Predictive Golf Analytics Versus the Daily Fantasy Sports Market

Claremont Colleges

Scholarship @ Claremont

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Predictive Golf Analytics Versus the Daily Fantasy

Sports Market

John O'Malley

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Claremont McKenna College

Predictive Golf Analytics Versus the Daily Fantasy Sports Market

submitted to

Professor Eric Hughson

John H. O’Malley

for

Senior Thesis in Economics

Fall-Spring 2018

April 19, 2018

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Acknowledgments

Thank you to the PGA Tour ShotLink Intelligence Program for their invaluable

assistance, it was greatly appreciated.

Thank you to all of my professors who have helped me along the way, especially

Professor Eric Hughson for his guidance throughout this project.

Thank you to my family and friends who have supported me throughout my life and

academic career.

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Table of Contents

Section I: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Section II: Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Section III: Data Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Section IV: Empirical Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Section V: Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Section VI: Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72

Appendix A: References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74

Appendix B: Table Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .79

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I. Introduction

Judging athletes by statistics has been common practice since the inception of

professional sports leagues. In recent years, however, advanced statistics have become a

part of the sports fan’s vernacular. In the 1980’s, Bill James created “sabermetrics,” which

is essentially a statistical analysis of baseball. The goal of sabermetrics is to identify which

player attributes and baseball strategies contribute most directly to winning games as a

team. The value of these statistics is being able to determine the market value of various

skills a baseball player can demonstrate.

“Sabermetrics” came to the forefront through

Michael Lewis’s book Moneyball, which described how the low budget Oakland Athletics

judged players to maximize expected wins and still fit their payroll.

Since Moneyball was

published in 2003, advanced statistics have exploded onto the scene across all major U.S.

sports, including golf. Indeed, in 1999, the PGA tour decided that advanced technology

was needed to track statistical performance, so they began the ShotLink program.

Until

2005, the system was only for PGA tour insiders use, when the ShotLink Intelligence

program began to allow access to professors and Ph.D. students.

The data supplied in the

ShotLink program contains common statistics, as well as advanced statistics called Strokes

Gained, which date back to the 2004 PGA season. Advanced statistics are generally used

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to judge a player’s true level of performance; however, they are just as useful when

attempting to predict a player’s future outcomes.

In this study, advanced PGA statistics will be used to create a predictive model for

a player’s score at a certain course. This model will be used to attempt to see if the daily

fantasy sports market for golf is efficient, specifically by testing if the players selected

based on the model can return a profit on DraftKings PGA contests. The PGA events that

will be analyzed are full field, 120 players or greater, stroke play events.

The PGA was established in 1916 by Rodman Wanamaker in New York. It was

created to grow the game of golf, by hosting tournaments and employing professional golf

instructors at clubs.

In 1968, the PGA Tour began as a subsection of the PGA, which was

for touring professionals instead of club professionals. The PGA is the largest professional

golf tour in North America, as it runs most week-to-week professional golf tournaments.

In 2018, there will be 47 tournaments hosted by the PGA Tour. Individual PGA

tournaments are held annually, generally being played at the same course year-after-year.

PGA tour events usually host 144 players, who compete for four days in what is called

stroke play. Stroke play is simply a competition in which the player who takes the least

total strokes wins. Each day, a player will play a round of eighteen holes, and after two

days, rounds, about half of the players will be cut from the event. The top 70 players,

including ties, will complete four rounds, and the individual who has taken the least strokes

over the totality of the four days will be named the winner. Certain events have modified

rules, for example the Career Builder Challenge has a cut after three days and is played on

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multiple courses, while the WGC-Dell Match Play is a match play event instead of stroke

play (meaning players compete head to head to move on in a seeded bracket). This paper

will focus on the standard tournaments.

The nature of golf is that each individual player is only indirectly competing against

one another, which is in stark contrast to most other professional sports. To win a

tournament, a golfer must shoot a lower score than all of his competitors, but there is

nothing a competitor can due to effect the play of any other individual. There is not an

offensive and defensive side to a golf tournament, as there is in baseball, basketball,

football, hockey, and soccer. Golf pits a collection of individuals against a course. This

should make statistical golf predictions more accurate than those of other sports. For

example, to predict the outcome of a baseball game there are many factors one must

forecast: How will the starting pitchers pitch? How will the defense play behind them?

Who will pitch after the starters? How well will whoever pitches after the starters pitch?

How will each individual hitter hit? The amount of possibilities that must be taken into

consideration is vast. In Golf, though, there is one question: Who will play best over the

course of four days? The “defense” is the course, and the player is on the offensive always,

as they attempt to shoot the lowest score possible. The “defense” in this case does not have

to be forecasted for as it would be in the other sports mentioned above, since it is a known

quantity. Most PGA Tour courses are played for multiple years, allowing for data to be

collected and analyzed. By analyzing said data, a course profile can be created, which is

entirely predictable from year-to-year. Since the courses are known, it should be possible

to predict which players will most likely play well at a given tournament, which can be

valuable information for someone trying to make money in the emerging Daily Fantasy

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Sports industry. With all this said, the idea that golf could be more predictable because of

less outside factors does not necessarily mean it is easier to win money in the fantasy sports

market, as one can assume that this would be an advantage for all skilled competitors.

Fantasy Sports began, loosely, in 1962 with rules for how fantasy football could

work being laid out. In 1963 the first draft occurred, with members of the Oakland Raiders

organization picking players from the NFL to make their own “fantasy” teams and compete

against each other based on how their drafted players perform on the field. By 1980,

Fantasy Football Leagues had become public and the idea of fantasy sports had spread to

baseball as well. With the internet boom in the 1990’s, fantasy sports went online and

spread rapidly. In 2006, the Unlawful Internet Gambling Enforcement Act (UIGEA)

became law, which took down the online poker industry, while allowing for fantasy sports

contests as they were deemed a game of skill and not chance. The language of the UIGEA

did not stipulate a difference between fantasy sports contests which lasted for the length of

the season and those that were solely for a given day. This lead to the rise of Daily Fantasy

Sports. FanDuel was founded in 2009, which was a platform designed for fans to pick a

roster of players competing on a given day in baseball, basketball, or football and wager

money on their lineup against other users of the site. Shortly after FanDuel was founded,

DraftKings was started in 2011, as their main competitor.

Both companies are now valued

at over a billion dollars.

As the companies’ user bases grew so did their creativity, with

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multiple different types of contests and additional sports added. DraftKings will be the

focus of this paper, as they were the first to offer Daily Fantasy Golf contests.

DraftKings offers many contests, but they can be grouped into two main categories:

Cash games and Guaranteed Prize Pool (GPP) games. Cash games are those with a greater

chance of winning, but with smaller overall prizes. Guaranteed Prize Pool contests are large

tournaments, with often thousands of players, in which only the top 20 or so percent make

money.

The payout scale is exponential, however, with the winner able to make many

thousand’s times their contest entry, for example the PGA Millionaire Maker Tournaments

pay $1,000,000 to the winner, with a lineup entry cost of only $20. DraftKings establishes

a limit to the amount of entries a single person can place in a contest, with some contests

allowing up to 150 entries. This study is focused on GPP tournaments, specifically the $3

entry fee, 150 lineups maximum, PGA Tournaments offered weekly.

Each $3 entry is a ticket to construct a lineup of golfers under a given salary cap.

DraftKings has a $50,000 salary cap for players, who they price on a scale generally from

around $6,000 to $14,000 based on DraftKings’ ranking of their ability. Each lineup must

consist of six golfers, and the total sum of the prices of the six must be $50,000 or less.

DraftKings Golf platform paired with the advanced statistics provided by the PGA

Tour and the nature of the game of golf yields an opportunity to possibly beat the market

in Daily Fantasy Sports and make a profit. This paper will look to analyze statistics of how

each course on the PGA Tour plays in order to create a regression equation that will predict

the player profile that should excel on the given course. The regression equation formed

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by regressing past statistical results on a specific course to a player’s score, coupled with

the regression of binary variables about a player’s history and form, should create a model

that predicts which players will generally score the lowest at a given tournament. Using

this information, players can be valued based on their DraftKings price and a group of

players can be identified as good selections. By distributing these chosen players in

different combinations throughout 150 lineups, hopefully, there will be a greater chance of

placing highly in GPP contests and making a profit. Ultimately, this study does show a

large positive profit, however, it is difficult to conclude success by the model with very

limited observable results.

This study is organized as follows: Literature Review, Section II, which details past

research on the predictability of golf through statistics, as well as how to value players and

create optimal lineups to win DraftKings contests for sports other than golf; Data Review,

Section III, which is an overview of the data used, detailing each variable and its

importance; Empirical Process, Section IV, which explains step-by-step the general

process for the creation of the predictive model for a certain tournament, as well as the

process for valuing and selecting players to create 150 DraftKings lineups; Results, Section

V, which gives a detailed explanation of the results of this study, looking at the most

successful week individually, as well as the overall net gains/losses; and Conclusion,

Section VI, which brings the results together and details the further research that could be

conducted and the information that would be needed to improve this model.

II. Literature Review:

Success on the PGA tour is often defined by a player’s overall earnings for the year,

so there have been many empirical studies as to what a player’s traits, statistics, yield the

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greatest dollar value. Davidson and Templin (1986) was the first published research

document that delved into the effect of different golf skills on a player’s success, which

they measured by earnings and season long scoring average. Their results showed that

specific skill set differences had a greater effect on scoring average than earnings but that

certain skills were clearly more beneficial.

In the years since Davidson and Templin (1986), many studies have been done to

attempt to show the effect of certain skills on PGA performance, with putting and accuracy

consistently being the skills most correlated to success. Some significant publications are

Shmanske (1992), Finley and Halsey (2004), Alexander and Kern (2005), and Peters

(2008), all of which are studies that show which statistics lead to the best year-long

performance, meaning, in large part, which statistics yield consistency. There is

significantly less published work on what may lead a golfer to be successful on any given

week.

Shmanske (1992) observes strong putting to be the most significant characteristic

of a successful golfer, in terms of earnings. As time goes on, the PGA tour and its courses

evolve, with the main change in the past decades being increased length. Alexander and

Kern (2005) attempted to review the previous publications claiming putting to be the key

to earnings, with the thought that longer courses may put a higher premium on driving

distance. Their results still showed putting to be the main contributing factor to earnings,

despite it becoming marginally less so than in past years. Peters (2008) further corroborated

the importance of putting on earnings, while also looking at the exterior factor of

experience, which proved to have a positive impact as well.

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Finley and Halsey (2004) looked into the effect of new stats, Bounce Back and

Scrambling, on scoring average, while also looking at Simple Scoring Average versus

Adjusted Scoring Average as a predictor of earnings. Simple Scoring Average is merely

the average score of each round an individual plays over the course of the season, while

Adjusted Scoring Average takes into account the average score of each player who played

the round and adjusts it to see if an individual played better or worse than his competitors.

