Individual tournament incentives in a team setting: the 2008-09 NBA MVP race.

Nutting, Andrew W.

You don't think [Le]Bron watches SportsCenter and files away those "Just wait until what I do tomorrow" vows every time one of the anchors is raving about Wade's latest 40-10 performance?

-- Bill Simmons, ESPN.com, April 1, 2009

Introduction

Sport economics has been fertile ground for empirical tests of tournament theory--the idea that tying compensation to ordinal performance rankings causes workers to be concerned with their performances relative to other workers rather than their objective performances (Lazear & Rosen, 1981). Tournament incentives have been shown to significantly affect athletes' performances in the individual sports of golf (Ehrenberg & Bognanno, 1990a, 1990b), running (Maloney & McCormick, 2000; Lynch & Zax, 2000), and weightlifting (Nutting, 2008). They have also been shown to explain teams' performances in the team sport of basketball (Taylor & Trogdon, 2002; Balsdon, Fong, & Thayer, 2007; Price et al., 2010). This paper furthers the empirical research of tournament theory by examining whether, in a team sport, individual players' performances are affected by individual tournament incentives. It also examines whether players' individual tournament incentives affect, positively or negatively, the performances of their respective teams.

Previous research has shown that, in team sports, individual performances of players are affected by pay incentives (Woolway, 1997; Stiroh, 2007). (1) To examine whether individual NBA performances are also subject to tournament incentives, this paper models the race for the 2008-09 NBA Most Valuable Player award as a winner-takes-all tournament between the top three finishers in the end-of-season MVP balloting: LeBron James of the Cleveland Cavaliers, Kobe Bryant of the Los Angeles Lakers, and Dwyane Wade of the Miami Heat. (2) James, Bryant, and Wade were the only feasible contenders of the MVP award: toward the end of the season, basketball writers had written that the contest for MVP was a "three-way battle" (Saraceno, 2009) and a "three-way race" (Wilbon, 2009). (3) Some writers additionally opined toward the end of the season that a rivalry had developed between James, Bryant, and Wade when they were teammates on the Summer 2008 USA Olympic basketball team, and therefore that the MVP race was all but limited to them even at the season's inception (DeShazier, 2008; Simmons, 2009; Wilbon, 2009). Other opinions published prior to the season seemed to limit the competition to James and Bryant specifically, because Wade's health was in question (Buffalo News, 2008; Winderman, 2008).

Tournament theory hypothesizes that effort increases when the marginal benefits of such effort--a combination of expected improvement in ordinal rank and the expected increase in benefits from any such improvement--outweigh its marginal costs. The NBA MVP tournament is winner-take-all, and presumably much of the utility derived from winning is associated with nonpecuniary factors such as the knowledge of being the very best player in the NBA or having an all-but-certain probability of being inducted into the Basketball Hall of Fame (Peterson, 2009). Pecuniary incentives may be less important, given the already-huge incomes of high-level NBA players, but winning an MVP award may lead to contract bonuses from teams (Schulman, 2002) or sponsors (Turner, 2009), or larger future endorsement deals. Winning an MVP award may also increase the probability of a player becoming a "superstar," which can lead to higher team revenues (Hausman & Leonard, 1997; Berri, Schmidt, & Brook 2004). Higher revenues could allow MVP winners (and other players) to receive higher-paying future contracts, (4) since the NBA's maximum contracts are tied to the team salary cap, which is itself a function of league revenue. (5)

Unlike the tournaments studied in previous sport economics research, ordinal rankings in the NBA MVP tournament are unknown until the season has ended. Nevertheless, since James, Bryant, and Wade were generally considered to be in a three-way battle for the MVP award, this paper assumes that each had an incentive to outdo the others' performances in order to improve or maintain his position in the ordinal MVP rankings. Therefore, this paper hypothesizes through tournament theory that during the season James, Bryant, and Wade improved their own performances in direct response to another MVP competitor playing well in his most recent game.

Empirical results show significant evidence of individual tournament incentives. James and Bryant significantly increased their scoring in response to Wade increasing his scoring, and James additionally significantly increased his scoring in response to Bryant increasing his scoring. In all cases, significant increases in point totals corresponded with significantly more free throws attempted, indicating more aggressive offensive play in response to a better game by an MVP competitor. There is very little evidence that pursuing better individual statistics hurt the probability of an MVP competitor's team winning. Indeed, James' increased scoring in response to Wade's increased scoring was correlated with significantly increased probabilities of his Cavaliers winning. Evidence that Wade increased his scoring in response to victories by James' Cavaliers is not robust to the inclusion of another possible MVP competitor to the tournament. So while Wade's individual statistics clearly affected Bryant's and James' performances, there is no robust, significant evidence that Bryant's and James' performances significantly affected Wade.

