Risk Taking Dynamics in Tournaments: Evidence from Professional Golf. Todd McFall 1 Department of Economics Wake Forest University

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1 Risk Taking Dynamics in Tournaments: Evidence from Professional Golf Todd McFall 1 Department of Economics Wake Forest University Kurt W. Rotthoff Stillman School of Business Seton Hall University Spring 2016 Abstract Analyzing strategies in tournaments can be difficult to analyze given data limitations. We analyze golfers risk taking strategies with a unique data-set from ten seasons of professional golf tournaments and present three major findings. First, as the value of taking on a risk rises, golfers become more likely to adopt risky strategies, a finding that aligns well with classic economic thinking. However, golfers exhibit signs of loss aversion as the total payouts increase. Second, golfers are influenced by a reference bias, which we measure as the difference in their standing in a tournament compared to their world ranking at the time of the tournament. This bias is dynamic throughout the tournament, as risk taking rises as payouts become more imminent. Last, in Tiger Woods s era of dominance ( in our dataset), golfers took on more risk when Woods was in the field compared to events in which he was not. This finding suggests that the superstar forced his rivals to take on more risk than they would have liked, providing an explanation for the superstar effect found in Brown (2011). Keywords: Risk Taking, Risk Strategies, Tournaments, Reference Bias, Superstar Effect JEL: 1 Todd McFall: Wake Forest University s Department of Economics, 223 Kirby Hall, Winston-Salem, NC He can be reached at d at mcfallta@wfu.edu, Kurt W Rotthoff: Seton Hall University s Stillman School of Business, 400 South Orange Ave, JH 674, South Orange, NJ He can be reached at Kurt.Rotthoff@shu.edu or Rotthoff@gmail.com. Thank you to Robert Tollison, Angela Dills, Rey Hernandez, Pete Groothuis, and the participants at the Eastern Economic Association s annual meetings in 2015 and the Appalachian State University seminar series for helpful comments. Any mistakes are our own.

2 I. Introduction The incentive effects provided by tournaments are an often studied topic. The overwhelming dimension of interest in these studies is how competitors choose different levels of effort in preparation or during the competition. Beginning with pioneering applied studies like Ehrenberg and Bognanno (1990a, b), a number of important studies have provided strong evidence in support of the theoretical propositions discussed in Lazear and Rosen (1981). Instead of analyzing effort choices, our study adds to the literature by analyzing the risk taking strategies of tournament participants. Sports studies allow for controlled settings where differences in behaviors can be measured. We utilize data on the decisions professional golfers face in nearly every competitive round they play the decision of how much risk to take with their second shots on par five holes. 2 This commonly made yet often critical decision forces golfers to consider the returns from hitting a longer second shot, a high-risk, high-reward activity, or playing a more conservative lay-up shot. 3 If executed correctly, a great second shot to a par five green can give a golfer a leg up on his competition, an action that increases the chances of a golfer receiving a valuable remunerative reward for strong relative performance. We use the extraordinary ShotLink database to test golfers risk choices on these shots and present three major findings. First, we analyze the extent to which golfers decisions align with traditional economic decision making models: within rank-order tournament settings, 2 On page 1323 of Ehrenberg and Bognanno (1990), the authors presage studies of this sort by writing, Players can also choose conservative (e.g., hit down the center of fairway) or risky (e.g., try to cut across a dogleg) strategies, and, depending on a player s ability to the rest of the field or his rank after each round, different strategies may be pursued. Models that also included the choice of strategies that differ in risk undoubtedly would yield additional empirical implications. 3 Each golfer faces the same optimal decision on the first shot; hit the ball as far as they can. To the extent that ability, distance of first shot, and where they land their first shot matter, these are controlled for in this study thus allowing us to focus on the risky decision of the second shot itself. 2

3 analyzing behavior biases, and under general risk taking strategies. Our findings are consistent with well-established beliefs of agents behavior. The likelihood of golfers taking a riskier shot increases with their ranking in a tournament. Golfers become more conservative when faced with conditions that enhance uncertainty, such as when there are more hazards on the hole or during worse weather. These findings align with previous studies of competitors behavior in rank-order tournaments: both Chevalier and Ellison (1997) and Mago, Sheremata, and Yates (2013) show that agents change the amount of risk they take depending upon their relative standing in a tournament. Similarly, Romer (2006) shows that head coaches in the National Football League are highly risk averse regarding their fourth down strategies. Coaches elected to punt or kick a field goal on many fourth downs despite strong evidence suggesting these decisions were economically inefficient. We also find evidence of loss aversion; golfers take less risk, on average, when the total prize payout increases at the tournament level. Second, we analyze golfers risk decisions relative to a reference point their world ranking. When comparing a golfer s world ranking prior to a tournament with their current standing in that tournament, we find that their risk levels change when they are playing at a level differing from their expected play. In particular, golfers who are playing above their standing in non-final rounds of tournaments tend to back away from adopting risky strategies in order to protect their surprising standing. 4 However in the final round golfers take on substantially more risk, no matter their tournament standing relative to their world ranking standing. This result shows that it is not only how someone is doing relative to their expectations that matters, but also what phase of the tournament, their career, or how much job security they have really do matter. 4 We use data from the Official World Golf Rankings, which are published weekly by a consortium of professional golfing tours located throughout the world. 3

