COLLEGE OF THE HOLY CROSS

Clutch Strokes: Performance Under Pressure in Golf

Jeffrey Paadre

This paper examines 10 years worth of PGA Tour Tournament data in order to examine whether or not clutch performance exists during the final round of a tournament. After controlling scores for differences in course difficulty, the paper finds no evidence of tangible clutch performance. The authors find that the perception of clutch performance is more likely attributable to talent differential between golfers. Assuming a normal distribution of golfer talent, it is possible that Tiger Woods can outshoot his opponents on the final day of a tournament as well as lose his lead to his competitors. Motivation and Literature

In professional sports, heroes can be created through the concept of clutch performance.

The perception of clutch performance occurs when an athlete raises his or her performance to an extraordinary level during the most important moments of a sporting event. Athletes such as

David Ortiz and Adam Vinatieri have been immortalized as legends due to their consistent ability to help their teams win baseball and football games during important games where the outcome was hanging in the balance. Conversely Bill Buckner and Scott Norwood are amongst the unfortunate athletes burdened with reputations as choke artists based on their inability to perform well when their teams needed a high performance the most.

One of the challenges that accompanies examining performance under pressure lies within trying to define which performances constitute clutch performance. For example, in 2005

John Henry, the owner of the Boston Red Sox, presented David Ortiz with a plaque inscribed

“David Ortiz: The Greatest Clutch Hitter in the History of the Boston Red Sox”. While Ortiz had played especially well late during close games, Nate Silver, recently famous for his Five Thirty

Eight blog where he accurately predicted the 2012 Electoral College by weighing various political polls, found that clutch hitting as he defined it, had no correlation from one season to another, implying that at least in baseball, it is difficult for a player to sustain clutch performance

(Silver 2006). Silver's definition of clutch included estimating a player's marginal lineup value, translating that figure into wins produced, accounting for how often a player appears at the plate in pressure situations and then estimating the expected amount of wins the player would produce given his talent and the scenarios he faces. Silver defines clutch as the difference between the amount of wins a player produced in a season and the amount of wins he could have been expected to produce given his ability. Silver found that through his definition of clutch, David

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Ortiz exhibited extremely clutch performances in 2005 but that in some other seasons, Ortiz actually performed worse in "clutch situations" than he should have been expected to. This implies that performance in the clutch may be random and that each player may have a mean expected performance in high pressure situations. As seen with Ortiz, his performance relative to this expected value fluctuates from season to season. While Ortiz's season in 2005 is ranked as the 5th best single season clutch score in Silver's analysis, Ortiz is not amongst the 25 players in baseball history with the highest clutch score. This suggests that each player could be expected to stay around their mean clutch score value and that any extreme fluctuation from that average could be random, thus the viewer should expect a regression to the mean in a subsequent season.

While baseball may be easier to measure potential clutch performance due to the individual battles occurring during a team game, other team sports typically have too many different factors contributing to the outcome of a game to assign substantial credit to one player’s performance. In basketball for example, whether or not a last second shot goes in is truly the result of the efforts of all 10 players on the court. The defense is equally responsible for the result of a shot attempt, and it would be truly subjective to determine whether a game winning shot should be credited to the offensive player or written off as a result of the opponent’s poor defensive play. The same problem holds true for most other team sports.

One study did attempt to examine clutch performance in basketball by observing the differences in free throw percentages for given times and score differentials in games. Free throws in basketball are the only way in which a player can add to his team’s score in a manner that is truly independent from the other 9 players on the court because the shooter stands at the line to take an uncontested shot. Zheng, Price, and Stone (2011) find that NBA players do shoot a worse free throw percentage than expected when their teams are winning or losing by small

3 margins late in games, indicating that if a player can underperform relative to their averages under pressure, or “choke”, other players may remain consistent or outperform their averages during high pressure situations. These players may be identified as clutch performers.

Another issue that faces identifying clutch performance is whether or not, based on a player’s abilities, performing well in a key moment should be expected. Streakiness can and often does occur during random events. For example, if a coin is flipped 100 times, the flipper should not be surprised if at some point, 5 or 6 consecutive heads results are obtained. Likewise, in sports, if a basketball player makes on average 50% of his shots, a viewer should not be surprised if that player makes 5 or 6 shots in a row. Extending this, a viewer should not necessarily be surprised if the same player happens to make 5 or 6 shots in a row in supposed

“clutch situations”. Monte Carlo simulations often attempt to address the likelihood of various streaks of consecutive successful events by running many simulations with a given probability in order to determine the likelihood of long streaks.

In order to combat these inherent problems with examining clutch performance, this paper examines PGA tournament performance. In golf, all elements of a golfer’s score can be attributed to the golfer’s performance. It is also reasonable to assume that all golfers competing in the same tournament are competing on equal playing conditions. The course layout and weather during the rounds are consistent for all of the competitors in a given tournament.

Additionally, using years worth of data on both courses and golfers, the statistical likelihood of a golfer’s performance given his ability and the course difficulty can be predicted.

In golf, no golfer is more widely regarded as a clutch performer than Tiger Woods. In

2008, Barker Davis of the Washington Post declared that “Fact is, golf has never had a player

4 who always rises to the moment like Woods. Never. Not Jack Nicklaus, not Ben Hogan, not

Byron Nelson, not Bobby Jones. Again this week, Woods has proved to be a transcendent player, a player in a pantheon all his own”i. This evaluation of Woods came following a 15 foot putt that

Woods made in order to force a playoff in the 2008 US Open against rival golfer Rocco Mediate, while in excruciating pain due to an injured knee. After Woods made the putt to force the playoff

Mediate stated "I knew he'd make that putt. That's what he does. He is so hard to beat. He's unreal"ii. The opinion following the made putt was that no golfer performed better under pressure than Woods.

Reputations in golf are no different than reputations in other sports; a player's entire career can be defined by single rounds or tournaments. Just as Woods is often known for his clutch play, another elite golfer, Greg Norman, has left a different lasting impression on his audience. In the 1996 Masters Tournament, Norman led Nick Faldo by 6 strokes heading into the final day of the tournament. Not only did Norman lose his lead, he lost to Faldo by 5 strokes.

Norman was outshot by his rival by 11 strokes on the final day and finished well behind a golfer he had led by a sizeable margin. For his loss to Faldo, Norman is often regarded as one of the great choke artists in golf, someone who cannot be counted on when the tournament is on the line. Conversely, Woods is known as one of the most clutch golfers in the history of the PGA

Tour. Brown (2011) found that Tiger’s mere presence in a tournament event will lead to worse scores by roughly .8 stokes, from each of the other players in the tournament field than they could be expected to score without Woods’ presence. Brown attributes this to many golfers believing that Woods will automatically win the tournament and that everyone else may as well compete for second place. Woods has a colossal reputation as a superstar golfer who performs well under pressure.

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One statistic often used to defend this point is that prior to the 2009 PGA Championship,

Tiger Woods had never lost a Grand Slam tournament where he entered the final round of play with at least a share of the lead. Tiger’s first surrendered lead in a tournament occurred when

Y.E. Yang outshot Tiger by 5 strokes in the PGA Championship, overcoming Tiger’s initial two stroke lead. While Tiger has consistently held leads going into the final round of a major tournament, he too has his limits. Tiger has yet to win a major tournament where he did not lead or hold a share of the lead entering the final round of play. While Woods has proven consistent at maintaining leads, he has not shown any ability to overtake leads in the crucial moments of a tournament.

This may cause a critic to question this accepted notion of Tiger’s brilliance under pressure. One may deconstruct this anointment of Woods as a clutch golfer by examining the circumstances. For much of his professional career, Tiger Woods has been widely accepted as the best golfer in the world. When distinguishing his ability from the rest of his peers, while also adding in the fact that Tiger has entered these final rounds of tournaments already ahead of his competitors, one should expect Woods to win the tournament. If a player who is already better than everyone else is given a lead, he should be expected to maintain it more often than not. This paper looks to use data from all PGA tournaments and 361 different PGA golfers to construct expected performance values and distributions for any golfer on any tournament course. Using these probabilities, one can examine whether Tiger’s consistent streak of holding off his foes was as statistically unlikely as may be expected given its assessment as clutch performance.

Conversely, the data can also be used to further examine certain tournaments where

Woods was within striking distance of overcoming a deficit entering the final round of a tournament. The data could lead to a newer interpretation of Woods’ abilities under pressure.

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Using the probabilities, the likelihood of Woods outshooting a rival golfer by a certain amount can be calculated and it can be determined whether Tiger should have been expected to have overcome a deficit by this point in his career. If it appears that Woods should have been expected to overtake a rival golfer’s lead going into the final round of a tournament at least once in his career by this point, the argument that Tiger Woods has underachieved relative to statistical expectations could be made.

Data

In order to attempt to determine whether or not clutch performance exists specifically in

Tiger Woods’ golf game, substantial PGA data had to be collected. This data set contains 10 full years of round by round data for any PGA Stroke Play Tournament in the years 2002-2011. This time set was chosen as a representation of the “Tiger Woods Era”. Tiger Woods turned professional in the 1996 PGA Season and the 2011 PGA season is the most recent fully completed golf season. The average year in this data set has between 40 and 50 stroke play tournaments per year. Many of these tournaments consist of 4 different rounds on the same course, typically during a Thursday through Sunday period. One notable consistent exception throughout the data is the Bob Hope Classic Tournament, which consistently has a 5 round format. This has been accounted for in the data. The round by round data for each PGA tournament was obtained through both ESPN and Yahoo Sports’ websites.

The data set examines golfers who have finished in the Top 100 on the PGA Tour Money

List in any given season in the data set. The Money List is a ranking system which ranks golfers based on their tournament winnings during a given year. In most golf tournaments, monetary prizes are given in relation to tournament standing amongst all entrants who have “made the

7 cut”. In many PGA events, after the second day of tournament play, the tournament trims the competition field to approximately the Top 70 golfers remaining, with those who are not amongst the Top 70 or tied for the Top 70 deemed as “missing the cut”. Other tournaments have a “within 10” system which deems that any golfer within 10 strokes of the leader after the second day is eligible to compete in the remainder of the tournament. PGA golfers are only financially compensated for winnings in tournaments where they “make the cut”, with better tournament finishes being rewarded with higher payouts.

The PGA Money List in any given year is a strong measure of the rankings of golfers with regards to consistency. The top golfers as well as the most consistent golfers can be expected to rank highly on a money list for a given year because they are the golfers routinely making the cut and also expect high tournament finishes, leading to higher payoffs than their peers. This data set includes any golfer whose name appears in the Top 100 for any year in the

“Tiger Woods Era” of 1996-2011. This includes a total of 361 different PGA golfers. This estimate is a sufficient proxy for talent because it includes any golfer that Tiger Woods could realistically be expected to compete against for tournament championships in the 15 year span.

This data was obtained from the PGA Tour Website in order to gain an accurate list.

Match play tournaments were omitted from this data set due to their inexact scoring nature. In a match play tournament, golfers are not scored based on how many aggregate strokes taken in a given round, but by how many holes in the round they have outperformed their opponent on. Due to the different nature of the scoring system and the different strategy involved in competing in a Match Play tournament, round by round stroke data is not readily accessible, nor is it a reliable measure of an individual golfer’s performance.

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Each individual tournament and individual golfer has been given an identifier variable for which to fix certain effects about either the competition or the competitor. The panel data will be used in an iterative deletion procedure in order to account for variations in golfer ability as well as course and tournament difficulty. For example, Tiger Woods plays in roughly 20 different

PGA sanctioned tournaments per year, most of which are notoriously tougher courses which also attract a higher competition pool. The differences in course difficulty from tournament to tournament, as well as other factors which affect scores, such as weather, will be accounted for through this process.

The final product of this process will be a normal distribution curve of player performance. This curve will be representative of both the golfer’s ability, the difficulty of the course, and how the player had performed in the rounds preceding the final round of a tournament. With this curve, the expected value or mean of a golfer’s ability as well as the expected variance of his performance is calculated. With the use of this data, multiple golfers’ performance probabilities can be analyzed, and the probabilities of any golfer shooting a specific score can be estimated. This process will attempt to normalize every 18 hole round of golf that a

PGA golfer competes in by creating weighted identical rounds of golf. By doing this, one can approximate the likelihood of Tiger Woods actually surrendering a lead he held going into the final round of a tournament by analyzing the probabilities that any of his competitors outshoot him in the final round of a tournament by a sufficient amount to overcome Tiger’s lead. These results will help to highlight whether Tiger’s consistency in holding a lead was clutch in the sense that it was statistically unlikely or improbable, or if statistically, it should have been expected given the size of the leads and the discrepancies in player ability.

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Methods

In order to try to identify the probabilities that a particular lead will be overtaken, this study initially aims to predict an expected score for a golfer in final round of a tournament based on his seasonal average for an 18 hole round. Given that PGA golfers play in many tournaments each year, almost all of which consist of 4 rounds, it is reasonable to assume that a golfer's 18 hole average can be thought of as a figure that will be normally distributed around a mean value with a certain standard deviation in the similar shape to a bell curve. For example, if a PGA golfer plays in 25 tournaments in a calendar year and makes the cut in all of them, he will be expected to have 100 different 18 round scores to analyze. Since it is impossible for a golfer to shoot a non-integer number during a round of golf, the normal distribution will resemble a step- function with a plateau at the integers near the golfer's average.