Their finding that Simple Scoring Average was not highly correlated to earnings is

significant, as in the past earnings and scoring had been used simultaneously as measures

of success on tour. Adjusted Scoring Average is shown to be more important for earnings.

More statistics evolved in the late 2000’s to be used to determine a golfer’s

performance. Brodie (2008) and (2012) delved into new data being provided by the PGA

tour, ShotLink data. The data was used to create a comparative metric for the relative value

of a single putt and then extrapolated that number to accumulate the relative number of

strokes gained or lost to the average player in a tournament. The idea of how many strokes

could be gained or lost in relation to the average player in a tournament field, would

become known as Strokes Gained statistics, which now are used for each shot on a golf

course, broken into Off the Tee, Approaching the Green, Around the Green, and Putting.

Despite the array of work highlighting which golf skills most affect success,

whether judged by scoring average or earnings, there is very little public research on which

statistics yield success at any of the specific courses played annually on the PGA Tour.

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With there being minimal work on course specific results for PGA tour players,

there is no published work on how to predict performance for PGA Daily Fantasy sports.

Daily Fantasy sports have exploded in the past decade behind leading companies,

DraftKings and FanDuel. Both companies provide contests for PGA events, however, there

is no work published on how to successfully profit off of said contests.

There is published work, however, on the merit of statistical modeling to profit off

of DraftKings NBA contests. Barry, Canova, and Capiz recently completed a study to see

if they could improve their chances of consistently winning money on DraftKings NBA by

analyzing projected statistics relevant to DraftKings point scoring, as well as factors that

could affect performance, such as rest and the opposing defenders. They managed to show

improved accuracy for their projections when taking into account these factors.

Hunter, Vielma, and Zaman studied how to maximize the ability to win a contest

with a top-heavy payout structure. They conducted this study using DraftKings Hockey

and Baseball contests, in which a large percentage of the prize pool was paid out to the

winner. Their hypothesis was that by putting in a large amount of entries, all of which

having a large expected point value, a large volatility, and minimal correlation to each

other, one would have the best chance of winning. Despite a small sample size, they yielded

large enough winnings to not reject their hypothesis.

My study will look to expand upon both research into PGA tour success and also

Daily Fantasy Sports success. There are no published papers which focus on PGA Daily

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Fantasy Sports. This study will provide new information as to which player statistics and

other exterior factors affect a PGA player’s success on a given course during a specific

week, while also exploring how these results can be used to profit on DraftKings PGA

contests.

III. Data Review

There were forty PGA Golf tournaments played during the 2017 Calendar season,

however, the sample used for this project is much smaller. Only tournaments which hosted

a full field of players, 144 or more, were considered. Furthermore, certain tournaments are

not played on the same course each year, for example the three majors (US Open, Open

Championship, and PGA Championship), which makes past years’ statistics irrelevant to

the coming year’s event. Beyond changes in course and number of participants, DraftKings

only provided the type of contest this model is created for (150 entry GPP) during the first

portion of the season, before changing the number of entries allowed into their contests.

Ultimately, there are nine tournaments, which fit the parameters necessary to test this

hypothesis for conclusive results, and another six which were simulated and can be looked

at to see general trends.

The data used was provided by the ShotLink® Intelligence Program, which began

in 2005 and expanded in 2008 with a partnership with CDW. The program allows for

professors and students to study advanced PGA statistics that are not made available to the

public. The ShotLink database contains common statistics dating back many years,

however, the highly advanced Strokes Gained statistics are only available since 2004.

Strokes Gained statistics were developed by Mark Broadie of Columbia University, as a

way of measuring a player’s performance in specific skills against those of his competitors.

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Strokes Gained Total takes a player’s score for a round and compares it to the average score

of the rest of the players in the competition during that round.

The winner of a tournament

will lead the field in Strokes Gained Total. Beginning in 2014, the PGA tour began to split

Strokes Gained Total into two categories: Strokes Gained Tee-to-Green and Strokes

Gained Putting.

For the purposes of this study, data before 2011 will not be examined. Individual

tournament data from past years is only provided for those players who make the cut, with

the cut being the top 70 players and ties, so for each year’s hosting of the event there are

70+ data points. The previous three years’ results at an event will be used to predict the

current year, so for each regression there will be 210+ data points used.

There are eight independent variables used to predict the dependent variable,

Scoring Average. Three binary variables: History, Form, and Weather, are regressed

against the difference between historical projections of the individual’s scoring averages

from 2014-2016 and the true outcomes they achieved to further adjust the predicted

dependent variable. These binary data points are collected from a review of the historical

section of the ShotLink database, which shows individual player’s finishing position results

at events. The data ultimately input into the regression equation to predict an individual’s

score is the player’s season long averages in the eight variables examined.

Dependent Variable – Adjusted Scoring Average: This is a weighted statistic of

how an individual player scored with an adjustment for how the rest of the players in the

field scored in the same round. The average score of each of the four rounds of the event

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will be subtracted from the course’s par score, with the four resulting differences being

added to the total strokes an individual took over the course of the tournament. The sum of

the total strokes and these adjusting differences is then divided by the number of rounds

played, four, yielding a weighted scoring average.

Independent Variable 1 – Driving Distance: A distance measured in total average

yards a player hits the ball off of the tee on all par 4 and par 5 holes, with the accuracy of

the shot being ignored. The statistic attempts to show how far on average a player will hit

the ball using a Driver. ShotLink uses GPS and laser measurement equipment to determine

the total amount of yards a drive covers. In 2016, 85% of the shots used to determine a

player’s average driving distance were confirmed to be shots hit with a Driver, however,

15% were unconfirmed which club the player used to hit the ball off the tee. Not knowing

what club was used by a player can skew the driving distance statistic, as a player who

chooses to hit 3-Wood would have hit the ball farther had he chosen to use a Driver, yet

the distance is attributed to his driving distance. Ultimately, this statistic is still the best

measure of a player’s ability to hit the ball a certain distance off of the tee.

Independent Variable 2 – Driving Accuracy Percentage: A percentage of how

many of a player’s tee shots on par 4 and par 5 holes end up on the fairway. The statistic

does not take into account the club hit off of the tee, so a player with a high percentage

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may not necessarily be hitting their Driver more accurately but may, in reality, just be using

a different club.

Independent Variable 3 – Strokes Gained Tee-to-Green: The sum of a player’s

Strokes Gained Off-the-Tee, Strokes Gained Approach-the-Green, and Strokes Gained

Around-the-Green. Conversely, it is a player’s Strokes Gained Total – Strokes Gained

Putting. Strokes Gained Total on a hole is determined by a player’s score minus the average

score on all holes of the same distance. In other words, hypothetically, if a hole is 450 yards

and the average score on holes of said length is 4.5, then a player who scores a 4 will have

accumulated .5 Strokes Gained Total. The par of the hole has no affect. In general, a

player’s Strokes Gained Tee-to-Green represents how effectively a player is at getting the

ball to the green at a distance closer than expected to the hole. The Strokes Gained Tee-to-

Green for each hole is added up to determine Strokes Gained Tee-to-Green for a round.

The season-long Tee-to-Green statistics are an average of each calculated round played.

See Strokes Gained Putting below for more details on what is subtracted from Strokes

Gained Total to find Strokes Gained Tee-to-Green.

Independent Variable 4 – Strokes Gained Putting: A measure of the number of putts

a player takes against the projected number of putts the average PGA tour player takes

from a certain distance from the hole. For example, hypothetically, if a player is 20 feet

from the hole and on average it takes a PGA Tour player 1.8 shots to get the ball in the

hole from 20 feet, then a shot made from 20 feet would yield .8 Strokes Gained Putting.

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The number of strokes gained or lost on each putt over the course of eighteen holes is

accumulated to find a Strokes Gained Putting for the round. The season-long Strokes

Gained Putting statistics are an average of a player’s Strokes Gained Putting over the

number of rounds played.

Independent Variable 5 – Scrambling Percentage: A measurement of how likely a

player is to make par or birdie after missing the green in regulation. To be on a green in

regulation is being on the green in two strokes less than the par of the hole. To miss a green

in regulation means that a player’s third shot on a par 5, second shot on a par 4, or first shot

on a par 3 lands off of the green. Scrambling percentage looks at every time a player is in

such a position and finds the percentage of times the player still makes birdie, by making

the shot from off of the green, or par, by making it in to the hole using just two shots from

off of the green. The statistic emphasizes players who are good at chipping and pitching

from around the green.

Independent Variable 6 – Greens in Regulation Percentage: The total amount of

times a player makes it onto a green in regulation divided by the number of holes played.

As explained above under Scrambling Percentage, a green in regulation is a player being

on the green in two strokes less than the par of the hole. This statistic highlights a player’s

ability to hit their irons or wedges onto the green.

Independent Variable 7 – Putts Per Round: The sum of the total number of putts a

player hits divided by the number of rounds he has played. Does not take into account

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distance of putt or how many strokes were hit before putting, both of which affect the total.

Players who hit the green in regulation more frequently will likely take more putts, whether

they are better putters or not, so the statistic can be skewed as to who the best putters truly

are.

Independent Variable 8 – Sand Save Percentage: A measurement of how likely a

player is to make par or birdie after missing the green in regulation with the ball sitting in

a sand bunker. Calculated in the same way as Scrambling Percentage, except with the

condition of the ball being in the sand instead of just off the green in any location. This

statistic highlights who is best at hitting the ball accurately out of a sand trap.

Binary Variable 1 – History: Certain players consistently play well at courses

which do not fit their statistical profile. In order to take this into account, a player’s past

performances at a course must be taken into account. If enough data was collected, each

individual who has played the event more than once could be projected for the given year

and observed to either underperform or outperform their projection. Those who continually

outperformed what was projected would be considered to have good history, which would

be taken into account for the current year. However, not enough data is being analyzed in

this study to be able to go back far enough to project each player’s individual average over

or under performance. With that being said, a player’s history is still significant, so it must

be incorporated in some other way. To do so, history is tracked for each past participant

and then a standard linear regression is run on the sample of players with the independent

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variable being a qualitative measure of a player’s history and the dependent variable being

the difference between the projection and real score. If the regression coefficient is

statistically significant and negative, then it will be taken account into the final projection

equation, as that means that players who were deemed to have good course history in the

past have generally outperformed their projection by the given coefficient. The following

chart dictates whether a player is given a 1 for good course history or a zero for poor history

or none:

Table 1: Course History

If a player has played the tournament four or more times, then they solely need to

have made the cut in 75% or better of the time. A player who has played the tournament

less times, though, needs to have performed better. Someone who has played only once

must have finished in the top five to be labeled a 1 for good course history. One that has

played the tournament twice must have made both cuts and finished in the top ten once.

