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Modeling NBA Defensive Minded Teams’ Wins during the Regular Season
Yujie Zi
University of California, Irvine

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Introduction
Coach Bear Bryant once claimed “Offense sells tickets but defense wins championships.”
Every season, more and more teams throughout the NBA are beginning to value defensive play
due to the gradual accumulation of more and more championship teams that have historically
focused on defense. The coaching staffs, NBA analysts, and even NBA commentators stress how
defense is very important, since defense is the only part of a basketball game that players have
consistent control over. Players who perform well defensively, or who have won defensive
recognitions are often praised in sports commentaries. Even the least talented players can earn
respect, as long as they put in the effort towards defense, because defense is equally important to
offense in securing a win, even though it is often overlooked. With the growing popularity in
sports statistical analysis, especially with the hiring of more analysts by more teams, defense is
one of the key aspects of a basketball game that the aforementioned analysts are studying to
hopefully provide their team owners with an advantage in games.
The focus of this paper is to study the significance of an NBA team’s defensive focus on
regular season game win percentages. 30 NBA teams’ offensive and defensive statistics for the
2005-2006 and 2007-2008 NBA regular seasons are regressed on the teams’ seasonal winning
percentages. A dummy variable is included in the regression to define a team’s mindset based on
the Hollinger efficiency rating system. Factors covering all aspects of a game that determine the
outcome of a game are controlled for when evaluating the significance of a team’s defensive or
offensive tendency. Wins or losses are determined by points, but both offensive statistics, such as
shooting percentages, and defensive statistics, such as block, steals, and rebounds, help explain
teams’ performances and win records.
Teams that focus on defense, or have a higher defensive rating, are predicted to perform
better in the regular season than teams that focus on offense, or have a higher offensive rating.
However, the final regression concludes that the dummy variable is insignificant and therefore, a
teams’ focus or tendency towards focusing on defense should not affect the team’s seasonal win
record. The insignificance of a team’s mindset could be explained by the fluidity of a game,
where hard to measure factors, such as momentum, could spark good offense from good defense,
regardless of the team’s defined mindset.

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Literature Survey
Literature in the field of sports economics is scarce as a relatively new area of research.
Few publicly available research projects focus on the effects of game statistics on win
percentages, since several factors of basketball games are hard to quantify, such as talent and
will power. Chatterjee (1994) and Oliver (2004) have produced the most concise and accurate
models by finding and accounting for the most important game statistics in determining wins.
Chatterjee (1994) is one of the first papers in the field of sports economics to analyze
winning percentages for NBA teams. Using OLS estimation and looking at individual NBA
game data from 1988 to 1992, Chatterjee (1994) found that field goals, free throws, rebounds,
and turnovers are found to be most significant when determining if a team loses or wins during a
regular season game, especially when used to predict future team seasonal performances. The
coefficients also seemed to reflect stableness and consistency when regressed from year to year.
Oliver (2004) focuses on evaluating individual players’ defensive statistics, but also looks
rigorously at how defense helps “win championships”. From data since the 1970’s, Oliver (2004)
has constructed OLS regressions whose results show that highly ranked defensive statistics do
significantly contribute to a team’s performance, but not to a great extent. Teams with good
offense that have relaxed on defense during the regular season, but can increase their defensive
performance in the playoffs are more likely to win championships. Lyons (2005) reviews
Oliver’s work and criticizes it, stating that the regressions’ variables are often “ambiguous” in
their terms of measurement, such as its unorthodox measurement of “talent” as a variable.
However, Lyons (2005) agrees with the conclusion that there is not a large difference in
performance between strong offensive teams and strong defensive teams.
Copenhaver (2009) makes an important observation that over the past decade (2000-
2010), the NBA had instituted numerous rule changes meant to aid offensive production. The
paper uses the results of OLS regressions to examine the effects of NBA home game attendance
on competing teams’ offensive output, using individual game statistics for the 2007-2008 NBA
regular season. Copenhaver (2009) concluded that a higher NBA home game attendance results
in increased offensive quality and production for the home team, which associates closely to the
outcomes of victory for the home team.