Data

Game-by-game regular season data for Bryant, James, and Wade are available from player game logs at ESPN.com. Table 1 summarizes the players' seasons. Bryant played all 82 regular-season games. James did not play Cleveland's last game of the season. Wade missed Miami's last two games and a mid-season game on March 18. Bryant, James, and Wade were the three highest-scoring players in the season: Wade averaged over 30 points per game, James averaged over 28 per game and Bryant fewer than 27. Wade attempted more field goals and free throws per game than either James or Bryant. Bryant took substantially fewer free throws than James or Wade, but made a larger percentage of them. (6) James averaged more than 7 rebounds and 7 assists per game, and Wade averaged over 7 assists and 2 steals per game. Bryant and James won approximately 80 percent of their games, while Wade's Miami team won only slightly more than half its games. (7)

Theoretical Model

Where i is player, t is team, and g is game, i's performance in g ([PERF.sub.ig]) is modeled as a function of whether i is playing an away game or a home game ([AWAY.sub.ig]), the quality of i's opponent ([Q.sub.(-t)g]), the performances of the other MVP competitors {[PERF.sub.-i(g-1)]) in their most recent games, and an unobserved component [v.sub.ig]. That is,

[PERF.sub.ig] = f([AWAY.sub.ig], [Q.sub.(-t)g], [PERF.sub.-i(g-1)], [v.sub.ig]). (1)

[PERF.sub.-i(g-1)] is the critical factor in determining whether the MVP race yielded tournament incentives. Its inclusion in the right-hand-side indicates that, in order to maintain or improve his positions in the MVP tournament, i may have improved his own performance in response to other competitors (-i) improving their performances in their most recent games. [PERF.sub.-i(g-1)] has two separate components: points scored ([POINTS.sub.-i(g-1)]) and team win/loss status ([WIN.sub.-i(g-1)]). Points scored is used because it is the most prominent individual statistic in basketball. It is especially appropriate considering that Bryant, James, and Wade were the three highest-scoring players in the 2008-09 NBA season. Win/loss status is included in [PERF.sub.-i(g-1)] because the hedonic model of Coleman, DuMond, and Lynch (2008) finds that NBA players earn MVP votes based not only on their personal statistics, but also on their team's overall win-loss record. An MVP competitor therefore may, to maintain or improve his position in the MVP tournament, increase his own performance in response to another competitor scoring more points, and/or when the other competitor's team wins a game. The unobserved component [v.sub.ig] is separated into two terms: [[alpha].sub.i], a season-invariant measure of individual player quality, and [[epsilon].sub.ig], a game-specific error term.

Empirical Strategy

To empirically determine whether Bryant, James, and Wade significantly altered their performances in response to each others' most recent performances, I estimate the equations

[PONTS.sub.ig] = [[delta].sub.1(-t)g] + [[beta].sub.1][AWAY.sub.ig] + [[phi].sub.1i][POINTS.sub.-i(g-1)] + [[gamma].sub.1i][WIN.sub.-i(g-1)] + [[alpha].sub.1i] + [[epsilon].sub.1ig] (2)

and

[WIN.sub.ig] = [[delta].sub.2(-t)g] + [[beta].sub.2][AWAY.sub.ig] + [[phi].sub.2i][POINTS.sub.-i(g-1)] + [[gamma].sub.1i][WIN.sub.-i(g-1)] + [[alpha].sub.2i] + [[epsilon].sub.2ig] (3)

where i is player, t is team, and g is game. [POINTS.sub.ig] is used as a dependent variable to determine whether an MVP competitor's individual statistics improved in response to another competitor scoring more points or winning a game. [WIN.sub.ig] is used as a dependent variable because, as mentioned above, both individual statistics and team wins are factors in the end-of-season MVP vote, and MVP competitors may exert more effort toward winning in response to another competitor improving his performance. Note also that an MVP competitor may reduce his team's probability of winning in response to a competitor's better play, if the individual incentives toward better personal statistics clash with the team's probability of winning. Such a result could occur, for example, if more effort toward scoring reduced scoring efficiency (Berri, Schmidt, & Brook, 2006).

[[delta].sub.1(-t)g] and [[delta].sub.2(-t)g] represents fixed effects for opposing team (hence the -t) in game g, which control for different-quality opponents affecting the performances of Bryant, James, and Wade. (8) [[alpha].sub.1i] and [[alpha].sub.2i] are season-invariant individual player fixed effects. [delta] and [alpha] coefficients in equations (2)-(3) are estimated via vectors of dummy variables. [AWAY.sub.ig] is a dummy variable equal to 1 if game g is an away game for player i. [POINTS.sub.-i(g-1)] is a vector representing the points scored by the two other competitors (-i) in this three-person tournament in their most recent respective games (g-1). [WIN.sub.-i(g-1)] is a vector of dummy variables representing whether the other competitors' teams won or lost their most recent games. Coefficients on [POINTS.sub.-i(g-1)] and [WIN.sub.-i(g-1)] have an i subscript to allow each MVP competitor to be differently impacted by each of the other two MVP competitors. Since equations (2) and (3) include individual-player fixed effects, coefficients on [POINTS.sub.-i(g-1)] and [WIN.sub.-i(g-1)] measure, for example, whether i scored more points than he normally did in response to MVP competitor -i scoring more points than he normally did. [[epsilon].sub.ig] is a random error term.

