superstar effect by jen brown

8/3/2019 Superstar Effect by Jen Brown

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Figure 1: Numerical Solutions for Three-Players and Two-Prize Model

0

0.05

0.1

0.15

0.2

0.25

1 2 3 4 5 6 7 8 9 10

EffortofNon-SuperstarPlayers

(x2andx3)

Relative Ability Measure (!)

alpha =1 alpha = 0.8 alpha = 0.6

Note: The figure illustrates numerical solutions to the system of equations presented in Section 2 for a tournament with three players competing for

two prizes. Alpha (!) describes the purse-sharing rule, where the winner receives fraction ! of the total purse, the second-place player receives

fraction (1-!) of the total purse, and the third-place player receives 0. The vertical axis measures the effort of the two, identical non-superstar players

in the tournament. The horizontal axis measures the relative ability advantage of the superstar player, where the superstar is " times more skilled than

the regular, non-superstar players.


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Figure 2: Mean Scores for PGA Tour Events 1999-2006

-16

-14

-12

-10

-8

-6

-4

-2

0

1999 2000 2001 2002 2003 2004 2005 2006

MeanTournamentScoresRelativeto

Par

Tiger Woods Ranked 1 to 20 Ranked 21 to 200 Unranked

Note: Only players who made the cut are included. Regular and major events are included; values for small-field and alternate events are not presented. Ranks reflect

players Official World Golf Ranking at the time of the event. Values for Tiger Woods are presented separately and, therefore, are omitted from the statistics for top-

ranked players.


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Figure 3: Scores Relative to Par Over Time for Tournaments With and Without Tiger Woods

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Figure 4: Differences in Tournament Scores for Events With and Without Tiger Woods

-2

0

2

4

6

8

10

1999 2000 2001 2002 2003 2004 2005 2006

MeanTournamentScoreinEventsWithWoodsMinus

MeanTournamentScoreinEventsWitho

utWoods

Rank 1 to 20 Rank 21 to 200 Unranked

Note: Only scores from players who made the cut are included in the calculations. Regular and major events are included; small-field and alternate events are

excluded. "With Tiger Woods" indicates that Woods played in the tournament, while "Without Tiger Woods" includes only tournament in which Woods did not

participate. Ranks reflect players Official World Golf Ranking at the time of the event. Scores for Tiger Woods are excluded.


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Figure 5 - Distribution of Tournament Scores for Barclays Classic and Wachovia Championship in 2005

Note: Only scores from players who made the cut are included. Woods's final score in the Wachovia Championship is excluded.

0

5

10

15

20

Frequency

-10 0 10 20Strokes Relative to Par

Barclays 2005 - Woods Did Not Participate

Wachovia 2005 - Woods Participated


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Average # Per

Round in

TournamentsWith Tiger

Average # Per

Round in

Tournaments

Without TigerWoods

H0: Equal number with

and without Tiger

(Unpaired t-test)

2 Strokes under par "Eagle" 0.080 0.093 p-value=0.065(0.004) (0.006)

1 Stroke under par "Birdie" 3.815 3.866 p-value=0.194(0.021) (0.033)

Equal to par "Par" 11.323 11.354 p-value=0.515(0.026) (0.038)

1 Stroke over par "Bogey" 2.510 2.448 p-value=0.069(0.020) (0.028)

2 Strokes over par "Double Bogeys 0.242 0.218 p-value=0.035(0.006) (0.009)

Table 1: Average Number of Eagles, Birdies, Pars, Bogeys and Double Bogeys in Tournaments With and

Without Tiger Woods from 2002 to 2006

Note: Values in parentheses are standard deviations. Only scores from players who "made the cut" are included.

Regular and major events are included; small-field and alternate events are excluded. "With Tiger Woods" indicatesthat Woods played in the tournament, while "Without Tiger Woods" includes only tournaments in which Woods didnot participate. Scores for Tiger Woods are excluded.


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2.1 2.2 2.3 2.4

Strokes Relative to Par for

Tournament types:

Superstar Effect for Players:

Ranked 1 to 20 0.596 ** 0.535 * 1.358 ** 0.996

(0.281) (0.302) (0.726) (0.786)

Ranked 21 to 200 0.161 0.141 0.804 *** 0.672 **

(0.113) (0.117) (0.318) (0.328)Unranked 0.202 0.212 0.596 0.311

(0.126) (0.131) (0.396) (0.400)

Other variable coefficients suppressed

# of obs 34986 29167 18805 15651

Adjusted R-squared 0.29 0.21 0.48 0.38

regulars & majors regulars regulars & majors regulars

Table 2: Regression Results for Scores in Regular and Major Tournaments 1999-2006

first round first round tournament tournament

Note: All specifications include controls for players' rank, strength of the field, wind, rain and temperature, purse size, television viewership, tournament

type, and course-player fixed effects.Values in parentheses are standard errors, clustered by player-year (e.g. Mickelson in 1999). *,**, and ***

represent statistical significance at p-values of 0.10, 0.05, and 0.01, respectively. "Major" events are the PGA Championship, US Open, British Openand Masters. Scores for Tiger Woods are excluded.