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Model
The theoretical framework for the model is heavily influenced by Chatterjee (1994) and
Oliver (2004). Both papers have found that using games’ box score statistics is enough to control
for, predict, and explain seasonal win percentages, and factors such as salary cap and superstar
presence would be reflected in teams’ seasonal performance statistics. The NBA provides
thousands of past game statistics, including individual games’ box scores, but both literatures
find that seasonal averages are less skewed and more consistent predictors of win records.
Therefore, the model only incorporates teams’ seasonal average statistics to regress on win
percentages.
Measurable factors influencing the outcome of games are controlled for in the model.
Wins are determined by a point system, where the winning team of a basketball game wins by
producing a larger amount of points than the other team. Other controlled factors include the
statistics of a basketball game that contribute to scoring, opportunity to score, and denial of
scoring, which can be split into the general categories of offense and defense. Offensive statistics
includes mostly scoring, or scoring related statistics, such as assists, or passes of the ball that
have resulted in made points (Asst), field goals (FG), free throws (FT), and 3-pointer field goal
percentages (3PFG). Defensive statistics include blocks (Blk), steals (Stl), defensive rebounds
(DefReb), and forced opponent turnovers, which is when the opponent loses the ball (OppTOV).
Opponent teams’ offensive statistics are also classified as defensive statistics, because the more
productive a team performs defensively, the less productive its opponent performs offensively.
The focus of the model is the variable defining a team’s mindset, or whether a team
focuses on defense or offense. The dummy variable “Def” is used to represent the characteristic
of a team having a defensive mindset. The mathematical definition of a team’s mindset will be
based on Hollinger’s efficiency rating system, which is used to rank teams defensively and
offensively in the NBA. The variable “Def” equals 1 if the ranking value of a team’s defensive
efficiency, which is defined as “the number of points a team allows per 100 possessions”, is less
than the ranking value of a team’s offensive efficiency, which is the “number of points a team
scores per 100 possessions”, and Def equals 0 otherwise. To clarify, the best ranked team would
have the lowest ranking value of 1, so a smaller ranking value represents a better ranking.
All variables with “Opp” in front are expected to have negative coefficients, since
logically, the worse a team’s opponent performs, the more likely that team would perform better

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and win. Therefore, the respective team would obtain a higher regular season winning
percentage. All other variables are expected to have positive coefficients, since they help
contribute positively to the team’s play and winning chances.
The hypothesis is that defensive-minded teams, or teams whose defensive efficiency is
ranked greater than their offensive efficiency, win more in the regular season than offensive-
minded teams, or teams whose defensive efficiency is ranked lower or equal to their offensive
efficiency. The dummy variable “Def” is expected to obtain a positive coefficient in the
regression to reflect a defensive mindset’s positive effect on a team’s win percentage.
Model Equation (*Refer to Table 1 for variable descriptions)
WIN = β0 + β1(Def) + β2(OppPt) + β3(OppAsst) + β4(OppFG) + β5(OppFT) + β6(Opp3PFG) +
β7(DefReb) + β8(Blk) + β9(Stl) + β10(OppTOV) + β11(OppOffReb) + β12(Pt) + β13(Asst) +
β14(FG) + β15(FT) + β16(3PFG)
Data
The cross-sectional data of 30 NBA teams’ seasonal statistical averages for both the
2005-2006 and 2007-2008 regular seasons contains a pooled amount of 60 observations. Both
seasons’ average statistics were generated from 82 games each season. All box scores were
entered manually and organized on an Excel spreadsheet. The data concerning teams’ win
percentages and point averages are retrieved from the ESPN database of past NBA box scores.
Team efficiencies and all other offensive and defensive statistics are retrieved from
www.teamrankings.com.
The “Def” variable was constructed using functions of Excel. Teams’ offensive and
defensive efficiencies’ seasonal rankings were copied onto an excel spreadsheet. Some teams
lacked a numerical value for ranking because of ties in efficiency rankings, so for each tie, the
same rank value was entered for all teams tied. Teams and their offensive and defensive
efficiencies’ seasonal rankings were then alphabetized using the “Sort & Filter” function. A new
column was constructed for the binary “Def” variable dummy. A value of 1 was manually
entered for each team that was higher ranked in defensive efficiency than offensive efficiency,
and a value of 0 was entered otherwise.