Simultaneous to the tournament for the MVP trophy was the NBA team tournament for better positions in the league win-loss standings. (9) If estimations of equation (3) show that i's team wins more often after -i's team wins, it may reflect incentives in the team tournament rather than the MVP tournament. In this three-man tournament, the most critical team tournament was probably between James' Cavaliers and Bryant's Lakers, who spent the 2008-09 season in close contest for overall home-court advantage in the playoffs. Wade's Heat finished 5th in the Eastern Conference and were not in competition with the Cavaliers or Lakers for home-court advantage.

In all estimations a competitor's "most recent game" is defined as the most recent game player -i played, given that the game began at least three hours before the beginning of player i's game g. Since the average length of an NBA game appears to be between two and two and a half hours, (10) and since many games appear to be played at 7:00 or 7:30 local time, (11) this definition allows, for example, Bryant (whose Lakers played 59.8% of their games in the Pacific Time Zone) to have been influenced by games James or Wade (both of whose teams played 76.8% of their games in the Eastern Time Zone) finished not long before Bryant's game started. (12)

Games in which either of player i's two MVP competitors did not play in their team's previous game or had not yet played a regular-season game are omitted from estimation samples. (13) All OLS equations are estimated with standard errors robust to heteroskedasticity.

Results and Implications

Points and Wins

Table 2 shows [PONTS.sub.-i(g-1)] and [WIN.sub.-i(g-1)] coefficients from estimations of equations (2) and (3). Column (1) shows results when the dependent variable is [POINTS.sub.-i(g-1)]. The points_bryant_on_james coefficient captures how James' point total was affected by Bryant's most recent point total. (When player i is James, the variable points_bryant_on_james is equal to the number of points Bryant scored in his most recent game. When i is Bryant or Wade, points_bryant_on_james is equal to zero.) The win_bryant_on_james coefficient captures how James' point total was affected by whether Bryant's Lakers won their most recent game. (When i is James, win_bryant_on_james is 1 if Bryant's Lakers won their previous game--assuming Bryant played--and 0 if they lost. When i is Bryant or Wade, win_bryant_on_james is 0.) All other variables in Table 2 are analogously defined.

All significant coefficients in Column 1 are positive. points_wade_on_bryant and points_wade_on_james are significantly positive and have similar point estimates, indicating that a 10-point increase in Wade's point total significantly increased the point totals of both of his MVP competitors by more than 2 points. (14) points_bryant_on_james is also significantly positive, so that James significantly increased his scoring in response to Bryant's scoring as well as Wade's scoring. Wade was the only player to not significantly increase his own scoring in response to a competitor's scoring, but he increase his own point totals by a significant and substantial margin--5.7 points--after James' Cavaliers team won. (15)

Column 2 shows marginal effects from a probit maximum likelihood estimation of equation (3), where the dependent variable is [WIN.sub.ig]. (16) These estimations determine whether the probability of an MVP competitor's team winning its next game was affected by his MVP competitors' most recent performances. Results show that increases in Wade's scoring significantly increased James' probability of victory. James, then, responded to high-scoring games by Wade by scoring more points (Column 1) and leading the Cavaliers to victory more often (Column 2). Wade, in turn, responded to wins by James' Cavaliers by scoring more points and leading the Heat to victory more often. The win probability of Bryant's Lakers were unaffected by the most recent performances of his MVP competitors, possibly because he had better teammates than either James or Wade, (17) and the Lakers' win probability was less dependent on Bryant's personal performance. No coefficient in Column 2 is significantly negative, so there is no evidence that the 3 MVP competitors reduced their teams' probability of winning by emphasizing their own statistics in response to better play by a competitor.

It is somewhat surprising that, in Column 2, win_james_on_wade is large and significantly positive while win_james_on_bryant and win_bryant_on_james are insignificant. Bryant's Lakers and James' Cavaliers were the best two teams in the NBA in 2008-09 and spent the season competing for overall home-court advantage in the playoffs. Team tournament incentives regarding the Lakers and Cavaliers would seem to suggest that Bryant's Lakers had more incentive to win after the Cavaliers had won and vice versa, but Column 2 shows no significant evidence of a team tournament between the Lakers and Cavaliers.

Columns 3-6 perform robustness checks on Columns 1-2. Columns 3-4 add a cubic control for game number (1-82) of the season to test whether the significant results in Column 1 capture secular trends towards different scoring at different times in the season instead of actual effects of an MVP tournament. All significant coefficients in Columns 1-2 are again significant in Columns 3-4. The time trend itself (not shown) is insignificant in both estimations. Columns 5-6 drop the last week of the season from the sample. It is possible that the three players put little emphasis on the latest-season games in their three-person MVP tournament, since James and Wade both skipped late-season games, and since Bryant's Lakers team had qualified for Western Conference playoff home-court advantage with several weeks remaining in the season (Bresnahan, 2009). All significant coefficients in columns 1-2 are again significant in Columns 5-6.

