patrickewingtheoryfinal.docx

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The Ewing Paradox

In the world of professional basketball, great players are often praised over

their high statistics. What often isnt highlighted on the nightly ESPN recaps are the

efficiencies of these playersonly, for example, that Allen Iverson scored a

triple-double, recording double-digit figures in three statistics such as points,

assists, and rebounds. While NBA superstars all have remarkable athletic ability

and talent, sometimes they do not help their teams win solely by recording such

inordinate statistics. If the superstar scores 40 points in a game but misses 15

shots, his high point total may outweigh his low scoring average. Other overlooked

examples may include lackadaisical defense or high turnovers, even if a player

shoots efficiently and boosts one of the five main statistics: points, rebounds,

assists, steals, and blocks.

Sportswriter Bill Simmons observed one superstar whose team played

better without him, Patrick Ewing's teams (both at Georgetown and with New

York) inexplicably played better when Ewing was either injured or missing

extended stretches because of foul trouble (Simmons, 2001). In this article,

Ewing Theory 101, Simmons identifies the paradoxical nature that some teams

improve after their superstar leaves the team. While Simmons claims these

counterintuitive phenomena exist in all professional team sports leagues, how

often do NBA teams actually improve after a superstar departs and can economics

explain these observations? The Ewing Theory may simply describe a series of

unlikely coincidences, which after all are statistically likely to occasionally occur.


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This paper will investigate the team value, measured in terms of player and team

efficiency and post-departure team wins, of 52 of the NBAs greatest players of all

time compiled from NBA all-star and MVP votes from fans dating back to 1960.

Sports media and sports fans often express strong cultural desires in sports

for the best possible performances. Sports fans demand to seeboth in game and

on televisionbetters players increasingly more as player skill rises; it comes as

no surprise that fans desire to see exciting highlights of NBA superstars, such as

dunks and alley-oops (when a players pass is dunked out of the air). This

consumer demandsatisfied by media sources like ESPNhas shaped the

professional style of play and maybe even the rules; additionally, it perhaps affirms

and reinforces egotistical or closed-minded styles of play. Additionally, the NBAs

reverse order entry draft ensures the worst teams can add the best college players

to their subpar rosters, thereby increasing this superstar effect. Throughout this

paper, I presume a superstar is the best player on a team and has relative absolute

and comparative advantages in many basketball proficiencies on his team. A

superstar may certainly be a smart asset to utilize during a final play or during

scoring droughts to regain game momentum; however, he may also be a detriment

to the team if defenses can adjust to his playing a major role in an offense.

Employing Berri et al.s win score calculation from Wages of Wins is a

statistical player evaluation (or team evaluation) based on nine basketball statistics

that lifts the superstar curtain and exposes each players efficiency (Berri,Schmidt

& Brook, Wages of Wins, 2004, page 99). According to the list of superstar data,


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some teams ironically improved in win score when calculating the aggregate team

win score after the superstars departed from their teams, in line with the Patrick

Ewing paradox. The teams increased performancealbeit not necessarily

through winscan be explained by economic theory of supply and demand. By

analyzing the comparison between superstars wins score and their respective

teams aggregate win score, I will bring to light truer values of each superstar. I

believe that superstars with higher win scores as a percentage of their overall team

win scores will correlate with non-optimal play at the team level and lower

numbers of team wins.

Assessing a players efficiency necessitates an understanding of

win-maximizing agents in basketball. Teams generate higher revenues, and thus

higher profits, by maximizing their win production. Since teams operate like

profit-maximizing firms, they seek to win as many games as possible in a season

and thus aim to maximize overall team win score efficiency. Berri et al. establish

that wins are solely a function of offensive and defensive efficiency (Berri et al.,

Wages of Wins, 2004, 99). Since each team alternates possessions back-and-forth

throughout the game, the team that plays with the highest combined offensive and

defensive efficiency will always win. Win-maximizing teams will maximize their

chances to score the most points possible each possession while minimizing the

opponents attempt at the same. Their coaching decisions should reflect this

assumption by calling for the most efficient scorer (or otherwise link to scoring),

whom is assumed to be the superstar, to shoot the ball.


