PERSISTENCE IN THE OFFICIAL WORLD GOLF RANKINGS

A THESIS

Presented to

The Faculty of the Department of Economics and Business

The Colorado College

In Partial Fulfillment of the Requirements for the Degree

Bachelor of Arts

By

Mason Bergh

December 2018

PERSISTENCE IN THE OFFICIAL WORLD GOLF RANKINGS

Mason Bergh

December 2018

Economics

Abstract

This paper builds on decades of hot hand effect research. Belief in persistent success or failure is common in sports despite a lack of statistical evidence supporting the phenomenon. Using weekly ranking data for 60 professional golfers around the world, this study deploys an ordinary least squares regression to analyze if persistent rank movement exists in the Official World Golf Rankings. This study hypothesizes that persistence does not exist outside of chance because significant evidence is needed to support the existence of streaks in golf ranks. Like previous studies, the results suggest that streaks do occur, but true statistical evidence to reject the hypothesis was not present.

KEYWORDS: (Persistence, Hot hand, Official World Golf Rankings, Golf) JEL CODES: Z21, L83

ii

ACKNOWLEDGMENTS

Thank you to my family for the continuous love and support that they have shown me.

Also, thank you to Neal Rappaport for his commitment and guidance throughout this process.

iii

ON MY HONOR, I HAVE NEITHER GIVEN NOR RECEIVED UNAUTHORIZED AID ON THIS THESIS

Mason Bergh

Signature

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TABLE OF CONTENTS

ABSTRACT…………………………………………………………………………. ii

ACKNOWLEDGEMENTS…………………………………………………………. iii

1 INTRODUCTION……………………………………………………………...... 1

2 LITERATURE REVIEW………………………………………………………… 3 2.1 Beginning of Streak Research………………………………………………... 4 2.2 Psychological Theories………………………………………………………. 6 2.3 Literature in Golf…………………………………………………………….. 8

3 THEORY……………………………………………………………………….... 12 3.1 Model………………………………………………………………………… 12

4 DATA……………………………………………………………………………. 14

5 RESULTS AND ANALYSIS……………………………………………………. 20

6 CONCLUSION…………………………………………………………………... 23

REFERENCES……………………………………………………………………….. 25

APPENDIX………………………………………………………………………...... 27

v Introduction

In sports, a general belief that players can produce sequences of consistently superior performance compared to their normal performance exists (Bar-Eli et al., 2006;

Heath et al., 2012). This occurrence is referred to as the hot hand effect, and despite its acceptance amongst sports fans, coaches, and players, there is little evidence supporting the hypothesis that it is a real phenomenon (Livingston, 2012).

The subject of this research is professional golf. Analyzing hot streaks in golf has proven to be difficult because judging success is not as simple as other sports. For example, basketball and other shooting sports contain a clear success (scoring) and fail

(missing) outcome. In golf, shots can be rated, but the score is player dependent and is impacted by factors such as environment, ability, course condition, and others (Heath et al., 2012; Rees and James, 2006). This makes examining two separate events difficult.

However, golf continues to be an area of interest for persistence investigation. Many studies have deployed approaches that analyze hole-to-hole performance with different criterion for judging success, but week-to-week linkage is rare.

Rosenqvist and Skans’ (2015) research on the effects of success on future performance in golf tournaments is closely related to this study, but their measure of success is defined differently. No previous studies have used rank movement as a measure of success. An ordinary least squares regression will be used to examine the impact that previous rankings have on current rankings for professional golfers. Using weekly rankings from the 2016 and 2017 periods, this study contributes to hot hand effects research in professional golf by looking at persistent rank movement in the

Official World Golf Rankings. What the results suggest is that although streaks of rank movement occur, significant statistical evidence was not found. This suggests that the persistence that does happen is random.

The study will be organized as follows: Literature Review, Theory, Data, Results, and Conclusion. The literature review will highlight previous research on hot hand effects in sports. Next, the theory will explain this study’s approach to answering the question of persistence in professional golf rankings. Following theory, the data will be described. Finally, the results of the research will be discussed and the study will be concluded.

2 Literature Review

The hot hand effect is an idea that has been studied extensively across numerous fields such as economics, mathematics, and psychology. It has evolved throughout years of research, but the primary focus continues to be whether the hot hand effect is present or not. Livingston (2011) describes it as a topic of interest because people believe strongly in its occurrence despite little evidence supporting that it is a real phenomenon.