Lastly, someone who has played the tournament three times must have made the cut at least

twice and must have a top ten finish.

Binary Variable 2 – Current Form: Certain players may not be statistically suited

for a certain course nor have played the course well in the past, however, if a player is

Times Played

Made Cuts

Top 10

Top 5

75%

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playing extremely well in past weeks, they may continue their hot streak. The “hot hand

fallacy” is often discussed by sports statisticians, as statistically players don’t get “hot,”

since streaks of success are shown to be merely random occurrences that are to be expected

from a large sample size.

In order to examine the “hot hand” in golf, current form will be

used as a binary variable. A player’s form is still possibly significant, so it must be

incorporated in some way. To do so, form is tracked for each past participant and then a

standard linear regression is run on the sample of players with the independent variable

being a qualitative measure of a player’s current form and the dependent variable being the

difference between the projection and real score. If the regression coefficient is statistically

significant and negative, then it will be taken into account in the final projection equation,

as that means that players who were deemed to have good current form leading into the

tournament in the past have generally outperformed their projection by the given

coefficient.

Since most PGA Tour golfers do not play every week, multiple weeks will have to

be looked at to determine who has been playing well recently. For the purpose of this study,

the past six weeks will be viewed and a player must have played in three of them to achieve

a 1. The following chart dictates the scenarios in which players will receive a 1 for good

current form:

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Table 2: Current Form

Times Played Past 6 Weeks

Made Cut

Top 10

Binary Variable 3 – Weather: Rain and wind can have a serious impact on PGA

Tour events. Certain players are more equipped to handle these challenges, so this needs

to be taken into account if possible. The problem is that weather is hard to predict, with

forecasts often being wrong. For the purpose of this study, tournaments that are expected

to have wind over 20 mph on three or four of the days, and tournaments that are given a

75% chance or greater of rain on the first two days will take weather into account. The

main issue with wind and rain is the affect it has on the ball when it is in the air. The longer

and higher a ball is traveling through the air the larger the effect of the inclement weather,

so players who naturally hit the ball lower are at an advantage.

When weather is deemed

to be a factor, players who have an average apex height of their shots in the bottom 50%

of the field will be given a 1 that indicates good play in bad weather. By looking at past

tournaments that had weather as a factor, player’s binary score for weather play based on

apex height can be regressed on the difference between their score and their projection. If

the result of this regression shows that apex height is significant to performance during the

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past tournaments with inclement weather, then it will be added into the projection for the

coming week with forecasted bad weather.

IV. Empirical Process

Executive Summary:

This study will create a model for identifying a portfolio of players to select for

weekly DraftKings PGA Golf tournaments. The process will first take historical

predictions of the past three years, in order to see how similar the projected scores were to

reality. The same standard linear regression equation that is used to predict the past three

seasons will also be the beginning of our predictive equation for the 2017 event, before

being adjusted to take into account binary variables. The binary variables will be found to

be significant or not based on if they had significance when regressing them against the

difference between projected and real past results. Once the binary variables have been

incorporated into the base projection equation for 2017, the player’s statistics for the

current season will be input to find an expected score. Twenty-five players will be selected

based on their projected scores and the value of them based on their given DraftKings’

prices. Selected players will be randomized into 150 lineups to meet the DraftKings Salary

Cap and the results will be judged based on the net returns.

1.1 - Historical Predictions

The first step in predicting a player’s performance in a specific upcoming PGA

tournament is to look at past results. Tournaments’ names change frequently with the

change of sponsors; however, the vast majority of PGA events are played at the same

course for a substantial number of years. The fact that many tournaments are always played

on the same course makes past statistics very significant to the event in any given year.

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Even when the players participating in an event change, the skills that are most necessary

for success on a certain course, at a specific tournament, should remain unchanged over

the years. The first step for predicting the success of participants in a coming year’s

tournament is to attempt to predict the performance of players in the event in past years.

For this model, the previous three year’s tournament results will be used to predict any

desired year. This test was done for the 2017 PGA Tour season, however, historical models

were made for the 2014, 2015, and 2016 seasons as well, so 2011-2016 data is relevant.

The general model for the standard linear regression used to predict success will

have the dependent variable of player n’s Scoring Average and the independent variables

being player n’s performance in the statistics listed in the data section: Driving Distance

(DD), Driving Accuracy (DA), Strokes Gained Tee-to-Green (SGTG), Strokes Gained

Putting (SGP), Scrambling Percentage (SCRAM), Greens in Regulation (GIR),

Putts/Round (PR), and Sand Save Percentage (SAND). Taking the data from 2011, 2012,

and 2013, the linear regression should produce an equation that will predict how a player

will score in the 2014 tournament:

(1)

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If certain variables are not shown to be significant, then they are removed from the

data set, and the regression is run once more, but this time with fewer independent

variables. Once an equation is found for 2014 with each statistic included being significant,

the process will be repeated again using the data from 2012, 2013, and 2014 to predict the

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2015 event, the data from 2013, 2014, and 2015 to predict the 2016 event, and finally from

2014, 2015, and 2016 to predict the upcoming 2017 event. These four regression equations

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historical equations are necessary for finding how much of a difference there was between

the projection and reality in 2014, 2015, and 2016, so, hopefully, other variables can be

added that will take into account some of this error. The 2017 equation is the base equation

for predicting the current year before being adjusted with binary variables.

1.2 – Independent Variable Inputs

Once equations are in place to predict a player’s performance for a given year,

inputs must be decided on. Players’ season long statistics will be used from 2013, 2014,

2015, and 2016 to predict specific events in 2014, 2015, 2016, and 2017, when the event

takes place during the first ten events of the calendar year, as players have not played

enough leading into those first events for their season long averages to be indicative of

their true skill set. By looking at the previous year, we are given a wider look at a player’s

skills, however, we do sacrifice the possibility that a player has improved or worsened

significantly since the end of the past season, which is always possible in sports. For the

event of the season and on, season long averages for the year of the event in question

will be used and input into the SCR equation. Accepting that players’ season long averages

are good predictors of their performance over multiple rounds still leaves a large margin

for error, however, it is the best way to define their skills. The result of inputting season

long average statistics for each individual should yield a projected score above or below

the tournament average based on how well the individual tends to perform in the significant

skills needed to optimize performance.

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1.3 – Binary Variables and Adjusting Projection

Using past data becomes significant for checking how well the model fits to the

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player’s actual Scoring Average was. This comparison can be expected to yield a small

positive or negative difference for each player depending on if they outperformed or

underperformed on their season averages during the given week’s tournament. Once these

differences are found, the question is why an individual may have outperformed or

underperformed from their season statistics. There are many factors that may play a role,

which are not quantifiable. Some examples of factors that almost certainly affect a player

are illness, travel/time change, sleep, family or personal problems, motivation, etc. There

are however other factors, which despite the PGA not offering directly as statistics, can be

used to try to diminish the error in the predicted Scoring Average and the player’s actual

one. The three that will be focused on are all binary variables, which are explained in the

Data section above, Course History, Current Form, and Weather. To determine the effect,

if any, that these variables may have on a player under or out performing his projected

score, a simple linear regression will be run with the dependent variable being player n’s

projection error (Real SCR – Projected SCR) and the independent binary variables Course

History, Current Form, and possibly Weather. The equation is:

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The variables must be in the 95% confidence interval to be considered for the final

equation. Along with being significant at the 95% level, the variables must also decrease

the average error between projection and real score for the past three years. To check if this

is the case, first the average error will be calculated based on our past results and then the

past projections must be altered to account for the binary variables effect. To account for

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depending on n’s individual performances. The adjusted past projected scores are then

subtracted from the player’s real score from that year’s event to find an individual’s new

projected difference, error. The adjusted errors are then averaged, and the average is

compared to the average error before accounting for the binary variables. If the newly

found adjusted average difference is less than the original average difference, then the

binary variables effects will be included in the predictive equation for 2017. The equation

to predict 2017 maintains the initial betas but now includes any significant binary variables

as well:

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1.4 – Player Selection

Once the predicted scoring averages are found based on the equation above, it is

time to figure out how to select the best core, portfolio, of players to use on DraftKings.

DraftKings typically posts its different contests, as well as player prices, on the Monday

before a tournament, so this step must be completed shortly before the tournament tees off.

As is discussed above, there are many different types of games on DraftKings, however,

for the purpose of this experiment the large guaranteed prize pool contests will be the focus.

In DraftKings largest weekly PGA contests, an individual player is allowed to submit up

to 150 lineups. Since payouts decrease exponentially from the top, with the top ten

finishing lineups securing a massive percentage of the overall winnings, the best way to

return a profit is to maximize your chance of having one or more lineups fall in that top

ten. In order to maximize potential winnings, this model will be used to create 150 distinct

lineups each week.

Each lineup on DraftKings is made up of six golfers, with a total salary cap of

50,000, so when constructing 150 lineups, there must be 900 players selected at a maximum

cost of $7,500,000. Players are given a different price on DraftKings each week. The 900

players must be made up of a portfolio that takes into account the individual’s projection,

expected ownership, and price. One of the main difficulties is deciding how many players

to pick and how many to fade entirely. For this model, 25 players will be selected each

week. Due to price constraints and errors, certain players will not be picked or will be

picked despite how they rank based on the SCRADJ equation.

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To maintain balanced teams, which are not solely based around the top priced

players and the highly volatile bottom priced ones, there are restrictions placed on how

many expensive players will be owned on any given week. The rules are as follows:

1. Only 3 Players above $10,000 can be owned;

2. 2 players over $11,000 can be owned when players in the field are priced over

$12,000; and

3. If highest priced player in the field is <$12,000 then only own one player above

$11,000.

These stipulations limit the amount of high priced players that will be picked. This

eliminates the possibility of fully diversifying among the top players, who all could

hypothetically win a tournament any week, however, this is accepted, as to fully benefit

from a player’s performance the player must be owned in a large percentage of lineups.

What is meant by this is that to beat the field on average an individual must have a higher

percentage of a player in his 150 lineups than is owned by the contest participants as a

whole. For example, if Player A produces the most points on DraftKings and is included

in ten of the 150 lineups you have entered, while Player A is owned in 50% of all lineups

entered in the contest, then Player A’s success is likely hurting your portfolio of lineups as

a whole. By selecting only a few of the high priced options, an individual can have them

highly concentrated throughout the 150 lineups, allowing for a massive advantage when

the players selected play up to their projection.

Along with the stipulations that reduce the players allowed to be picked for this

model, there are also qualitative measures for picking certain players, who for some reason

are not projected to perform well at the event. These rules are purely based off of

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DraftKings being a predictive model itself, and one that frequently has errors. Players who

are priced under $7,000 on DraftKings but that reside in the top 50 of the Official World

Golf Rankings (OWGR) will be automatically selected to be one of the 25 players used. A

low price on a top 50 player can generally be attributed to recent poor play or time off,

however, said players are deemed by this model too talented to not be selected when near

the minimum price.