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In the supply-and-demand curve in Graph 1 below, superstars are assumed

to shoot a higher shot percentage than an average player. Following the model, as

this superstar increases his supply of shot percentage of overall team shots each

game, defensive demand for guarding the superstar will rise with it. The defensive

coach will respond to guard this scoring superstar more tightlyperhaps by

double covering himthereby forcing him to either take some more difficult shots

and increase his missed shot percentage (lowering his field goal percentage) or

forcing him to shoot less. The superstars field goal percentage will fall as a result

so much that the win-maximizing offensive coach will decide to suppress his

original scoring option and instruct him to shoot less. Meanwhile, assuming the

rest of the team has a lower field goal percentage than the superstar, it will rise as

long as the superstar contributes some shots. Eventually though, if the defense

guards the superstar much more, the overall team field goal percentage will fall,

potentially even below the team average without the superstar in the first place

(Gravity and Levity, 2006). The gray area on the graph is the low team field goal

percentage that is one graphical possibility of the Patrick Ewing Effect. One

example of this scenario is the performance of the Cleveland Cavaliers with Lebron

James. Although James has been dubbed by many the greatest player in the NBA, if

the defense could adjust and guard his many shots each game, then the Cavaliers

field goal percentage would fall as a team and they would often lose due to this

inefficiency (Kubatko, 2011). The equilibrium of this coaching strategy is

illustrated by the following models, the first of which I created:


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Graph 1 Graph 2 (Gravity and Levity,

2006)

Given the aforementioned assumptions of the superstar field percentage

and the supply/demand curves relationship between superstars and defenses,

teams with superstars have the potential to be more efficient than teams without.

However, mainly due to talent, superstar hype, and major statistics without

efficiency, the models gray area shows some superstars may not only irrationally

ignore the teams opportunity cost during game-play but may actually lower the

teams productivity altogether had they not been playing. While shot percentage is

not the only example of superstar (or perhaps coach) overzealousness on the

courtdefenses could, for instance, adjust to box out superstar rebounder Dwight

Howard if he never left the paintit serves as a good example with actual data to


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back it up. The second graph shows a negative correlation between field goal

percentage and shots per game, illustrating data of superstars Kobe Bryant and

Shaquille ONeal (Gravity and Levity, 2009). Superstar presence may also prevent

a team from achieving its optimal efficiency by impeding the efficiencies of other

individuals, who may even have higher opportunity costs at certain specialized

roles. Since there is only a single ball used in a game, according to the law of

diminishing returns, increasing the scoring productivity at one position must

decrease it at another. Moreover, superstars may impede team cohesionwhich

could increase each players productivityby monopolizing ball control,

preventing the team from firing on all cylinders.

One implication of the Ewing Paradox on profitability is that bad teams may

be better off distributing payroll more evenly than acquiring a single superstar.

Theoretically, if a team can produce a higher win score without a superstar, they

may lose some close games without a strong finisher, but they could very well win

more games in a season with an increased team win score. However,

championships are rarely won without at least one superstar, so better teams may

need to seek acquiring one if they are contending for a championship.

With the goal of uncovering more potential, Patrick Ewings who may have

reduced or not added efficiency value to their teams, I used a list of 84 all-stars

compiled through a formula based on MVP and All-NBA votes since 1960.

McChesney (2006) assigned the ranks of each annual MVP vote since 1960 (first

place earns ten points, second earns nine points, etc.) and added the All-NBA votes


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(first-team earns five points, while second and third-teams both earned 3 points).

When the list was made in 2006, only 84 players received nine or more total

points, below which the threshold was deemed too frequently reached to be

considered the best ever. Next, I researched the statistics of each player that was

traded or otherwise left a team (permitting multiples), only including players that

played at least 2000 minutes in both of the two preceding seasons. I then compiled

the statistics for each original team for those two years with superstars and the

two years following their departures. Teams whose number of wins increased

after their superstars departure may have been home to somepotentialPatrick

Ewings. Assessing the new number of wins for each of these 70 instances

provided a glimpse of what a further efficiency analysis could uncover.

In order to analyze the compiled list of NBA superstars, I utilized Berri et

al.s wins production formula, a close variant on his win score formula that he

developed based on years of historical statistics in the NBA. Note that Berri et al.

do have a more precise model, based on regressions of very complex statistics that

were not readily available. Likewise, payroll is an obvious candidate as an

independent variable in regressions, but team payroll and salary information can

only be found for few years until 2000, often accompanied with a disclaimer that

the information is based on estimates.

Berri et al. argue that wins are simply a result of a teams efficiency since

teams alter possessions and thus control the ball the same amount of timesgive

or take one possessionper game. He notes the simple coefficient of possession


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in relation to team points: Over the years we examine (1993 94 to 2004 05) this

ratio [points per possession] tended to hover around one, hitting a high of 1.05

points per possession in 1994 95 and a low of 0.99 points per possession in

1998 99 (Berri et al., Wages of Wins, 212). Each change of possession or point

scored is recorded by one of the statistics in his equation so that the overall

efficiency can be feasibly calculated at both the individual and team levels. He

claims to be able to moderately calculate the efficiency of a player based on nine

statistics in the following formula:

(Berri et al., Wages of Wins, 113)