After gathering a golfer's average and standard error on an 18 hole round for a specific year, using the rules of probability, the study can predict the likelihood of a golfer shooting any particular score in the final round of a tournament based on his yearly performance. This study will treat each golfer in a different year as a unique golfer; that is to assume that Tiger Woods' averages in 2008 will not be counted towards predicting how he may perform in a given round in

2009. This allows the study to more accurately gauge a golfer's level of talent while they are competing in the tournament of interest. For example, if an elite golfer is suffering from nagging injuries in a given year, which negatively affect his play, the study will capture that effect.

Rather than using career data, which may cancel out the negative effects of an injury or the positive effects of improved ability over time, the yearly approach will be able to more accurately predict a golfer's performance in a specific year.

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In order to calculate the likelihood that a golfer will relinquish his lead on the final day of the tournament, the study examines joint probabilities between multiple golfers. For example, if

Tiger Woods enters the final day of a tournament with a 3 stroke lead on Phil Mickelson and a 4 stroke lead on Rory McIlroy, the odds that Woods loses his lead will consist of the probabilities that Mickelson will outshoot Woods by 3 strokes on the final day of the tournament or McIlroy will outplay Woods by 4 strokes on the last round. Conversely, the likelihood that Woods does not blow his lead and wins the tournament will be the probability that Tiger will not shoot 3 or more strokes worse than Phil on the last day while also not shooting 4 or more strokes worse than Rory on the final day of a tournament. Given the talent of the golfers included in the study as well as their typical range of scores, this study examines the likelihood of any score between

58 and 85 strokes in a round of golf.

This study will look at two particular possibilities: the possibility that the golfer in the lead is outright beaten as well as the possibility that the golfer in the lead is tied or beaten. This study will return both the odds that the golfer in the lead loses the tournament on the final day and the probability that another golfer is at least able to tie his score on the final day. In PGA

Tour events, after the final round of a tournament, if multiple golfers are tied with the same score, the tournament is decided on playoff holes. Over the course of an entire tournament, it is rare that two or more golfers will shoot the same aggregate score, however, there are measures to break the tie. There are three different types of playoff systems: an 18 hole playoff, a sudden death playoff, and an aggregate playoff. An 18 hole playoff requires the golfers who are tied to play an additional 18 hole round the following day with the golfer with the lowest stroke total named the winner. The sudden death playoff requires the deadlocked golfers to play one playoff hole at a time. If a golfer needs more strokes than his competitors on a playoff hole, he is

11 eliminated and the process continues until one golfer is remaining. Lastly, an aggregate playoff is a playoff system that requires the tied golfers to play a set number of holes, typically 3 or 4, and the lowest cumulative score wins. If any golfers are tied after that process, the playoff reverts to a sudden death playoff.

Due to the tournament by tournament inconsistencies in a playoff system, this study does not aim to predict the results of playoff holes and will consider a scenario where a golfer leads going into the final day of a tournament and needs to play a playoff hole to break a tie to be a blown lead. While the golfer who entered the final round of a tournament with the lead may win the playoff system, and thus the tournament, he will have squandered his initial lead by being outperformed on the tournament's final full day of play.

It is insufficient however to simply calculate the 18 hole round average of each player given his performance over a calendar year and assume that it can be compared seamlessly to other golfers across the board. The PGA Tour holds between 44 and 48 tournaments per year on average. The golfers on tour are not obligated to play in every tournament during the course of the year; they are more or less allowed to pick and choose which tournaments to enter. In some years, two tournaments have been held on the same weekend, making it impossible for a golfer to compete in every tournament in a full season. Certain tournaments have different rules regarding qualifications or entry, but it can be assumed that the golfers in this data set are able to choose the tournaments in which they play.

There are many factors that a golfer can consider when determining whether or not to enter a given tournament including, but not limited to, time of year, course difficulty, prize payouts, and expected competition the tournament. Tiger Woods, for instance, is notable for

12 playing a smaller number of tournaments per year on average than some of his competitors.

Tiger Woods has typically played around 20 PGA Tour events per season. Tiger Woods is also notorious for choosing to play in the harder tournaments, including the four Grand Slam tournaments. If the averages were counted without any adjustment for course or tournament the data would not be accurate for predictions. For example, Tiger Woods, an elite golfer may choose to play in 20 hard tournaments during a calendar year which could lead a year average of

72 strokes per an 18 hole round. A different golfer may choose to also play in 20 tournaments during the course of the PGA season. However, it is possible that this golfer may choose to play in tournaments he feels may be easier, maybe to increase his prize money potential. He may also average 72 strokes during an 18 hole round for the year but his scores are based on different courses than Woods'. For this reason, it is insufficient to simply compare a golfer's raw average score and spread of scores to another golfer's and assume that given their averages, they are similarly skilled.

Additionally, it is also insufficient to simply apply a tournament average score as a proxy for course difficulty in adjusting the round by round data. The problem with using this tactic for a course is very similar to the issue with applying this to golfers. Tougher tournaments typically have higher prize payouts and typically attract better golfers than easier tournaments. The tournament average per round is based on both the difficulty of the course itself and the talent of the golfers competing. A notoriously difficult tournament, like the Masters tournament, attracts the world's top golfers every year. The Masters' course average could be very similar to the course average of an easier tournament course. If this is the case, it can be unclear as to why the courses have similar average scores. The Masters and this other tournament's course may actually be of comparable difficulty. It is also possible that the Masters is more difficult than the

13 other course but the averages are the same between the two because elite golfers may be able to earn average scores on a very hard Masters course while lesser golfers struggle on an easy course and also receive average scores.

For this reason, this study compares each tournament in a PGA calendar season to every other tournament based on the common golfers that chose to compete in both events. Every golfer's performance in each round of every tournament he performed in will be averaged to get a tournament average for each tournament for each player who competed in the tournament. In most cases, this will be the result of the four day average for the golfers who competed in all four rounds of the tournament or the two day average for the golfers who competed in the first two days of the tournament before missing the cut because they were not amongst the Top 70 golfers.

In instances where players compete in only 1 round or 3 rounds due to factors such as withdrawal due to injury or disqualification from the tournament, the average will be calculated based on the amount of rounds the player played in the tournament.

The first tournament of the year, Tournament 1, will be compared in difficulty to the second event of the year, Tournament 2, by comparing the differences between the Tournament 1 and Tournament 2 averages of only the golfers that chose to compete in both Tournament 1 and

Tournament 2. Tournament 1 will then be compared to Tournament 3 by the same criteria.

Eventually after Tournament 1 is compared to every other tournament on the PGA Tour during the season, the average of the differences between Tournament 1 and every other tournament will be calculated. This average will then be calculated for the second Tournament of the year,

Tournament 2, by the same process and eventually every tournament is compared to every other tournament through the scores of their common golfers. This calculation allows for a quantifiable measure for relative difficulty for each tournament while removing the ways in which a golfer's

14 tournament selection biases could prevent the data from being interpreted accurately. In short, applying these course difficulty averages to each round for each golfer in the tournament, and then taking the golfer's yearly average will provide the study with a golfer yearly average weighted for course difficulty. By examining each golfer's course-neutral averages and deviations, as seen in Appendices G, H, and I, the study can better quantify differences in golfer talent independent of the courses they play in order to most accurately use a player's ability to predict his scoring probabilities.

Applying these probabilities is a bit more complicated than it may seem on the surface.

This study will calculate the chance that any particular golfer has of overcoming a deficit on the final round of a tournament as if the golfer in the lead and the golfer chasing him are the only two golfers competing. For example, if Tiger Woods leads Phil Mickelson by 2 strokes and

Vijay Singh by 3 strokes, this study will calculate the odds that Phil can outshoot Tiger by at least 2 as well as the odds that Vijay can outshoot Tiger by at least 3. However, calculating the odds of Woods blowing his lead is more complicated than simply multiplying the odds that

Mickelson does not beat Woods by the odds that Singh does not beat Woods. This number would theoretically represent the odds that Tiger Woods would be playing two separate rounds, one against each golfer, and could feasibly shoot two separate scores in the final round, which is not possible.

To aggregate a golfer's ability to hold the lead, this study forms a matrix that will calculate the golfer's odds of winning the tournament relative to the field for every golf score between 58 and 85 strokes. This probability is the likelihood that no other golfer catches the leading golfer. This can be calculated by taking the products of the complements of the probabilities that each golfer in the field catches the golfer in the lead. For example, if Phil

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Mickelson has a 50% chance of catching Tiger Woods and Vijay Singh has a 20% chance of catching Woods, it can also be expressed that Woods has a 50% chance of not being caught by

Mickelson and an 80% chance of not being caught by Singh. Therefore, by taking the product of those two probabilities, there is a 40% chance that Woods is not caught by either Mickelson or

Singh and thus there is a 40% chance he keeps his lead. This probability will then be multiplied by the likelihood of a golfer actually attaining that score. For example, if Tiger Woods has a 1 stroke lead heading into the final round of a tournament, and shoots a 58, the odds he wins that tournament are essentially 100%. That said, even though Woods is a great golfer, the odds he shoots that 58 are astronomically small, leaving the product of the two probabilities to also be small. This represents that Tiger Woods has a very small chance going into the final day of both shooting a 58 and winning the tournament. This matrix will then sum up the odds that no one catches the leading golfer given every feasible round score for the golfer in the lead to get an aggregate measure of how likely it is that the golfer keeps the lead. These matrices, seen in

Appendices J and K, for the 2006 PGA Championship will measure how likely it is that Tiger

Woods will shoot a specific number, how likely it is that any golfer in contention will catch him given his score, how likely it is that no golfer in contention catches Woods given his score, as well as the overall likelihood that Woods' lead should be expected to be safe on the last day of a tournament.

Results

The course-neutral golfer averages as well as the tournament differences for 2006, 2008, and 2009 can be seen in Appendices D through I. It is no surprise that difficult tournaments, such

16 as the Masters consistently have large positive differences coefficients, meaning that golfers who play in the Masters find the tournament to be harder than the other courses they place during the season. It is also unsurprising that golfers such as Tiger Woods have lower course-neutral round averages than unadjusted round averages given the difficulty of tournaments played which indicates that he plays a tougher slate of tournaments than the average golfer. Lastly, it is expected that Woods has the lowest course-neutral average for each of the three years in the study, this indicates that should be expected to shoot a lower score than any of his opponents, regardless of which course they play.

Applying these averages to select tournaments can begin to identify the probabilities of

Tiger Woods winning a tournament in which he holds at least a share of the lead heading into the final round. The 2008 US Open Championship, the 2006 PGA Championship and the 2009 PGA

Championship are all tournaments of note in Tiger Woods' career to examine further.

One interesting tournament to look at is the earlier mentioned 2008 United States Open

Tournament. Tiger Woods entered the tournament 1 stroke ahead of Lee Westwood, 2 strokes ahead of Rocco Mediate, and 4 strokes ahead of Geoff Olgivy and DJ Trahan. Tiger also had a five stroke lead heading into the final round over Robert Allenby, Robert Karlsson, Hunter

Mahan, and Camilo Villegas. Due to injuries in 2008, Woods did not play in very many tournaments that year. Woods only played in 5 tournaments in 2008, the US Open being his last, before ending his year with knee surgery. Woods was in considerable pain throughout the duration of the tournament. Most fans remember this tournament for Tiger Woods' dramatic putt on the 18th hole to force a playoff with Rocco Mediate. Many experts use this putt and this tournament as another example for defending the idea that Tiger Woods is a clutch golfer. Tiger went on to win the 18 hole playoff the next day over Mediate and secure the US Open title.

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While many saw Tiger's display as a clutch performance, it is worth noting that he had entered the day with a one stroke lead over Westwood and a two stroke lead over Mediate, his two closest competitors. During 2008, Woods' course-neutral 18 hole average was a 67.93 with a standard deviation of 2.37. Lee Westwood had a course-neutral 18 hole average of 70.97 with a standard error of 2.8 during the same year. Mediate, who Woods ended up tying on the last hole had an average in 2008 of 71.21 with a 2.87 standard deviation. When normalizing these numbers, as well as the averages and standard errors for the previously mentioned golfers as well as the other golfers within 5 strokes of Woods entering the final day, there was expected to be only a 28.1% chance that any of the golfers in contention would either tie or defeat Woods.

Given his lead, as well as his ability relative to the field in contention, Woods was roughly 3 strokes better than Westwood and about 3.3 strokes better than Mediate, it should have been expected that 71.9% of the time, Woods would do no worse than a tie, either winning or playing in a playoff the next day. It also should have been expected that Woods would not lose the tournament outright, without a playoff hole with a likelihood of 81.1%. Without his last putt on the 18th hole to force a playoff, Woods would have lost the tournament outright, an outcome with a likelihood of only 18.9%.

This was a tournament that Woods could have been expected to win. The data suggests that the probability that Woods won outright, without a playoff, was around 70%. More interestingly, the data suggests that Rocco Mediate, given his yearly statistics, had only a 7.74% chance of outshooting Woods by at least 2 on that given day. Given Woods' lower expected round score as well as his 2 stroke lead over Mediate, there was a very slim chance that Mediate would even force a playoff, let alone almost win the tournament outright without Woods' last putt. Given their averages, Mediate had only a 4.63% chance of outshooting Woods by 3 or more

18 strokes, which he would have had Woods' last putt not dropped in. While Tiger's putt on the 18th hole to tie Mediate was a dramatic moment, Mediate's performance during the final round should have been the more unexpected event of the final round. While Mediate did not get the ultimate win of winning the US Open in 2008, he did outshoot Woods by 2 strokes in a round, something that should be unexpected 92.26% of the time.