4 Third, we consider a strategic explanation for the superstar effect described in Brown (2011). We compare golfers penchant for taking risks in tournaments with and without Tiger Woods. We analyze this effect both before and after his salacious behavior was made public (in November 2009), an event which seemingly exhausted his supernatural golfing powers. We find that prior to his public shaming, golfers in the tournaments he entered took on added risk on par five holes. This behavior became much less likely after his return to competition following the scandal. This evidence suggests that the presence of the superstar in his era of dominance pushed golfers to take on risks for which they were uncomfortable and/or ill-prepared. By doing so, we posit that they carded higher scores because of these excess risks, and offer at least a partial explanation of the superstar effect found in Brown (2011). This paper is divided into four sections following this introduction. The second section discusses risk taking in golf and presents a simple model of second shot decisions. The third section describes the data and the model we employ to analyze golfers decisions. The fourth section presents the three sets of results that comprise our findings and the final section offers concluding remarks. II. Risk in Golf Excellent professional golfers are masters of the game and understand the many risks inherent in the sport. They have developed the ability to gauge when it is best for them to adopt appropriately risky strategies and, often, follow through on their decision with their incredible physical gifts. This section describes a particular decision that professional golfers of all qualities face in nearly every round: the decision of what to do with their second shot on par five holes. Par five holes are generally the longest holes on a golf course, with par three and par four holes being the shortest and second longest types of holes. On all holes, golfers start by hitting a 4

5 shot from the tee box, which is a well-manicured area on which it is legal for golfers to improve the conditions from which they strike the shot by using a short wooden peg called a tee. Par three holes are designed such that the golfer is supposed to reach the green with his first shot and then take two putts to complete the hole in par. Par four and five holes are designed such that the golfer hits a long shot from the tee, often with a club called a driver, which is designed to launch the ball further than other clubs the golfer might carry. 5 On par four holes, golfers second shots should reach the green, where they should take two putts to complete the hole in par. Following this pattern, par five holes are designed such that the second shot is played short of the green, which sets the stage for a short third shot to the green. However, professional golfers tend to be able to hit a golf ball a very long way, and this often leads to them facing the option of attempting to reach the par five green with their second shot. The benefit of this decision is that with a successful, aggressive second shot the golfer stands a chance to earn a relatively low score on the hole, which helps him gain ground over his competition, a must-do for those wanting to be successful in rank-order tournaments. The trade-off, though, comes in the form of the golfer losing some control over the direction of the second shot, a cost the golfer must reconcile when he chooses to hit a ball a relatively long way. Attempting to reach the green in two shots opens the golfer to the possibility of low and high scores on the hole, depending upon the success of that second shot. 6 Laying up is the more conservative strategy, and it 5 The Rules of Golf stipulate that golfers can use up to 14 clubs in a competitive round (These clubs vary by length to leverage imparted changes positively with length and the angle of the club face - the part of the club that strikes the ball to the ground where launch angle varies with this characteristic). Golfers can hit a driver the furthest of all clubs because they can impart the most leverage with the lowest launch angle with this club compared to the other clubs, which are shorter and launch the ball higher after impact. 6 Well-designed par five holes force golfers to deal with extreme temptation on the second shot. A successful second shot could lead to a low score for the hole. However, a small hiccup on the holecan ruin a tournament. Of course, the more harrowing the shot, the more exciting it is for fans to watch golfers attempt risky gambits. 5

6 eliminates tail end risks golfers face but at the cost of perhaps making it more difficult to earn a low score and gain ground on the competition. Of course, professional golfers play for prize money, so the efficacy of their risk strategies affect the money they earn in an event. In this study, we use data from ten seasons of play on the Professional Golf Association (PGA) Tour ( ), which uses the same payout structure for all of the tournaments that comprise the dataset. The prize structure in PGA events is highly nonlinear, which means small advantages over the course of a tournament can lead to large increases in compensation. Given that the PGA Tour rewards golfers for their relative performance, a golfer who posts a lower score on a par five hole increases his chances for a bigger prize at the end of the tournament. 7 Given this prize structure, the successful execution of a risky second shot can boost quickly a golfer s earnings. The best professional golfers thrive on par five holes. Long hitters, like Tiger Woods in the prime of his career, had many opportunities to play smart, aggressive second shots into par five greens, thereby gaining strokes on the competition by leveraging one of his strengths. But golfers who favor a safer approach to playing the game (Jim Furyk, for instance) also have played par five holes well in their successful seasons. Table 1 illustrates the strong relationship between golfers earnings and their performance on par five holes. The table lists the leading money winners for each season from 2004 to 2013 and those golfers absolute and relative performances on par five holes during those seasons. In those ten years, only one golfer, Luke Donald, managed to top the money list while performing outside of the top five golfers on par five holes. [Table 1] 7 The purses for many tournaments were over $6 million in the 2013 season. See for a description of the way prize money is distributed in PGA Tour events. 6