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Results
Descriptive Statistics
All of the data points appear to be normally distributed with minimal standard deviations.
Most extremes are not greater than one standard deviation away from averages. Table 1 lists the
descriptive statistics of all variables used in the regression. The mean of the win percentage
being so close to .5 confirms that the data is not skewed, since for all games, there is always a
winning team and a losing team, so win percentages have to average to .5 since no ties are
allowed. The “Def” dummy has a mean of 5.1667, which means more teams were labeled as
having a defensive mindset, than teams with offensive mindsets.
All variables regarding the production of a team on both the offensive and defensive end
are predicted to have positive correlations to win percentage and all variables regarding the
opponent’s productivity are predicted to have negative correlations to win percentage, which is
consistent with the correlation table in Table 5. Intuitively, offensive production, such as higher
field goal percentages, leads to scoring points and defensive production leads to denial of points
for the opponent, which would increase a team’s final point count more than an opponent’s final
point count to secure a win. Defensive production decreases the opposing team’s final point
count, which also helps a team win. Steals, blocks, and forcing turnovers deny the opponent
opportunities to score. Offensive and defensive production from an opposing team would
naturally hurt the respective team’s score, so they would be negatively correlated with winning
percentage.
Multicollinearity exists among a few pairs of variables, but the “Def” variable has
relatively low correlation with other variables, as seen in Table 5. Therefore, multicollinearity
can be ignored in analyzing the “Def” variable and its presence does not change any conclusions
about the dummy’s significance.
No observations are excluded from the final estimation because none showed extreme
outlier effects. Potential outliers include Indiana ’05, Sacramento ’07, and Toronto ’07 data
points, which correspond to win percentages of .5, .463, and .5, respectively, however, their
residuals were not further than about one standard deviation away, as shown in Figure 1.
Interestingly, all three teams were borderline playoff competitors, with Indiana ranking 16
overall in the league and making the playoffs, Sacramento ranking 18 overall and not making the
playoffs, and Toronto ranking 16 overall in league and making the playoffs. These teams’

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performance could be due to chance or other hard to measure factors, such as momentum or will
power in close game wins/losses. They might not have performed as well or have performed
much better than their stats can reflect in close games, which would explain the variability. The
observations still remained in the final estimation because they did not deviate too far from the
regression line and can be justified by pure chance.
Regression Analysis
The regression of “Def” and controls on win percentage shows that the coefficient of
“Def” is both negative and insignificant, as seen in Table 2. The regression produces a high R-
squared of .948 so the model is effective in explaining win percentages. The coefficient of “Def”
is not significant, even at the α = .1 level, and the only significant statistics at α = .05 are block,
points, and opponent points. The variable blocks’ significance and positive coefficient are due to
the fact that each block results in a complete denial of points, which is certain in lowering an
opposing team’s opportunities of scoring. The variable points’ coefficient’s positive sign and
opponent points’ coefficients’ negative sign are consistent with predictions since games’ winners
are decided on which team has more points. Their great significance is also expected due to the
fact that games’ victors are determined on which team has more points.
The result of “Def’s” insignificance can be more emphasized due to the fact that the two
seasons selected for the study border on a time during which there was a change in philosophy in
NBA gameplay execution, which was to focus on defense. In 2005-2006 and prior years, defense
was rarely stressed or focused on in the league. However, in 2007-2008 the “Big 3” concept was
formed and applied when creating a new Boston Celtics team, which resulted from a study that
historically, teams with 3 superstars are more inclined to win championships. One of the
members of the “Big 3” was a great defensive player named Kevin Garnett. The Celtics, known
as one of the premier defensive teams, seeded as #1 entering the playoffs and won the 2008 NBA
Championship with Coach Doc Rivers, who is also famous for stressing heavily on defense.
Separate regressions on each of the seasons were run to check for robustness of results,
which are displayed in Table 3 and 4. Betas on “Def” remained insignificant and the signs also
remained negative for each season so the results are consistent with the pooled data regression.
Therefore, there are no seasonal changes in defensive-minded teams’ performances, even though
many teams in the NBA became more prone to focusing on defense in the 2007-2008 season.