Other robustness checks are available from the author upon request. One check changes the POINTS variables in equations (2) and (3) to variables equal to (Points + Rebounds + Assists + Steals + Blocks), to better account for players' overall performances. The other robustness checks maintain the points variables on the right- and left-hand sides of equation (1) but changes the "previous game" definitions to a "two-hour" definition (where a competitor's most recent game must have started no less than two hours before player i's game) and a "full-day" definition (where a competitor's most recent game must have taken place on a previous day). The results for both sets of estimations are again largely consistent with those in Table 2, though fewer coefficients are significant. In all robustness checks, the right-hand-side variables that reflect competitors' recent performances never yield a significant negatively impact on points scored, win probability, or (Points + Rebounds + Assists + Steals + Blocks).

How points increased

Table 3, Column 1 reproduces Table 2, Column 1. The rest of Table 3 re-estimates equation (2) but alters the dependent variable to field goal attempts (Column 2), free throw attempts (Column 3), field goal percentage (Column 4), and free throw percentage (Column 5). When the dependent variables are field goal attempts and field goal percentage, estimations are OLS with robust standard errors. Since 5 observations feature 0 free throw attempts, Column 3 is estimated using a left-censored Tobit ML model. When the dependent variable is free throw percentage, the estimation is a Tobit lower-bounded at 0% and upper-bounded at 100%. (18)

Every significant Column 1 increase in points corresponds with a significant increase in free throw attempts in Column 3. Since free-throw attempts involve getting fouled, and getting fouled is generally associated with more aggressive interior offense, it appears that in response to an MVP competitor playing well, Bryant, James, and Wade increased their scoring via significantly more aggressive interior offense. (19) Note, though, that the sizes on the positive coefficients in the free throw estimations are not large enough to fully explain the scoring increases. None of the coefficients when the dependent variable is field goal percentage are significant, indicating no change in offensive efficiency correlated with individual tournament incentives. (20)

To summarize: Table 2 indicated that that Bryant, James, and Wade all in some way responded to individual MVP tournament incentives. Bryant increased his scoring in response to Wade increasing his scoring, James increased his scoring in response to both Bryant and Wade increasing their scoring, and Wade increased his scoring after James' Cavaliers won. There is no evidence that these scoring increases came at the expense of team performance; in fact, James' Cavaliers won more often in response to Wade scoring more points and Wade's Heat won more often in response to James' Cavaliers winning. Every significant increase in scoring corresponded with an increase in free throw attempts, suggesting that scoring increases in response to competitors' scoring increases were due in part to more aggressive offensive play.

Allowing other potential MVP competitors

To further clarify whether Bryant, James, and Wade participated in an MVP tournament where they responded only to each others' performances, equations (2) and (3) are re-estimated while adding data for other elite NBA players as explanatory variables. Table 4, Columns 1-3 show results when POINTSig is the dependent variable and when [POINTS.sub.-i(g-1)] and [WIN.sub.-i(g-1)] values for, respectively, Dirk Nowitzki of the Dallas Mavericks, Antawn Jamison of the Washington Wizards, and Dwight Howard of the Orlando Magic are added to the right-hand-side of equation (2). Columns 4-6 show analogous marginal effects from probit estimations where [WIN.sub.ig] is the dependent variable. Nowitzki and Jamison were chosen because they were the two highest 2008-09 scorers after Bryant, James, and Wade who played at least 79 games (Wade's total games played). Howard was chosen because he finished 4th in the MVP voting. (21)

In Table 4, the 4th_player variables refer to the respective player whose data is included as explanatory variables. Critically, Columns 1-3 show no significant evidence that Bryant, James, or Wade scored more points in response to Nowitzki, Jamison, or Howard scoring more points. Increases in Wade's scoring still prompt increases in Bryant's and James' scoring (the Column 3 coefficient on points_wade_on_james has a two-sided p-value of 0.106 and is significant in a one-sided test), and James still scores more points in response to Bryant scoring more points (the Column 1 coefficient on points_bryant_on_james has a two-sided p-value of 0.110 and is significant in a one-sided test). Therefore, Columns 1-3 strengthen the idea that the MVP tournament was effectively limited to James, Bryant, and Wade. Scoring increases by Wade led to scoring increases by his two MVP competitors, scoring increases by Bryant led to scoring increases by James, and the scoring by these three players was not affected by the scoring of other elite NBA players.

The Table 2 finding that Wade scored more points and won more often in response to James' Cavaliers winning is not robust to the inclusion of Howard's data. Indeed, adding Howard's data shows that Wade's point totals significantly increased after wins by Howard's Magic, not James' Cavaliers, perhaps because the Magic and Heat were rivals in the NBA Southeast Division. There is also, surprisingly, some evidence in Column 3 that Bryant scored fewer points after Wade's Heat won.