7 We view golfers decisions over their second shot on par five holes as an example of agents deciding between the marginal value of a risk against the expected return from their alternative lay-up strategy. The size of the value of adopting a risky strategy varies across golfers, who have different strengths and weaknesses, and holes, which have different design characteristics that may heighten the risk golfers face. To model golfers second shot decisions, we assume a golfer wants to adopt a level of risk that enables him to maximize the value of the score he earns on a hole, which he does by minimizing the number of strokes he takes to complete the hole. We view the level of risk that a golfer chooses for his second shot as being chiefly a function of the distance he must cover in order for a second shot to be successful. 8 Assume that the marginal cost of risk increases at an increasing rate with the distance a shot must traverse because the choice of heightened aggressiveness means the golfer has less and less control over the ball. We are able to observe several circumstances in which the value of risk shifts. Perhaps most influential of these circumstances is a golfers position in the tournament standings at the time of a decision. The closer a golfer is to the top of the tournament standings, the more valuable a successful second shot becomes, thereby shifting up the value of risk at all distances to the hole. Similarly, the design of a hole can vary the cost of a penalty for the loss of control of an aggressive option play. We used golf course maps to identify holes on which golfers faced water or sand-filled bunkers on a second shot decision. Also, golfers have different strengths and weaknesses when it comes to golfing skills, such as putting, power, and playing from sand. 8 Aggressiveness in this context is related to how far a golfer wants to hit the ball with his second shot. To hit a ball a longer distance, a golfer needs to select a club that is more unwieldy to use (a 3-wood, say) compared to a club used to hit a shot a shorter distance (a pitching wedge, for instance). Therefore, we can view golfers moving along their marginal cost curve the further they wish to hit the ball. We contrast this view of aggressiveness with one in which a golfer simply swings harder in order to get the ball to go longer distances. 7

8 Depending on the golfers relative skill-sets the cost of each unit of risk can vary by golfer. Additionally, the conditions of the shot itself can change the cost of aggression (the type of oncourse environment upon which the ball rests can affect tremendously a golfers ability to control a shot, as does the weather conditions that prevail at the time a shot was struck). 9 Finally, as Brown (2011) shows, the addition of superstars in a field (Tiger Woods, in the case of that study) can affect a golfer s performance and implicitly their choice of risk. We view the level of risk a golfer adopts on the second shot as a choice between a relatively high or low level of risk (r h or r l ), a view that is similar to models of choices made in contract decisions (Laffont and Martimort, 2002). A golfer choosing to attempt to reach the green requires an adoption of a high level of risk. Golfers must estimate four key values to arrive at their optimal level of risk. These values are 1) the probability of hitting a successful risky second shot, 2) the value of the score they believe they will earn given a successful risky second shot, 3) the value of the score they will earn given an unsuccessful risky second shot, and 4) the value of the score they estimate they will earn if they play with a low level of risk, the golfer s reference value for the hole. Let the probability of playing a successful shot, given a high level of risk, r h, be Prob(success r h ), which falls at an increasing rate with the size of r h. Let V[E(score r h )] be the weighted average of what the perceived likelihood that he will strike successfully with a high level of risk. Finally, define ΔV = V[E(score r h )] - V[E(score r l )], where r l represent occasions in which golfers choose a low level of risk. When ΔV = 0, we assert a risk neutral golfer is indifferent between going for the green and laying up. Equation (1) shows our view of a golfer s second shot decision: 9 Air is more dense in more humid conditions. This increased density causes the ball to travel reduced distances because the ball meets more resistance compared to drier conditions. Wind is a golfer s worst enemy, especially when gusty conditions prevail. Small deviations in wind speed can impact a ball s trajectory in enormous ways. 8

9 V[E(score r h )] = Prob(r h )(V(E(score success)) + (1-Prob(r h ))(V(E(score unsuccessful)) = V(E(score unsuccessful) + Prob(r h )(ΔV h ) (1), where ΔV h = V(E(score success)) V(E(score unsuccessful) is the risk premium the golfer faces over the second shot. Figure 1 depicts the values of the two strategies at various levels of aggression and ΔV. To illustrate the possibility of the effects exogenous shifts might have on a golfer s strategy decision, consider in Figure 1 that the same level of aggression, r h, leads to two different expected values of adopting r h, V 1 [E(score r h )] and V 2 [E(score r h )]. The rightmost line represents a situation in which the value of a successful shot is larger for all levels of risk than the line on the left. Figure 1- Golfers Second Shot Decision Can Vary With Shot Conditions V[E(score)] V 2 [E(score r h )] V[E(score r l )] V 1 [E(score r h )] V 2 V 1 r h Quantity of Risk Thus, holding constant the distance a successful shot needs to travel, differences in the likelihood that golfers adopt a risky strategy can be explained by differences in the environment from which shots are struck, differences in design characteristics of a hole, and differences in a golfer s 9