Now the remaining 25 spots must be filled. The top 15 lowest projected scoring

players based on SCRADJ will be selected, taking into consideration the rules stipulated

above. Generally this yields fairly high priced players, as better players tend to be projected

to score better on any given week. In order to pick cheaper players to fill out the rest of the

player portfolio a simple value ratio is used, which reads:

(4)

VALUE = DK PRICE/(PROJRANK/DKRANK)

DK PRICE, DraftKings price, is given. PROJRANK, projection rank, is a 1 to 144

ranking based on the projected scoring average from SCRADJ for each player in the field.

DKRANK, DraftKings rank, is a rank from highest to lowest price, with the highest price

being 1 and any players of equal price being tied for the same rank. For example, if the top

three players were priced $11,000; $10,000; $10,000, then the $11,000 player would be

DraftKings Rank 1, while the two $10,000 players would each be DraftKings Rank 2. This

value ratio will highlight players who are less expensive on DraftKings than the projected

score would indicate. The remaining spots from the initial 25 are filled by the top ranked

VALUE players. This equation could yield flaws based on scale if comparing players of

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drastically different prices/ranks, however, because it is only selecting the final ten players

who will be chosen, each is generally from the lowest price range, so the issue of scale is

less of a concern.

1.5 – Weighting

Above touched upon the idea of needing to have a higher concentration of a player

than the overall participants have in order to gain an advantage if said player performs well.

The determination of how much of each player to own is tricky, since it cannot be known

exactly how popular a pick a player will be on a certain week. For this reason, to simplify

the process, instead of looking at individual player’s average ownership, this study will

focus on price tier ownership. Historically, players on DraftKings who are priced higher

will also be owned at a higher percentage on average. This is in large part because there

are less players in the top price tiers than in the lower ones. While there may only be four

players above $10,000, it is likely there are around ten players in the $8,000’s, more in the

$7,000’s, and even more in the sub $7,000 range. This unequal dispersion causes less

differentiation among high priced players and more among low priced ones, so naturally

high priced players are owned in a larger amount of lineups, while the low priced ones are

more randomly strewn throughout. Once determining projected ownerships by tier, there

must be an adjustment to have a higher percentage in the 150 lineups being created. In

other words, to gain an advantage a higher percentage of each player will be held than is

projected to be held by the total entries to the contest. To go massively overweight the goal

will be to have twice the percentage amount of each player picked. The ownership

percentages that will be used for the projection for the overall contest and also in the 150

lineups being created are as follows:

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Table 3: Ownership Percentages

Player Price

Expected Ownership

Portfolio Ownership

Percent

>$9,990

20%

40%

$8,900<Price<$10,000

15%

30%

$7,900<Price<$9,000

12%

24%

$6,900<Price<$8,000

10%

20%

Price<$6,900

10%

In an ideal scenario, these weights will allow for 150 lineups to be created within

the $7,500,000 total salary cap, however, far more frequently adjustments have to be made.

1.6 Adjusting Weights

To check for whether adjustments need to be made for player weighting, first it

must be determined if the salary cap has been passed and by how much. First, multiply a

player’s percentage ownership by 150 and then, take the resulting number and multiply it

by the player’s DraftKings price. For example, a $10,000 player would be in 40% of

lineups, so .40*150=60 total and 60*$10,000=$600,000. Once the total overall cost of

owning each player is found, they can be summed, and if the resulting number exceeds

$7,500,000, then adjustments must be made to how much of each player is owned. The

first step to do this adjustment is to move ownership from the most expensive players to

the least expensive by price tier. Remove five from each of the top price tier players and

disperse them to the next price tier. For example, if your top tier is above $9,900, then

remove five of the 60 lineups from each member of this tier and disperse the additional

five or more slots to each player in the $8,900 to $10,000 tier. If the total salary is still

higher than $7,500,000, then take five off of each of the second-tier players and redistribute

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them to the third tier. Continue this process of redistribution until the total salary is under

$7,500,000.

1.6 – Lineup Creation

Now that the portfolio of 25 players has been established, as well as how many

times each player will be used in a lineup while fitting the salary cap ($7,500,000) and total

number of players (900), lineups must be created. In order to eliminate selection bias,

lineups ought to be randomized. In order to randomize the lineups efficiently, they must be

done in tiers, so that they do not grossly exceed the $50,000 salary cap. Excel’s

RANDBETWEEN(x,y) function can be used to randomize once players are allotted a

number. In order to create tiers, start from the highest owned players and work down. Tier

1 will be comprised of the highest owned player, followed by the next highest owned

players until the total number of lineup slots allotted to tier one surpasses 150. For example,

if the top two players are in 60 lineups each and the third player is in 45 lineups, then these

three players would comprise tier 1, as 60+60+45=165, which is greater than 150. Tier 2

and so on will be formed in the same way, with the remaining highest owned players being

added together until their total amount of selections exceeds 150 or is the last remaining

players. Once the tiers are created they will be randomized individually. Tier 1 is

randomized throughout the first column of excel, with the spillover past 150 being

randomized into the second column. Tier 2 will then be randomized into the second column

with the spillover being randomized into column 3. This process will continue until six

columns are filled with 150 players. The sum of the prices of each row are then summed

to make sure the players fit in the $50,000 salary cap. For the lineups which are too

expensive, players will be switched with the lineups that are the farthest under the salary

!"#$%%&'(*+(

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cap, so that all 150 are playable on DraftKings. In the case of duplicate lineups, players

can be switched from lineups that are under the salary cap to create greater randomness.

The lineups would then be entered into the DraftKings system.

V. Results

Week 1 - Sony Open

The Sony Open is the first full field PGA event of the calendar year. The tournament

has been played at Waialae Country Club in Honolulu, Hawaii since 1965.

Regressing

the chosen statistics from the 2014-2016 gives the predictive base equation for the 2017

event:

(5)

!"#

/PQR>?@E

( STUVVWW X U SYYZ !232 X U WS[\ !25 X ]U\SWW^2:# * ]UTYVY^5#

* =

((((((((((((((((((((((((((((((((((((((((((((((((((((((((

(J2&G7(X&%%&'3(45/G'(!?&G(8G(W$E$88(T/%I(]/L2G$6&G73;(-,(b$GL$2'()@-A3(34&9=4/M&0#&13($99& : : &< (-=(

>?28%()@-A3(https://www.thoughtco.com/sony-open-in-hawaii-golf-tournament-1565848.(

!"#$%%&'(*,(

(

!!!!!!!!!!!!!!!!!!!!!!!Table!4:!

!!!!!!!!Sony!Regression!Output!

(

7(=.(<<*&",5/+/*</*#<,

.(5fL$2&(

@FV*=-(

(

><K(.(5fL$2&(

@FV*,V(

(

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Strokes Gained Tee-to-Green, Strokes Gained Putting, Greens in Regulation, and

Putts/Round were significant statistics at the 95% level, while Driving Distance, Driving

Accuracy, Scrambling, and Sand Save Percentage were insignificant. This equation

emphasizes players who are very good at hitting approach shots to the green and putting,

while devaluing off the tee driving and accuracy skills. Waialae Country club is 7044 yards,

making it one of the ten shortest courses played annually on the PGA Tour.

Being such

a short course, any player on the PGA tour can hit the ball far enough off the tee to reach

the green easily with their second shot on par 4’s, and because it is a par 70, there are only

two par 5 holes which would require a long drive off the tee to reach the green in two shots.

These aspects of the course make a player whose strength is hitting the ball onto the green

((((((((((((((((((((((((((((((((((((((((((((((((((((((((

(4]B&(-@(P/GQ&:7($G<(-@(5B/27&:7([/L2:&:(/G(7B&(ST>(]/L2(8G()@-,h-O3;(-O(Y&9&60&2()@-O3(

34(>&%@N(?<N(/0#&12,$99&::&<(-=(>?28%()@-A3(

https://thegolfnewsnet.com/golfnewsnetteam/2016/12/16/longest-shortest-courses-pga-tour-2015-2016-

101774/.(

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close to the hole with their approaches and putting well once on the green the ideal player.

A player’s ability to hit a drive far off the tee or to be accurate off the tee with a drive is

insignificant when the course is so short, as most players will be able to hit their more

accurate irons off the tee and still reach the green with their next shot. Scrambling is also

understandably insignificant, as with such an emphasis on reaching the green in regulation,

those who are continually scrambling are likely not scoring well no matter how successful

they are being. In other words, players need to be on the green in regulation for a chance

to make birdies, and scrambling to make pars will not let a player compete.

In order to sharpen the equation to take into account a player’s history at the course,

the 2014, 2015, and 2016 tournaments must be back checked. Linear regressions of the key

statistics from 2011-2013 to predict 2014, from 2012-2014 to predict 2015, and from 2013-

2015 to predict 2016 are found to have the same four significant variables with slightly

differing coefficients depending on the year. The player’s season long averages from the

year in question for the four statistical categories are then inserted as the independent

variables to predict their score for the tournament. Then, subtracting the projections from

their real average scores from the event differences are found, which are regressed on each

player’s individual binary course history. Current form and weather are not analyzed for

this tournament, as it is the first tournament of the year so there is no current form data and

the weather is not expected to be a factor. The regression yields:

(6)

-:F ( X]U_`W_[^H:!3 * =

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Table 5:

Adjusted Sony Regression Output

So now, adding this to the initial 2017 projection equation:

(7)

!"#

/PQR>?@E

( STUVVWW X U SYYZ !232 X U WS[\ !25 X ]U\SWW^2:# * ]UTYVY^5#

X U _`W_ H:!3 * =

The players playing the 2017 tournament are then projected by inputting their 2016 season

long statistics into the equation, as well as a 0 or 1 for course history depending on whether

they had met the qualifications detailed. Valuation based on the projections and lineup

creation detailed above leads to the 150 lineups that were set for the DraftKings Sony Open

$3 GPP contest.

The net result of the $450 investment was a loss of $356. Eighteen of the 150

lineups placed in the money. Four of the lineups returned the $3 investment along with $3

of profit. Fourteen lineups returned the $3 investment along with $2 of profit. Fifteen of

the twenty-five players selected made the cut for a 60% made-cut rate. This percent is too

low to be profitable without extreme luck in the randomization of rosters, as rosters

generally need at least five of six players to make the cut. Justin Rose who was the top

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projected value by the model and the seventh highest priced player on DraftKings finished

second in the event, however the cheaper value players did not perform to the projections,

resulting in a losing week.