Wins produced is a statistic that Berri created to calculate the amount of

wins produced that a player contributes to a teams wins each season. Adding all

of the statistics within the parentheses above yields what he calls win score,

which is converted to wins produced per season by dividing by the number of

games. By instead dividing the win score by the number of minutes that player

played in a season, the calculation yields the wins production per minute played, or

per game productivity (WP48) (Berri et al., Wages of Wins, 2004). For instance,

Michael Jordan had a high wins produced with almost 12 in back-to-back seasons, a

season average 0.25 win production for each 48 minutes he played, while Allen

Iverson performed the least efficiently on the 52 player list, ranging from 2.8 to 3.5


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in win production with WP48s of 0.6 and 0.7. Steve Nash performed averagely

among the superstars with results of 8.1 and 9.3 in wins produced. The superstar

list ranged from wins produced of -1.3, during Pete Maravichs unsuccessful 1978

season, to Wilt Chamberlains 28 wins produced in 1966 (Kubatko, 2011). Table 1

shows win scores for some of these individual players:

Individual Win Score (Table 1)*

Player Team

Games

Played Minutes Points

Rebound

s Assists Steals

Michael

Jordan

CHI199

2 80 3102 2404 511 489 182

Jordan

CHI199

3 78 3067 2541 522 428 221

Allen

Iverson PHI2004 75 3174 2302 299 597 180

Iverson PHI2005 72 3099 2377 232 532 140

Steve Nash

DAL200

2 82 2711 1455 234 598 85

Nash

DAL200

3 78 2612 1128 232 687 67

Blocks

Turnove

rs

Person

al

Fouls

FG

Attempt

s FG Made

WINS

PRODUCE

D WP48

Michael

Jordan 75 200 201 1818 943 11.90.25

Jordan 61 207 188 2003 992 11.90.25

Allen

Iverson 9 344 140 1818 771 3.60.07

Iverson 10 248 121 1822 815 2.90.06


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Steve Nash 6 192 134 1114 518 8.10.17

Nash 8 209 139 845 397 9.30.19

*Data from Kubatko, 2011

The wins produced can also be investigated over all four years at the team

level to show whether the team achieved a more efficient level of playregardless

of wins for those seasonswith or without its superstar. Think of this as an

aggregation: adding each players wins produced or WP48 would produce the

same result as calculating it from the team statistics. Revisiting Simmons article,

Elgin Baylor is listed as a great example of the Ewing paradox, as Simmons cites the

Lakers 33-game win streak after Baylor abruptly retired (Simmons, 1999). Notice

that the team wins produced and real wins actually improve after Baylor and

Cowens leave their teams. However, the opposite is true for Shaq because his team

became much worse after he left.

Team Win Score (Table 2)*

Player

Tea

m Year Won Lost WIN SCORE WINS PROD.

Elgin Baylor LAL 1968 55 27 4500 54.87

LAL 1969 46 36 3875.5 47.26

*Early Retire LAL 1970 48 34 4312.5 52.59

LAL 1971 69 13 5031.5 61.35

Shaquille

O'Neal ORL 1994 57 25 4462 54.41

ORL 1995 60 22 4073.5 49.67

*Traded to ORL 1996 45 37 3175 38.71


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Lakers

ORL 1997 41 41 2894 35.29

Dave Cowens BOS 1978 29 53 3029 36.93

BOS 1979 61 21 3911.5 47.70

*Early Retire BOS 1980 62 20 3812.5 46.49

BOS 1981 63 19 3899.5 47.55

Player

WINS

PRODUCE

D

Average

Wins

Prod.

Wins Produced

Differential

Before/After

Avg

Wins

Win Diff.

Before/After

Elgin Baylor 54.9 51.1 50.5

Lakers 1968-1971 47.3 5.9 8.0

*Early Retire 52.6 57.0 58.5

61.4

Shaquille O'Neal 54.4 52.0 58.5

Magic 1994-1997 49.7 -15.0 -15.5

*Traded to Lakers 38.7 37.0 43.0

35.3

Dave Cowens 36.9 42.3 45.0

Celtics 1978-1981 47.7 4.7 17.5

*Early Retire 46.5 47.0 62.5

47.6

*Data from Kubatko, 2011

Table 2 shows the overall team wins produced compared to actual wins

over a span of four listed years. While the amount of wins produced by Berri et

al.s win score estimate did not equal the exact wins that a team had in a season,

regressing a teams aggregate win score, with the wins as the dependent variable


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and win score as the independent variable, returned a very high correlation.

Additionally, in almost all cases, the win score and wins either both increased or

both decreased after a superstar departure, though not always proportionally.