There remains strong significant evidence in Columns 4-6 that James' Cavaliers won significantly more often in response to Wade scoring more points. In Column 4, Bryant's Lakers won more often in response to James scoring more points. Also in Column 4, though, James' Cavaliers won less often in response to Bryant scoring more points. This result may indicate that, by attempting to score more points in order to maintain position in the MVP race over Bryant, James hurt his teams' chances of winning.

There are some surprisingly significant coefficients in Column 6, when Howard's performance data are added to the right-hand-side. Higher point totals by Howard are correlated with significantly lower win probabilities for Bryant's and Wade's teams, even though Howard was nowhere near the league leaders in points scored. Wins by Howard's Magic were correlated with higher winning probabilities for James' Cavaliers and lower winning probabilities for Bryant's Lakers. That the Cavaliers won more often after the Magic won may reflect team tournament incentives, since both the Cavaliers and Magic were both division champions in the Eastern Conference.

Concluding Comments

This paper adds to the empirical research of tournament theory and player incentives by determining whether there are individual tournament incentives within the confines of a team sport. Examining the 2008-09 NBA MVP race as a tournament between LeBron James (the eventual MVP winner), Kobe Bryant, and Dwyane Wade shows significant and robust evidence that James and Bryant scored more points in response to Wade scoring more points in his most recent game, and that James also scored more points in response to Bryant scoring more points. James also led his Cavaliers team to victory more often in response to Wade scoring more points. In all cases, increases in point totals were determined in part by significantly more free throw attempts, suggesting that the MVP competitors exhibited significantly more aggressive offense after other MVP competitors had better games.

The effect of Wade's scoring on Bryant and James' scoring and the effect of Bryant's scoring on James' scoring are robust when allowing for the possibility that other elite players' performances may have influenced these three players' performances. These estimations also reveal no evidence that James, Bryant, and Wade scored more points in response to Dirk Nowitzki, Antawn Jamison, or Dwight Howard scoring more points. However, it does show some evidence that James' Cavaliers lost more often in response to Bryant scoring more points, suggesting that individual performance incentives may have come at the expense of a team.

That Bryant and James were so responsive to Wade, while Wade was not responsive to them, is an interesting finding. It might be related to Wade being on a decidedly worse team that Bryant or James. Wade's candidacy for MVP was based almost entirely on his personal statistics, and not on his being an outstanding player on a top-flight team. Therefore, his position in the ordinal MVP rankings may have, compared to Bryant and James, experienced a relatively large boost when he accumulated especially high point totals. Bryant and James, then, may have been especially wary of Wade's scoring totals, and may have tried to increase their own scoring when Wade did.

There are many other opportunities to further examination of individual tournament incentives in team sports. It is possible, for example, to test whether Magic Johnson and Larry Bird improved their own performances in response to each others' performances in the 1980s, when Johnson or Bird won six MVP trophies in seven years and their teams won eight NBA titles in nine years. (22) There is also the possibility of examining whether the intensity of individual tournaments affect league revenues in team sports. Ryan (2010), for example, writes that rivalries between individual players have been good for basketball's growth in popularity. The validity of such sentiments could, perhaps, be empirically determined.

More sports economics research could also exist in the field connecting individual performance incentives--whether related to MVP tournaments, contract incentives, or other factors--to team outcomes and revenues. This paper finds that team performance is more likely to be positively correlated with positive individual-performance incentives, but cases in which incentives lead players to chase individual statistics to their team's detriment seem feasible.

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Endnotes

(1) Stiroh (2007) finds that NBA players improve their performances the season before they sign multi-year contracts, and worsen them the season after such contracts have been signed. Woolway (1997) finds similar results for Major League Baseball, but Maxcy, Fort, and Krautmann (2002) analyze Major League Baseball and do not find evidence of post-contract shirking.

(2) James received 1,172 total points and 109 of 121 first-place votes, Bryant received 698 points and 2 first-place votes, and Wade received 680 points and 7 first-place votes.

(3) The fourth-highest vote-getter was Dwight Howard of the Orlando Magic, who received fewer than half as many total points (328) as the third-place Wade.

(4) Kahn and Sherer (1988) show that NBA players with better statistics receive greater pay, though they do not explicitly examine the effect of winning an MVP award on pay.

(5) The NBA collective bargaining agreement is available at http://www.nbpa.org/cba/2005.

(6) The field goal and free throw percentages in Table 1 are individual-game observations, not overall season percentages. This is because estimations in this paper use game-level data.

(7) Wins and losses are only summarized for games in which the player actually played.

(8) These fixed effects also implicitly control for games in which the competitors play against each other.

(9) There is also a tournament among teams teams competing for a worse record in order to receive a better draft position (Taylor & Trogdon, 2002; Price et al., 2010). The three teams in this paper, though, all made the playoffs and were not competitors in that tournament.