10 relative standing at the time the shot is struck, which alters the value of a successful shot because of the PGA Tour s reward structure. Given that we all face risks and risky decisions on a daily basis, understanding when we take risks and when we change our risk levels is vital to understanding human behaviors. Many non-professional athletes face tournament pay structures that decide their compensation levels, which means they have to decide how much risk to take on any given work project. These decisions are dependent upon who else workers are stacked against and the compensation structures under which they are employed. The next section discusses the data and methodology that will allow us to analyze these risk decisions. III. Data and Methods Using data from the ShotLink database allows us to recreate aspects of nearly every shot taken on the PGA Tour. ShotLink has fields that show the distance from the hole a golfer was when he struck a shot, the type of environment from which the ball was struck (fairway, rough, or sand, for instance), and the place where a shot ends. From these data, characteristics about the nature of every shot can be determined. Additionally, we calculate measures of golfers skill sets as golfer specific characteristics within different facets of the game. These include: how far a golfer can hit a ball (driving distance), how accurately a golfer can hit a ball (driving accuracy and a number of measures on iron and wedge play), and the efficacy of a golfers short game (pitching, chipping, and putting). These controls are measures of each golfer s abilities, which controls for the endogeneity issues from the first shot; where the quality of the first shot influences the ability of the golfer to take more risks in the second shot (we control for golfer ability and other factors of the shot, but we also assume that every golfer hits the first shot as far 10

11 as they can we also exclude shots that are not close enough to be in the feasible set of shots where a golfer can decide how to play their second shot). The most difficult part of the estimation procedure is determining when a golfer decided to go for a green in two. No field exists that explicitly describes the golfers action. Although we cannot tell what club the golfer hit or how hard he swung at a ball, we can determine the distance from the pin the second shot started and ended. We can also determine if the shot ends near the green because ShotLink contains a binomial variable that describes whether or not a shot ended around the green. 10 From the distance measures available and the qualitative response of the volunteer who entered the data, we use this measure to analyze occasions in which a golfer decided to go for the green in two. When this variable takes on a value of one, we conclude that a golfer tried to reach a green in two, and a value of zero means he did not. Skepticism regarding the efficacy of around the green is expected. If the variable only detects the occasions of successful attempts to reach the green, then we would be overstating the benefits of a successful risk (or simply not measuring risk taking at all). However, this skepticism is misplaced for this measure. Our measure is based on the distance relative to the hole and the course location golfers shots ended not only if it was successful. Additionally, we created an algorithm that captured occasions in which golfers were penalized after hitting wayward second shots. These occasions would not be found in around the green because the penalties golfers had to incur inevitably forced them to be outside of the zone considered to be around the green. As a final layer of insurance, we also compared our empirical results against a variable that identifies the occasions when a shot ended inside of a circle of 30 and 40 yards, separately, from the hole or when a golfer was penalized following a wayward second shot. 10 Listed as aroundthegreen in the ShotLink data. We limit the data as shots that exceed 275 yards on the second shot. These results are robust to higher limits; specifically results are similar at 325 yards. 11

12 None of these results differed from the results we report using around the green. Therefore, we believe that the variable does what its intent is it allows us to identify when golfers attempted to reach a green with their second shot or when they take a risky second shot. 11 [Table 2] In total, we analyze ten seasons of data in this study ( ). Table 3 displays some useful statistics regarding the par five holes that comprise the dataset. The dataset contains 376 tournaments in total, with 4116 par five holes played across 1506 rounds. The average score on a par five holes in these tournaments is 4.69 shots per hole. The hardest hole was the 2011 version of 14th hole at Pebble Beach Golf Links. The easiest hole was the first hole at Trump National Doral in There were five occasions in which a golfer scored a two on a par five (an albatross) and one occasion in which a 13 was carded. We model golfers second shot decisions with a regression model that includes the shot and player characteristics discussed above. Our baseline model, equation 2, is: (2) Where the probability of going-for-it (one if they go for it, zero otherwise) is estimated with the yards-to-pin, also with a squared term, for each golfer, i, at time, t. The specification treats golfers as considering risk along cost and benefit of risk curves that change on the margin with yardage. They go for the green with their second shot when their perception of the marginal benefit taking a gamble exceeds the marginal cost of doing so. 11 More than 40% of the shots are listed as around the green in the ShotLink dataset. We also include any shots that landed on the green or in the water/had a penalty involved, increases the number of shots listed as around the green to almost 60%. See Table A1 in the appendix. 12 The first hole at Doral has since been re-designed. It is no longer the pushover that it once was. 12