For example, in a study performed by Gilovich et al. (1985), there was no evidence that a hot hand effect exists in basketball, however, they found strong evidence that basketball fans believe in it. In their study, 91 percent of their sample believed that a player “has a better chance of making a shot after having made his last two or three shots than he does after having just missed his last two or three shots.”

Due to the fact that there is such a strong popular belief in it, there is a wide variety of strategies that have been deployed to evaluate the impact of past successes on future performances. Bar-Eli et al. (2006) compiled both supportive and non-supportive studies throughout years of research. Their literature review resulted in thirteen non- supportive studies and eleven supportive studies, but stressed that the results of the non- supportive studies weigh heavier than the supportive. However, since that review of hot hand research was released, further evaluation has been conducted and more supportive studies have surfaced. This literature review will look at hot hand research in its entirety.

To do so, the literature review will be broken up into three sections: The beginning of streak research, psychological theories, and golf specific studies. Each section will analyze and discuss relevant literature to better understand the research that has been conducted.

3

2.1 Beginning of Streak Research

Most people in the world of sports acknowledge that streaks happen. For example, a baseball player could put together ten straight hits, or a basketball player could make six straight shots, but what motivates streakiness studies across major sports is whether the observed superior performance is different than what could occur by chance (Bar-Eli et al., 2006).

Gilovich et al. (1985) is acclaimed for initiating research on the hot hand effect in sports. Like many subsequent studies, Gilovich and his partners set out to obtain statistical data that supports the existence of streakiness in the sport of basketball. The first step entailed surveying basketball fans to determine if a belief in streak shooting exists. After establishing that there was an acceptance of persistence in the game of basketball, this belief was translated into a statistical hypothesis that could be tested (Bar-

Eli et al., 2006). Two primary studies were introduced in this portion of their research.

The first study analyzed professional basketball field goal data. Individual field goal records were compiled from 48 home games during the 1980-1981 season for both the

Philadelphia 76ers and their opponents. This data was used to determine that the probability of making a shot was usually lower after having made shots than having missed shots, providing evidence against the hot hand (Bar-Eli et al., 2006 & Gilovich et al., 1985). Although evidence against streak shooting from the field is presented, shot selection and the opponent’s defensive efforts are factors introduced that could be responsible for the negative correlation between successive shots (Gilovich et al., 1985).

To avoid these confounding factors, the second study looked at professional basketball

4 free-throw data. Free throws are most commonly shot in pairs from the same location without defensive pressure. All pairs of free throws by Boston Celtics players during the

1980-1981 and the 1981-1982 seasons were collected for this analysis. However, the data again showed that the outcome of the second free throw is not influenced by the outcome of the first free throw, providing no statistical support for persistence in basketball shots.

Although Gilovich and his colleagues presented statistical evidence against streakiness in basketball, it has served as a foundation for research to develop and extend across many sports. In addition to basketball, research on streakiness continues to surface in baseball (Kvam & Chen, 2017; Vergin, 2000), tennis (Page & Coates, 2017), and like this study, golf (Clark, 2005a; Clark 2005b; Heath et al., 2012; Rees and James,

2006; Livingston, 2012; Rosenqvist & Skans, 2015).

2.2 Psychological Theories

How an athlete reacts to certain events can have a lasting effect on the athlete’s psychological state (Adler, 1981; Bar-Eli et al., 2006; Compte & Postlewaite, 2004;

Gilovich et al., 1985; Livingston, 2011; Taylor & Demick, 1994). Sports has been a topic of interest in psychology because performance varies as the game progresses. It is a series of small events that can be perceived by an athlete in different ways, impacting a player’s psychological and physiological states. For example, a basketball player making a basket can be viewed as a positive event, while missing a shot is perceived negatively.

A lot of research analyzing the linkage between these events exists. Adler (1981),

Gilovich et al. (1985), and Livingston (2011) explain that the connection made between past performance and current performance is called psychological “momentum”. This

5 theory of momentum introduces the idea that a current shot will be influenced by a previous shot. Literature on psychological momentum is extensive, however the multidimensional model of momentum deployed by Taylor and Demick (1994) closely aligns with this paper’s study on persistence in golfers’ performance because their research covers professional golfers from week to week.

