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Yujie Zi Econ 123CW Research Paper - NBA Defensive Teams

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Yujie Zi Econ 123CW Research Paper - NBA Defensive Teams

  1. 1. Zi 1 Modeling NBA Defensive Minded Teams’ Wins during the Regular Season Yujie Zi University of California, Irvine
  2. 2. Zi 2 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.
  3. 3. Zi 3 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.
  4. 4. Zi 4 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
  5. 5. Zi 5 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.
  6. 6. Zi 6 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’
  7. 7. Zi 7 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.
  8. 8. Zi 8 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.
  9. 9. Zi 9 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
  10. 10. Zi 10 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
  11. 11. Zi 11 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
  12. 12. Zi 12 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
  13. 13. Zi 13 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.

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