13 The other controls shift the benefit or cost of risk at all yardage levels. The N-vector controls for golfer-specific characteristics like their ability to hit the ball long distances, accurately, as well as to manage themselves on the green (putting) and on occasions in which they are close to the green in regulation (known as scrambling). The S-vector controls for shotspecific characteristics like the weather faced over a shot, the on-course environment from which a shot was struck (fairway, rough, or bunker, for instance), and the hazards arrayed around the green (water or bunkers) to which the golfer was deciding to attempt to reach with his second shot. We also control for yearly fixed effects, captured in the Y vector, to hold constant technology changes that have occurred in golf. We add controls to equation (2) to test for changes in risk given golfers ranking in tournaments, their relative standing in a tournament compared to their world ranking, and peer effects that might affect their risk calculation. IV. Results We analyze golfers decisions to take on risk with different controls in order to measure the way golfers willingness to undertake risky strategies changes given different situations they face. After looking at the general model (equation 2), we estimate a number of specifications related to the base model. Following Levitt and Miles (2011), we introduce different rank variables to see how a golfer is performing in a given round, relative to their world ranking, influences their risk taking behaviors. Like Chevalier and Ellison (1997), we separate out the entire tournament from the last round of each tournament in order to determine the extent to which golfers strategies change as they approach the end of a tournament. We also test the results presented in Brown (2011) to determine if Tiger Woods s presence in a tournament influence a golfer s strategy. In the primary regressions we use golfer s shot choices that are 13

14 taking their second shot from the fairway. Finally, as a robustness check, analyzing the same procedures as above, for golfers that are taking their second shot from anyplace and not just fairway (i.e. fairway, rough, etc.). It is arguable that golfers that hit a bad first shot may change their strategy because they have to hit their second shot from a less desirable location (i.e. the rough). The general model measures golfers that are going-for-it if the golfer was able to place the ball near the green after their second shot. This is a dummy variable, so the marginal effects of probit regressions are reported. As is shown in table 3, in all columns, the yards-to-pin is positive with the yards-to-pin-squared term being negative. The peak for this measure is very early (too close to the pin for it to be in the feasible set), showing that the further a golfer is from the pin, the less likely they are to play the risky shot. We also find that as the purse size (measured in millions) increases, golfers are less likely to play an aggressive shot. For example in all rounds of golf, column four, for a tournament with a $10 million purse the players are 5.75 percent less likely to play the aggressive shot than a tournament with a $4 million purse. This percentage also changes during the last round of the tournament, as shown in column 5. During the last round of the same $6 million change in tournament purse, golfers are percent less likely to take the risky shot. Thus players playing for larger purses are less risky and show evidence of risk aversion (Tversky and Kahneman, 1974 and Kahneman and Tversky, 1996). [Table 3] Columns two through five also have measures of relative score within a given tournament, field score, and a difference in ranking measure that captures their current standing in the tournament relative to their world rank. Columns two and four have the entire sample, while columns three and five are restricted to the last round of the tournament. Columns four and 14

15 five also have standard errors that are clustered by round. Chevalier and Ellison (1997) find that mutual fund managers respond to relative performance and Mago, Sheremata, and Yates (2013) show that players change their strategy depending on their relative performance. We find that golfers with lower field scores are more likely to take the risky shot; thus, those golfers doing better in a given tournament are more likely to take the risky shot. This result is both statistically and economically significant. We also find that golfers with a more positive difference in rankings are more likely to play aggressively. So those golfers that are performing worse than their world ranking take on more risk than if they are performing at or above their expected level (given their world rank) a form of loss aversion on their relative status. These results are consistent when looking at all rounds of golf and at only the last round. In table 4 we replicate the last two columns of the previous table, but include an interaction of the golfer rank in the tournament with the tournament purse. This measure captures the value of a given shot, especially late in the tournament as in columns two and four. We find that, other than the unit purse variable, the other results are similar. The estimate of the interaction term on tournament rank and purse size is important, as the results suggest that golfers who are near the top of the leaderboard are more inclined to take risks, and that their inclination for doing so increases with the purse. So as the purse size increases, those nearest to the high payouts are the most likely to take on additional risky shots. This result is important because it shows that golfers respond by taking more risk when the marginal benefit of doing so increases. [Table 4] In the last two columns of Table 4 we include controls for the average temperature at the time of play (and average temperature squared) and two hole specific controls (if there are 15