Another interesting Grand Slam tournament victory for Woods came in the 2006 PGA

Championship tournament. Woods entered the final round of the tournament tied with Luke

Donald, 2 strokes ahead of Mike Weir, 3 strokes ahead of Geoff Olgivy, 4 strokes ahead of

Shaun Micheel and Sergio Garcia, and 5 strokes ahead of KJ Choi. This tournament was expected to be close finish due to the fact that Woods entered the final day tied for the lead with strong competitors closely behind him. However, Woods won the tournament by 5 strokes ahead of the second place finisher, Micheel. Tiger also outshot Luke Donald, who he was tied with entering the day, by 6 strokes to significantly pull away from Donald. According to their course- neutral rankings, there was only an 11.4% chance that Tiger Woods would outshoot Luke

Donald by 6 strokes, so Tiger certainly pulled off a feat that was unexpected.

During 2006, Tiger Woods had a course-neutral average of 68.19 strokes per 18 hole round with a standard deviation of 2.57 strokes. Luke Donald had an average of 69.37 stokes and a standard deviation of 2.68 strokes. Weir averaged 70.3 strokes per 18 holes with a standard error of 2.86 strokes. Olgivy had a stroke average of 70.22 and a standard deviation of 2.64.

Micheel, who came the closest to Woods averaged 70.76 strokes per round with a standard error of 2.8. Garcia and Choi had averages of 70.44 and 70.45 respectively with standard errors of

2.87 and 2.63 respectively.

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Given these averages and distances away from Tiger's score, Woods was one stroke better than Donald and around 2 strokes better than the rest of the field per round, there was a

53.1% chance that a contending golfer would either remain tied with Woods or surpass him by the end of the final round. Luke Donald had a 44.66% chance of at least tying Woods' score on that round. Weir had an 18.2% chance and Olgivy had an 11.18% chance of at least tying Woods by overcoming their deficits. Tiger Woods, given his 2006 statistics, had roughly a coin flip chance of winning that tournament outright. Woods won the tournament, by a large margin, an occurrence that was statistically about a 50-50 chance given the scores and the golfers heading into the final round.

However, Tiger Woods has proven that he is also capable of squandering a lead heading into the final round as well. In the 2009 PGA Championship Tournament, Woods entered the final day with a two stroke lead over both Padraig Harrington and Y.E. Yang. Woods also led

Lucas Glover and Henrik Stenson by 4 strokes each and led Ernie Els by 5 strokes. Given

Woods’ reputation as an elite closer, this was a tournament many expected Woods to win given his lead. However, Woods did not win the tournament; Woods was outshot by 5 strokes by Y.E.

Yang on the final day to finish in second, 3 strokes behind Yang.

During 2009, Woods posted a course-neutral scoring average of 67.89 with a standard error of 2.65 strokes per 18 holes. Harrington averaged 70.06 strokes per 18 holes with a standard error of 2.92. Yang’s average in 2009 was 70.3 strokes per 18 holes with a standard deviation of 2.87 strokes. Glover averaged 70.03 strokes per round with a deviation of 2.95 strokes. Stenson had a higher average and a higher deviation than Glover; his numbers were

70.16 and 3.55 respectively. Lastly, Els had a scoring average of 70.05 strokes and a standard error of 2.86 strokes. Given these numbers, Woods was about 2.5 strokes per round better than

20 his peers, and Tiger’s leads over his competitors, it is estimated that 73.03% of the time he would have finished the tournament without being tied or passed, winning the tournament. Woods’ greatest individual threat was Harrington. Woods should have been expected to win the tournament outright from this point without the use of playoff holes.

A couple of interesting pieces of information stand out from this tournament. First, Y.E.

Yang given his standardized scores should only have been expected to tie Woods given the two stroke deficit, 12.55% of the time. More impressive is that Yang only would have been expected to outshoot Woods by 3 strokes, thus beating Woods by 1 in the tournament, 8% of the time.

Lastly, the probability that Yang would go on to outshoot Woods by 5 strokes during an 18 hole round, to give Yang a 3 stroke lead over Tiger was 2.8%. Given the data available, there was a

97.2% chance that Woods would not be outshot by Yang by 5 strokes. However, this is exactly what happened; Y.E. Yang converted and achieved a level of golf that was highly statistically unlikely. The odds that Woods would have lost the tournament outright were 18.3% while the odds that any golfer in contention would have at least tied Woods were 27%.

While the most interesting piece of information from this tournament comes from Yang’s improbable overtaking of Woods’ lead, another piece of data also stands out. Both Lucas Glover and Henrik Stenson were 4 strokes back of Woods heading into the final round of play. Both had similar averages, although Stenson’s was .13 strokes per 18 roles less than Glover’s. However, when calculating the data, Stenson had a 2.16 percentage point better chance of outshooting

Woods by 4 strokes to tie his total than Glover did.

The main reason for this dramatic increase is the .6 stroke differential between the two golfers in terms of their standard deviations. Stenson’s standard error was about .6 strokes more

21 than Glover’s which can mean that Stenson’s totals fluctuate more than Glover did. In short,

Glover in 2009 was a more consistent golfer around his mean average than Stenson was.

However, when calculating the probability for a one day score of 4 strokes better than Woods,

Stenson had the better chance. This is Stenson’s probability density was more spread out, with a higher variance. Stenson’s range of scores between 1 standard deviation in 2009 was between

66.61 strokes and 73.71. By comparison, Glover’s range of scores in 2009 within 1 standard deviation was between 67.08 and 72.98. While Stenson’s slightly higher mean score harmed his probability of overtaking Woods’ lead, his increased variance around the mean gave him a better opportunity in a random draw of drawing a very low number, or shooting a very low score.

When comparing the three tournaments, it is evident that Tiger Woods is capable of winning tournaments that are hotly contested on the final day. Tiger is also capable of failing to win a tournament with which he holds a multiple stroke lead heading into the final day. The results could lead a reader to believe that Woods in 2006 was extremely clutch while Woods in

2008 and 2009 was less clutch, losing leads that he had less than a 30% chance to lose either to a playoff hole or an outright loss. A more realistic interpretation of this data is that Tiger Woods as a golfer has an expected value for an 18 hole round with variance just like every other golfer on tour. While each golfer has unique standardized mean and deviation values, every golfer has a probability of shooting any given score; some scores may just be less realistic for different golfers. While Woods outperformed a packed field in the final round of the 2006 PGA

Championship, yet coughed up a lead in both the 2008 US Open and 2009 PGA Championship it is likely that Tiger was neither clutch in 2006 nor a choke artist in 2008 or 2009.

Woods is a very talented golfer, by all accounts best golfer since Jack Nicklaus, however just like every other golfer, he has a normalized average score and variance which make it

22 possible that he will shoot any given score. Because of Woods’ talent, his scores are likely to be on the lower end than most of his peers. In 2006, Tiger won the PGA tournament because he essentially drew a good round score from his random distribution, while his competitors drew worse round scores from their deviations. In 2008 and 2009, Woods lost his leads on the final day due to drawing poorer scores from his expected range of scores while his competitors drew very good scores, scores that were both good enough to beat Tiger outright as well as overcome any initial deficit the golfer had. For this reason, it can be assumed that Woods is not a clutch golfer; clutch performance likely does not exist. What can be determined is that Woods is a very talented golfer. Because of his talent relative to his peers, if a tournament is within striking distance, Woods will always have a decent probability of winning the tournament, but it is no certainty.

Conclusion and Discussion

While the concept of clutch performance always makes for a fascinating story, the data suggests it may be closer to fiction than reality. With PGA Tour golf data, most golfers play enough rounds in a season that their abilities can be standardized to a normal expected round score. Golfers can be expected to fluctuate around their mean scores to have better than expected rounds as well as worse than expected rounds. However, with enough data, it is reasonable to assume that there will be an eventual regression to the mean, meaning that if a golfer outperforms his expected round average by three strokes in a round, it should not be a surprise if sometime later in the year, his performances average out back to his expected value. This can come from a single round that is three strokes worse than expected or 3 independent rounds that are each one stroke worse than the golfer’s average.

23

Tiger Woods is an extremely talented golfer, perhaps the most talented in the history of the sport. However it is likely that Tiger’s high levels of performance, as seen by consistently holding onto leads heading into the final round of a major tournament, are more a function of his talent than any intangible aspect of being able to perform under pressure. Woods shoots great scores during these scenarios because he is a great golfer. The rest of the PGA Tour competing field often fails to catch up to Tiger because they shoot worse scores than Woods on the final round because of Woods’ talent advantage. Occasionally in these scenarios, Woods is outshot on the final round of a tournament but can maintain his lead due to outshooting his competition by more strokes during the first three tournament rounds than he loses the fourth round by.

Given the talent differential, Woods should be expected to win a lot, but not all, of the tournaments he leads going into the final round. When he loses, it is not because he has choked but because in a random one round sample, an outcome where his competitor overtakes his lead has been selected through Woods’ and his competitor’s scores; in the cases seen in the paper, these outcomes vary in likelihood. When Woods wins these tournaments it is not necessarily because he has risen to the occasion and achieved clutch performance under pressure but likely that Tiger can be expected to outplay any golfer on any day given his ability. On the final days of a tournament where Woods does not outperform his opponent, Woods can often still win the tournament based on the fact that he held a lead and pacing one’s score with Tiger Woods straight up is typically unlikely, therefore outshooting Woods by specific margin becomes even less likely.

In team sports such as football, enough different variables can go into whether or not a kicker makes a clutch field goal. The length of the kick as well as other factors like the wind, whether or not the ball was cleanly snapped, or how talented the respective blockers and kick

24 rushers are all contribute to whether a kick can go in. It is uncertain to this point whether Adam

Vinatieri’s reputation as a clutch kicker is well-earned due to uncertainty over how often he should have been expected to make his playoff field goal attempts because every scenario is different. Additionally, it is unclear whether or not Scott Norwood actually did choke when he failed to make a field goal attempt that would win the Buffalo Bills a Super Bowl because it is unclear how to model the likelihood he would have succeeded in that given scenario.

However, due to the individual nature of golf, after teasing out the effects that course selection biases have on scores, it is evident that clutch performance is a highly unlikely phenomenon. While it makes for a good story, it is more likely that clutch performance exists in golf. This implies that at least in golf, Woods should not be labeled as a clutch golfer, nor should

Greg Norman get the reputation as a choke artist based on his performance. Since every action in golf is dependent on the golfer’s ability as well as playing conditions that are uniform for all golfers in a given tournament, the key determinant in attaining golf success is talent, not an interpretation of clutch performance.

An additional question to examine given the analysis is whether or not athletes earn significantly different amounts of money based on their perception of clutch ability. In golf, this may be tougher to attain due to the fact that golfers are compensated mainly by prize money rather than through contract offers from teams. However, it would be interesting to see if golfers with a high perception of clutch ability receive a significantly higher amount of money through endorsements, indicating that sponsors may be willing to pay a premium to associate their product with a player the public believes performs best under pressure.

25

Acknowledgements

This paper would not have been completed without the contributions and helpful suggestions of Professors Victor Matheson and Joshua Congdon-Hohman at the College of the

Holy Cross. Their help was integral in the completion process of this research.

26

References

Brown, J (2011). Quitters Never Win: The (Adverse) Incentive Effects of Competing with Superstars. Journal of Political Economy Vol. 119, No. 5, 982-1013. Silver, Nate. "Is David Ortiz a Clutch Hitter." Baseball Between the Numbers: Why Everything You Know about the Game Is Wrong. New York: Basic, 2006. 14-34. Zheng, C, Price, J, and Stone, D F. (2011). Performance Under Pressure in the NBA. Journal of Sports Economics Vol. 12, No. 3, 231-252.

i Davis, Barker. "He’s Clutch, Even in Pain." Washington Times 16 June 2008 ii Shipnuck, Alan. "A Gritty Playoff on a Bum Knee ... but Tiger Woods Wins the 2008 U.S. Open." Golf Magazine 16 June 2008

27

Appendix A- 2006 PGA Championship Through 3 Rounds Golfer Strokes Back Round Average Round Dev CN Average CN Dev Chance of Tie/Beat Tiger Chance Beat Tiger Tiger Woods 0 68.73 3.22 68.19 2.57 Luke Donald 0 70.06 2.95 69.37 2.68 44.66% 34.36% Mike Weir 2 70.76 2.94 70.30 2.86 18.20% 12.16% Geoff Olgivy 3 71.19 2.66 70.22 2.64 11.18% 6.84% Shaun Micheel 4 70.91 2.96 70.76 2.80 7.45% 4.40% Sergio Garcia 5 71.45 3.11 70.44 2.87 4.62% 2.61% KJ Choi 5 70.65 3.17 70.45 2.63 3.90% 2.10% Aggregate 53.10% 41.27%

