient players

Point Guards = 14% of the 50 most efficient players

Centers = 10% of the 50 most efficient players

These statistics suggest that the most valuable position in the NBA is indeed the power forward. Power forwards had the highest efficiency and PER ratings, and were second in overall NBA statistics last season.

Let’s now look at the top NBA salaries for this season on each team to determine what value teams place on positions (data obtained from To account for team spending preferences, the positions of the top 2 highest paid players on each team were compiled to determine which positions are paid the highest. Shaq being the highest paid player in the NBA is an exception and definitely not a rule. In general, teams see the importance of the power forwards and spend the most money on these players.

Power Forwards = 25% of top 2 highest paid players

Small Forwards = 23% of top 2 highest paid players

Point Guards = 20% of top 2 highest paid players

Shooting Guards = 20% of top 2 highest paid players

Centers = 12% of top 2 highest paid players

For now power forwards reign.

To be continued....................