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Event: Personal Issues

Years: 2009-2010

Months: July August March

Ranked 1 to 20 with Woods -4.00 4.51 4.60(3.61) (7.29) (4.16)

# of obs 5 35 5

without Woods -8.00 -0.17 -1.00

(5.24) (5.06) (6.04)

# of obs 9 18 9

Ranked 21 to 200 with Woods 2.01 3.84 5.84

(4.70) (10.05) (5.20)

# of obs 86 136 44

without Woods -5.97 2.63 1.87

(4.93) (6.44) (5.07)

# of obs 73 57 47

Unranked with Woods 4.13 -2.68 6.48

# of obs (4.69) (11.43) (4.14)

53 59 23

without Woods -4.09 5.80 3.21

(4.58) (7.82) (5.75)

# of obs 70 5 19

2007-2009

Table 3: Tournament Scores in Selected Events with and without Tiger Woods

Knee Surgery

Note: Values in parentheses are standard deviations. Months and years of interest reflect the timing

of Woods's unexpected absences from competition. Only scores from players who made the cut are

included."With Woods" indicates that Woods played in the tournament, while "Without Woods"includes the same tournaments when Woods did not participate in the year of interest. Scores for

Tiger Woods are excluded.


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Event:

Period included:

Strokes Relative to Par for:

Superstar Effect for Players:

Ranked 1 to 20 0.244 3.919 *** 1.125 2.754

(0.614) (1.462) (0.930) (2.038)

Ranked 21 to 200 0.317 5.647 *** 1.510 *** 3.519 ***

0.309 0.956 0.447 1.050

Unranked 0.119 5.755 *** 1.210 *** 3.554 ***

(0.377) (1.094) (0.484) (1.351)


# of obs 2676 1616 2339 1172Adjusted R-squared 0.21 0.58 0.18 0.36

Table 4: Regression Results for Woods's Unexpected Absences

First-Round Tournament First-Round

Knee Surgery in 2008 Personal Issues in 2009 and 2010

July - Sept 2007-2009 January - March 2009-2010

Tournament4.1 4.2 4.3 4.4

Note: All specifications include controls for wind, rain and temperature, purse size, course- and player-level fixed

effects.Values in parentheses are standard errors, clustered by player-year (e.g. Mickelson in 1999). *,**, and ***

represent statistical significance at p-values of 0.10, 0.05, and 0.01, respectively. Scores for Tiger Woods areexcluded.


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Strokes Relative to Par for

Tournament types:

Ranked 1 to 20 Typical Superstar Effect 0.358 0.381 1.016 0.792

(0.302) (0.332) (0.833) (0.927)

Hot Superstar Effect 0.982 *** 1.388 *** 2.074 *** 2.276 ***

(0.321) (0.379) (0.775) (0.961)

Cool Superstar Effect 0.279 -0.418 0.500 -0.753(0.439) (0.501) (1.049) (1.330)

Ranked 21 to 200 Typical Superstar Effect -0.088 -0.065 0.669 ** 0.519

(0.127) (0.130) (0.365) (0.373)

Hot Superstar Effect 0.611 *** 0.744 *** 1.377 ** 1.414 ***

(0.139) (0.152) (0.369) (0.400)

Cool Superstar Effect -0.220 -0.299 * -0.332 -0.265

(0.171) (0.173) (0.486) (0.519)

Unranked Typical Superstar Effect 0.129 0.222 0.433 0.310

(0.152) (0.153) (0.460) (0.465)

Hot Superstar Effect 0.523 *** 0.602 *** 1.387 *** 0.974 *

(0.149) (0.159) (0.504) (0.522)

Cool Superstar Effect -0.294 -0.342 -1.151 * -1.110 *

(0.216) (0.215) (0.663) (0.632)


# of obs 34986 29167 18805 15656

Adjusted R-squared 0.29 0.58 0.48 0.38

egulars & majors regularsregulars & majors regulars

Table 5: Regression Results for "Typical", "Hot" and "Cool" Periods

5.3 5.45.1

tournament tournamentfirst round first round

5.2

Note: All specifications include controls for players' rank, strength of the field, wind, rain and temperature, purse size, television viewership,

tournament type, and course-player fixed effects.Values in parentheses are standard errors, clustered by player-year (e.g. Mickelson in 1999).

*,**, and *** represent statistical significance at p-values of 0.10, 0.05, and 0.01, respectively. "Major" events are the PGA Championship,US Open, British Open and Masters. The difference between the average score posted by ranked players and the score posted by Tiger

Woods was calculated for all months. "Cool" and "Hot" periods represent the first and fifth quintile of these values, respectively, lagged by

one month. Missing percentile values were replaced with data from the previous available month. Scores for Tiger Woods are excluded.


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Dependent Variable:

Ranked 1 to 20 0.001 0.016

(0.023) (0.055)

Ranked 21 to 200 -0.005 -0.005

(0.009) (0.039)

Unranked 0.013 0.025

(0.012) (0.041)

Round 2 -0.002 0.003

(0.006) (0.072)

Round 3 0.027 *** -0.013

(0.008) (0.078)

Round 4 0.034 *** -0.017

(0.008) (0.046)


# of obs 29166 7423

Adjusted R-squared 0.29 0.41

"Went for it" Measure

(Greens attempted /

Total opportunities)

Regulars 2002-2006

Table 6: Regression Results for Risky-Strategy Measures

6.26.1

Variance of Strokes

Relative to Par in

Regular Events

2001-2006

Note: All specifications include controls for wind, rain and temperature, purse size, and player-course

fixed effects. Values in parentheses are standard errors, clustered by player-year (e.g. Mickelson in

1999). *,**, and *** represent statistical significance at p-values of 0.10, 0.05, and 0.01, respectively.Only data from players who made the cut are included.

superstar effect by jen brown

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