Appendix B- 2008 US Open Through 3 Rounds Golfer Strokes Back Round Average Round Dev CN Average CN Dev Chance of Tie/Beat Tiger Chance Beat Tiger Tiger Woods 0 68.90 2.57 67.93 2.37 Lee Westwood 1 72.07 3.55 70.97 2.80 17.92% 11.88% Rocco Mediate 2 71.61 3.12 71.21 2.87 7.74% 4.63% Geoff Olgivy 4 71.38 3.35 70.67 3.13 5.47% 3.24% DJ Trahan 4 70.89 3.42 70.81 2.91 4.77% 2.72% Robert Allenby 5 70.64 2.97 70.02 2.74 2.33% 1.20% Robert Karlsson 5 71.43 2.36 70.20 2.37 1.63% 0.77% Hunter Mahan 5 70.78 3.69 70.70 2.98 2.86% 1.56% Camilo Villegas 5 70.60 3.27 70.04 2.79 2.45% 1.28% Aggregate 28.10% 18.88%

Appendix C- 2009 PGA Championship Through 3 Rounds Golfer Strokes Back Round Average Round Dev CN Average CN Dev Chance Tie/Beat Tiger Chance Beat Tiger Tiger Woods 0 68.84 2.81 67.89 2.65 Padraig Harrington 2 71.05 3.17 70.06 2.92 12.77% 8.23% Y.E. Yang 2 70.72 2.94 70.30 2.87 12.55% 8.03% Lucas Glover 4 70.34 3.28 70.03 2.95 5.10% 2.96% Henrik Stenson 4 71.21 3.06 70.16 3.55 7.16% 4.56% Ernie Els 5 70.76 2.83 70.05 2.86 2.76% 1.49% Aggregate 26.97% 18.32% Appendix D- 2006 Tournament Corrections Number Tournament Name Average Relative to Others 1 Mercedes Championships 3.474 2 Sony Open -0.748 3 Bob Hope Chrysler Classic -1.292 4 Buick Invitational 0.627 5 FBR Open -1.007 6 AT&T Pro Am 0.474 7 Nissan Open 0.113 8 Chrysler Classic of Tucson -1.712 9 Ford Championship at Doral -0.794 10 Honda Classic 2.128 11 Bay Hill Invitational 0.872 12 The Players Championship 2.304 13 BellSouth Classic 0.485 14 The Masters 2.553 15 Verizon Heritage -0.271 16 Shell Houston Open 0.803 17 Zurich Classic of New Orleans -0.859 18 Wachovia Championship 2.234 19 EDS Byron Nelson Championship -0.932 20 Bank of America Colonial -1.447 21 FedEx St Jude Classic 0.687 22 Memorial Tournament 1.872 23 Barclays Classic 0.714 24 US Open 3.594 25 Booz Allen Classic -0.990 26 Buick Championship -0.930 27 Cialis Western Open -0.138 28 John Deere Classic -1.432 29 B.C. Open -1.535 30 British Open 0.557 31 US Bank Championship -2.450 32 Buick Open -1.170 33 PGA Championship 1.110 34 Reno Tahoe Open -0.656 35 WGC- Bridgestone Invitational -0.615 36 Deutsche Bank Championship 1.110 37 Bell Canadian Open -1.244 38 84 Lumber Classic 1.060 39 Valero Texas Open -1.109 40 Southern Farm Bureau Classic 0.296 41 WGC- American Express Championship -1.251 42 Chrysler Classic of Greensboro -0.134 43 Frys.com Open -2.127 44 Funai Classic -1.643 45 Chrysler Championship 0.802 46 The Tour Championship -0.200 Appendix E- 2008 Tournament Corrections Number Tournament Name Average Relative to Others 1 Mercedes Benz Championship -0.563 2 Sony Open -1.455 3 Bob Hope Chrysler Classic -1.674 4 Buick Invitational 1.513 5 FBR Open -1.048 6 AT&T Pro Am 0.786 7 Northern Trust Open 0.950 8 Mayakoba Classic -0.815 9 Honda Classic 0.459 10 PODS Championship 1.632 11 Arnold Palmer Invitational -0.450 12 WGC CA Championship -1.076 13 Puerto Rico Open 0.027 14 Zurich Classic 0.603 15 Shell Houston Open 0.563 16 The Masters 2.181 17 Verizon Heritage 0.221 18 EDS Byron Nelson Championship 0.552 19 Wachovia Championship 1.438 20 The Players Championship 3.190 21 AT&T Classic 0.333 22 Crowne Plaza Invitational -0.996 23 Memorial Tournament 3.303 24 Stanford St. Jude Championship 1.295 25 US Open 2.663 26 Travelers Championship -2.553 27 Buick Open -0.899 28 AT&T National -0.878 29 John Deere Classic -1.308 30 British Open 2.947 31 US Bank Championship -2.866 32 RBC Canadian Open -0.830 33 WGC Bridgestone Invitational -1.505 34 Reno-Tahoe Open 0.197 35 PGA Championship 2.803 36 Wyndham Championship -2.763 37 The Barclays 0.405 38 Deutsche Bank Championship -1.344 39 BMW Championship -1.936 40 Viking Classic -0.942 41 The TOUR Championship -0.103 42 Turning Stone Championship 1.723 43 Valero Texas Open -2.250 44 Shriners Hospital Open -2.486 45 Frys.com Open -2.437 46 Ginn sur Mer Classic 1.602 47 Childrens Miracle Network Classic -1.735 Appendix F- 2009 Tournament Corrections Number Tournament Name Average Relative to Others 1 Mercedes Benz Championship -0.992 2 Sony Open -0.845 3 Bob Hope Classic -3.035 4 FBR Open 0.028 5 Buick Invitational 2.329 6 AT&T Pro Am 0.635 7 Northern Trust Open -0.230 8 Mayakoba Classic -0.608 9 Honda Classic 0.336 10 WGC- CA Championship -0.332 11 Puerto Rico Open 0.173 12 Transitions Championship 1.203 13 Arnold Palmer Invitational 1.192 14 Shell Houston Open 1.117 15 The Masters 1.223 16 Verizon Heritage 0.534 17 Zurich Classic of New Orleans 0.898 18 Quail Hollow Championship 1.632 19 The Players Championship 1.897 20 Valero Texas Open -1.871 21 HP Byron Nelson Championship -1.425 22 Crowne Plaza Invitational -1.614 23 Memorial Tournament 2.798 24 St. Jude Classic -0.871 25 US Open 1.615 26 Travelers Championship -2.449 27 AT&T National 0.046 28 John Deere Classic -1.384 29 British Open 1.097 30 US Bank Championship -1.799 31 RBC Canadian Open -0.465 32 Buick Open -0.532 33 WGC- Bridgestone Invitational -0.658 34 Legends Reno Tahoe Open 0.712 35 PGA Championship 3.336 36 Wyndham Championship -2.273 37 The Barclays 1.956 38 Deutsche Bank Championship -0.665 39 BMW Championship 0.734 40 The TOUR Championship -0.091 41 Turning Stone Resort Championship 0.037 42 Shriners Hospital Open -1.859 43 Frys.com Open -2.295 44 Childrens Miracle Network Classic -0.351 Appendix G - 2006 Average and Course Neutral Round Scores for Top Golfers Golfer Rounds Average Round Average Dev CN-Average Round CN-Dev Aaron Baddeley 76 71.41 3.29 71.38 2.94 Adam Scott 68 70.02 3.27 69.24 2.84 Alex Cejka 91 70.97 3.39 71.55 3.02 Anders Hansen 4 71.00 0.82 69.89 0.82 Andres Romero 6 71.17 3.06 70.43 2.86 Andrew Magee 47 72.43 3.03 72.96 2.87 Angel Cabrera 38 70.92 2.38 70.17 2.21 Anthony Kim 8 68.63 2.67 69.03 2.25 Arjun Atwal 95 71.27 3.40 71.77 2.96 Arron Oberholser 79 70.37 3.56 70.21 3.16 Bart Bryant 86 71.24 3.34 71.01 2.92 Ben Crane 81 71.24 3.81 70.92 2.99 Ben Curtis 86 71.59 3.44 71.37 3.12 Bernhard Langer 72 71.13 3.00 71.17 2.60 Bill Glasson 45 71.38 3.18 72.16 2.94 Bill Haas 96 70.96 3.02 71.31 2.80 Billy Andrade 74 71.10 3.34 71.06 2.92 Billy Mayfair 94 71.00 3.25 70.94 2.85 Blaine McCallister 29 73.38 3.49 73.90 3.55 Bo Van Pelt 102 70.79 3.09 70.66 2.92 Bob Burns 23 71.65 2.95 72.58 3.02 Bob Estes 85 70.68 3.06 70.98 2.69 Bob May 62 70.81 3.00 71.44 2.74 Bob Tway 78 71.47 3.08 71.90 2.76 Brad Elder 2 76.00 2.83 76.75 2.83 Brad Faxon 78 72.23 3.22 71.94 2.98 Bradley Hughes 2 73.50 2.12 72.94 2.12 Brandt Jobe 88 71.21 3.15 70.98 2.93 Brent Geiberger 97 70.96 2.90 71.39 2.79 Brett Quigley 105 70.31 3.19 70.30 2.74 Brett Wetterich 82 70.68 3.18 70.85 2.96 Brian Bateman 65 71.57 2.83 72.02 2.83 Brian Davis 90 71.11 2.77 71.26 2.47 Brian Gay 107 70.32 2.88 70.68 2.63 Brian Henninger 39 71.21 3.08 71.95 2.64 Briny Baird 77 70.51 2.25 70.75 2.31 Bubba Watson 79 70.66 3.29 71.07 2.91 Cameron Beckman 48 70.71 3.61 71.48 3.25 Camilo Villegas 93 71.08 3.36 70.88 2.88 Carl Pettersson 93 71.31 3.28 70.79 2.97 Carlos Franco 86 71.87 2.92 72.09 2.86 Chad Campbell 87 70.90 3.65 70.82 3.27 Charl Schwartzel 26 72.58 2.94 71.73 2.72 Charles Howell III 93 71.46 3.10 71.04 2.63 Charles Warren 90 70.69 2.68 70.77 2.54 Charley Hoffman 98 70.62 3.28 70.70 2.90 Charlie Wi 2 72.50 3.54 73.25 3.54 Chez Reavie 2 76.00 0.00 77.01 0.00 Chip Beck 4 71.75 2.63 73.29 2.63 Chris Couch 75 71.56 3.40 71.93 3.02 Chris DiMarco 78 71.04 2.93 71.05 2.67 Chris Perry 6 75.00 2.19 76.21 2.39 Chris Riley 82 71.07 3.51 71.68 3.18 Chris Smith 67 71.37 3.07 71.73 3.01 Clark Dennis 2 76.00 0.00 76.93 0.00 Colin Montgomerie 18 72.89 3.03 71.55 3.39 Corey Pavin 70 70.91 3.55 71.19 3.10 Craig Barlow 73 71.22 3.38 71.11 3.03 Craig Parry 44 72.09 2.85 72.28 2.81 Craig Perks 37 75.43 4.03 75.47 4.01 Craig Stadler 10 73.70 3.34 73.20 3.03 D.A. Points 80 71.50 3.33 71.73 3.17 D.J. Trahan 90 71.48 3.52 71.72 3.01 Daisuke Maruyama 79 71.01 3.30 71.41 3.04 Dan Forsman 43 71.33 2.86 71.78 2.73 Daniel Chopra 107 70.65 3.53 70.80 3.24 Darren Clarke 26 72.08 3.76 70.81 3.73 David Berganio Jr. 5 73.80 4.03 73.39 2.24 David Duval 69 72.10 3.77 71.83 3.45 David Edwards 9 72.11 3.52 72.77 2.78 David Frost 23 71.35 3.88 72.59 3.31 David Gossett 19 72.79 2.72 73.56 2.61 David Howell 45 71.67 4.12 70.90 3.89 David Ogrin 2 73.50 3.54 75.04 3.54 David Peoples 9 72.44 3.43 72.81 3.93 David Toms 69 70.57 3.72 70.22 3.34 Davis Love III 76 71.11 3.62 70.70 3.31 Dean Wilson 111 70.71 3.09 70.96 2.66 Don Pooley 2 71.50 0.71 73.21 0.71 Dudley Hart 83 71.07 2.99 71.37 2.79 Duffy Waldorf 92 71.03 3.13 71.29 2.89 Eric Axley 89 71.03 3.51 71.49 3.25 Ernie Els 64 70.63 3.13 69.88 2.69 Esteban Toledo 7 71.57 3.74 72.25 3.20 Frank Lickliter II 97 70.47 3.34 70.79 3.01 Franklin Langham 4 71.00 1.41 70.52 1.41 Fred Couples 50 71.72 3.66 71.02 3.36 Fred Funk 105 70.90 3.34 70.88 2.67 Fredrik Jacobson 56 71.32 3.47 71.13 3.15 Fuzzy Zoeller 2 79.50 2.12 76.95 2.12 Gabriel Hjertstedt 46 71.02 3.05 71.53 2.84 Garrett Willis 27 71.22 2.87 72.21 2.65 Geoff Ogilvy 70 71.19 2.66 70.22 2.64 George McNeill 2 79.50 3.54 75.91 3.54 Glen Day 30 71.27 2.69 72.00 2.72 Graeme McDowell 43 71.72 3.23 71.16 2.95 Grant Waite 21 71.91 3.16 72.21 2.80 Greg Chalmers 67 72.24 3.12 72.58 3.01 Greg Kraft 75 71.60 3.47 71.87 3.31 Greg Owen 77 71.00 2.84 70.77 2.70 Guy Boros 14 72.36 2.79 73.35 2.71 Hal Sutton 2 74.50 0.71 74.39 0.71 Hank Kuehne 25 73.76 3.85 73.35 3.57 Harrison Frazar 91 70.77 3.43 71.15 3.25 Heath Slocum 93 71.04 3.17 71.20 2.65 Henrik Stenson 32 71.88 3.31 70.96 3.25 Hidemichi Tanaka 73 73.27 3.16 73.60 3.09 Hunter Mahan 99 70.81 3.07 71.05 2.85 Ian Leggatt 76 71.90 3.04 72.32 2.67 Ian Poulter 52 71.04 3.39 70.21 3.12 J.B. Holmes 77 71.44 3.90 71.36 3.41 J.J. Henry 93 70.84 3.17 70.64 2.75 J.L. Lewis 57 72.00 3.15 71.97 2.91 J.P. Hayes 55 71.24 3.12 71.76 2.97 