RSEM 7110 Tournament Validity Paper - LinkedIn

Running Head: MODELS EXPLAINING PLAYER SUCCESS

Modeling Success for the 2012 U.S. Open and Masters

Kenneth Hee

8 December 2012

RSEM 7110

MODELING SUCCESS FOR THE 2012 U.S. OPEN AND MASTERS 2

Background, Terms and Research Problem:

Assessments are difficult to design and validate, both in education and in

sports. The use of slope is common in both item response theory and the slope of a

golf course. In the two-parameter logistical model of item response theory, the

discrimination factor is introduced (add citations). The discrimination factor ai

alters the slope of any given question in an exam. Which is analogous to the slope

rating of a golf course. In this way, a golf tournament is essentially a test similar to

an academic test (Sachau et al., 2009). The four major events on the PGA tour are

highly coveted events that should, in theory, be the best tests in golf. They should be

valid tests, in the competency area they intend to test.

This paper aims to determine the skill set tested in the 2012 U.S. Open and

Masters championship tournaments. The Professional Golf Association (PGA) has a

clear idea on how a championship course should play, difficult (improve and add

citation). In order to increase course difficulty, the rough grows long and the greens

are trimmed short. Courses even take extremes to increase their distance and

narrow fairways (Klein, 2012). All of these preparations increase the slope of the

course. Which in effect intentionally tests different skill areas of golf.

The players are compared across the four skill areas in each tournament to

explain player success. The four shot making areas and other golf definitions are

presented in Table 1. Increasing the slope of courses tends to decrease the

tournaments reliability (Sachau et al., 2009). The research problem then asks, if the

intentionally difficult tests of golf identify the best golfer in the intended skill areas.


Table 1 The Four Shot Making Areas and other Golf Definitions

Terms Definition

Putting* Average number of putts per hole Greens in Regulation (GIR)* The percentage of the player reaching the green in regulation.

Meaning one hits the green in 2 on a par 4, or 3 on a par 5.

Driving Distance* Average yards per drive Driving Accuracy* Percentage of driving the ball into the fairway

Slope The difficulty or discrimination factor of the course Drive Players initial tee shot into the fairway

Fairway The intended area for landing the drive Rough The area outside of the intended area for landing the drive

* Shot Making Area

Background, Research Questions and Hypothesis:

In the case of the Olympic Club, the 2012 U.S. Open venue, the course was

cited to have narrow fairways and small greens (Klein, 2012). This means that

players who drove the ball accurately and hit greens in regulation should perform

well. However, did this test of golf actually test the intended skills? The hypothesis

is that the Olympic Club course will discriminate players according to their

performance in the greens in regulation and driving accuracy skill areas. These two

factors will be the most significant in explaining player success in the 2012 U.S.

Open.

In the case of Augusta National, the 2012 Masters venue, the course had a

more intangible difficulty. Especially since the course does not have an official slope

(Knuth, 2010). Without disclosed course manipulation the research question takes

a different focus. Simply asking, what shot making area best explains player

success? The hypothesis is that putting and greens in regulation will be the most

significant in explaining player success in the 2012 Masters.


Delimitations, Limitations and Assumptions:

The field was delimited to players who participated and finished in both the

U.S. Open (N=27) and Masters (N=42) championships. This criterion limited the

study to a smaller sample size and the study is delimited to assessing the top players

in the world who compete in these two specific events. An independence of

observation was assumed between rounds and between tournaments. Meaning that

player groupings or weather conditions did not affect the results on any given day of

the four-round tournament. Also meaning that performance in the 2012 Masters

did not have implications on player performance in the subsequent 2012 U.S. Open.

A limitation associated with the driving distance statistic must be

acknowledged. Players are only assessed on two random holes per round to

determine their average distance. The other three skill areas are assessed on every

hole, and are more reliable indicators of player competence.

Need for Significance and Researcher’s Perspective:

As with any measure or test, the results are intended to be reliable and valid.

With such immense implications placed on the four major PGA tournaments, the

results should be highly reliable and valid. Studies have examined the reliability of

the results by correlating scores on courses with similar difficulty (Sachau et al.,

2009). However, I feel these results neglect to identify what was more difficult

about each course; failing to provide an explanation for success. In my opinion, a

comparison across the four skill areas will provide an accurate indicator on why

players are succeeding.