Week 2 – CareerBuilder Challenge

The CareerBuilder Challenge is the second full field PGA event of the calendar

year. The tournament is played at three courses in the Coachella Valley in Southern

California. Despite being played at three courses, each have similar layouts, as the dessert

golf courses are made in the same style. The PGA West Stadium course is played twice, so

a player’s ability on it is most significant.

Regressing the chosen statistics from the 2014-

2016 gives the predictive base equation for the 2017 event:

(8)

!"#

6a6>?@E

( YWU_[W` X U \T_V -- X U \VZ -. X U VT !232 X U \W_[ !"#.8

X U \_T[ 2:# * ]USS[T^5# * =

((((((((((((((((((((((((((((((((((((((((((((((((((((((((

(45/G'(!?&G(8G(W$E$883;(-)h-,(b$GL$2'()@-=3(>&%@M4+""(%0#&12,$99&::&<(-=(>?28%()@-A3(

https://www.golfchannel.com/tours/pga-tour/2017/sony-open-hawaii/.(

(4>0/L7(7B&(]/L2G$6&G73;(M+.((.-9*%)(.M4+%%("=(0#&12,$99&::&<(-=(>?28%()@-A3(

https://www.careerbuilderchallenge.com/about-the-tournament.(

!"#$%%&'(*V(

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!!!!!!!!!!!!Table!6:!

CareerBuilder!Regression!Output!

(

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Driving Distance, Driving Accuracy, Strokes Gained Tee-to-Green, Scrambling

Percentage, Greens in Regulation, and Putts/Round were significant statistics at the 95%

level, while Strokes Gained Putting and Sand Save Percentage were insignificant. The

courses played for this tournament are all listed in the ten easiest courses played on tour,

so in order to be successful a player must be well under par, so birdie making is key. The

courses are all about the same length, around tour average, and all are par 72.

Par 5

scoring is key, as players will play sixteen par 5’s over the four days. The emphasis on par

5 scoring makes Driving Distance and Driving Accuracy significant factors, since those

who can potentially hit their drive far enough and accurate enough to be close enough to

((((((((((((((((((((((((((((((((((((((((((((((((((((((((

(S$7289N(#$'/3(4U$G7$:'(T/%I(S89N:C()@-=([$2&&20L8%<&2([B$%%&GQ&(5%&&?&2:3(57$27:(`(S2&a8&E3;(-O(b$GL$2'(

)@-=3(7&/&!O'(./<0#&12,$99&::&<(-=(>?28%()@-A3(http://rotoexperts.com/118134/2017-careerbuilder-

challenge-picks-fantasy-golf-picks-sleepers-starts-course-preview-careerbuilder-picks/.(

!"#$%%&'(+@(

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the green to hit their second shot onto it will have the best chance to make birdie or even

eagle. Scrambling Percentage would not seem to be highly valuable on a course where

making birdies is so vital, however, the Bermuda grass rough at the Stadium Course is

difficult to get out of and can lead to bogey and double bogey, so being able to get up and

down from it is important. Strokes Gained Putting being insignificant is odd, however, it

is likely correlated to the fact that in order to play well a player must make so many birdies

that being close to the hole and having easy putts for birdie is more important than being

able to make longer birdie putts. Even the best putters do not consistently make long birdie

putts over four rounds, however, great ball strikers can hit it close to the hole frequently

when their game is clicking, so when a massive number of birdies is necessary, the players

giving themselves more close-range opportunities at birdie are generally more successful

than those hoping to make many long putts. The players who have historically won this

tournament in the past have likely hit it close enough to the hole repeatedly that they have

not had to out putt their competitors on a Strokes Gained basis. Sand Save Percentage is

likely insignificant, as those who win rarely hit it into the sand, whether they get up and

down from the sand at a high rate or not has minimal impact on their score.

In order to sharpen the equation to take into account a player’s history at the course,

the 2015 and 2016 tournaments must be back checked. 2014 is not reviewed as there is not

enough data from the previous three years to do so, since the tournament had a different

format up until 2012. Linear regressions of the key stats from 2012-2014 to predict 2015

and from 2013-2015 to predict 2016 are found to have the same significant variables with

slightly differing coefficients depending on the year. The players’ season long averages

from the year in question for the four statistical categories are then inserted as the

!"#$%%&'(+-(

(

independent variables to predict their score for the tournament. Then, by subtracting the

projections from their real average scores from the event differences are found, which are

regressed on each player’s individual binary course history. Current form and weather are

not analyzed for this tournament, as it is only the second tournament of the year, so there

is not enough significant current form data and the weather was not expected to be a factor.

The regression yields:

(9)

-:F ( X]WUYY`^H:!3 * =

Table 7:

Adjusted CareerBuilder Regression Output

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.(5fL$2&(

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(

><K(.(5fL$2&(

@F-V=*(

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h-F==V-(

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h,F)*-=(

So now adding this to the initial 2017 projection equation:

(10)

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X U \_T[ 2:# * ]USS[T^5# X WUYY` H:!3 * =

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The players playing the 2017 tournament are then projected by inputting their 2016 season

long statistics into the equation, as well as a 0 or 1 for course history, depending on whether

they had met the qualifications detailed. Valuation based on the projections and lineup

creation detailed above leads to the 150 lineups that were set for the DraftKings

CareerBuilder Challenge $3 GPP contest.

The net result of the $450 investment was a loss of $22. Fifty-eight of the 150

lineups placed in the money. All 58 lineups returned the $3 investment with profit

dispersion as follows: two lineups yielded $22, one $12, three $9, three $7, eleven $5,

nineteen $3, and nineteen $2 of profit. Fifteen of the twenty-five players selected made the

cut for a 60% made-cut rate, which is the same as the past week at the Sony Open. This

percent is too low to be profitable without extreme luck in the randomization of rosters, as

rosters generally need at least five of six players to make the cut. Three of the top four

finishers in the tournament were selected, however, the winner of the event was not. Having

these high finishers allowed the lineups to almost break even, with just a minimal loss,

despite the high number of missed cuts. The majority of the missed cuts stem from the low

DraftKings priced value plays selected. Of the eight players selected who were priced

below $7000 on DraftKings only one made the cut. Bud Cauley, who was $6000, was

ranked third by the projection model despite being priced above only eighteen of the 156

players in the larger field. Unfortunately, Cauley was the lone stand out from the low-price

selections, and since most lineups contain at least one of the cheap players, there were very

few which had enough players make the cut to return significant profit. Overall having

!"#$%%&'(+*(

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three players in the top four mitigated losses that were to be expected based on the 60%

made-cut percentage.

Week 3 – Farmers Insurance Open

The Farmers Insurance Open is the third full field PGA event of the calendar year.

The tournament has been played at Torrey Pines Country Club in La Jolla, California since

1968. Torrey Pines has a South and North course. Players will play one round at each

course before the cut, however, both rounds after the cut will be played at the South

Course.

The three rounds of data from the South course will be analyzed. Regressing the

chosen statistics from the 2014-2016 gives the predictive base equation for the 2017 event:

(11)

!"#

Ibcdecf>?@E

( SZUZW`V X U V_W !232 X U \_ZZ !25 X U \WVW !"#.8 X

]UWTWV^2:# * ]UZV_W^5# * =

((((((((((((((((((((((((((((((((((((((((((((((((((((((((

(4[$2&&2JL8%<&2([B$%%&GQ&3;(-Vh))(b$GL$2'()@-=3(>&%@M4+""(%0#&12,$99&::&<(-=(>?28%()@-A3(

https://www.golfchannel.com/tours/pga-tour/2017/careerbuilder-challenge/.(

(4]B&(U$26&2:(RG:L2$G9&(!?&G(.&7L2G:(7/(P$(b/%%$(b$GL$2'(),7B3;(C+P&%%+0#&12,$99&::&<(-=(>?28%()@-A3(

https://www.lajolla.com/article/regional-attractions/farmers-insurance-open-torrey-pines-san-diego/.(

!"#$%%&'(++(

(

Table 8:

Farmers!Insurance!Regression!Output!

(

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Strokes Gained Tee-to-Green, Strokes Gained Putting, Greens in Regulation, Scrambling

and Putts/Round were significant statistics at the 95% level, while Driving Distance,

Driving Accuracy, and Sand Save Percentage were insignificant. Torrey Pines is

consistently one of the toughest tournaments on tour to score low at, so bogey avoidance

is at a premium. Players who can stay close to par and make a few birdies without hurting

themselves with bogey or worse will be able to contend. This is due to the length of the

South Course, at 7,698 yards it is one of the longest on tour, and the wind can wreak havoc,

being situated near the ocean.

The predictive equation emphasizes players who get to the

green in regulation and putt well, while also being proficient at making par when they do

((((((((((((((((((((((((((((((((((((((((((((((((((((((((

(S$7289N(#$'/3(4U$G7$:'(T/%I(S89N:C(()@-=(U$26&2:(RG:L2$G9&(!?&G(5%&&?&2:3(57$27:(`(S2&a8&E3;()*(

b$GL$2'()@-= 3(7&/&!O'(./<0#&12,$99&::&<(-=(>?28%()@-A3(http://rotoexperts.com/118284/fantasy-golf-picks-

2017-farmers-insurance-open-picks-sleepers-starts-preview-tiger-woods/.(

!"#$%%&'(+,(

(

miss the green in regulation. Driving Distance and Accuracy are not significant, which at

first seems odd based on the length of the course. Taking the wind into account, though, it

is highly likely that the players who drive the ball the farthest might be most affected due

to the higher apex and longer time in the air. Sand Save Percentage is yet again not

significant, possibly due to players who win being on the green in regulation a high enough

percentage that their few trips to the sand to not have a great effect on their scorecard.

History, Current Form, and Weather are all insignificant for this tournament.

Despite having certain players who have dominated the course year after year, most notably

Tiger Woods who has won there eight times, a player’s history does not show up as

significant when back testing. This is likely because of the difficulty of the course, as even

players who have games which should yield success on the course have a very slim margin

for error. Form is insignificant again as it is the third week of the season, and although

some players will be teeing off for a third straight week, many are making their season

debut. Weather has already been discussed as a factor on this course, with extreme wind

always being possible when located on the water, however, the variability of wind is too

difficult to predict for. The standard equation before adjusting for History, Current Form,

or Weather is used to predict success.

The players playing the 2017 tournament are then projected by inputting their 2016

season long statistics into the equation. Valuation based on the projections and lineup

creation detailed above leads to the 150 lineups that were set for the DraftKings Farmers

Insurance Open $3 GPP contest.

The net result of the $450 investment was a loss of $401. Eight of the 150 lineups

placed in the money. One of the lineups returned the $3 investment along with $6 of profit.