James Driscoll 80 72.31 3.33 72.51 3.35 Jason Bohn 104 70.82 3.18 70.60 2.79 Jason Day 20 70.20 3.02 71.16 2.48 Jason Dufner 6 73.17 2.79 70.82 2.55 Jason Gore 84 72.20 3.75 71.98 3.24 Jay Delsing 36 71.58 3.44 71.78 3.24 Jay Haas 25 72.72 3.78 71.40 3.86 Jeff Brehaut 96 71.38 3.04 71.68 2.89 Jeff Maggert 81 71.65 3.33 71.52 3.13 Jeff Overton 88 70.80 2.83 71.18 2.74 Jeff Sluman 101 70.93 3.16 70.95 2.75 Jerry Kelly 100 70.80 3.53 70.93 3.01 Jerry Smith 92 70.90 2.59 71.41 2.43 Jesper Parnevik 84 70.64 2.87 70.59 2.57 Jim Carter 7 74.29 3.86 74.38 3.82 Jim Furyk 88 69.46 2.78 69.04 2.42 Jim Gallagher Jr. 10 72.10 2.38 73.01 2.16 Jimmy Walker 58 71.62 2.88 71.95 2.55 Joe Durant 101 70.75 3.59 70.77 3.29 Joe Ogilvie 91 70.84 3.77 71.03 3.38 Joel Edwards 10 72.40 3.20 73.50 3.15 Joey Sindelar 90 71.60 3.18 71.58 2.72 Joey Snyder III 14 73.29 4.34 73.90 4.03 John Cook 67 71.05 3.32 71.30 3.06 John Daly 49 72.82 3.25 72.25 2.85 John Huston 73 71.41 3.20 71.67 2.88 John Mallinger 8 73.13 1.96 71.74 1.30 John Riegger 2 71.00 5.66 71.79 5.66 John Rollins 91 71.12 3.57 71.16 3.07 John Senden 93 70.51 2.73 70.55 2.41 Jonathan Byrd 66 69.97 3.15 70.18 2.82 Jonathan Kaye 92 71.25 2.55 71.50 2.38 Jose Coceres 38 70.40 3.72 70.95 3.78 Jose Maria Olazabal 58 71.09 2.92 70.21 3.00 Justin Leonard 79 71.28 3.02 71.14 2.55 Justin Rose 95 70.35 3.39 70.51 3.18 K.J. Choi 92 70.65 3.17 70.45 2.63 Kelly Gibson 4 75.25 4.99 76.45 4.85 Ken Duke 8 70.50 1.20 69.78 1.21 Kenny Perry 72 70.94 3.25 71.02 2.59 Kevin Na 31 71.45 2.61 71.35 2.28 Kevin Stadler 22 72.64 4.04 71.66 3.61 Kevin Sutherland 96 70.68 2.76 70.98 2.43 Kirk Triplett 56 71.55 3.60 71.69 3.36 Larry Mize 51 71.80 2.74 71.90 2.29 Larry Nelson 2 76.00 5.66 74.89 5.66 Lee Janzen 79 71.95 3.65 72.02 3.34 Lee Rinker 4 74.50 2.08 74.34 2.84 Lee Westwood 41 71.93 3.31 71.23 3.20 Len Mattiace 59 72.44 3.00 72.77 2.89 Loren Roberts 14 70.79 2.29 70.54 1.62 Louis Oosthuizen 6 71.50 3.39 72.15 3.08 Lucas Glover 101 70.56 3.43 70.33 3.07 Luke Donald 63 70.06 2.95 69.37 2.68 Marco Dawson 87 71.01 2.73 71.25 2.48 Mark Brooks 90 72.04 3.33 72.26 3.13 Mark Calcavecchia 94 72.04 4.03 71.75 3.47 Mark Hensby 44 72.98 4.16 72.40 3.86 Mark O'Meara 50 72.38 3.79 72.29 3.39 Mark Wilson 76 70.80 3.13 71.22 2.94 Mathew Goggin 70 71.57 3.55 71.54 3.24 Matt Gogel 34 71.35 3.17 72.22 2.62 Matt Kuchar 21 73.14 3.02 72.52 2.51 Michael Allen 84 71.06 3.09 71.37 3.00 Michael Bradley 15 71.80 3.78 72.55 3.39 Michael Clark II 10 72.80 2.53 74.05 2.40 Michael Sim 2 71.00 2.83 71.93 2.83 Mike Hulbert 15 73.87 4.12 74.21 4.04 Mike Sposa 66 71.91 3.24 72.33 2.90 Mike Standly 2 71.50 0.71 73.04 0.71 Mike Weir 85 70.77 2.94 70.30 2.86 Nathan Green 104 70.96 3.42 71.09 2.85 Neal Lancaster 43 71.84 2.79 72.32 2.39 Nicholas Thompson 93 71.97 3.48 72.36 3.22 Nick Faldo 13 74.39 3.45 73.51 3.19 Nick O'Hern 46 70.65 3.27 70.62 2.92 Nick Price 43 72.40 3.16 71.96 2.72 Nick Watney 95 70.82 3.13 70.94 3.05 Nolan Henke 2 75.50 2.12 77.04 2.12 Notah Begay III 31 71.74 2.72 72.21 2.67 Olin Browne 104 71.35 3.17 71.27 2.68 Omar Uresti 59 70.81 2.80 71.55 2.44 Padraig Harrington 50 70.92 2.91 70.30 2.60 Parker McLachlin 8 70.88 2.90 71.01 2.88 Pat Perez 50 71.62 3.56 71.35 3.57 Patrick Sheehan 100 71.40 3.28 71.73 3.06 Paul Azinger 87 71.03 2.94 71.23 2.80 Paul Casey 22 72.09 3.27 71.23 3.49 Paul Goydos 72 71.24 3.29 71.57 3.19 Paul Lawrie 4 75.25 0.96 74.54 0.92 Paul Stankowski 70 71.47 3.40 71.74 3.18 Peter Jacobsen 12 72.25 2.90 71.71 2.32 Peter Lonard 76 71.79 3.07 71.48 2.71 Phil Blackmar 2 77.00 1.41 76.20 1.41 Phil Mickelson 69 70.07 2.87 69.41 2.83 Phil Tataurangi 46 73.54 3.75 73.57 3.67 Retief Goosen 60 70.98 2.97 70.24 2.87 Rich Beem 83 71.54 3.61 71.51 3.12 Richard S Johnson 96 70.96 3.03 71.00 2.66 Ricky Barnes 7 70.71 2.22 71.49 1.86 Robert Allenby 77 70.48 2.76 70.05 2.46 Robert Damron 91 71.55 3.19 71.82 2.87 Robert Gamez 94 71.51 3.13 71.70 2.82 Robert Garrigus 84 71.64 3.23 71.84 3.18 Robert Karlsson 20 71.30 2.83 71.12 2.95 Rocco Mediate 50 72.12 2.97 71.78 2.52 Rod Pampling 84 70.98 2.95 70.63 2.82 Rory Sabbatini 83 70.80 3.32 70.54 2.95 Russ Cochran 2 71.50 3.54 73.04 3.54 Ryan Moore 65 71.03 3.14 71.22 3.20 Ryan Palmer 99 70.95 3.35 71.22 3.10 Ryuji Imada 102 70.77 2.89 70.96 2.90 Scott Dunlap 2 73.00 0.00 72.52 0.00 Scott Gump 28 71.96 3.13 72.64 2.76 Scott McCarron 47 71.85 3.15 71.85 2.62 Scott Piercy 20 70.55 2.93 71.33 2.92 Scott Simpson 3 73.67 2.52 73.19 2.52 Scott Verplank 86 70.57 3.03 70.77 2.53 Sean O'Hair 98 71.62 3.52 71.25 2.99 Sergio Garcia 55 71.46 3.11 70.44 2.87 Shaun Micheel 93 70.91 2.96 70.76 2.80 Shigeki Maruyama 92 70.72 3.18 70.84 2.73 Skip Kendall 72 71.10 3.28 71.43 2.98 Spencer Levin 4 70.00 2.45 70.99 2.45 Stephen Ames 62 70.79 3.26 70.36 3.15 Stephen Leaney 84 70.79 2.69 71.02 2.52 Steve Elkington 51 70.86 2.81 71.26 2.63 Steve Flesch 115 70.79 3.36 70.98 3.03 Steve Jones 82 71.79 3.41 71.70 2.98 Steve Lowery 97 71.22 3.37 71.18 3.01 Steve Pate 4 73.50 1.29 74.60 1.39 Steve Stricker 62 69.55 2.04 69.58 1.99 Stewart Cink 88 70.30 2.89 70.06 2.44 Stuart Appleby 78 70.87 3.32 70.21 3.10 Tag Ridings 100 71.77 3.48 72.02 3.13 Ted Purdy 101 71.50 3.29 71.12 3.18 Ted Tryba 2 72.50 4.95 71.81 4.95 Thomas Bjorn 26 72.77 3.48 71.59 3.16 Tiger Woods 52 68.73 3.22 68.19 2.57 Tim Clark 79 71.04 3.08 70.57 3.07 Tim Herron 81 71.70 3.40 71.50 2.97 Tim Petrovic 91 71.68 2.93 71.68 2.75 Todd Fischer 100 71.47 2.94 71.74 2.77 Todd Hamilton 72 73.21 3.65 72.98 3.27 Tom Byrum 28 72.57 3.64 72.50 3.20 Tom Gillis 2 73.00 4.24 74.17 4.24 Tom Kite 2 74.50 0.71 75.49 0.71 Tom Lehman 60 71.60 3.04 71.14 2.77 Tom Pernice Jr. 4 69.50 1.73 70.29 1.73 Tom Scherrer 9 73.44 2.35 73.86 2.27 Tom Watson 6 73.67 3.33 72.44 2.61 Tommy Armour III 65 71.48 3.07 71.45 2.83 Trevor Dodds 4 73.75 0.96 74.59 1.05 Trevor Immelman 86 69.93 2.76 69.76 2.44 Troy Matteson 101 71.21 3.36 71.47 3.10 Vaughn Taylor 88 70.86 2.88 70.58 2.68 Vijay Singh 100 70.21 3.01 69.69 2.95 Webb Simpson 2 73.50 2.12 72.63 2.12 Wes Short Jr. 94 72.28 3.39 72.45 3.26 Will MacKenzie 88 71.14 3.10 71.46 2.94 Willie Wood 26 72.42 2.40 73.07 2.60 Woody Austin 107 71.11 3.48 71.14 3.02 Zach Johnson 88 70.85 2.69 70.68 2.44 Appendix H- 2008 Average and Course Neutral Round Scores for Top Golfers Golfer Rounds Average Round Average Dev CN-Average Round CN-Dev Aaron Baddeley 73 70.86 3.21 70.41 2.68 Adam Scott 49 71.45 3.64 70.61 3.42 Alex Cejka 75 71.69 3.23 71.47 3.02 Anders Hansen 16 72.63 3.93 71.39 3.25 Andres Romero 67 71.85 3.23 71.36 3.14 Andrew Magee 9 72.44 2.83 72.56 2.77 Angel Cabrera 51 71.94 3.44 71.49 2.87 Anthony Kim 81 70.22 3.31 69.94 2.79 Arron Oberholser 31 71.16 3.16 71.28 2.73 Bart Bryant 81 71.22 3.23 70.74 2.87 Ben Crane 87 70.39 2.89 70.62 2.39 Ben Curtis 80 70.96 3.17 70.44 2.79 Bernhard Langer 6 73.67 3.78 70.81 4.00 Bill Haas 99 70.66 3.11 70.99 2.60 Billy Andrade 71 72.16 3.65 72.48 3.26 Billy Mayfair 103 70.76 3.06 71.00 2.64 Blaine McCallister 4 78.75 5.19 78.37 5.16 Bo Van Pelt 101 70.96 3.26 71.29 2.83 Bob Burns 17 74.71 3.18 74.65 3.15 Bob Estes 90 70.69 3.50 71.09 3.00 Bob May 15 70.73 2.82 70.36 2.55 Bob Tway 70 69.94 3.15 70.71 2.75 Boo Weekley 83 71.12 3.64 70.76 3.33 Brad Bryant 2 78.00 1.41 75.34 1.41 Brad Elder 67 71.25 2.99 72.00 2.57 Brad Faxon 6 74.50 3.21 73.97 2.54 Brandel Chamblee 3 74.00 5.57 73.21 5.57 Brandt Jobe 52 71.48 2.65 71.50 2.42 Brandt Snedeker 84 71.27 2.81 70.94 2.63 Brenden Pappas 66 70.80 3.15 71.54 2.67 Brent Geiberger 26 73.31 3.99 73.92 3.92 Brett Quigley 80 71.28 2.92 71.07 2.53 Brett Wetterich 36 73.03 3.57 72.53 3.15 Brian Bateman 48 72.23 3.12 71.89 2.91 Brian Davis 108 70.73 3.50 71.11 3.14 Brian Gay 102 70.11 2.94 70.57 2.59 Briny Baird 113 70.44 3.15 70.57 2.83 Bryce Molder 2 71.50 2.12 72.96 2.12 Bubba Watson 97 71.07 3.44 71.23 2.80 Cameron Beckman 87 71.09 3.43 71.62 2.94 Camilo Villegas 78 70.60 3.27 70.04 2.79 Carl Pettersson 110 70.84 3.06 70.60 2.67 Carlos Franco 73 71.16 2.47 71.48 2.20 Chad Campbell 94 70.37 3.48 70.64 2.87 Charl Schwartzel 4 73.75 2.99 70.95 2.99 Charles Howell III 99 71.15 3.27 70.97 2.65 Charles Warren 79 72.08 4.25 72.29 3.55 Charley Hoffman 94 71.16 3.55 71.54 2.88 Charlie Wi 97 70.41 3.14 70.80 2.75 Chez Reavie 102 71.03 3.39 71.50 2.94 Chris DiMarco 87 71.70 3.32 71.79 2.67 Chris Kirk 11 73.09 2.91 72.27 2.03 Chris Riley 51 70.92 3.11 71.65 2.65 Chris Smith 13 73.08 3.48 73.25 3.29 Chris Stroud 81 71.54 3.78 72.11 3.07 Cliff Kresge 84 71.54 3.94 71.43 3.49 Colin Montgomerie 18 74.67 3.33 74.03 2.84 Corey Pavin 69 70.67 2.92 71.04 2.54 Craig Barlow 43 72.79 3.14 72.16 2.78 Craig Parry 14 74.93 2.97 74.44 2.98 Craig Stadler 5 75.40 3.13 74.06 3.41 D.A. Points 12 72.00 3.16 71.00 2.54 D.J. Trahan 94 70.89 3.43 70.81 2.91 Daisuke Maruyama 12 71.75 2.60 72.10 2.81 Dan Forsman 36 71.50 2.16 71.67 2.30 Daniel Chopra 83 71.51 3.49 71.42 3.00 Darren Clarke 6 70.67 4.32 70.74 2.64 David Berganio Jr. 2 72.50 0.71 73.55 0.71 David Duval 51 73.73 3.57 73.43 3.37 David Frost 9 73.00 1.73 71.65 1.32 David Howell 10 72.80 3.68 72.31 4.21 David Ogrin 2 70.00 1.41 72.25 1.41 David Peoples 4 73.25 2.99 73.62 2.73 David Toms 68 71.13 3.35 70.85 2.81 Davis Love III 78 71.21 3.55 70.70 2.73 Dean Wilson 109 70.98 3.42 71.06 2.97 Dennis Paulson 4 72.75 2.36 72.55 2.36 Derek Lamely 4 74.75 5.12 73.12 5.12 Dudley Hart 74 70.84 3.18 70.95 3.14 Duffy Waldorf 11 73.73 2.94 73.14 2.90 Dustin Johnson 92 71.50 3.55 71.58 2.96 Eric Axley 113 71.31 3.51 71.72 3.17 Ernie Els 50 71.44 3.14 70.64 2.83 Esteban Toledo 12 70.58 2.94 70.74 2.73 Frank Lickliter II 108 71.25 3.14 71.71 2.72 Fred Couples 60 71.22 2.98 70.76 2.85 Fred Funk 42 71.31 3.31 71.89 2.81 Fredrik Jacobson 78 71.26 3.28 70.82 2.82 Fuzzy Zoeller 2 80.00 1.41 77.82 1.41 Gabriel Hjertstedt 10 73.30 2.41 73.31 2.62 