The phase of interest in the model by Taylor and Demick is the relationship between precipitating events and changes in competitive outcome. The phase begins with no momentum, followed by an event that they call the “precipitating event”. The precipitating event may be perceived by the athlete as either positive or negative. The development of momentum from the precipitating event is the area of interest. They define momentum as a positive or negative change in cognition, physiology, affect, and behavior caused by a precipitating event or series of events that will result in a shift of performance. They found that the two events can influence an athlete in three main areas: cognition, affect, and physiology. The first is cognition. The perception of an event can impact a player’s sense of control and have a lasting impact. It affects their belief in their abilities, motivation, and their ability to focus on the task. The second area they discuss is affect. When speaking about the precipitating event, changes in cognition create positive or negative emotions. Put simply, positive emotions are expected to increase the chance of a good outcome in future performance, and negative emotions are expected to increase the chance of a bad outcome. Finally, physiology can be influenced by the precipitating event. A positive or negative emotion can influence things like heart rate, adrenaline, and cognition (Taylor & Demick, 1994).

6 They conclude that there can be momentum from the precipitating event to the subsequent event for a player, but explain that it is not enough evidence to begin a positive or negative momentum change. It suggests that the precipitating event is correlated changes in cognition, affect, and physiology, but it cannot demonstrate that positive precipitating events will result in positive momentum and a hot hand effect, or negative precipitating events will result in negative momentum and a cold hand effect

(Heath et al., 2012; Livingston, 2012; Taylor & Demick, 1994). Similarly, Compte and

Postlewaite (2004), they stress that different athletes can have different reactions to the same event. Koehler and Conley (2003) argue that hot hand and cold hands may exist, but their presence is affected by some psychological variable and further research is necessary before any conclusions can be made.

Another tested psychological link between past performance on future performance is confidence (Bénabou & Tirole, 2002; Compte & Postlewaite, 2004;

Rosenqvist & Skans, 2015). Like the theory of momentum, having or lacking confidence can influence performance. Probability of success can create a sense of confidence and positive emotions that can improve performance. Likewise, possibility of failure can have psychological consequences that can impair an athlete’s performance (Compte &

Postlewaite, 2004; Taylor & Demick, 1994). Robert Hooke (1989) expresses this feeling of confidence well: “In almost every competitive activity in which I’ve ever engaged

(baseball, basketball, golf, tennis, even duplicate bridge), a little success generates in me a feeling of confidence which, as long as it lasts, makes me do better than usual. Even more obviously, a few failures can destroy this confidence, after which for a while I can’t

7 do anything right” (p. 35). Since athletes experience this sensation of confidence or failure, there is a strong belief in persistence of success or failure (Bar-Eli et al., 2006).

Understanding the role psychology plays in hot hand effect and streak research works as motivation for further studies on how recent successes or failures can impact future performance outcomes. There is evidence that athlete behavior and psychological state is altered depending on the perception of the event, but evaluating streakiness and persistence in sports is elusive and complex (Heath & Smart, 2012; Bar-Eli et al., 2006).

2.3 Literature in Golf

Throughout years of investigation, there have been many different approaches to analyzing hot and cold streaks in golf. One of the most widely deployed methods is analyzing hole to hole performance (Heath et al., 2012; Livingston, 2012). Golf is structured so that each player records 18 performance values (hole scores) in a round.

One round of golf produces 18 scores that can be used to evaluate any unusual performance that could be deemed streaky. However, where research differs is how studies assess performance based on individual hole scores. Golf uses a simple structure for this in that each hole has a given number of target shots in which the hole should be completed, called the par. Par for the hole is determined by the distance of the hole. The three par scores awarded are 3, 4, or 5 (Heath et al., 2012). Livingston (2012) adopts the built-in performance measure of par, but instead of focusing on a player’s raw score, the analysis focuses on whether the player performed exceptionally well or exceptionally poorly. He explains that a birdie, or better (one stroke or more below par), is defined as having a “good” hole, scoring a bogie or worse (one stroke or more above par) is defined

8 as having a “bad” hole, and scoring a par is a neutral outcome that has no positive or negative impact on momentum.