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The characteristic of being defined as defensive-minded is shown to be insignificant in
determining a team’s regular season performance possibly because good defensive plays usually
lead to good offensive plays due to momentum. Therefore, defensive and offensive statistics can
even out even if a team plans to play every game with a focus on defense. Luck and willpower
are also hard to measure and include in a model, but are also important factors in determining
gameplay and can sometimes contribute enough to tip a team’s score by one point higher than
their opponent’s to result in a win.
Conclusion and Future Research
The regression of the effects of a team’s offensive or defensive mindset on two seasons’
regular season win percentage shows that a team’s mindset is insignificant to its regular season
winning record. The coefficient of the “Def” dummy, signaling the presence of a defensive
mindset, was predicted to be positive and significant, but results show the opposite, where the
coefficient is both insignificant and negative. Even when the regression was run on each separate
season, no significant results were obtained so seasonal effects were not a factor in determining
the benefits of having a defensive mindset. Therefore, defensive minded teams do not
statistically perform better than offensive minded teams during the regular season and being
defensive minded does not benefit a team in gameplay production.
Future research could include a regression of the number of wins involving either
overcoming a deficit in the last half of the fourth quarter to evaluate the usefulness of being more
defensively active. Another study could focus on teams’ performances in games overcoming
leads of 20 points or more to try to determine if defense is the spurring factor in winning games.

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References
Table 1 Mean Median Maximum Minimum Std. Dev. Description
WIN 0.49998 0.5 0.805 0.183 0.152093
Pooled NBA teams’ win
percentages for the
2005-2006 and 2007-
2008 regular seasons
DEF 0.51667 1 1 0 0.503939
Def = 1 if a team’s
Defensive Efficiency is
ranked higher than a
team’s Offensive
Efficiency, and Def = 0
otherwise
OPPPT 98.435 98.85 108.8 88.5 4.994466
Average opponent points
allowed per game
OPPASST 21.1333 21.4 25.8 16 2.009019
Average opponent
assists
OPPFG 0.45543 0.456 0.491 0.421 0.014918
Average opponent field
goal percent
OPPFT 0.75042 0.749 0.777 0.729 0.012436
Average opponent free
throw percent
OPP3PFG 0.3595 0.359 0.386 0.319 0.014061
Average opponent 3-
point field goal percent
DEFREB 30.1967 30.1 33.2 26.9 1.532027
Average defensive
rebounds per game
BLK 4.69167 4.8 6.6 2.6 0.820767
Average blocks per
game
STL 7.18167 7.15 10 5.5 0.839792 Average steals per game
OPPTOV 13.5933 13.4 17.4 11.3 1.12142
Average opponent
turnovers
OPPOFFREB 11.1683 11.1 13.2 9.4 0.812924
Average opponent
offensive rebounds
PT 98.2383 97.4 111 88.8 4.708668
Average points scored
per game
ASST 21.005 20.9 26.2 17.4 1.941118 Average assists
FG 0.45545 0.454 0.5 0.433 0.014391
Average field goal
percent
FT 0.75075 0.7535 0.814 0.689 0.029121
Average free throw
percent
3PFG 0.35855 0.3575 0.399 0.317 0.019518
Average 3-point field
goal percent