!"#$%%&'(+O(

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Five lineups returned the $3 investment along with $3 of profit. Two of the lineups returned

the $3 investment along with $2 of profit. Twelve of the twenty-five players selected made

the cut for a 48% made-cut rate. This percent is far too low to be profitable. The model

selected the winner of the tournament, Jon Rahm, as well as one of the players who tied

for second, Charles Howell, but the lineups never stood a chance with such a poor made-

cut percentage. Forty-Seven percent of players in the field made the cut, and the model

only managed to have 48% make it, so it was incredibly unsuccessful for this week leading

to a major loss.

Week 4 – Waste Management Phoenix Open

The Waste Management Phoenix Open is the fourth full field PGA event of the

calendar year. The tournament has been played at TPC Scottsdale in Scottsdale, Arizona,

since 1987.

Regressing the chosen statistics from the 2014-2016 gives the predictive base

equation for the 2017 event:

(12)

!"#

L74>?@E

( Y\U`VW_ X U `_T !232 X U V[VV !25 * =

((((((((((((((((((((((((((((((((((((((((((((((((((((((((

(4U$26&2:(RG:L2$G9&(!?&G3;()Oh)V(b$GL$2'()@-=3(>&%@M4+""(%0#&12,$99&::&<(-=(>?28%()@-A3(

https://www.golfchannel.com/tours/pga-tour/2017/farmers-insurance-open/.(

(4]/L2G$6&G7(W8:7/2'3;(?1B4&("*OQ'("0#&12,$99&::&<(-=(>?28%()@-A3(

https://wmphoenixopen.com/spectator-info/tournament-history/.(

!"#$%%&'(+=(

(

!!!!!!!!!!!!!!!!!!!!!!!!!!Table!9:!

WM!Phoenix!Open!Regression!Output!

(

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Only the Strokes Gained statistics, both Tee-to-Green and Putting were significant statistics

at the 95% level, with all other statistics being insignificant. TPC Scottsdale generally ranks

in the middle of PGA Tour courses in difficulty, with a score in the teens under par likely

to win.

Driving Distance is insignificant, likely due to the dry Arizona climate, which

allows for players to hit the ball farther than they generally would. A desert course, TPC

Scottsdale is wide open, where missing the fairway could leave your ball at the base of a

cactus or in a dry patch with a view of the green. Being on the fairway consistently always

helps, but at this type of course, luck in relation to where a player misses the fairway could

make driving accuracy ultimately insignificant. At a course where scoring significantly

under par is necessary to win, scrambling to make par is less valuable, as hitting greens

and making birdies is necessary. The greens at TPC Scottsdale are Bermuda grass, which

are generally slower and thus easier to two-putt on. This is because a player’s first putt is

((((((((((((((((((((((((((((((((((((((((((((((((((((((((

(S$7289N(#$'/3(4U$G7$:'(T/%I(S89N:C(()@-=(Z$:7&(#$G$Q&6&G7(!?&G(5%&&?&2:3(57$27:(`(S2&a8&E3;(*@(

b$GL$2'()@-= 3(7&/&!O'(./<0#&12,$99&::&<(-=(>?28%()@-A3(http://rotoexperts.com/118466/fantasy-golf-picks-

2017-waste-management-open-picks-sleepers-starts-preview/.(

!"#$%%&'(+A(

(

unlikely to roll well past the hole on slow greens, so most players should be able to avoid

three-putting. Putts/round is insignificant due to the ease of two-putting, however, Strokes

Gained Putting is still significant as players who can make birdies will excel. Strokes

Gained Tee-to-Green is the most significant variable, as those who are able to get close to

the hole in regulation will be able to amass the most birdie opportunities.

In order to sharpen the equation to take into account a player’s history at the course,

the 2014, 2015, and 2016 tournaments must be back checked. Linear regressions of the key

stats from 2011-2013 to predict 2014, 2012-2014 to predict 2015, and from 2013-2015 to

predict 2016 are found to have the same significant variables with slightly differing

coefficients depending on the year. The players’ season long averages from the year in

question for the four statistical categories are then inserted as the independent variables to

predict their score for the tournament. By then subtracting the projections from their real

average scores from the event, the differences are found, which are regressed on each

player’s individual binary course history. Current form and weather are not analyzed for

this tournament, as it is only the fourth tournament of the year so there is not enough

significant current form data and the weather in Arizona is expected to be warm and clear,

which should benefit all. The regression yields:

(13)

-:F ( X]US`[S^H:!3 * =

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(

Table 10:

Adjusted WM Phoenix Open Regression Output

7(=.(<<*&",5/+/*</*#<,

.(5fL$2&(

@F--V,(

(

><K(.(5fL$2&(

@F--+)(

(

57<F(g22/2(

-F-VAO(

(

!0:&2a$78/G:(

-AV(

(

M&(@@*#*("/<,

5/+")+.),

!..&.,

/,5/+/,

WR5](

h@FOV+O(

@F-*=,(

h,F@,))(

So now adding this to the initial 2017 projection equation:

(14)

!"#

L74>?@E

( Y\U`VW_ X U `_T !232 X U V[VV !25 X U S`[S H:!3 * =

The players playing the 2017 tournament are then projected by inputting their 2016 season

long statistics into the equation, as well as a 0 or 1 for course history, depending on whether

they had met the qualifications detailed. Valuation based on the projections and lineup

creation detailed above leads to the 150 lineups that were set for the DraftKings Waste

Management Open $3 GPP contest.

The net result of the $450 investment was a gain of $609. Ninety-three of the 150

lineups placed in the money. All 93 lineups returned the $3 investments with profit

dispersion as follows: one lineup yielded $147, one $97, two $72, one $47, one $37, one

$24, four $9, seven $6, six $5, five $4, twenty-eight $3, and thirty-six $2 of profit. Nineteen

of the twenty-five players selected made the cut for a 75% made-cut rate. This percent was

high enough to be profitable. Ten of the top 23 finishers in the tournament were selected,

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(

including the players who finished first, second, third, and one of two players who tied for

fourth. Having these high finishers allowed for a large profit, however, unfortunately, the

randomization did not create any lineups with all four of the selected top finishers, which

would have exponentially increased the profit. Course history seemed to be the key to

success this week, as each of the top players had past success at the course, with Winner

Hideki Matsuyama having a particularly stellar past record at TPC Scottsdale.

Week 5 – AT&T Pebble Beach Pro-Am

The AT&T Pebble Beach Pro-Am is the fifth full field PGA event of the calendar

year. The tournament is played at three courses around Pebble Beach, California. Despite

being played at three courses, each are fairly similar, particularly in length. Pebble Beach

is a par 72 measuring 6,816 yards, Spyglass Hill is a par 72 measuring 6,953 yards, and

Monterey Peninsula is a par 71 measuring 6,914 yards.

Regressing the chosen statistics

from the 2014-2016 gives the predictive base equation for the 2017 event:

(15)

g!"#

4a>?@E

( SSUZZW\ X U TT_Y !232 X U WTWY !25 X U \WV !"#.8

X U \[_T 2:# * ]UV_ZZ^5# * =

((((((((((((((((((((((((((((((((((((((((((((((((((((((((

(b/BG(Y$a8: 3(4Z $ :7&(#$G$Q&6&G7(SB / &G 8i(! ? &G C((W8< &N8(#$7:L'$6$(]$N& :(> 86 ($7(*hS&$73;(*@(b$GL$2'(

)@-A3(+RM("/.+%0#&12,$99&::&<(-=(>?28%()@-A3(https://www.azcentral.com/story/sports/golf/phoenix-

open/2018/01/30/waste-management-phoenix-open-hideki-matsuyama-takes-aim-3-peat/1081419001/).(

(4>]`](S&00%&(J&$9B(S2/h>6C((]/L2G$6&G7(RGI/26$78/G3;(B(66%(-(+#40#&12,$99&::&<(-=(>?28%()@-A3(

https://www.pebblebeach.com/events/att-pebble-beach-pro-am/.(

!"#$%%&'(,-(

(

!!!!!!!!!Table!11:!

Pebble!Beach!Regression!Output!

(

7(=.(<<*&",5/+/*</*#<,

.(5fL$2&(

@FOO+V(

(

><KL:7&<(.(5fL$2&(

@FO,O-(

(

57$G<$2<(g22/2(

@FO)*V(

(

!0:&2a$78/G:(

-VO(

(

M&(@@*#*("/<,

5/+")+.),

!..&.,

/,5/+/,

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OOF,,-@(

-F+*A=(

+OF),OA(

5T]T(

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h@F-*-=(

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h@F@+A*(

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@F)A,,(

@F@+VV(

,F=-=@(

Strokes Gained Tee-to-Green, Strokes Gained Putting, Scrambling Percentage, Greens in

Regulation, and Putts/Round were significant statistics at the 95% level, while Driving

Distance, Driving Accuracy, and Sand Save Percentage were insignificant. With these

three courses being extremely short by PGA standards and also the possibility of coastal

winds, players can choose to hit very few drivers off the tee. Most players will be able to

hit a long iron off the tee and still have a wedge or a short iron shot left to make the green

in regulation. Due to players ability to not hit driver as frequently at this tournament,

Driving Distance and Accuracy are both insignificant statistics. The challenge of these

courses are the tiny greens, which are incredibly difficult to hit. The small greens make

hitting the green in regulation, as well as being able to scramble to make par when a green

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is missed, extremely significant.

Gaining strokes tee-to-green and putting are significant

factors, as despite the small greens, the length of the courses allow for players to have many

birdie opportunities in good conditions, which must be taken advantage of by gaining

strokes against the field. Yet again, Sand Save Percentage is not significant, likely due to

the small sample of times players who score well end up in the sand.