Like Taylor and Demick’s (1994) theory of momentum, Livingston (2012) uses regressions to examine whether positive or negative momentum affect player performances by examining how previous “good” and “bad” holes affect the likelihood that players have additional good and bad holes. The study uses player data from four golf tours: the PGA Tour, the LPGA Tour, the Champions Tour, and the Nationwide

Tour. The PGA Tour and the LPGA Tour are the top tier professional tours for male and female golfers. The Champions Tour, now known as the PGA Tour Champions, is a men’s professional senior golf tour. The Nationwide Tour is golf’s equivalent to AAA minor baseball, meaning it is one step below the PGA Tour. Using these tours, four separate streak categories were created. The categories consisted of exactly one good hole, a streak of two or more good holes, exactly one bad hole, and a streak of two or more bad holes. Of the four major tours, only the Nationwide Tour showed evidence of players being susceptible to hot or cold hand effects. On the Nationwide Tour, players that recorded streaks of good holes decreased the likelihood of future bad scores and increased the chances of good scores. However, despite evidence for hot hand effects on the Nationwide Tour, Livingston (2012) extends the study to analyze the effects player experience has on susceptibility to good and bad holes. This showed that competitive experience has an impact on a player’s reaction to past performance. Moreover, the only players who showed evidence of streakiness are those that make up the Nationwide Tour, the least experienced and least skilled of the three male tours researched (Livingston,

2012; Taylor & Demick, 1994). Livingston (2012) concludes that streakiness and hot

9 hands can be hidden through psychological factors and degrees of experience, but examples of statistically significant effects of previous performance on future performance were found in the study. He argues that hot and cold hand effects are a real phenomenon.

Rosenqvist and Skans (2015) use a method to analyze streakiness that is most comparable to this study because they focus on performance across tournaments. Using player data from the male European Tour, they analyze performance based on the “cut” in tournaments. A typical tournament is played in four days, with 18 holes each day.

After 36 holes, the cut is determined based on players’ scores. The cut eliminates players in the field that are positioned below 65th, while the qualifying players complete another

36 holes to determine final payout. Rosenqvist and Skans (2015) assume that making the cut can be described as a success, and missing the cut is a failure. To assess the impact of current performance on future performance, they deploy a two-period model that consists of a treatment tournament (period one), and an outcome tournament (period two). By using data of the players who finished within a six-stroke window on either side of the cut in the treatment tournament, they created a situation where players who performed almost equally well in the first period are split into successes (making the cut) and failures (missing the cut). They use the outcome tournament to analyze the estimation that success breeds confidence and that confidence in turn influences future performance

(Compte & Postlewaite, 2004; Rosenqvist & Skans, 2015).

The results of Rosenqvist & Skans (2015) indicate that the impact of present success on future performance is substantial. They show that players who marginally succeeded in making the cut in the treatment tournament substantially increased their

10 performance in the outcome tournament relative to players who marginally failed to make the cut in the treatment tournament. In fact, players that made the cut in the treatment tournament increased their probability of doing so in the outcome tournament by three percentage points. They also provided evidence showing that previous success matters the most when a player is competing in an outcome tournament that involves more prize money.

This literature review brings together various studies across multiple fields to demonstrate the complexity of hot hand effects research. Streakiness in sports has been a topic of interest for decades, and previous investigations have shown that psychological states of momentum and confidence can link past performance and future performance.

Studies have been conducted across a wide range of sports, but golf specifically has introduced signs of hot and cold hand effects. However, evidence supporting the phenomenon is often not substantial and the question of whether current performance impacts future performance remains unanswered. This study will build on the foundation of hot hand research in golf, and will aim to answer the question: Does persistence exist in the professional golf world rankings? That is, does a player experience a streak of rank movement that could occur outside of chance?

11 Theory

The purpose of this analysis is to uncover any persistent patterns in world golf rankings during a single year. Golf rankings are intriguing because they are developed based off player success on any given week throughout the period. With rankings updated weekly, it is reasonable to assume that there can be streaks of movement either up or down, but the motivation for this study is to see if persistence in rank movement is different than what could occur by chance (Bar-Eli et al., 2006). As it has been shown in previous studies on this topic, streakiness in sports can be complicated and difficult to support statistically, meaning the null hypothesis for this study is that persistence does not exist in the Official World Golf Rankings. The methodology for this study is an ordinary least squares (OLS) regression.

3.1 Model

The model is as follows:

RankDiff =0 + 12to1 + 2 3to2 + 3 4to3 + i

Where:

 RankDiff is created by differencing the current rank variable (Rankt – Rankt-1).