(10) For example, the 14 games played on April 15, 2009, averaged 2 hours 19 minutes, with a minimum length of 2:04 and maximum of 2:45. When omitting that day's 3 overtime games the average length was 2:15 and the maximum was 2:23.

(11) NBA.com shows that 938 of 1,230 (76.3%) regular-season games in 2008-09 began at either 7:00 or 7:30 p.m. local time. All but 92 (7.5%) began between 6:00 and 8:30 p.m. local time.

(12) Game times are available via the 2008-09 schedule at NBA.com. In this paper, all game times are recorded according to their Eastern time zone start times.

(13) Nine of 246 potential games are omitted: the four games the players missed (one by James and three by Wade), Bryant's and James' first games of the season, Bryant's and James' first games after Wade missed a game due to injury, and Bryant's last game of the season (which occurred after Wade had skipped his most recent game).

(14) The elasticity of Bryant's point total to Wade's most recent point total is 0.24. The elasticity of James' point total to Wade's most recent point total is 0.23.

(15) The elasticity of Wade's point total with respect to James' win status is 0.16.

(16) The reduction in observations results from perfect classification issues involving opposing-team fixed effects. The [R.sup.2] value in Column 2 is a pseudo-[R.sup.2] value.

(17) Knott (2009) refers to the Cavaliers as a "one-man gang," and Cunningham (2008) says the Heat had "deficiencies in experience and personnel" that led to Wade "struggling"

(18) The reported [R.sup.2] values for Columns 3 and 5 are Pseudo-[R.sup.2] values.

(19) An alternative explanation is that referees themselves are aware of the three-man MVP tournament and deliver these three players to the foul line more often after a competitor has had a good game. Price and Wolfers (2007) and Price, Remer, and Stone (2009) show that referees possess biases that can be revealed in the numbers and types of fouls called.

(20) That Wade's free throw percentage fell after Bryant's Lakers won is curious. Using free throw percentages as a dependent variable serves somewhat as a falsification test: reasons to intentionally miss free throws rarely occur in games, and there is little reason to believe a player would shoot a worse free throw percentage in response to a competitor's play. Price and Wolfers (2007) use free throw percentage as a falsification test when studying racial discrimination among NBA referees.

(21) Nowitzki played 81 games and averaged 25.9 points per game, 4th in the NBA. Jamison played 81 games and averaged 22.2 points per game, 11th in the NBA. Howard played 79 games and averaged 20.6 points, 18th in the NBA.

(22) MacMullen (2009) writes of Johnson and Bird, "Both checked the box scores each morning to see how their rival had fared, but that was only a small part of their obsessive need to chart their dueling milestones."

Andrew W. Nutting [1]

[1] University of Idaho

Andrew W. Nutting is an assistant professor in the College of Business and Economics. His research interests include sport economics, the economics of education, and law and economics.

Author's Note

The author wishes to thank Eric Stuen, Jon Miller, Stephen Wu, and anonymous referees for helpful comments on previous drafts. All remaining errors are his own.

Table 1: Summary Statistics

Games Bryant James Wade

 82 81 79

 Mean St. Dev Mean St. Dev Mean St. Dev

Points 26.8 8.6 28.4 8.8 30.2 8.9
FG Attempts 20.9 5.8 19.9 5.3 22 5.2
FT Attempts 6.9 4.1 9.4 4.3 9.8 4.4
FG Percentage 47.1 10.9 49.1 9.9 49.4 11.2
FT Percentage 85.4 16.8 77.1 16.4 74.6 17.8
Rebounds 5.2 2.6 7.6 3 5 2.1
Assists 4.9 2.5 7.2 2.9 7.5 3.2
Steals 1.5 1.2 1.7 1.3 2.2 1.5
Blocks 0.5 0.7 1.1 1 1.3 1.2
Team Win 0.79 0.41 0.81 0.39 0.53 0.5

Table 2: Estimation Results

Robust standard errors: Columns 1, 3, 5; Standard
errors: Columns 2, 4, 6

 1 2 3

points_bryant_on_james 0.189 * -0.009 0.173 *
 [0.100] [0.007] [0.103]
points_bryant_on_wade 0.097 0.002 0.072
 [0.127] [0.006] [0.134]
points_james_on_bryant -0.049 0.009 -0.051
 [0.081] [0.007] [0.081]
points_james_on_wade -0.041 0.005 -0.042
 [0.114] [0.006] [0.117]
points_wade_on_bryant 0.210 ** -0.001 0.199 *
 [0.103] [0.007] [0.102]
points_wade_on_james 0.224 ** 0.027 *** 0.222 *
 [0.114] [0.009] [0.117]
win_bryant_on_james 1.682 -0.115 1.757
 [2.204] [0.183] [2.229]
win_bryant_on_wade 1.362 -0.007 1.599
 [2.886] [0.135] [2.903]
win_james_on_bryant 0.997 0.163 1.065
 [2.238] [0.143] [2.131]
win_james_on_wade 5.737 ** 0.274 * 5.888 **
 [2.414] [0.141] [2.420]
win_wade_on_bryant -2.578 -0.033 -2.327
 [1.716] [0.115] [1.690]
win_wade_on_james -0.981 -0.190 1.326
 [2.328] [0.150] [2.445]