Originally, I hypothesized that superstars wins produced would be

inversely related to their teams aggregate wins produced, representing the

inefficiency of allowing one player to serve such a major role on a team. I also

hypothesized that win score differential would be positively correlated with win

differential because a team performing more optimally should earn more wins. I

modified my original hypothesis by creating percentages for each ratio of player

win score compared to overall team wins (I created another for team win score

that predictably produced the same correlation). This percentage represents the

statistical involvement of each superstar throughout the season, ranging from Bob

Cousys 3.2% with the 1962 Celtics to Dikembe Mutombos 63.6% with the 1999

Hawks (Kubatko, 2011). By regressing team wins as a function of individual win

score, the analysis returned a negative fit line with a coefficient of -15.11 at a 10%

significance level. Every increase of 1% of the player win score : team wins ratio

decreased the number of wins in a season by 0.15%.

*Created with STATA

In other words, teams that have one player that consistently has a high

percentage of involvement, in terms of all the stats that win score measures, the


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lower that teams wins and overall win score. Despite contributing large amounts

of wins for a team, superstars that monopolize team possessions generally dont

seem to do as well as superstars that are smaller roles of a greater team. And this

result makes sensethe lower wins produced can be most likely be explained by

presence of other very good players or if the superstar settles into a niche which

does not churn out high win scores.

Graph 3, produced by STATA

Contrary to my first hypothesis, results showed lower win scores for

players whose teams performed better after they left. Regressions showed that


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there is no correlation between wins produced by a teams superstar compared to

the teams wins before after that player left his team. The players at the top of the

list, such as Michael Jordan and Kareem Abdul-Jabbar, were parts of extremely

good teams and exhibited high win scores, throwing off my original hypothesis:

Jordans team had little room for improvement after setting the NBA season win

record and winning six titles. Interestingly, my second hypothesis, that as the

player wins produced : team wins produced ratio rose that team wins would fall

was correct. While correlation is not causation, it seems as though due to the

decreasing marginal returns of employing high talent in basketball, having a

superstar detracts from other players contributions. I must also consider that this

trend may occur partially due to the reverse order entry draft that forces some

superstars into producing high win score ratios while playing for teams with bad

records. The sheer number of players in the data set that were observed in the

data set to follow a Patrick Ewing paradox was 21%. Among the 52 superstars, 11

of these players teams recorded better team win scores and overall wins in the

regular season after the superstars left their teams: Kemp, Parish, Richmond,

McGinnis, Hill, McGrady, Archibald, Cowens, Ewing, Malone, and Baylor. According

to this list, an inordinate number of the best NBA players ever actually played on

teams that perhaps improved after their departures.

While unique player characteristics can boost a great NBA player into the

realm of superstardom, fans are generally most attracted to players who post high

statistics and touch the ball often. Superstars have the most opportunities to make


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plays for the team and thus increase the demand for defense for that particular

player. In doing so, the players efficiency, in statistics such as field goal percentage

and turnovers, worsens because defenses adjust to guard the superstar. The

superstar may consequently shoot too often and lower the teams productivity to

below the optimal level. Aside from the motivation of remaining post-departure

players to fill the superstar void and play better in games, the teams optimal

efficiency decreases but the actual win score efficiency may counter intuitively

increase. An initial glance at the NBA superstar list over the last 50 years would

not seem to contain many inefficient players, but improving team win scores and

team records has revealed these relevant findings. Likewise, the negative

correlation between the player wins produced : team win produced ratio and

overall wins helps verify the inefficiency of many team scenarios. Multiple forms

views of the win score data show that Patrick Ewing paradox manifests itself at

even the highest level of play in the NBA.


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Bibliography

Berri, D. (2004). On The Road With the National Basketball Associations Superstar

Externality.Journal of Sports Economics, 7(347), 1-13.

Berri, D. (2006). Stars at the Gate: The Impact of Star Power on NBA Gate

Revenues.Journal of Sports Economics, 7(33), 1-13.

Berri, D., Brook, S., & Schmidt, M. (2004). Wages of Wins (Vol. 7). Stanford, CA:

Stanford University Press.

Gravity and Levity. (2009, 5 28). Braesss Paradox and The Ewing Theory.

Retrieved April 11, 2011, from Gravity and Levity:

http://gravityandlevity.wordpress.com/2009/05/28/braesss-paradox-and-the-ewi

ng-theory/

Kubatko, J. (2011). NBA & ABA Player Statistics. Retrieved April 15, 2011, from

Kubatko, 2011: http://www.basketball-reference.com

McChesney, R. (2006, 8 13). The Gold Medal Superstar Theory and Championship.

Retrieved April 11, 2011, from NBADraft.net:

http://www.nbadraft.net/mcchesney001.html

Simmons, B. (2001). Ewing Theory 101. Retrieved April 11, 2011, from ESPN.com:

http://sports.espn.go.com/espn/page2/story?page=simmons/010509a

Simmons, B. (2009). The Book of Basketball. New York, New York: ESPN Books.

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