16 bunkers and/or water present). We find that the general results hold and that holes with water induce fewer risky shots, whereas holes with bunkers induce more risk taking shots. We expect these results on water and bunkers because hitting into the water is significantly more costly. When golfers hit a shot in the water they have to take a one stroke penalty, whereas golfers have the chance to play their way out of a bunker, without invoking a penalty. So the costs of navigating most bunkers are minimal relative to the sink or swim nature of contending with water hazards. We also find a significant effect on the difference in the player s tournament rank and world rank, which leads us to look at how a players relative rank impacts their risk taking with different ways to measure these rank differences. Around the green with Relative Rank Controls The previous findings show that the best golfers, golfers with the lowest field ranks, and the golfers with the most money on the line are the most likely to take the risky shot. In table 5 we continue to look at what determines the risk taking strategies of golfers. Each column represents the last two columns of each of the previous table. They include all the same controls and have standard errors that are clustered by the round. We use this to further examine the impact of the difference in rank, a golfer s tournament rank relative to their world ranking, and how that impacts their risk taking strategies. In order to measure how rank impacts the strategic risk taking decision, we measure risk in three different ways. At first, in columns one and two of Table 5, we look at both golfers difference in tournament rank, relative to their world rank entering the tournament, and add a difference in rank squared term to measures any non-linearities that could exist. Second, in columns three and four, we look at golfers who are having a good (bad) day. This measure is created by looking at golfers that are 50 or more (less) ranks above (below) their world rank 16

17 entering the tournament at the time of the shot. The third measure, presented in columns five and six, is golfers having a really good (bad) day. This measure looks at golfers 100 ranks above (below) their world rank entering the tournament. [Table 5] We find that these different measures do not change the general findings already presented. However, we do find that those golfers that are performing well in a given tournament are more likely to take risks in the early rounds of the tournament. Which is significant in all rounds, column one, but not in the last round, column two. An interesting result is found for those players who are having a really good or really bad day. We find that players having a really good day take the safer option and are less likely to take the risky shot during the early rounds of the tournament. However, their desire for taking additional risks changes in the last round. A player having a really good day in the last round is significantly more likely to take the risky shot. Those players having a really bad day are also more likely to take risks in the last round of the tournament, but only at one-third of the magnitude of the increased risk taking by those having a really good day. Thus, it appears golfers who are performing surprisingly well are willing to play it safe until they make the cut, then, just before the moment paychecks are cut, they take on additional risks to (potentially) secure a higher paycheck. We also continue to find that golfers with the most valuable shot are the more likely to take risky shots. Given that we find that golfers that are having a really good, or really bad, day increase their risk levels in the last round. This shows a finding of a U-shaped risk change those having a really bad day are 28.5 percent more likely to take risks, whereas those having a really good 17

18 day are 71.5 percent more likely to take risks (relative to those having an anticipated day shown in figure 2). Figure 2 Risk Relative Rank Tiger Woods s Impact on Risk Taking There has been evidence that Tiger Woods was such a dominating golfer that his presence at a tournament impacted the play of other golfers. Specifically, Brown (2011) finds that golfers play worse when Tiger Woods was present, in his prime, in a tournament. This can occur because other non-superstar participants are nervous and miss-hit the ball more often when he is present. Or, this outcome could exist when these other golfers feel they need to take on additional risks, with a higher potential for reward, when Tiger Woods is present because this is their only chance to beat him. Also, Ehrenberg and Bognanno (1990a, b) reference the importance of strategies and effort. In Tables 6 we look at the impact of Tiger Woods on risk taking by including a dummy variable for Tiger Woods presence, there is no evidence that golfers take more (or less) risky 18

19 shots when Tiger Woods is present. This is true for all rounds and last rounds where Tiger Woods is still in the last round of the tournament. 13 Tiger Woods is present in 27.4 percent of the observations in this data (and 24.7 percent of the last round observations). [Table 6] In Table 7 we interact the Tiger Woods variable with different rank, good/bad days, and really good/bad days. When Tiger Woods is present, the average golfer takes more risk when controlling for different rank and different rank squared, specifically those that are doing better than their world ranking, columns one and two, are statistically more likely to take risks in the early rounds (but not in the last round). When looking at players having a good or bad day, in columns three and four, we find that Tiger Woods only has an impact on the last round. Here we find that his presence, in general, has a negative impact on the risks taken. When interacting Tiger Woods on those players having a good or bad day, those players are significantly more likely to take risky shots when Tiger Woods is present. However, when he is not in the last round of the tournament, those players are less likely to take risks. Thus, Tiger Wood s presence causes people playing at their national rank to play more conservatively, whereas those deviating from their national rank are taking more risky shots when he is present. When looking at players that are having really good/bad days, columns five and six in Table 7, we find that Tiger Woods s presence causes more risks to be taken relative to when he is not present for all rounds (there is not enough variation in really good/bad days in the last round to estimate the interaction with really good/bad days and Tiger Woods). [Table 7] On November 30, 2009 Tiger Woods wrecked his SUV outside his Florida mansion. This turned out to be the beginning of a series of events that changed the overall quality of his game. 13 Of the 103 tournaments Tiger Woods played in, he made it to all but nine of the final rounds. 19