Garrett Willis 34 71.50 3.70 71.72 3.05 Geoff Ogilvy 64 71.38 3.36 70.67 3.13 George McNeill 97 70.94 2.86 71.06 2.34 Glen Day 64 70.61 2.54 71.19 2.26 Graeme McDowell 16 72.00 2.68 71.21 3.00 Grant Waite 17 73.00 2.06 72.86 2.14 Greg Kraft 63 71.56 3.62 71.60 3.08 Greg Norman 11 74.00 4.20 72.80 4.84 Greg Owen 3 72.67 4.51 71.88 4.51 Guy Boros 17 72.71 2.97 72.78 2.70 Harrison Frazar 73 71.48 3.10 72.07 2.74 Heath Slocum 104 71.17 3.35 71.09 2.99 Henrik Stenson 30 72.07 2.82 70.83 3.09 Hunter Haas 2 75.00 7.07 72.34 7.07 Hunter Mahan 85 70.78 3.69 70.70 2.98 Ian Leggatt 17 72.06 2.84 71.78 2.39 Ian Poulter 50 71.72 2.59 70.66 2.48 J.B. Holmes 85 71.39 3.27 70.96 2.97 J.J. Henry 108 71.07 3.09 71.39 2.67 J.L. Lewis 41 73.85 2.79 73.88 2.42 J.P. Hayes 67 72.09 3.43 72.37 2.88 James Driscoll 85 71.60 3.76 71.94 3.43 Jason Bohn 45 71.76 3.27 71.03 2.79 Jason Day 81 71.06 3.44 71.51 3.10 Jason Dufner 49 70.96 3.10 71.66 2.67 Jason Gore 94 71.03 3.49 71.57 2.85 Jay Delsing 19 73.00 3.00 73.31 2.64 Jay Haas 2 75.00 2.83 72.20 2.83 Jean Van De Velde 4 73.50 4.51 70.55 4.51 Jeff Maggert 86 71.29 3.33 71.66 3.18 Jeff Overton 103 71.29 3.44 71.23 3.07 Jeff Quinney 88 71.42 3.14 71.08 2.94 Jeff Sluman 6 71.50 2.43 73.10 2.36 Jerry Kelly 88 71.49 3.66 71.41 3.19 Jesper Parnevik 88 71.25 3.19 71.37 2.86 Jhonattan Vegas 4 68.50 1.00 70.75 1.00 Jim Furyk 94 70.56 3.02 70.11 2.47 Jim Gallagher Jr. 17 74.82 4.56 75.37 3.98 Jimmy Walker 73 71.45 3.52 72.03 3.25 Joe Durant 92 71.24 3.28 71.68 2.88 Joe Ogilvie 100 70.92 3.13 71.24 2.75 Joel Edwards 2 76.50 2.12 76.47 2.12 Joey Sindelar 15 73.07 4.06 72.60 3.73 John Daly 43 73.28 4.58 73.36 3.55 John Huston 56 70.48 3.20 71.13 2.90 John Mallinger 95 71.02 3.35 71.03 2.87 John Merrick 98 70.97 3.49 70.98 3.12 John Morse 21 73.19 2.94 73.26 2.39 John Rollins 94 71.54 3.53 71.36 3.13 John Senden 92 70.90 3.17 70.80 2.83 Johnson Wagner 83 71.65 3.45 71.44 3.13 Jonathan Byrd 85 71.37 3.07 71.32 2.65 Jonathan Kaye 22 72.41 2.99 72.51 3.03 Jose Coceres 37 72.27 3.63 72.04 3.37 Jose Maria Olazabal 12 73.33 3.14 71.48 2.79 Justin Leonard 95 70.41 3.04 70.24 2.58 Justin Rose 45 71.80 3.55 70.70 3.12 K.J. Choi 70 71.01 3.78 70.73 3.02 Ken Duke 116 70.61 3.30 70.77 2.82 Kenny Perry 97 70.21 3.29 70.28 3.02 Kevin Chappell 4 71.50 1.29 74.01 1.19 Kevin Na 97 70.81 3.32 71.02 2.79 Kevin Stadler 90 71.56 3.57 71.62 3.34 Kevin Streelman 114 70.63 3.88 71.14 3.31 Kevin Sutherland 98 70.22 2.85 70.50 2.44 Kirk Triplett 25 71.80 3.78 73.18 3.59 Kyle Stanley 2 75.00 4.24 72.34 4.24 Larry Mize 46 72.17 4.35 72.52 3.68 Lee Janzen 89 71.46 3.35 71.71 2.87 Lee Rinker 2 75.50 0.71 75.47 0.71 Lee Westwood 30 72.07 3.55 70.97 2.80 Len Mattiace 31 72.19 2.34 72.46 2.04 Louis Oosthuizen 10 74.90 3.14 74.10 2.77 Lucas Glover 91 70.95 3.23 71.08 2.51 Luke Donald 33 71.18 3.02 69.85 2.81 Marc Turnesa 87 71.16 3.28 71.52 2.87 Marco Dawson 64 71.42 3.12 71.65 2.79 Mark Brooks 48 71.81 3.38 72.41 2.59 Mark Calcavecchia 66 71.86 3.60 71.68 2.99 Mark Hensby 71 71.85 3.84 72.18 3.24 Mark O'Meara 14 74.07 3.91 73.01 3.33 Mark Wilson 107 70.44 2.89 70.76 2.37 Martin Kaymer 22 73.82 3.32 72.86 3.06 Martin Laird 98 70.81 3.14 71.63 2.76 Mathew Goggin 91 70.73 3.08 70.65 2.87 Matt Jones 95 71.40 3.25 71.67 2.86 Matt Kuchar 88 71.03 3.24 70.85 2.87 Michael Allen 92 71.17 3.20 71.08 2.55 Michael Bradley 40 71.08 2.83 71.46 2.45 Michael Clark II 2 75.50 2.12 75.30 2.12 Michael Letzig 88 71.01 3.50 71.28 3.05 Michael Sim 27 70.93 3.03 70.91 2.47 Mike Hulbert 2 77.00 1.41 77.45 1.41 Mike Standly 2 73.50 6.36 73.30 6.36 Mike Weir 87 70.68 3.11 70.46 2.63 Nathan Green 95 71.33 3.15 71.40 3.23 Neal Lancaster 28 70.96 2.17 71.92 2.11 Nicholas Thompson 113 71.38 3.53 71.45 3.32 Nick O'Hern 80 70.89 2.99 70.62 2.43 Nick Price 4 70.00 2.83 70.82 2.83 Nick Watney 96 71.02 3.22 70.85 2.73 Nolan Henke 2 77.50 3.54 77.30 3.54 Notah Begay III 24 72.38 4.07 73.16 3.44 Olin Browne 77 71.81 3.10 72.22 2.53 Omar Uresti 74 71.05 3.01 71.67 2.73 Padraig Harrington 50 70.70 2.97 69.70 3.13 Parker McLachlin 88 71.07 3.39 71.09 2.97 Pat Perez 92 70.70 3.68 70.41 3.04 Patrick Sheehan 124 70.93 3.23 71.34 2.85 Paul Azinger 21 73.19 3.33 72.66 2.18 Paul Casey 52 71.75 3.58 70.75 3.07 Paul Goydos 78 71.60 3.41 71.58 3.20 Paul Lawrie 2 75.00 2.83 72.05 2.83 Paul Stankowski 38 71.50 3.25 72.39 3.21 Peter Jacobsen 3 75.33 2.52 74.55 2.52 Peter Lonard 92 70.94 3.37 71.22 2.93 Phil Mickelson 78 70.28 3.01 69.54 2.58 Phil Tataurangi 13 74.00 2.48 74.40 2.26 Retief Goosen 58 71.71 3.31 70.83 2.86 Rich Beem 90 71.39 3.37 71.44 2.70 Richard S Johnson 60 71.13 2.99 71.72 2.35 Rick Fehr 4 75.50 5.80 75.30 5.80 Rickie Fowler 6 73.83 3.71 71.98 3.71 Robert Allenby 107 70.64 2.97 70.02 2.74 Robert Damron 22 71.77 3.32 72.13 3.36 Robert Garrigus 90 71.02 3.48 71.24 2.80 Robert Karlsson 28 71.43 2.36 70.20 2.37 Rocco Mediate 87 71.61 3.12 71.21 2.87 Rod Pampling 80 71.39 3.49 71.17 3.09 Ronnie Black 6 73.17 2.79 73.04 2.64 Rory Sabbatini 76 71.05 3.25 71.04 2.78 Russ Cochran 2 78.00 1.41 76.71 1.41 Ryan Moore 72 71.50 3.42 71.44 3.27 Ryan Palmer 69 70.48 3.36 71.22 3.28 Ryuji Imada 80 71.13 3.06 70.84 2.80 Scott Dunlap 2 72.50 3.54 72.17 3.54 Scott Gump 4 74.50 0.58 74.39 0.59 Scott Hoch 4 72.00 2.45 71.54 2.45 Scott McCarron 63 71.22 3.50 71.77 2.94 Scott Piercy 6 72.50 2.88 72.16 1.78 Scott Verplank 81 70.84 3.29 70.97 2.68 Sean O'Hair 81 71.25 3.20 70.98 2.70 Sergio Garcia 70 70.60 2.92 69.76 2.66 Shaun Micheel 45 72.89 2.98 72.29 2.55 Shigeki Maruyama 50 71.78 3.21 71.94 2.95 Skip Kendall 15 72.93 2.22 73.28 2.29 Spencer Levin 4 70.00 2.94 71.46 2.94 Stephen Ames 82 70.67 3.21 70.53 2.67 Stephen Leaney 53 72.23 2.40 72.08 2.25 Steve Elkington 84 70.67 3.09 70.70 2.80 Steve Flesch 95 71.17 3.14 71.23 2.76 Steve Lowery 74 71.96 3.72 71.96 3.20 Steve Marino 119 70.29 3.09 70.61 2.41 Steve Pate 7 74.00 1.83 73.51 1.82 Steve Stricker 72 70.83 3.68 70.51 3.24 Stewart Cink 81 70.65 2.94 70.30 2.63 Stuart Appleby 84 70.86 2.91 70.22 2.62 Tag Ridings 88 71.34 3.38 71.68 3.04 Ted Purdy 69 71.75 2.95 72.23 2.69 Tiger Woods 20 68.90 2.57 67.93 2.37 Tim Clark 89 70.87 3.93 70.91 3.05 Tim Herron 97 70.66 3.60 71.18 3.12 Tim Petrovic 97 71.23 3.23 71.31 2.86 Tim Wilkinson 95 71.02 3.51 71.23 3.07 Todd Hamilton 92 71.83 3.07 71.37 2.62 Tom Byrum 36 71.03 2.97 71.76 2.52 Tom Gillis 10 72.80 3.12 71.79 2.85 Tom Kite 2 75.50 2.12 75.47 2.12 Tom Lehman 51 71.98 2.63 71.22 2.49 Tom Pernice Jr 54 71.57 3.36 70.85 3.02 Tom Scherrer 56 71.64 3.17 72.31 3.01 Tom Watson 4 75.00 0.82 72.44 0.93 Tommy Armour III 77 70.99 3.90 71.36 3.43 Tommy Gainey 60 71.95 3.79 72.55 3.22 Trevor Dodds 4 75.00 4.24 76.28 3.33 Trevor Immelman 68 71.85 3.25 71.24 3.01 Troy Matteson 94 71.40 3.64 71.53 3.17 Vaughn Taylor 103 70.85 3.25 71.08 2.88 Vijay Singh 78 70.27 3.25 70.13 2.62 Webb Simpson 18 70.89 2.30 71.61 1.91 Will MacKenzie 62 71.63 3.51 72.18 3.04 Willie Wood 11 74.64 2.01 74.49 2.03 Woody Austin 105 71.11 3.44 71.13 2.73 Y.E. Yang 89 71.53 3.09 71.89 2.69 Zach Johnson 84 71.06 3.56 70.96 2.78 Appendix I - 2009 Average and Course Neutral Round Scores for Top Golfers Golfer Rounds Average Round Average Dev CN-Average Round CN-Dev Aaron Baddeley 67 71.16 3.47 70.82 3.21 Adam Scott 52 72.06 3.76 71.71 3.11 Alex Cejka 82 70.81 3.44 70.88 3.05 Anders Hansen 8 72.38 3.46 71.60 3.18 Andres Romero 58 71.48 3.55 71.37 3.11 Andrew Magee 5 72.80 2.17 71.94 2.16 Angel Cabrera 54 71.15 3.57 70.29 3.16 Anthony Kim 74 70.62 3.13 70.49 2.73 Arjun Atwal 31 71.90 2.66 72.08 2.75 Arron Oberholser 11 69.46 2.66 70.38 1.99 Bart Bryant 58 71.33 3.20 71.32 2.83 Ben Crane 93 70.34 3.06 70.23 2.71 Ben Curtis 62 71.63 3.50 70.70 3.09 Bernhard Langer 2 75.00 7.07 73.78 7.07 Bill Haas 91 70.36 3.10 70.48 2.71 Bill Lunde 83 70.43 3.16 70.88 2.66 Billy Andrade 40 72.43 3.16 72.90 2.42 Billy Mayfair 83 71.89 3.31 72.05 3.10 Bo Van Pelt 100 70.12 3.44 70.40 3.00 Bob Burns 4 72.25 2.63 73.10 1.48 Bob Estes 78 70.49 3.12 70.51 2.66 Bob Tway 30 71.77 3.01 71.67 2.59 Boo Weekley 77 70.88 3.09 70.55 2.80 Brad Faxon 59 72.71 3.70 73.14 3.19 Brandt Jobe 28 70.07 2.68 70.32 2.40 Brandt Snedeker 81 70.57 3.31 70.50 2.89 Brendon de Jonge 90 70.93 2.88 71.29 2.72 Brent Geiberger 11 73.18 3.95 73.65 3.67 Brett Quigley 92 70.69 3.30 70.78 2.80 Brian Bateman 55 71.80 2.97 72.34 2.46 Brian Davis 104 70.47 3.07 70.76 2.50 Brian Gay 96 70.34 3.63 70.58 3.21 Briny Baird 89 70.40 3.31 70.74 2.94 Bryce Molder 69 70.12 3.65 70.63 3.10 Bubba Watson 73 70.82 3.15 70.46 2.91 Cameron Beckman 87 70.68 3.09 70.98 2.66 Cameron Tringale 2 73.50 4.95 71.89 4.95 Camilo Villegas 73 70.82 2.77 70.00 2.68 Carl Pettersson 87 71.46 3.14 71.53 2.71 Carlos Franco 31 71.32 3.20 71.58 2.87 Chad Campbell 90 70.31 3.03 70.46 2.42 Charl Schwartzel 16 72.44 2.99 70.39 2.96 Charles Howell III 99 70.62 2.98 70.40 2.54 Charles Warren 63 70.87 3.14 70.95 3.07 Charley Hoffman 97 70.32 3.60 70.30 3.16 Charlie Wi 92 70.46 3.01 70.57 2.55 Chez Reavie 81 70.94 3.10 71.44 2.48 Chris Couch 21 71.14 3.58 71.50 3.29 Chris DiMarco 97 70.49 2.71 70.91 2.38 Chris Kirk 5 73.20 2.86 72.17 2.50 Chris Riley 77 70.13 3.35 70.67 2.82 Chris Smith 9 71.22 2.17 71.13 2.44 Chris Stroud 88 70.52 3.44 70.96 2.79 Cliff Kresge 78 70.86 2.97 71.15 2.62 Colin Montgomerie 4 74.50 2.89 72.28 2.01 Corey Pavin 73 70.58 2.94 70.95 2.55 Craig Barlow 13 72.31 3.07 72.57 2.75 Craig Stadler 2 75.50 2.12 74.28 2.12 D.A. Points 99 70.73 3.40 70.88 3.11 D.J. Trahan 96 70.50 3.53 70.83 2.90 Daniel Chopra 89 71.03 3.07 71.23 3.08 Darren Clarke 22 72.23 3.10 71.60 2.49 David Berganio Jr. 43 71.14 3.43 71.58 3.03 David Duval 56 72.23 3.40 72.34 3.24 David Gossett 11 72.46 3.48 73.11 3.20 David Howell 4 72.25 3.30 71.15 3.30 David Ogrin 2 71.00 1.41 72.87 1.41 David Peoples 18 70.50 2.81 71.38 2.47 David Toms 98 