The current rank variable gives the ranking for each week for every player within

the dataset. By differencing the left-hand side variable, we can look at the change

in ranking from the current week and the previous week,

 2to1 denotes the first of the three lag variables in the regression. It is the

difference of the lag variable (Rankt-1 – Rankt-2) that allows us to look at the

12 impact that the change in the rankings from week two and week one has on the

change in the current ranking,

 3to2 is the second of the three lag variables. It embodies the difference in the

rankings from week three and week two (Rankt-2 – Rankt-3),

 4to3 is the final lag variable period. It explains the difference in the rankings

from week four and week three (Rankt-3 – Rankt-4).

13 Data

The data for this research was obtained through the Official World Golf Ranking system. The OWGR system is an archive of rankings for professional golfers around the world dating to 1986. The ranking system is updated weekly throughout the year to provide a comparison of players. Players compete in tournaments from the leading

Eligible Golf Tours, as well as Major Championships, World Golf Championships,

Olympic Games, and the World Cup of Golf to be eligible for world ranking points.

There are currently 20 Eligible Golf Tours included in the OWGR system, meaning hundreds of players are awarded world ranking points weekly.1 The world ranking points for each player are accumulated over a two-year period with the points awarded for each tournament maintained for a 13-week phase, rewarding recent performance. Strength of field also plays a role in determining the number of points allocated to an event. Simply, a tournament with a superior field distributes more world ranking points to finishers than a weaker event on a less challenging tour. For example, players receive the most points for winning a major tournament on the PGA Tour compared to lesser events. The PGA Tour has four major tournaments each season. The majors are the Masters, the PGA Championship, the U.S. Open and the British Open, and are considered the most important events in professional golf. The victor of a major tournament receives 100 world ranking points, while a standard PGA Tour or European

Tour event rewards the winner with 24 points. The points earned by players determines their positioning among the top 300 professional golfers around the world each week.

1 List of Eligible Tours seen in Appendix A.

14 For this study, using the OWGR system, the top 100 players for every week from

2016 and 2017 were collected. The data includes each player’s ranking from any week throughout the year, the ranking they held the previous week, their ranking at the beginning of the year, and the collection of world ranking point statistics that determine their rankings. The world ranking point statistics are the basis of the final rankings.

They tell the story of movement and exactly how many points a player needs to improve their positioning among their competitors. Knowing that, the locations of the most volatile spots are revealed.

For example, when looking at the top 100 players from week one of 2016, the number one player in the world was Jordan Spieth, with 11.334 average points per week.

Sitting at 20th from that same week was Matt Kuchar, with 3.604 average points per week. The OWGR system uses average points to determine final rankings. Jordan

Spieth held a 7.73 point advantage over the number 20 player in the world, Matt Kuchar.

Now, 7.73 points does not seem like a lot, but when compared to the difference between the 20th position and the 80th position, it is eye opening. In that same week, Brendon

Todd was the 80th ranked golfer in the world with 1.808 average points. That is 1.796 points behind the 20th ranked player. So, the number one player in the world held a 7.73 point lead over a player only 20 spots below him, while the 20th ranked player only held a 1.796 point lead over a player 60 spots below him. This explains that a player ranked in the 20-80 range has a better chance to move up or down in the OWGR, than a player ranked in the top 20. These results are consistent across all weeks of the two years analyzed.

15 Using this knowledge, the top and bottom 20 players were eliminated from the dataset, leaving the 60 players from the first week of 2016 in the model to assess persistence in rank movement across a year.2 However, players do not stay within the

20-80 range throughout a given period; therefore, 60 observations were not present each week, which explains the variation in number of observations for the lag variables. Table

1 presents the descriptive statistics for the variables used in the model.

Table 1: Descriptive Statistics for Variables

Variable Obs. Mean Std. Dev. Min. Max.

RankDiff 4,581 .33 3.26 -34 14

2to1 4,492 .30 3.27 -34 10

3to2 4,425 .29 3.29 -34 10

4to3 4,355 .28 3.29 -34 10

All players analyzed experienced movement in ranking during the year 2016. In fact, of the 60 players included in the dataset, none finished in the same position that they started the year in. The following figures show the rank movement of three professional golfers within the dataset. In the graphs, movement down signifies an improvement in ranking. Figure 1 shows the movement patterns throughout the year for Shane Lowry, who started in the 21st position. At year’s end, Lowry was ranked 43rd in the world.