In order to sharpen the equation to take into account a player’s history at the course,

the 2014, 2015, and 2016 tournaments must be back checked. Linear regressions of the key

stats from 2011-2013 to predict 2014, 2012-2014 to predict 2015, and from 2013-2015 to

predict 2016 are found to have the same significant variables with slightly differing

coefficients depending on the year. The players’ season long averages from the year in

question for the four statistical categories are then inserted as the independent variables to

predict their score for the tournament. By then subtracting the projections from their real

average scores from the event differences are found, which are regressed on each player’s

individual binary course history. Current form and weather are not analyzed for this

tournament, as it is only the fifth tournament of the year so there is not enough significant

current form data and it is not projected to rain and wind is too difficult to predict. The

regression yields:

(16)

g-:F ( X]UZ_S^H:!3 * =

((((((((((((((((((((((((((((((((((((((((((((((((((((((((

(S$7289N(#$'/3(4U$G7$:'(T/%I(S89N:C(()@-=(>]`](S&00%&(J&$9B(S2/h>6(5%&&?&2:3(57$27:(`(S2&a8&E3;(O(

U&02L$2'()@-=3(7&/&!O'(./<0#&12,$99&::&<(-=(>?28%()@-A3(http://rotoexperts.com/118602/fantasy-golf-

picks-2017-pebble-beach-picks-sleepers-starts-preview-pro-am/.(

!"#$%%&'(,*(

(

Table 12:

Adjusted Pebble Beach Regression Output

7(=.(<<*&",5/+/*</*#<,

.(5fL$2&(

@F-@O@(

(

><K(.(5fL$2&(

@F@VA*(

(

57$G<$2<(g22/2(

-F@++V(

(

!0:&2a$78/G:(

-*-(

(

M&(@@*#*("/<,

5/+")+.),!..&.,

/,5/+/,

WR5](

h@F,AO@(

@F-+V*(

h*FV),=(

So now adding this to the initial 2017 projection equation:

(17)

!"#

4a>?@E

( SSUZZW\ X U TT_Y !232 X U WTWY !25 X U \WV !"#.8

X U \[_T 2:# * ]UV_ZZ^5# X U Z_S H:!3 * =

The players playing the 2017 tournament are then projected by inputting their 2016 season

long statistics into the equation, as well as a 0 or 1 for course history depending on whether

they had met the qualifications detailed. Valuation based on the projections and lineup

creation detailed above leads to the 150 lineups that were set for the DraftKings Pebble

Beach $3 GPP contest.

The net result of the $450 investment was a loss of $221. Thirty-eight of the 150

lineups placed in the money. All 38 lineups returned the $3 investments with profit

dispersion as follows: one lineup yielded $13, one $9, three $5, two $4, eight $3, and

twenty-three $2 of profit. 14 of the twenty-five players selected made the cut for a 56%

made-cut rate, which is the same as the past week at the Sony Open. This percent is too

!"#$%%&'(,+(

(

low to be profitable without extreme luck in the randomization of rosters, as rosters

generally need at least five of six players to make the cut. Four of the top seven finishers

in the tournament were selected, including Jordan Spieth, the winner of the event. Having

these high finishers allowed the lineups to make back slightly more than 50% of the initial

investment, however, the low percentage of made-cuts still left a relatively large net loss.

The top three rated players by the model: Dustin Johnson, Jason Day, and Jordan Spieth

finished 3

, T-5

, and 1

respectively.

Only four of the top fifteen projected players

missed the cut, however, seven of the next ten did make the cut. Of the ten players who

were selected that were priced below $7,000 on DraftKings only three made the cut. This

shows a failure by the model to predict sleeper plays this week, with only the top-end

players selected performing as expected.

Week 6 – Genesis Open

The Genesis Open is the sixth full field PGA event of the calendar year. The

tournament has been played at Riviera Country Club in Pacific Palisades, California,

consistently since 1973.

Regressing the chosen statistics from the 2014-2016 gives the

predictive base equation for the 2017 event:

(18)

!"#

1eQefhf>?@E

( YWUZ_\V X WU\W[Y !232 X U VZSZ !25 * =

((((((((((((((((((((((((((((((((((((((((((((((((((((((((

(4>]`](S&00%&(J&$9B(S2/h>63;(Vh-)(U&02L$2'()@-=3(>&%@M4+""(%0#&12,$99&::&<(-=(>?28%()@-A3(

https://www.golfchannel.com/tours/pga-tour/2017/att-pebble-beach-pro-am/.(

(R08<F(

(4]/L2G$6&G7(W8:7/2'3;(>("(<*<Q'("0#&12,$99&::&<(-=(>?28%()@-A3(http://genesisopen.com/tournament-

history.(

!"#$%%&'(,,(

(

!!!!!!!!!!!!!!!!!!!!!!!Table!13:!

Genesis!Open!Regression!Output!

(

7(=.(<<*&",5/+/*</*#<,

.(5fL$2&(

@FVVO*(

(

><K(.(5fL$2&(

@FVVO*(

(

57$G<$2<(g22/2(

@F@=O=(

(

!0:&2a$78/G:(

)),(

(

M&(@@*#*("/<,

5/+")+.),

!..&.,

/,5/+/,

BG8+%9(,

RG7&29&?7(

=-F,A@)(

@F)@V-(

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Only the Strokes Gained statistics, both Tee-to-Green and Putting were significant statistics

at the 95% level, with all other statistics being insignificant. The equation for the Genesis

is eerily similar to that of the Waste Management Phoenix Open, which despite being very

different courses in terms of terrain makes some sense. Both courses generally have

winners who score in the teens under par, and both can be conquered by players of very

different skill sets. Riviera Country Club is 7,322 yards, which is around the average PGA

tour yardage, however, the difference between holes’ distances makes it more interesting.

Six of the eleven par 4 holes are over 450 yards, which are long by tour standards, while

one of the par 4 holes is 315 yards which is incredibly short. The course also features a

short par 5, which is easily reachable in two strokes even for the tour’s shorter hitters off

the tee.

Driving distance would appear to be important with six long par 4’s, but distance

((((((((((((((((((((((((((((((((((((((((((((((((((((((((

(S$7289N(#$'/3(4U$G7$:'(T/%I(S89N:C(()@-=(T&G&:8:(!?&G(5%&&?&2:3(57$27:(`(S2&a8&E3;(-*(U&02L$2'()@-=3(

7&/&!O'(./<0#&12,$99&::&<(-=(>?28%()@-A3(http://rotoexperts.com/118793/fantasy-golf-picks-2017-genesis-

open-picks-sleepers-starts-preview/.(

!"#$%%&'(,O(

(

can get players into trouble as well. On the short par 4 if long hitters decide to try to make

the green in one stroke and fail, then they may wind up in the surrounding bunkers, which

can be very penal. Players who do not drive the ball but are accurate can be just as effective

as those driving the ball a long way. With that said, accuracy is not shown to be significant

either, which can be attributed to the lack of accuracy needed by long hitters, as those who

hit it a long way often will be able to reach the green even if they miss the fairway. In other

words, there is more than one way to be successful driving the ball at Riviera. The Strokes

Gained statistics are as usual the most indicative of success, with a player gaining strokes

on his competitors in both facets of the game being vital.

In order to sharpen the equation to take into account a player’s history at the course,

the 2014, 2015, and 2016 tournaments must be back checked. Linear regressions of the key

statistics from 2011-2013 to predict 2014, 2012-2014 to predict 2015, and from 2013-2015

to predict 2016 are found to have the same significant variables with slightly differing

coefficients depending on the year. The players’ season long averages from the year in

question for the two statistical categories are then inserted as the independent variables to

predict their score for the tournament. By then subtracting the projections from their real

average scores from the event differences are found, which are regressed on each player’s

individual binary course history. Current form and weather are not analyzed for this

tournament, as it is only the sixth tournament of the year so there is not enough significant

current form data and the weather in the Pacific Palisades is expected to be sunny and clear,

which should benefit all. The regression yields:

(19)

-:F ( X]USWV^H:!3 * =

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(

Table 14:

Adjusted Genesis Open Regression Output

7(=.(<<*&",5/+/*</*#<,

.(5fL$2&(

@F@==*(

(

><K(.(5fL$2&(

@F@=-=(

(

57$G<$2<(g22/2(

-F+@A*(

(

!0:&2a$78/G:(

-=V(

(

M&(@@*#*("/<,

5/+")+.),!..&.,

/,5/+/,

WR5](

h@FO-)@(

@F-,A+(

h*FAO),(

So now adding this to the initial 2017 projection equation:

(20)

!"#

1eQefhf>?@E

( Y\U`VW_ X U `_V_ !232 X U V[VW !25 X U SWV H:!3 * =

The players participating in the 2017 tournament are then projected by inputting their 2016

season long statistics into the equation, as well as a 0 or 1 for course history depending on

whether they had met the qualifications detailed. Valuation based on the projections and

lineup creation detailed above leads to the 150 lineups that were set for the DraftKings

Genesis Open $3 GPP contest.

The net result of the $450 investment was a gain of $45,623. Seventy-seven of the

150 lineups placed in the money. All 77 lineups returned the $3 investments with profit

dispersion as follows: one lineup yielded $24,997, one $14,997, one 2,497, one $747, three

$497, one $297, one $147, one $97, two $67, two $47, two $27, four $17, five $9, four $7,

five $5, fourteen $4, ten $3 and nineteen $2 of profit. Twenty of the 25 players selected

made the cut for an 80% made-cut rate. This percent was high enough to be profitable.

Seven of the top 15 finishers in the tournament were selected, including the players who

!"#$%%&'(,A(

(

finished first, one of two players tied for second, and two of four players tied for fourth.

Having these high finishers allowed for a large profit, and with the benefit of some luck in

the randomization process creating more than one lineup with all four of the top selected

finishers, the Genesis Open provided the greatest win to-date. The top two entries would

have won and finished second in the entire GPP tournament. This one week would be able

to pay for at least 451 weeks of future contest entries, however, due to the small sample it

is impossible to know if this was a result of luck or the skill of the model.

Week 7 – Honda Classic

The Honda Classic is the seventh full field PGA event of the calendar year. The

tournament has been played at PGA National Golf Club Championship Course in Palm

Beach Gardens, Florida, since 2007.

Regressing the chosen statistics from the 2014-2016

gives the predictive base equation for the 2017 event:

(21)

!"#

GPQib>?@E

( S`U``YT X U ```S !232 X U ```S !25 X U \\\\V !"#.8

X ]U\\\\S^2:# * ]U\\\T^5# * =

((((((((((((((((((((((((((((((((((((((((((((((((((((((((

(4T&G&:8:(!?&G3;(-Oh-V(U&02L$2'()@-=3(>&%@M4+""(%0#&12,$99&::&<(-=(>?28%()@-A3(

https://www.golfchannel.com/tours/pga-tour/2017/genesis-open/.(

(4W/G<$([%$::89(Z8GG&2:($G<(W8:7/2'3;(),(U&02L$2'()@-A3(>&%@-%&==(.0#&12,$99&::&<(-=(>?28%()@-A3(

https://golfblogger.com/honda_classic_past_winners_and_history/.(

!"#$%%&'(,V(

(

!!!!!!!!!!!!!!!!!!!!!!Table!15:!

Honda!Classic!Regression!Output!

(

7(=.(<<*&",5/+/*</*#<,

.(5fL$2&(

@FVVVVVVA(

(

><KL:7&<(.(5fL$2&(

@FVVVVVVA(

(

57$G<$2<(g22/2(

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(

!0:&2a$78/G:(

)-=(

(

M&(@@*#*("/<,

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OVFVV=*(

@F@@-+(

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5T]T(

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h@F@@@-(

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Strokes Gained Tee-to-Green, Strokes Gained Putting, Scrambling, Greens in Regulation,

and Putts/Round were significant statistics at the 95% level, while Driving Distance,

Driving Accuracy, and Sand Save Percentage were insignificant. The Championship

Course has only been outside of the top ten most difficult courses on the PGA schedule in

two seasons, solidifying it as one of the most challenging courses on tour with the average

score being above par. The course is a par 70, which plays 7,140 yards and is littered with

sand traps and water hazards.