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Table 2:
(Note: Eviews’ function of White’s test is used to test for heteroskedasticity and to adjust
standard errors.)
DependentVariable:WIN
Method: LeastSquares
Sample:30 NBA teams’ regular season 2005-
2006,2007-2008 statistics
Included observations:60
White heteroskedasticity-consistentstandard errors & covariance
Variable Coefficient Std. Error t-Statistic Prob.
C 0.945960 1.026316 0.921704 0.3618
DEF -0.008782 0.016797 -0.522836 0.6038
OPPPT -0.032285 0.004810 -6.711663 0.0000
OPPASST -0.004318 0.005287 -0.816658 0.4186
OPPFG 0.095043 1.312861 0.072394 0.9426
OPPFT 0.301639 0.475939 0.633777 0.5296
OPP3PFG 0.240747 0.556200 0.432842 0.6673
DEFREB -0.004178 0.010537 -0.396466 0.6937
BLK 0.017387 0.007028 2.473887 0.0174
STL 0.010046 0.014979 0.670670 0.5060
OPPTOV -0.015441 0.012646 -1.221026 0.2287
OPPOFFREB -0.008292 0.009154 -0.905844 0.3701
PT 0.033737 0.003703 9.111938 0.0000
ASST 0.005701 0.004526 1.259597 0.2146
FG -0.893602 0.660698 -1.352512 0.1833
FT -0.271187 0.232157 -1.168119 0.2492
3PFG -0.214369 0.417364 -0.513625 0.6101
R-squared 0.948143 Mean dependentvar 0.499983
Adjusted R-squared 0.928847 S.D. dependentvar 0.152093
S.E. of regression 0.040570 Akaike info criterion -3.338047
Sum squared resid 0.070775 Schwarz criterion -2.744649
Log likelihood 117.1414 Hannan-Quinn criter. -3.105936
F-statistic 49.13745 Durbin-Watson stat 1.758261
Prob(F-statistic) 0.000000
Table 3:
DependentVariable:WIN
Method: LeastSquares
Sample (adjusted):2005-2006 Regular Season
Included observations:30
White heteroskedasticity-consistentstandard errors & covariance
Variable Coefficient Std. Error t-Statistic Prob.
C -2.645382 1.777190 -1.488520 0.1605
DEF -0.043380 0.023280 -1.863415 0.0851
OPPPT -0.045492 0.009826 -4.629956 0.0005
OPPASST -0.000129 0.009643 -0.013355 0.9895