2 Full list of players in dataset seen in Appendix B.

16 The question is, did he experience persistence of ranking movement from week to week that could occur outside of chance? The one significant jump in rankings occurred when he finished tied for second place at the US Open in week 24, moving him up to 25th from

41st, but it didn’t result in another increase in ranking the following week.3 In fact, aside from that jump, Lowry experienced a relatively consistent drop in rankings throughout the year.

Figure 1: Shane Lowry Rank Movement 2016

Shane Lowry (21) 50 45 40 35 30 25 20

WorldRanking 15 10 5 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 Week

Source: Official World Golf Ranking

Figure 2 presents another interesting movement pattern in 2016. The chart follows the rankings of the 50th ranked player in the world at the start of the year, Brandt

Snedeker. Snedeker started the year extremely well, and his ranking shows it. In the first week, Snedeker placed third in the Hyundai Tournament of Champions, moving him up

3 http://www.espn.com/golf/player/results/_/id/4587/year/2016.

17 16 positions to 34th in the world. The following week, he finished tied for second in the

Sony Open in Hawaii, shooting him up another 10 spots to 24th. After not playing the third week of the year, he won the Farmers Insurance Open in the fourth week, landing him at number 12 in the world.4 After that initial jump in rankings, Snedeker remained rather consistent for the year, hovering around the 20th position and never going above

30. What makes this figure so intriguing is the consecutive weeks of rank improvement that Snedeker had at the start of the year. This illustrates that persistence can exist, but it does not provide statistical evidence that it is not a random occurrence.

Figure 2: Brandt Snedeker Rank Movement 2016

Brandt Snedeker (50) 60

50

40

30

20 WorldRanking

10

0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 Week

Source: Official World Golf Ranking

Finally, Figure 3 shows the rank movement of Luke Donald, ranked 78th in the world at the start of 2016. Donald finished 2016 in the 81st position, and had a year like

4 http://www.espn.com/golf/player/results/_/id/1222/year/2016.

18 Shane Lowry in terms of rank movement. Outside of his second-place finishes at the

RBC Heritage in week 15 and the Wyndham Championship in week 33, Donald held a steady ranking and did not experience any noteworthy improvements.5 Donald had two separate events where he played exceptionally well, but that success was not replicated in the weeks following.

Figure 3: Luke Donald Rank Movement 2016

Luke Donald (78)

100 90 80 70 60

50 40

WorldRanking 30 20 10 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 Week

Source: Official World Golf Ranking

5 http://www.espn.com/golf/player/results/_/id/601/year/2016.

19 Results and Analysis

This section discusses the results of the OLS regression used to analyze how previous performances impact current performance in professional golf. The testable hypothesis for this study is that persistence does not exist in the Official World Golf

Rankings, and the alternative hypothesis is that persistence does exist. This means that significant evidence is necessary to support that streaks outside of chance occur. Prior to regression analysis, the model was tested for econometric issues, and it was concluded that the model suffered from heteroskedasticity. To correct for that, the regression uses standard errors that are robust to heteroskedasticity. The periods were sorted to analyze each year individually. The regression results for both years can be found in Table 2

(2016) and Table 3 (2017).

Table 2: OLS Regression Results 2016

RankDiff Coef. Std. Err. t P>| t | [95% Conf. Interval]

2to1 -.007424 .0170701 -0.43 0.664 -.0408977 .0260497

3to2 .0263761 .0253099 1.04 0.297 -.0232555 .0760076

4to3 .0333678 .0199467 1.67 0.094 -.0057469 .0724825

_cons .2980027 .0672308 4.43 0.000 .166166 .4298395

Observations = 2,394 F (3, 2390) = 1.34 Prob > F = 0.2604 R-squared = 0.0019

20 Table 3: OLS Regression Results 2017

RankDiff Coef. Std. Err. t P>| t | [95% Conf. Interval]

2to1 .0198216 .0211213 0.94 0.348 -.0216013 .0612444

3to2 .0166356 .0244557 0.68 0.496 -.0232555 .064598

4to3 .0299033 .0177003 1.69 0.091 -.0057469 .064617

_cons .3285621 .0712285 4.61 0.000 .166166 .468255

Observations = 1,934 F (3, 2390) = 1.55 Prob > F = 0.2002 R-squared = 0.0016

When the regression was sorted by year, the results lead to a failure to reject the null hypothesis. To start, the R-squared values were low for both periods at .0019 (2016) and .0016 (2017), suggesting that the previous weeks had little impact on the current ranking of players in the dataset. In both years, the three lag variables proved to be statistically insignificant with no T-values above 2 or below -2, and no T-values significant above the 95% confidence level. The main strength of the study is demonstrated by the consistency across two periods. The 2016 and 2017 periods produced almost identical conclusions, suggesting that the model was built correctly.