Being in Florida, weather can also play a large factor at the

tournament, however, for this year’s installment, rain is not in the forecast and winds are

only expected to be ferocious on Sunday afternoon. The Strokes Gained statistics are key

((((((((((((((((((((((((((((((((((((((((((((((((((((((((

(S$7289N(#$'/3(4U$G7$:'(T/%I(S89N:C(()@-=(W/G<$([%$::89(5%&&?&2:3(57$27:(`(S2&a8&E3;()@(U&02L$2'()@-=3(

7&/&!O'(./<0#&12,$99&::&<(-=(>?28%()@-A3(http://rotoexperts.com/119146/fantasy-golf-picks-2017-honda-

classic-picks-sleepers-starts-honda-classic-preview/.(

!"#$%%&'(O@(

(

as usual, with players needing to beat their competitors in how they reach the green and

how they get the ball in the hole in order to compete. Driving Distance and Accuracy are

both insignificant, which can likely be attributed to the water hazards. With so many

chances to lose a ball into the water off the tee, many players will resort to hitting irons

instead of a driver off the tee in order to more likely keep the ball in play. Despite the many

bunkers, Sand Save Percentage is still insignificant, however, scrambling is important and

includes player’s success out of the sand. The many bunkers make hitting the green in

regulation a priority, as a missed green could result in a tough test to get up and down for

par from the sand.

In order to sharpen the equation to take into account a player’s history at the course,

the 2014, 2015, and 2016 tournaments must be back checked. Linear regressions of the key

statistics from 2011-2013 to predict 2014, from 2012-2014 to predict 2015, and from 2013-

2015 to predict 2016 are found to have the same five significant variables with slightly

differing coefficients depending on the year. The players’ season long averages from the

year in question for the four statistical categories are then inserted as the independent

variables to predict their score for the tournament. By then subtracting the projections from

their real average scores from the event differences are found, which are regressed on each

player’s individual binary course history. Weather is not analyzed for this tournament, as

it is not expected to take effect until late Sunday. Current Form is analyzed for this week;

however, results are insignificant, likely due to an influx of European players who come to

Florida to begin to prepare for the Masters and have little trackable form. The regression

yields:

!"#$%%&'(O-(

(

(22)

-:F ( X]UZ_S^H:!3 * =

Table 16:

Adjusted Honda Classic Regression Output

7(=.(<<*&",5/+/*</*#<,

.(5fL$2&(

@F-*-,(

(

><K(.(5fL$2&(

@F-),*(

(

57$G<$2<(g22/2(

-F@AA=(

(

!0:&2a$78/G:(

-O)(

(

M&(@@*#*("/<,

5/+")+.),!..&.,

/,5/+/,

WR5](

h@F,AVV(

@F--V,(

h+FV*O,(

So now adding this to the initial 2017 projection equation:

(23)

!"#

GPQib>?@E

( S`U``YT X U ```S !232 X U ```S !25 X U \\\\V !"#.8

X ]U\\\\S^2:# * ]U\\\T^5# X U Z_S H:!3 * =

The players playing the 2017 tournament are then projected by inputting their 2016 season

long statistics into the equation, as well as a 0 or 1 for course history depending on whether

they had met the qualifications detailed. Valuation based on the projections and lineup

creation detailed above leads to the 150 lineups that were set for the DraftKings Honda

Classic $3 GPP contest.

The net result of the $450 investment was a gain of $403. Eight-four of the 150

lineups placed in the money. All 84 lineups returned the $3 investments with profit

!"#$%%&'(O)(

(

dispersion as follows: one lineup yielded $97, two $47, one $37, two $27, three $17, three

$12, one $9, one $7, seven $6, five $5, seven $4, nineteen $3, and thirty-one $2 of profit.

Nineteen of the 25 players selected made the cut for a 75% made-cut rate. This percent was

high enough to be profitable. Eight of the top 20 finishers in the tournament were selected,

including the player who finished first, one of two players who tied for second, and two of

six players tied for fourth. Having these high finishers allowed for a large profit, but the

randomization process did not produce the best possible lineup which could have been

formed out of the 25 players selected. Seven of the ten players below $7,500 that were

selected made the cut, with Billy Horschel, priced at $7,200, placing in a tie for fourth.

Furthermore, the number two ranked player by the model, Rickie Fowler, won the

tournament, which shows that this week it was successful in picking the top players, as

well as cheap value players.

Week 8 – Valspar Championship

The Valspar Championship is the eighth full field PGA event of the calendar year,

which falls in week nine of the season. The WGC- Mexico is played during week seven,

which only has a field of approximately sixty players, so was not analyzed. The Valspar

Championship began in 2000 and is played at Copperhead Course at Innisbrook Resort in

Palm Harbor, Florida.

Regressing the chosen statistics from the 2014-2016 gives the

predictive base equation for the 2017 event:

((((((((((((((((((((((((((((((((((((((((((((((((((((((((

(4]B&(W/G<$([%$::893;()*h)O(U&02L$2'()@-=3(>&%@M4+""(%0#&12,$99&::&<(-=(>?28%()@-A3(

https://www.golfchannel.com/tours/pga-tour/2017/honda-classic/.(

(4\$%:?$2([B$6?8/G:B8?(Z8GG&2:($G<(W8:7/2'3;(--(#$29B()@-A3(>&%@-%&==(.0#&12,$99&::&<(-=(>?28%()@-A3(

https://golfblogger.com/valspar_championship_past_winners_and_history/.(

!"#$%%&'(O*(

(

(24)

!"#

jbkflbc>?@E

( Y\U`__T X U `_Y !232 X U `_[` !25 * =

!!!!!!!!!!!!!!!!!!!!!Table!17:!

!!!!!!Valspar!Regression!Output!

(

7(=.(<<*&",5/+/*</*#<,

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(

!0:&2a$78/G:(

)-O(

(

M&(@@*#*("/<,

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Only the Strokes Gained statistics, both Tee-to-Green and Putting were significant

statistics at the 95% level, with all other statistics being insignificant. Similar to at the

Honda Classic, the second Florida tournament is also very challenging.

The challenge of

the Honda Classis was water hazards throughout, however, at the Valspar Championship

it is tree lined fairways, which can keep a player from being able to reach the green in

regulation if hit into. Driving accuracy would seem to be significant, however, so few

players elect to hit their driver off the tee that driving statistics are actually inconsequential.

Greens in Regulation and Scrambling are insignificant as well, despite seemingly being

important when looking at the difficulty of the course. The key to success at Copperhead

((((((((((((((((((((((((((((((((((((((((((((((((((((((((

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is avoiding making double bogey or worse in order to keep a score close to par, as most

players will be over par for the tournament. Gaining strokes on the field on the way to the

green and also by making difficult putts, to either save par or make birdie, is the path to

victory.

In order to sharpen the equation to take into account a player’s history at the course,

the 2014, 2015, and 2016 tournaments must be back checked. Linear regressions of the key

statistics from 2011-2013 to predict 2014, from 2012-2014 to predict 2015, and from 2013-

2015 to predict 2016 are found to have the same five significant variables with slightly

differing coefficients depending on the year. The players’ season long averages from the

year in question for the two statistical categories are then inserted as the independent

variables to predict their score for the tournament. By then subtracting the projections from

their real average scores from the event differences are found, which are regressed on each

player’s individual binary course history. Weather is not analyzed for this tournament, as

rain is not in the forecast and wins is not expected to be a constant. Current Form is

analyzed for this week however results are insignificant. The regression yields:

(25)

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Table 18:

Adjusted Valspar Regression Output

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So now adding this to the initial 2017 projection equation:

(26)

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The players playing the 2017 tournament are then projected by inputting their 2016

season long statistics into the equation, as well as a 0 or 1 for course history, depending on

whether they had met the qualifications detailed. Valuation based on the projections and

lineup creation detailed above leads to the 150 lineups that were set for the DraftKings

Valspar Championship $3 GPP contest.

The net result of the $450 investment was a loss of $229. Thirty-nine of the 150

lineups placed in the money. All 39 lineups returned the $3 investments with profit

dispersion as follows: two yielded $6, one $5, two $4, eleven $3, and twenty-three $2 of

profit. Seventeen of the 25 players selected made the cut for a 68% made-cut rate. This

percent could have been high enough to be profitable with high finishers and some luck in

the randomization process, but unfortunately it was not this week. Only two of the top ten

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players were selected this week, with none in the top five. Charl Schwartzel and Henrik

Stenson finished sixth and seventh respectively in the tournament, with both being

projected to be in the top five, however, mediocre results from the middle and lower tier

players selected and failing to pick the winner, Adam Hadwin, resulted in a losing week.

Week 9 – Arnold Palmer

The Arnold Palmer Invitational is the ninth PGA event of the calendar year, and

although not a full field event, the 120 players invited and the standard two day cut make

this tournament similar enough to a full field event that it can be modeled. The invitational

began in 1966 under the name, the Florida Citrus Open Invitational. The tournament has

been played at Bay Hill Club and Lodge since 1979 and took on the name the Arnold

Palmer Invitational in 2007.

Regressing the chosen statistics from the 2014-2016 gives

the predictive base equation for the 2017 event:

(27)

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Driving Accuracy, Strokes Gained Tee-to-Green, Strokes Gained Putting, Scrambling,

Greens in Regulation, and Putts per Round were all significant, while Driving Distance and

Sand Save Percentage were not. Bay Hill is a par 72 course that measures 7,419 yards.

The four par 5’s provide many scoring opportunities, but the course has plenty of water

and sand to ruin a player’s round. Similar to the Honda Classic there is water that must be

avoided, however, unlike a few weeks back, Bay Hill is generally too long to not hit a

driver off the tee on most holes. Instead of hitting irons to avoid the water like they did at

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#$29B()@-=3(7&/&!O'(./<0#&12,$99&::&<(-=(>?28%()@-A3(http://rotoexperts.com/119817/fantasy-golf-picks-

2017-arnold-palmer-invitational-picks-sleepers-starts-bay-hill-preview-predictions/.(

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the Honda Classic, here players must be accurate with their drivers. The Strokes Gained

statistics are significant as always, as if a player hopes to win, they must make enough

birdies by gaining strokes against their competitors. Scrambling and Greens in Regulation

are likely both significant for the same reason, which is the multitude of bunkers

surrounding the greens. Being able to hit the green in regulation and avoid scrambling out

of the bunkers or thick rough is a huge advantage. If a player is to miss the green, though,

he had better be scrambling at a high level given the difficult conditions. Driving Distance

is insignificant, as this course is more reliant on accuracy.