Dependent Variable Points Win Points

Observations 237 223 237
R-squared 0.26 0.357 0.268

 4 5 6

points_bryant_on_james -0.009 0.201 * -0.009
 [0.007] [0.110] [0.007]
points_bryant_on_wade 0.003 0.09 0.003
 [0.006] [0.131] [0.007]
points_james_on_bryant 0.009 -0.057 0.009
 [0.007] [0.081] [0.007]
points_james_on_wade 0.005 -0.039 0.005
 [0.006] [0.117] [0.006]
points_wade_on_bryant 0.000 0.243 ** -0.001
 [0.007] [0.105] [0.007]
points_wade_on_james 0.028 *** 0.203 * 0.026 ***
 [0.009] [0.122] [0.010]
win_bryant_on_j ames -0.116 1.656 -0.12
 [0.184] [2.306] [0.187]
win_bryant_on_wade -0.005 2.441 0.009
 [0.134] [2.903] [0.140]
win_james_on_bryant 0.161 0.596 0.181
 [0.143] [2.322] [0.147]
win_james_on_wade 0.274 * 5.553 ** 0.287 *
 [0.141] [2.457] [0.145]
win_wade_on_bryant -0.045 -2.365 -0.052
 [0.117] [1.767] [0.120]
win_wade_on_j ames -0.180 -0.893 -0.162
 [0.154] [2.472] [0.157]

Dependent Variable Win Points Win

Observations 223 230 216
R-squared 0.359 0.245 0.344

Note: R-squared values in Columns 2, 4, and 6 are
pseudo-R-squared values.

* signification at 10%; ** signification at 5%;
*** significant at 1%

Table 3: Estimation Results

Robust standard errors: Columns 1, 2, 4; Standard
errors: Columns 3, 5

 1 2 3

points_bryant_on_james 0.189 * 0.054 0.114 **
 [0.100] [0.067] [0.049]
points_bryant_on_wade 0.097 0.110 -0.062
 [0.127] [0.067] [0.058]
points_james_on_bryant -0.049 0.019 -0.054
 [0.081] [0.071] [0.052]
points_james_on_wade -0.041 0.040 -0.073
 [0.114] [0.068] [0.051]
points_wade_on_bryant 0.210 ** 0.031 0.121 **
 [0.103] [0.068] [0.054]
points_wade_on_james 0.224 ** 0.111 * 0.141 ***
 [0.114] [0.060] [0.051]
win_bryant_on_j ames 1.682 -0.222 1.299
 [2.204] [1.677] [1.160]
win_bryant_on_wade 1.362 -0.383 1.770
 [2.886] [1.628] [1.172]
win_james_on_bryant 0.997 0.211 -0.018
 [2.238] [1.654] [1.226]
win_james_on_wade 5.737 ** 2.204 * 3.349 ***
 [2.414] [1.141] [1.201]
win_wade_on_bryant -2.578 -1.746 -0.499
 [1.716] [1.285] [0.922]
win_wade_on_j ames -0.981 0.709 -0.839
 [2.328] [1.307] [0.958]

 FG FT

Dependent Variable Points Attempts Attempts

Observations 237 237 237
R-squared 0.260 0.333 0.068

 4 5

points_bryant_on_james -0.001 0.004
 [0.001] [0.003]
points_bryant_on_wade 0.001 -0.002
 [0.002] [0.003]
points_james_on_bryant -0.001 0.002
 [0.001] [0.003]
points_james_on_wade -0.001 0.002
 [0.001] [0.003]
points_wade_on_bryant 0.003 0.003
 [0.002] [0.003]
points_wade_on_james -0.001 0.001
 [0.001] [0.003]
win_bryant_on_j ames -0.021 0.002
 [0.031] [0.062]
win_bryant_on_wade 0.024 -0.107 *
 [0.034] [0.062]
win_james_on_bryant -0.003 -0.045
 [0.040] [0.068]
win_james_on_wade 0.032 -0.085
 [0.041] [0.064]
win_wade_on_bryant -0.008 -0.034
 [0.026] [0.052]
win_wade_on_j ames -0.025 0.024
 [0.025] [0.051]

 FG FT


Dependent Variable Pct. Pct.

Observations 237 232
R-squared 0.18 0.746

Note: R-squared values in Columns 3 and 5 are
pseudo-R-squared values.