69.76 3.07 69.85 2.62 Davis Love III 87 70.69 2.59 70.37 2.56 Dean Wilson 82 70.63 2.93 71.08 2.65 Dennis Paulson 2 76.00 2.83 73.67 2.83 Derek Lamely 6 71.00 4.15 71.09 4.28 Dudley Hart 38 71.79 2.66 71.40 2.28 Dustin Johnson 84 70.48 3.24 70.16 2.95 Eric Axley 71 72.93 3.63 73.25 3.39 Ernie Els 66 70.76 2.83 70.05 2.86 Esteban Toledo 6 72.33 3.01 72.68 2.81 Frank Lickliter II 37 70.87 3.72 71.55 3.46 Fred Couples 54 70.65 3.63 70.57 3.04 Fred Funk 14 74.29 3.54 73.51 3.29 Fredrik Jacobson 83 70.65 3.26 70.65 2.93 Fuzzy Zoeller 2 77.50 2.12 76.28 2.12 Gabriel Hjertstedt 2 75.00 2.83 74.83 2.83 Garrett Willis 19 70.32 3.06 71.33 2.40 Gary Woodland 53 71.93 3.54 72.25 3.20 Geoff Ogilvy 72 70.68 3.39 70.10 3.07 George McNeill 82 70.42 3.08 70.34 2.63 Glen Day 79 70.99 3.24 71.62 3.02 Graeme McDowell 39 71.10 2.67 70.30 2.57 Grant Waite 6 71.67 3.01 71.82 3.08 Greg Chalmers 85 69.99 3.15 70.69 2.65 Greg Kraft 51 72.77 2.96 72.66 2.80 Greg Norman 8 73.75 4.37 72.61 4.37 Greg Owen 98 70.28 3.13 70.67 2.71 Guy Boros 22 70.86 2.55 71.65 2.39 Harrison Frazar 93 70.19 2.81 70.66 2.54 Heath Slocum 95 70.53 3.08 70.86 2.87 Henrik Stenson 34 71.21 3.06 70.16 3.55 Hunter Mahan 92 70.11 2.95 69.63 2.63 Ian Leggatt 4 73.25 0.96 73.13 0.99 Ian Poulter 56 70.84 3.03 69.87 2.82 J.B. Holmes 74 71.99 3.40 71.42 3.37 J.J. Henry 97 70.44 3.38 70.50 2.85 J.L. Lewis 10 72.90 3.78 73.23 3.62 J.P. Hayes 43 70.93 3.14 71.52 3.00 James Driscoll 49 71.20 3.86 71.56 2.98 James Nitties 86 70.67 3.28 70.72 2.94 Jason Bohn 88 70.41 3.14 70.80 2.60 Jason Day 61 70.08 2.99 69.89 2.75 Jason Dufner 90 70.48 3.21 70.31 2.83 Jason Gore 74 71.26 3.10 71.73 2.83 Jay Delsing 21 72.43 2.75 72.73 2.91 Jeff Brehaut 4 74.25 4.79 72.64 4.79 Jeff Klauk 97 70.57 3.16 70.70 2.75 Jeff Maggert 79 70.84 3.62 71.36 3.26 Jeff Overton 93 71.03 3.12 70.49 2.96 Jeff Quinney 78 71.01 3.05 71.31 2.54 Jeff Sluman 6 69.00 2.28 70.48 1.98 Jerry Kelly 90 70.01 3.02 70.23 2.61 Jesper Parnevik 38 71.42 3.52 72.02 3.20 Jim Furyk 83 70.02 3.24 69.40 2.96 Jim Gallagher Jr. 4 73.00 2.16 73.85 2.17 Jimmy Walker 74 70.95 3.57 71.43 3.39 Joe Durant 62 70.77 3.09 71.36 2.69 Joe Ogilvie 85 70.59 2.70 70.99 2.50 John Daly 16 72.81 5.17 73.10 5.02 John Huston 39 71.67 3.32 71.46 2.96 John Mallinger 90 70.77 3.27 70.67 2.82 John Merrick 91 70.84 3.29 70.90 2.84 John Rollins 92 71.17 3.18 70.97 3.14 John Senden 100 70.18 3.25 69.94 2.75 Johnson Wagner 81 70.93 2.99 71.32 2.44 Jonathan Byrd 89 70.32 2.66 70.28 2.69 Jonathan Kaye 50 70.96 3.25 71.04 3.12 Jose Coceres 13 74.23 4.34 74.37 4.74 Jose Maria Olazabal 14 70.86 2.96 69.98 2.72 Justin Leonard 91 69.91 3.28 70.14 2.74 Justin Rose 70 70.79 3.29 70.40 2.74 K.J. Choi 64 71.52 2.84 70.87 2.65 Ken Duke 87 71.32 2.96 71.44 2.58 Kenny Perry 91 70.14 3.13 69.74 2.73 Kevin Chappell 7 73.71 6.13 72.71 5.41 Kevin Na 92 70.21 3.30 70.02 3.16 Kevin Stadler 65 70.43 3.08 70.82 2.77 Kevin Streelman 97 70.51 3.40 70.72 2.71 Kevin Sutherland 95 70.71 3.12 70.42 2.79 Kirk Triplett 60 71.10 3.28 71.77 3.01 Kris Blanks 60 70.70 3.54 71.59 3.12 Kyle Stanley 24 70.13 3.08 71.19 2.35 Larry Mize 4 71.75 3.69 70.53 3.69 Lee Janzen 74 70.72 2.93 70.90 2.77 Lee Rinker 2 79.50 2.12 76.16 2.12 Lee Westwood 28 70.89 2.99 69.84 3.09 Len Mattiace 3 70.33 1.53 69.70 1.53 Loren Roberts 10 69.50 2.51 70.74 2.34 Louis Oosthuizen 14 72.64 3.20 71.59 2.72 Lucas Glover 93 70.34 3.28 70.03 2.95 Luke Donald 76 70.47 2.81 69.82 2.59 Marc Leishman 91 70.60 3.20 70.73 2.84 Marc Turnesa 77 72.23 2.96 72.33 2.63 Marco Dawson 14 71.93 2.92 72.33 1.90 Mark Brooks 55 71.11 3.11 71.65 2.67 Mark Calcavecchia 72 71.14 3.70 71.37 3.45 Mark Hensby 14 70.50 2.44 71.53 2.26 Mark O'Meara 6 74.33 3.78 73.19 3.76 Mark Wilson 99 70.21 2.92 70.35 2.63 Martin Kaymer 36 71.86 2.39 70.49 2.52 Martin Laird 72 70.94 3.68 71.24 3.23 Mathew Goggin 74 71.07 3.39 70.93 3.11 Matt Jones 56 70.32 3.42 70.77 3.29 Matt Kuchar 82 70.10 3.01 69.89 2.63 Michael Allen 69 70.81 3.09 70.74 2.52 Michael Bradley 45 71.13 3.52 71.71 3.17 Michael Letzig 98 70.47 2.55 70.71 2.39 Michael Sim 12 71.75 2.63 70.09 2.23 Mike Hulbert 2 75.00 4.24 74.83 4.24 Mike Weir 84 70.42 3.33 70.27 2.88 Nathan Green 104 71.05 3.63 71.27 3.21 Neal Lancaster 15 71.07 2.12 71.55 2.16 Nicholas Thompson 96 71.06 3.12 71.24 2.92 Nick Faldo 2 75.50 3.54 74.40 3.54 Nick O'Hern 90 70.39 2.99 70.65 2.52 Nick Watney 86 70.38 2.64 69.86 2.57 Nolan Henke 2 76.50 3.54 78.37 3.54 Notah Begay III 41 72.17 2.79 72.65 2.59 Olin Browne 24 72.08 2.72 72.71 2.30 Omar Uresti 27 70.48 2.49 71.03 2.27 Padraig Harrington 65 71.05 3.17 70.06 2.92 Parker McLachlin 71 72.24 3.54 72.24 3.14 Pat Perez 72 70.82 3.56 70.81 2.75 Patrick Sheehan 51 70.49 2.60 71.12 2.15 Paul Azinger 17 72.18 3.45 71.92 2.74 Paul Casey 36 70.86 3.35 70.02 2.86 Paul Goydos 79 71.04 3.85 70.80 3.36 Paul Lawrie 4 72.00 3.37 70.90 3.37 Paul Stankowski 24 71.46 3.02 71.81 2.55 Peter Lonard 86 71.51 3.15 71.93 2.72 Phil Mickelson 63 70.83 3.47 70.01 3.19 Phil Tataurangi 4 74.50 2.38 75.08 2.48 Retief Goosen 73 70.71 2.95 69.90 2.77 Rich Beem 77 70.74 3.64 71.20 3.18 Richard S Johnson 54 71.22 2.84 71.44 2.64 Rickie Fowler 20 69.40 4.06 70.38 3.62 Ricky Barnes 67 71.31 2.96 71.69 2.67 Robert Allenby 70 70.81 3.13 70.05 2.92 Robert Damron 13 73.31 4.11 73.37 4.00 Robert Gamez 25 74.40 3.59 75.11 3.18 Robert Garrigus 84 70.32 3.58 70.74 2.98 Robert Karlsson 17 71.71 2.89 70.66 2.76 Rocco Mediate 79 71.25 3.48 71.15 3.13 Rod Pampling 71 70.85 3.53 70.31 3.16 Ronnie Black 12 69.75 1.96 70.58 2.00 Rory McIlroy 38 71.26 2.33 70.29 2.48 Rory Sabbatini 80 70.61 3.62 70.41 3.09 Russ Cochran 2 73.00 2.83 72.10 2.83 Ryan Moore 89 70.46 3.86 70.55 3.36 Ryan Palmer 78 71.10 3.46 71.40 3.00 Ryuji Imada 85 71.17 3.15 71.11 2.83 Scott McCarron 91 70.56 3.52 70.75 2.79 Scott Piercy 86 70.76 3.79 70.88 3.41 Scott Verplank 88 69.99 2.97 70.20 2.67 Sean O'Hair 76 70.45 3.44 69.96 3.04 Sergio Garcia 58 70.62 3.31 70.23 2.89 Shaun Micheel 49 71.39 3.01 71.18 2.75 Shigeki Maruyama 15 69.60 2.87 70.08 2.88 Skip Kendall 11 71.73 3.95 71.78 3.11 Spencer Levin 75 70.44 3.05 70.92 2.69 Stephen Ames 73 70.19 3.32 70.16 2.73 Stephen Leaney 26 72.58 2.70 73.14 2.47 Steve Elkington 71 70.65 3.22 71.01 2.77 Steve Flesch 78 71.10 2.85 70.96 2.49 Steve Lowery 83 71.18 3.13 71.54 2.79 Steve Marino 98 70.09 3.29 69.98 2.87 Steve Pate 10 72.70 3.09 72.80 3.28 Steve Stricker 79 69.51 3.62 69.20 3.10 Stewart Cink 73 71.10 2.75 70.53 2.61 Stuart Appleby 78 71.77 3.08 71.44 2.85 Tag Ridings 51 70.12 3.14 70.79 2.85 Ted Purdy 101 70.68 3.13 70.78 2.86 Tiger Woods 62 68.84 2.81 67.89 2.65 Tim Clark 79 69.62 3.16 69.74 2.55 Tim Herron 87 70.59 3.46 71.09 3.00 Tim Petrovic 97 70.42 3.46 70.67 2.91 Tim Wilkinson 42 70.93 2.92 71.30 2.55 Todd Fischer 9 70.11 3.26 70.57 2.40 Todd Hamilton 83 71.54 3.19 71.45 2.87 Tom Byrum 10 71.20 2.44 71.61 2.15 Tom Gillis 2 72.50 3.54 73.11 3.54 Tom Lehman 55 71.42 2.99 70.85 2.46 Tom Pernice Jr 28 71.14 3.63 71.07 3.01 Tom Scherrer 7 71.57 2.23 71.20 2.19 Tom Watson 6 72.50 5.96 71.36 5.91 Tommy Armour III 58 71.09 3.01 71.22 2.80 Tommy Gainey 46 71.04 2.81 71.47 2.73 Trevor Dodds 2 75.00 7.07 76.87 7.07 Trevor Immelman 40 72.30 3.09 71.94 3.19 Troy Matteson 95 70.57 3.26 70.68 3.02 Vaughn Taylor 88 70.50 3.34 70.95 3.08 Vijay Singh 69 71.13 2.97 70.76 2.54 Webb Simpson 94 70.71 3.06 70.78 2.67 Wes Short Jr. 7 72.43 4.83 73.82 3.25 Will MacKenzie 69 71.55 3.38 71.60 3.14 Willie Wood 4 72.00 4.97 72.85 4.97 Woody Austin 84 70.68 3.02 70.43 2.50 Y.E. Yang 83 70.72 2.94 70.31 2.87 Zach Johnson 92 69.82 3.24 69.56 2.72 Appendix J - 2006 PGA Championship Odds Tiger Woods Beats or Ties Contending Golfers Given Relative Positions Before Last Round If Tiger Shoots Likelihood Donald Weir Olgivy Micheel Garcia Choi Field Chance Tiger Wins or Ties 58 0.005% 99.998% 100.000% 100.000% 100.000% 100.000% 100.000% 99.998% 0.005% 59 0.018% 99.990% 100.000% 100.000% 100.000% 100.000% 100.000% 99.990% 0.018% 60 0.070% 99.960% 99.999% 100.000% 100.000% 100.000% 100.000% 99.959% 0.070% 61 0.230% 99.857% 99.994% 100.000% 100.000% 100.000% 100.000% 99.851% 0.230% 62 0.656% 99.548% 99.976% 99.998% 99.999% 100.000% 100.000% 99.522% 0.653% 63 1.608% 98.737% 99.918% 99.992% 99.996% 99.999% 100.000% 98.642% 1.586% 64 3.396% 96.887% 99.743% 99.967% 99.982% 99.994% 99.999% 96.582% 3.280% 65 6.175% 93.210% 99.282% 99.877% 99.935% 99.975% 99.993% 92.337% 5.701% 66 9.668% 86.836% 98.206% 99.597% 99.787% 99.915% 99.969% 84.656% 8.185% 67 13.036% 77.210% 95.982% 98.844% 99.381% 99.735% 99.883% 72.520% 9.454% 68 15.138% 64.539% 91.908% 97.081% 98.397% 99.266% 99.613% 56.028% 8.481% 69 15.138% 50.000% 85.295% 93.502% 96.298% 98.175% 98.877% 37.276% 5.643% 70 13.036% 35.461% 75.787% 87.196% 92.351% 95.932% 97.143% 20.168% 2.629% 71 9.668% 22.790% 63.673% 77.551% 85.810% 91.838% 93.596% 8.300% 0.802% 72 6.175% 13.164% 50.000% 64.749% 76.256% 85.215% 87.313% 2.418% 0.149% 73 3.396% 6.790% 36.327% 50.000% 63.956% 75.714% 77.663% 0.464% 0.016% 74 1.608% 3.113% 24.213% 35.251% 50.000% 63.629% 64.819% 0.055% 0.001% 75 0.656% 1.263% 14.705% 22.449% 36.044% 50.000% 50.000% 0.004% 0.000% 76 0.230% 0.452% 8.092% 12.804% 23.744% 36.371% 35.181% 0.000% 0.000% 77 0.070% 0.143% 4.018% 6.498% 14.190% 24.286% 22.337% 0.000% 0.000% 78 0.018% 0.040% 1.794% 2.919% 7.649% 14.785% 12.687% 0.000% 0.000% 79 0.004% 0.010% 0.718% 1.156% 3.702% 8.162% 6.404% 0.000% 0.000% 80 0.001% 0.002% 0.257% 0.403% 1.603% 4.068% 2.857% 0.000% 0.000% 81 0.000% 0.000% 0.082% 0.123% 0.619% 1.825% 1.123% 0.000% 0.000% 82 0.000% 0.000% 0.024% 0.033% 0.213% 0.734% 0.387% 0.000% 0.000% 83 0.000% 0.000% 0.006% 0.008% 0.065% 0.265% 0.117% 0.000% 0.000% 84 0.000% 0.000% 0.001% 0.002% 0.018% 0.085% 0.031% 0.000% 0.000% 85 0.000% 0.000% 0.000% 0.000% 0.004% 0.025% 0.007% 0.000% 0.000%