The insignificant results of the tour dummy variable in Table 2 also support the consistency within the model. With a Prob > F of 0.26 in 2016 and 0.20 in 2017, we fail to reject that persistence does not exist and acknowledge that consistent rank movement can be random in the Official World Golf Rankings.

The regression was also run without separating the years and including a dummy variable for the year. This variable is “yeardummy” within the results and it was

21 insignificant. The dummy variable being insignificant leads to a failure to reject the null hypothesis that the year has no effect on the results. It is another sign that the results are statistically equivalent across the two periods analyzed and the model was built correctly.

The complete results from the overall regression can be found in Table 4.

Table 4: Complete OLS Regression Results

RankDiff Coef. Std. Err. t P>| t | [95% Conf. Interval]

2to1 .004296 .0132642 0.32 0.746 -.0217087 .0303006

3to2 .022339 .0178949 1.25 0.212 -.0127441 .0574221

4to3 .0318546 .0136936 2.33 0.020 .005008 .0587011 yeardummy .0352414 .0989 0.36 0.722 -.1586533 .229136

_cons .0352414 .0672798 4.40 0.000 .1640167 .4278227

Observations = 4,328 F (3, 4324) = 1.85 Prob > F = 0.1165 R-squared = 0.0016

22 Conclusion

It is widely recognized that streaks occur in the world of sports. Due to this belief, research on the topic of hot hand effects is plentiful. However, despite an abundance of studies, many lack statistical support of streakiness. This paper aimed to answer the question: Does persistent rank movement exist in the Official World Golf

Rankings? This study contributes to the hot hand research by using ranking as a performance measurement, an approach that is not widely used. After running the model for two periods, the results of this study suggest that persistence does not exist in the

OWGR.

However, this does not mean that streaks do not occur in golf rankings. In fact, patterns of consistent improvement or decline occurred numerous times in the periods studied, but, like many hot hand studies before this, a lack of significant statistical evidence implies that those streaks can be a product of random variation. There are several reasons that could account for the randomness of rank movement. One key reason is the performance of other players. Due to the fact that the OWGR system includes 20 tours, many players are provided with the opportunity to score world ranking points each week. This means that just playing well in an event does not guarantee that you move up in the rankings because someone else might play equally well elsewhere.

Another reason is the psychological component that was mentioned earlier. Player’s reactions to similar events differ, meaning if two players finish in the same position, one might develop confidence and carry that into the next weekend, and the other might be unaffected (Compte & Postlewaite, 2004; Taylor & Demick, 1994). Finally, competitive experience has been suggested to impact persistence. Players that have more experience

23 in professional golf are less susceptible to streaks, suggesting that moving up in ranking during a single week will have no impact on their performance the following week

(Livingston, 202).

After conducting this study, there is still opportunity for improvement that could benefit future streak research. One limitation is the movement of players outside of the specific range used to collect the data (20-80 in the world). Throughout the year, some players within the dataset might not be in the designated range for a specific week, and that observation was lost. The goal behind the rank range was to focus primarily on the golfers that experience the most movement, but future studies could analyze rank movement on all players. Moreover, including more than two years of rankings would help to round out the research and provide more data to determine if the pattern is consistent across multiple years. Although this study revealed some conclusions, further research is necessary to continue to analyze the relationship between past performance on current performance.