20 As such, we can measure if other golfers responded to this event as truly an event that changed his ability to play, and implicitly his superstar effect (Brown, 2011) on other golfers. We split the sample into two time periods: pre-event ( ) and post-event ( ). In these results we allow for a one year gap at the time of the event to allow time for the other players to adjust to the new level of play, if any, by Tiger Woods. In tables 8 and 9 we present the same estimation results from table 7, but split in and , respectively. [Table 8] [Table 9] In Table 8 we find that the results that are driving the changes in risk, and possibly the superstar effect found in Brown (2011), are driven primarily by the impact of Tiger Woods in the tournament before the event. When splitting the data, we find that the results are stronger for the period before the event, from The statistical significance is consistent with the previous results, but the magnitudes are larger in the earlier period then in the entire sample. When looking at the later sample, in Table 9, we find that the magnitudes of the coefficients decrease and there are less variables that are significantly significant. This shows that as early as 2011 professional golfers saw a difference in Woods game and responded by changing the way they played. The results in Tables 8 and 9 provide clear evidence in that there is a superstar impact on the risky decisions of professional golfers, which should be taken into account for all tournaments that have a superstar present. When Tiger Woods was in his prime, players responded by changing their risk levels to take on additional risks when Tiger Woods was present, and played more safe shots when he was not present. These results drastically decrease when the expected quality of Tiger Woods play decreased after the event (i.e. the reduced expectation that they were competing against a superstar). 20

21 Robustness: Shots from anywhere (not only the Fairway) The previous estimates limit the data to only those golf shots that landed on the fairway after the first tee. We can include all golf shots, controlling for the environments the second shot comes from, as a robustness check. In tables 10 and 11 we replicate the results found in Tables 4 and 5, but estimate in this sample control for the environment the shot is being taken from (fairway, rough, etc.). [Table 10] The golfers that are playing better rounds, and those with the lowest field-score, continue to take more risks and the coefficient on purse size continues to be negative and significant. Those with the most money on the line are the ones taking on the risk. When looking at those golfers having a really good or really bad day, columns five and six in table 11, we continue to find that in the early rounds of the tournament, those that are playing really well play more conservatively. However, during the last round of the tournament this response flips. Those that are having a really good or really bad day are significantly more likely to take risks. This shows that the golfers risk levels shift when their relative rankings shift and when they are closer to the actual payout. [Table 11] V. Conclusions In this study, we analyze risk taking strategies in professional golf with data from the ShotLink database, which has over 200,000 shots made in PGA tournaments from 2004 to With these data we analyze the option golfers face when playing their critical second shot on a par five holes. 21

22 Our findings support a number of previous studies on risk taking, both in and out of rankorder contests. We find that better golfers, golfers who have a longer drive, are more likely to take risks and tournaments with larger purses induce less risky shots. We also find evidence that golfers that have the most money on the line are also more likely to take the risky shot. When looking at golfers that are performing outside of the expected levels (when their tournament ranking varies from their world rankings), golfers that were having either a really good or really bad day are also significantly more likely to take the risky shot, but only in the last round. In fact, we find evidence that those golfers that are having really good days early in the tournament play a more safe game until they make the last round. Showing how the risk strategies switch as they near the payout portion of the tournament. Although there is no evidence that golfers respond to Tiger Woods s presence in the early rounds of a tournament, we do find that when he is present in the final round golfers having a good or bad day relative to their world ranking take on more risks; when without him in the last round they would play a more safe game. This risk shift in the presence of a superstar influences the impact of the tournament itself, has implications for all tournaments that have a superstar present, and might help to explain some of the findings in Brown (2011). 22

23 Works Cited Aseff, Jorge G. and Santos, Manuel S. (2005). Stock options and managerial optimal contracts Economic Theory Volume 26, Issue 4, pp Black, Fischer and Scholes, Myron (1973). The Pricing of Options and Corporate Liabilities Journal of Political Economy, Vol. 81, No. 3, pp Brown, J. (2011). Quitters never win: The (adverse) incentive effects of competing with superstars. Journal of Political Economy, 119(5), doi: / Chevalier, Judith A. and Ellison, Glenn D. (1997). Risk Taking by Mutual Funds as a Response to Incentives Journal of Political Economy, Vol. 105, no.6 (1997): Core, John E. and Guay, Wayne R. (2001). Stock option plans for non-executive employees Journal of Financial Economics 61 (2001) Ehrenberg, R.G., & Bognanno, M.L. (1990a). Do tournaments have incentive effects? Journal of Political Economy, 98(6), Ehrenberg, R.G., & Bognanno, M.L. (1990b). The incentive effects of tournaments revisited: Evidence from the European PGA tour. Industrial and Labor Relations Review, 43(3), 74S-88S. doi: / Blume, Marshall E. and Friend, Irwin. (1974). Risk, Investment Strategy and the Long-Run Rates of Return The Review of Economics and Statistics Vol. 56, No. 3 (Aug., 1974), pp Kahneman, D., and A. Tversky, (1996). On the reality of cognitive illusions Psychological Review, 103, Knoeber, Charles R. (1989). "A Real Game of Chicken: Contracts, Tournaments and the Production of Broilers," Journal of Law, Economics and Organization 5: Knoeber, Charles R. and Thurman, Walter N. (1994). "Testing the Theory of Tournaments: An Empirical Analysis of Broiler Production," Journal of Labor Economics 12: Laffont, Jean Jacques and Martimort, David. (2002). The Theory of Incentives: The Princpal- Agent Model Princeton University Press Lazear, E. and S. Rosen. (1981). Rank Order Tournaments as Optimum Labor Contracts. Journal of Political Economy 5: Levitt, Steven and Miles, Thomas J. (2014). "The Role of Skill Versus Luck in Poker: Evidence from the World Series of Poker" Journal of Sports Economics 31 23