* signification at 10%; ** signification at 5%;
*** significant at 1%

Table 4. Estimation Results when addina 4th MVP Contender

Robust standard errors: Columns 1, 3, 5; Standard errors:
Columns 2, 4, 6

 1 2

bryant_points_on_james 0.175 0.194 *
 [0.109] [0.104]
bryant_points_on_wade 0.075 0.100
 [0.132] [0.129]
j ames_p oints_on_bryant -0.059 -0.055
 [0.081] [0.085]
j ames_p oints_on_wade -0.032 -0.049
 [0.115] [0.118]
wade_points_on_bryant 0.208 ** 0.195 *
 [0.105] [0.109]
wade_points_on_james 0.234 ** 0.215 *
 [0.111] [0.112]
4th_player_points_on_bryant 0.023 0.015
 [0.110] [0.135]
4th_player_points_on_james 0.087 0.121
 [0.172] [0.234]
4th_player_points_on_wade -0.112 -0.051
 [0.126] [0.182]
bryant_win_on_james 1.909 1.700
 [2.506] [2.337]
bryant_win_on_wade 1.579 1.600
 [2.954] [3.006]
james_win_on_bryant 0.698 0.478
 [2.433] [2.263]
james_win_on_wade 4.531 * 5.224 **
 [2.488] [2.501]
wade_win_on_bryant -2.527 -2.547
 [1.743] [1.691]
wade_win_on_james -0.703 -0.711
 [2.366] [2.264]
4th_player_win_on_bryant 1.069 2.305
 [2.181] [3.289]
4th_player_win_on_james 0.242 1.275
 [2.785] [3.292]
4th_player_win_on_wade 0.774 0.466
 [2.441] [2.785]

4th Player Nowitzki Jamison

Dependent Variable Points Points

Observations 232 235
R-squared 0.2681 0.2714

 3 4

bryant_points_on_james 0.178 * -0.015 *
 [0.101] [0.008]
bryant_points_on_wade 0.096 0.002
 [0.119] [0.006]
j ames_p oints_on_bryant -0.067 0.015 **
 [0.086] [0.007]
j ames_p oints_on_wade 0.017 0.003
 [0.114] [0.006]
wade_points_on_bryant 0.191 * -0.006
 [0.106] [0.007]
wade_points_on_james 0.190 0.031 ***
 [0.117] [0.009]
4th_player_points_on_bryant 0.111 0.006
 [0.128] [0.007]
4th_player_points_on_james -0.172 -0.015
 [0.161] [0.010]
4th_player_points_on_wade 0.015 -0.007
 [0.128] [0.007]
bryant_win_on_james 2.392 -0.103
 [2.578] [0.183]
bryant_win_on_wade 1.109 -0.056
 [2.715] [0.129]
james_win_on_bryant 0.238 0.244
 [2.359] [0.150]
james_win_on_wade 3.178 0.219
 [2.558] [0.143]
wade_win_on_bryant -3.011 * 0.031
 [1.813] [0.120]
wade_win_on_james -0.309 -0.232
 [2.468] [0.160]
4th_player_win_on_bryant -2.383 0.358 ***
 [2.442] [0.134]
4th_player_win_on_james -1.696 0.011
 [2.923] [0.180]
4th_player_win_on_wade 4.752 * 0.097
 [2.704] [0.107]

4th Player Howard Nowitzki

Dependent Variable Points Win

Observations 230 210
R-squared 0.2895 0.396

 5 6

bryant_points_on_james -0.012 -0.01
 [0.008] [0.008]
bryant_points_on_wade 0.003 0.002
 [0.007] [0.007]
j ames_p oints_on_bryant 0.006 0.013
 [0.007] [0.008]
j ames_p oints_on_wade 0.005 0.004
 [0.006] [0.007]
wade_points_on_bryant 0.001 -0.007
 [0.007] [0.008]
wade_points_on_james 0.029 *** 0.038 ***
 [0.010] [0.012]
4th_player_points_on_bryant -0.015 -0.028 ***
 [0.011] [0.011]
4th_player_points_on_james -0.009 0.000
 [0.013] [0.012]
4th_player_points_on_wade -0.009 -0.023***
 [0.009] [0.009]
bryant_win_on_james -0.128 -0.097
 [0.201] [0.201]
bryant_win_on_wade 0.017 0.074
 [0.141] [0.158]
james_win_on_bryant 0.213 0.114
 [0.152] [0.168]
james_win_on_wade 0.294 * -0.044
 [0.158] [0.163]
wade_win_on_bryant -0.072 -0.124
 [0.123] [0.144]
wade_win_on_james -0.230 -0.585 **
 [0.160] [0.247]
4th_player_win_on_bryant 0.019 -0.310
 [0.162] [0.164]
4th_player_win_on_james -0.003 0.639 ***
 [0.205] [0.243]
4th_player_win_on_wade 0.121 -0.216
 [0.137] [0.137]

4th Player Jamison Howard

Dependent Variable Win Win

Observations 213 194
R-squared 0.358 0.426

Note: R-squared values in Columns 4, 5, and 6 are
pseudo-R-squared values.

* signification at 10%; ** signification at 5%;
*** significant at 1%