24 References Bar-Eli, M., Avugos, S., & Raab, M. (2006). Twenty years of “hot hand” research: Review and critique. Psychology of Sport and Exercise, 7(6), 525-553. Bénabou, R., & Tirole, J. (2002). Self-confidence and personal motivation. The Quarterly Journal of Economics, 117(3), 871-915. Broadie, M., & Rendleman, R. J. (2013). Are the official world golf rankings biased? a. Journal of Quantitative Analysis in Sports, 9(2), 127-140. Carlson, K. A., & Shu, S. B. (2007). The rule of three: How the third event signals the emergence of a streak. Organizational Behavior and Human Decision Processes, 104(1), 113-121. Clark III, R. D. (2005a). Examination of hole-to-hole streakiness on the PGA tour. Perceptual and Motor Skills, 100(3), 806-814. Clark III, R. D. (2005b). An examination of the “hot hand” in professional golfers. Perceptual and Motor Skills, 101(3), 935-942. Compte, O., & Postlewaite, A. (2004). Confidence-enhanced performance. American Economic Review, 94(5), 1536-1557. Cotton, C., & Price, J. (2006). The hot hand, competitive experience, and performance differences by gender. Crust, L., & Nesti, M. (2006). A review of psychological momentum in sports: Why qualitative research is needed.Athletic Insight, 8(1), 1-15. “ESPN Golf.” ESPN. Retrieved from http://www.espn.com/golf/. Gilovich, T., Vallone, R., & Tversky, A. (1985). The hot hand in basketball: On the misperception of random sequences. Cognitive Psychology, 17(3), 295-314. Hooke, R. (1989). Basketball, baseball, and the null hypothesis. Chance, 2(4), 35-37. Koehler, J. J., & Conley, C. A. (2003). The “hot hand” myth in professional basketball. Journal of Sport and Exercise Psychology, 25(2), 253-259. Kvam, P. H., & Chen, Z. (2017). A comprehensive analysis of team streakiness in major league baseball: 1962-2016. Livingston, J. A. (2012). The hot hand and the cold hand in professional golf. Journal of Economic Behavior & Organization, 81(1), 172-184. Page, L., & Coates, J. (2017). Winner and loser effects in human competitions. evidence from equally matched tennis players. Evolution and Human Behavior, 38(4), 530- 535. “Past Rankings.” Official World Golf Rankings. Retrieved from http://www.owgr.com/.

25 Rabin, M., & Vayanos, D. (2010). The gambler's and hot-hand fallacies: Theory and applications. The Review of Economic Studies, 77(2), 730-778. Rees, C., & James, N. (2006). A new approach to evaluating streakiness in golf. Performance Analysis of Sport, 7, 352-360. Rosenqvist, O., & Skans, O. N. (2014). Confidence enhanced performance-evidence from professional golf tournaments. Work Pap, 1-32.

26 Appendix

Appendix A: Eligible Tours

Tour Name

Alps Tour Golf Asian Development Tour Asian Tour Big Easy Tour China Tour EuroPro Tour European Challenge Tour Japan Golf Tour KPGA Korean Tour MENA Golf Tour Nordic Golf League PGA European Tour PGA Tour PGA Tour Canada PGA Tour China Series PGA Tour Latinoamérica PGA Tour of Australasia ProGolf Tour Sunshine Tour Web.com Tour

27 Appendix B: Player List

Player Rank Start Shane Lowry 21 Paul Casey 22 Kevin Na 23 J.B. Holmes 24 Marc Leishman 25 Jimmy Walker 26 Thongchai Jaidee 27 Martin Kaymer 28 Byeong Hun An 29 Russell Knox 30 Bernd Wiesberger 31 Emiliano Grillo 32 Victor Dubuisson 33 Andy Sullivan 34 Charl Schwartzel 35 Phil Mickelson 36 Justin Thomas 37 Kiradech Aphibarnrat 38 Robert Streb 39 Anirban Lahiri 40 Billy Horschel 41 Matthew Fitzpatrick 42 Bill Haas 43 Chris Wood 44 Soren Kjeldsen 45 Jamie Donaldson 46 Danny Lee 47 Scott Piercy 48 Chris Kirk 49 Brandt Snedeker 50 Lee Westwood 51 Daniel Berger 52 Charley Hoffman 53 Matt Jones 54 David Lingmerth 55 Ian Poulter 56 Graeme McDowell 57

28 Shingo Katayama 58 K.T. Kim 59 Ryan Palmer 60 Ryan Moore 61 Gary Woodland 62 Jason Bohn 63 Kristoffer Broberg 64 Jaco Van Zyl 65 Russell Henley 66 Francesco Molinari 67 Hunter Mahan 68 Cameron Tringale 69 Keegan Bradley 70 Steven Bowditch 71 Marc Warren 72 Webb Simpson 73 Smylie Kaufman 74 Patton Kizzire 75 Thorbjorn Olesen 76 Tommy Fleetwood 77 Luke Donald 78 John Senden 79 Brendon Todd 80

29