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OPPFG 2.687832 2.413780 1.113537 0.2856
OPPFT 3.033359 0.738306 4.108542 0.0012
OPP3PFG 2.009788 1.039369 1.933662 0.0752
DEFREB 0.010648 0.018650 0.570959 0.5778
BLK 0.009412 0.010996 0.855932 0.4075
STL 0.022347 0.028500 0.784113 0.4470
OPPTOV -0.011528 0.020862 -0.552597 0.5899
OPPOFFREB -0.008026 0.016040 -0.500358 0.6252
PT 0.031048 0.005070 6.124517 0.0000
ASST 0.021098 0.004708 4.481460 0.0006
FG 0.631896 1.165572 0.542134 0.5969
FT -0.605990 0.402967 -1.503820 0.1565
_3PFG -0.449321 0.735254 -0.611110 0.5517
R-squared 0.967503 Mean dependentvar 0.500000
Adjusted R-squared 0.927507 S.D. dependentvar 0.136325
S.E. of regression 0.036705 Akaike info criterion -3.474736
Sum squared resid 0.017514 Schwarz criterion -2.680724
Log likelihood 69.12104 Hannan-Quinn criter. -3.220725
F-statistic 24.19004 Durbin-Watson stat 1.512761
Prob(F-statistic) 0.000000
Table 4:
DependentVariable:WIN2007
Method: LeastSquares
Sample:2007-2008 Regular Season
Included observations:30
White heteroskedasticity-consistentstandard errors & covariance
Variable Coefficient Std. Error t-Statistic Prob.
C 1.602965 1.349993 1.187387 0.2563
DEF7 -0.008958 0.046050 -0.194523 0.8488
OPPPT7 -0.032201 0.008512 -3.782838 0.0023
OPPASST7 -0.002055 0.007322 -0.280734 0.7833
OPPFG7 -0.286673 2.708140 -0.105856 0.9173
OPPFT7 -0.631682 0.828572 -0.762374 0.4594
OPP3PFG7 0.040352 0.588273 0.068593 0.9464
DEFREB7 -0.000680 0.020846 -0.032606 0.9745
BLK7 0.013912 0.018150 0.766529 0.4571
STL7 0.001937 0.023832 0.081266 0.9365
OPPTOV7 -0.005440 0.031053 -0.175198 0.8636
OPPOFFREB7 0.000977 0.012228 0.079899 0.9375
PT7 0.032272 0.005602 5.760943 0.0001
ASST7 6.14E-05 0.010798 0.005682 0.9956
FG7 -0.830307 0.992336 -0.836719 0.4179
FT7 -0.035803 0.354778 -0.100915 0.9212
_3PFG7 -0.134666 0.583695 -0.230712 0.8211
R-squared 0.972738 Mean dependentvar 0.499967
Adjusted R-squared 0.939186 S.D. dependentvar 0.168754
S.E. of regression 0.041616 Akaike info criterion -3.223592
Sum squared resid 0.022514 Schwarz criterion -2.429580
Log likelihood 65.35388 Hannan-Quinn criter. -2.969581

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F-statistic 28.99125 Durbin-Watson stat 1.870109
Prob(F-statistic) 0.000000
Table 5:
WIN DEF
WIN 1.000000 -0.139865
DEF -0.139865 1.000000
OPPPT -0.536435 -0.290139
OPPASST -0.564256 -0.107701
OPPFG -0.649698 -0.314353
OPPFT -0.220652 -0.172864
OPP3PFG -0.586318 -0.106442
DEFREB 0.399624 0.019831
BLK 0.355660 0.117129
STL 0.073101 0.138905
OPPTOV -0.038369 0.180150
OPPOFFREB -0.164739 -0.116604
PT 0.359254 -0.464202
ASST 0.368336 -0.004418
FG 0.548080 -0.448610
FT 0.171179 -0.390665
_3PFG 0.413147 -0.344720
Figure 1:
-.08
-.04
.00
.04
.08
.12
5 10 15 20 25 30 35 40 45 50 55 60
WIN Residuals

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Chatterjee S, Campbell MR, Wiseman. F. 1994. Take that jam! An analysis of winning
percentage for NBA teams. Managerial and Decision Economics 15: 521–535.
Copenhaver, Todd, “Does NBA Attendance Respond to Increased Offensive Quality and
Production?” (2009). Honors Projects. Paper 21.
http://digitalcommons.macalester.edu/economics_honors_projects/21
Galletti, Arturo, Win Regression for the NBA « Arturo’s Silly Little Stats. (2010). Retrieved
June 2, 2012, from http://arturogalletti.wordpress.com/2010/07/01/win-regression-for-the-
nba-2/
Lyons, Tom, What Wins Basketball Games, a Review of “Basketball on Paper: Rules and Tools
for Performance Analysis” By Dean Oliver. (2005). Retrieved June 2, 2012, from
http://www.sfandllaw.com/CM/Articles/Articles10.asp
Oliver, Dean, Basketball on Paper: Rules and Tools for Performance Analysis, Potomac Books,
Dulles, 2004.