Total Chance No One Beats or Ties Woods 46.904% Appendix K - 2006 PGA Championship Odds Tiger Woods Beats Contending Golfers Given Relative Positions Before Last Round If Tiger Shoots Likelihood Donald Weir Olgivy Micheel Garcia Choi Field Chance Tiger Wins 58 0.005% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 100.000% 0.005% 59 0.018% 99.998% 100.000% 100.000% 100.000% 100.000% 100.000% 99.998% 0.018% 60 0.070% 99.990% 100.000% 100.000% 100.000% 100.000% 100.000% 99.990% 0.070% 61 0.230% 99.960% 99.999% 100.000% 100.000% 100.000% 100.000% 99.959% 0.230% 62 0.656% 99.857% 99.994% 100.000% 100.000% 100.000% 100.000% 99.851% 0.655% 63 1.608% 99.548% 99.976% 99.998% 99.999% 100.000% 100.000% 99.522% 1.601% 64 3.396% 98.737% 99.918% 99.992% 99.996% 99.999% 100.000% 98.642% 3.350% 65 6.175% 96.887% 99.743% 99.967% 99.982% 99.994% 99.999% 96.582% 5.963% 66 9.668% 93.210% 99.282% 99.877% 99.935% 99.975% 99.993% 92.337% 8.927% 67 13.036% 86.836% 98.206% 99.597% 99.787% 99.915% 99.969% 84.656% 11.036% 68 15.138% 77.210% 95.982% 98.844% 99.381% 99.735% 99.883% 72.520% 10.978% 69 15.138% 64.539% 91.908% 97.081% 98.397% 99.266% 99.613% 56.028% 8.481% 70 13.036% 50.000% 85.295% 93.502% 96.298% 98.175% 98.877% 37.276% 4.859% 71 9.668% 35.461% 75.787% 87.196% 92.351% 95.932% 97.143% 20.168% 1.950% 72 6.175% 22.790% 63.673% 77.551% 85.810% 91.838% 93.596% 8.300% 0.513% 73 3.396% 13.164% 50.000% 64.749% 76.256% 85.215% 87.313% 2.418% 0.082% 74 1.608% 6.790% 36.327% 50.000% 63.956% 75.714% 77.663% 0.464% 0.007% 75 0.656% 3.113% 24.213% 35.251% 50.000% 63.629% 64.819% 0.055% 0.000% 76 0.230% 1.263% 14.705% 22.449% 36.044% 50.000% 50.000% 0.004% 0.000% 77 0.070% 0.452% 8.092% 12.804% 23.744% 36.371% 35.181% 0.000% 0.000% 78 0.018% 0.143% 4.018% 6.498% 14.190% 24.286% 22.337% 0.000% 0.000% 79 0.004% 0.040% 1.794% 2.919% 7.649% 14.785% 12.687% 0.000% 0.000% 80 0.001% 0.010% 0.718% 1.156% 3.702% 8.162% 6.404% 0.000% 0.000% 81 0.000% 0.002% 0.257% 0.403% 1.603% 4.068% 2.857% 0.000% 0.000% 82 0.000% 0.000% 0.082% 0.123% 0.619% 1.825% 1.123% 0.000% 0.000% 83 0.000% 0.000% 0.024% 0.033% 0.213% 0.734% 0.387% 0.000% 0.000% 84 0.000% 0.000% 0.006% 0.008% 0.065% 0.265% 0.117% 0.000% 0.000% 85 0.000% 0.000% 0.001% 0.002% 0.018% 0.085% 0.031% 0.000% 0.000%

Total Chance No One Outright Beats Woods 58.726%