24 Mago, S., R. Sheremata, and A. Yates. (2013). Best-of-three contest experiments: Strategic versus Psychological Momentum. International Journal of Industrial Organization 3 (2013): Pope, D.G. and M. Schweitzer. (2011). Is Tiger Woods Loss Averse? Persistent Bias in the Face of Experience, Competition, and High Stakes. American Economic Review 1: Romer, David. (2006). Do Firms Maximize? Evidence from Professional Football Journal of Political Economy Vol. 114, No. 2, pp Tversky, A. and D. Kahneman, Judgment and uncertainty: Heuristics and biases Science 185,

25 Table 1- Leading Money Winners Perform Very Well on Par 5 Holes Year Leading Money Winner Average Score- Par 5 Holes Par 5 Scoring Rank 2004 Vijay Singh Tiger Woods Tiger Woods Tiger Woods Vijay Singh Tiger Woods Matt Kuchar Luke Donald Rory McIlroy Tiger Woods

26 Table 2- Summary Statistics of Par Five Holes Analyzed Year Number Tournaments Number Holes Completed Average Score Average Score Easiest Hole Average Score Hardest Hole Total

27 Table 3 (1) (2) (3) (4) (5) VARIABLES gambled gambled gambled gambled gambled yards-to-pin *** *** *** *** *** (0.001) (0.001) (0.002) (0.001) (0.003) yards-to-pin *** *** *** *** *** (0.000) purse size *** *** *** *** *** (0.001) (0.001) (0.002) (0.002) (0.005) field score *** *** *** *** (0.009) (0.019) (0.022) (0.046) difference in ranking *** *** *** *** Environmental Fixed Effects Yes Yes Yes Yes Yes Golfer Ability Controls Yes Yes Yes Yes Yes Sample Full Full Last Round Full Last Round Standard Errors Clustered by Round ID No No No Yes Yes Observations 244, ,641 48, ,641 48,111 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 27

28 Table 4 (1) (2) (3) (4) VARIABLES gambled gambled gambled gambled yards-to-pin *** *** *** *** (0.002) (0.004) (0.002) (0.004) yards-to-pin *** *** *** *** purse size *** *** *** *** (0.002) (0.005) (0.002) (0.005) field score *** *** *** *** (0.024) (0.044) (0.024) (0.047) difference in ranking *** *** *** *** Interaction *** ** *** * (Rank x purse size) water *** *** (0.007) (0.014) bunker *** ** (0.013) (0.023) average temperature (0.004) (0.008) average temperature Sample Full Last Round Full Last Round Observations 157,148 30, ,625 30,285 Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1 All columns control for Environmental Fixed Effects, Golfer Ability Controls, and the Standard Errors are Clustered by the Round ID. 28

29 Table 5 (1) (2) (3) (4) (5) (6) VARIABLES gambled gambled gambled gambled gambled gambled yards-to-pin *** *** *** *** *** *** (0.002) (0.004) (0.002) (0.004) (0.002) (0.004) yards-to-pin *** *** *** *** *** *** purse size *** *** ** *** ** *** (0.002) (0.005) (0.002) (0.005) (0.002) (0.005) field score *** *** *** *** *** *** (0.024) (0.047) (0.024) (0.047) (0.024) (0.047) Interaction *** * *** * *** * (Rank x purse size) water *** *** *** *** *** *** (0.007) (0.014) (0.007) (0.014) (0.007) (0.014) bunker *** ** *** ** *** ** (0.013) (0.023) (0.013) (0.024) (0.013) (0.024) Average Temperature Controls Yes Yes Yes Yes Yes Yes difference in ranking *** difference in ranking ** goodday (0.040) (0.127) badday (0.039) (0.146) realgoodday ** *** (0.063) (0.006) realbadday *** (0.095) (0.006) Sample Full Last Round Full Last Round Full Last Round Observations 153,625 30, ,625 30, ,625 30,285 Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1 All columns control for Environmental Fixed Effects, Golfer Ability Controls, and the Standard Errors are Clustered by the Round ID. 29