Literature Review:

Seemingly, the four major PGA tournaments have enormous implications on

a player’s perceived success. Therefore these tournaments should be designed

fairly and identify the best golfer. In order to do so the PGA increases the slope, or

discrimination, of the course by growing out the rough, narrowing fairways and

speeding up the greens (Schaap, 1974). Making the test harder for the best players

in the world makes sense.

The 2012 U.S. Open at the Olympic Club was an intentionally difficult test o f

golf. The director of golf course maintenance at the Olympic Club, Pat Finlen,

narrowed the fairways and created fast putting conditions (Belkin, 2012; Farris,

2012). Likewise Augusta National officials altered the course to account for the wet

and soft conditions in order to maintain the course’s difficulty (Greenberg, 2012). A

course with a high slope, or high discrimination, should in theory identify the best

golfer without question.

However, as seen in the four major 2003 PGA events the results have

diminished reliability (Sachau et al., 2009). The Sachau paper looked at the

correlation between a player’s overall adjusted average score and their

championship performance (2009). This provided an indication of tournament

validity by correlating scores on courses with similar slopes. By comparison, in this

paper the players are compared across four shot making areas to explain player

success.


Research Design, Rational and Measures:

The reason for selecting the Master and U.S. Open were simply because of

their prestige. The best players in the world strive to excel in these few

tournaments. Therefore a more difficult than average test of golf is required.

Examining a player across different shot skills provided an explanation for success

in each tournament.

These four factors have regularly been studied and provide significant

indicators on player success (Belkin et al., 1994; Quinn, 2006). Since the slopes of

the courses are unknown, comparing the overall difficulty of each tournament did

not make sense. Therefore each course was examined individually to determine

what specific skills each course tested. The study was designed to perform a

backwards regression. Using the four shot making areas as independent predictor

variables and the dependent variable the player’s finish in the tournament. In this

way a model for explaining player success was created for both the U.S. Open and

Masters championships.

Participants and Site:

The 2012 U.S. Open was held at the Olympic Club in San Francisco, CA and

the Masters was held at Augusta National in Augusta, GA. Only players who

completed all four rounds of each tournament were included in the analysis.


Procedures for Data Collection and Analysis:

The PGA publishes a seemingly infinite amount of statistics (PGA Tour,

2012). Inspection of the literature helped narrow down the wealth of published

statistics (Belkin et al., 1994; Quinn, 2006). In the case of this study, the four

significant predictor variables were: putting, greens in regulation, driving distance

and driving accuracy. Data on the four shot making areas and the final results were

gathered from each tournament’s website (The Masters, 2012; The U.S. Open, 2012).

The numbers were simply copied and pasted into an Excel document, then

exported into IBM SPSS Statistics, Version 21. The results were analyzed using the

linear regression function. A backwards multiple regression was conducted on both

tournaments using the four shot making areas as predictor variables. The resulting

models were examined for the largest adjusted R2 value in order to find the best

model to explain player success. Player success, or the dependent variable, was the

player’s finish in each tournament.

Assumptions for the multiple regressions include: a) normal distribution of

variables, b) independence of observations, c) multicolinearity, d) errors are

normally distributed and variance of the residual being constant. The normality of

variables was assessed using the frequencies function in SPSS Statistics.

Independence of observations was assumed. Multicolinearity was checked by

ensuring tolerance levels were greater than 1 – R2. Finally, plotting the

standardized residuals and predicted values checked the normal distribution of

errors and the variance residuals being constant.


Results of the U.S. Open Backwards Multiple Regression:

In order to determine which of the four shot making areas explained player

success in the 2012 U.S. Open a backwards multiple regression was performed. The

four shot making areas constitute the predictor variables. Assumptions were

checked and met. The means, standard deviations and inter-correlations can be

found in Table 2. Notice that greens in regulation and driving accuracy are

significantly correlated, r = .67, p < .001. The overall model significantly explained

player success, F(4, 22) = 19.74, p < .001. The results of the backwards regression

indicate that greens in regulation (t = -7.70, p < .001) and putting (t = 7.26, p < .001)

significantly contributed to the model. The adjusted R2 value was .74 indicating the

model explains 74% of the variance in the players finish in the U.S. Open. This is a

large effect according to the literature. The equation for the best model was:

U.S. Open Finish = – 218.71 + 311.12putting + .60accuracy – 4.20gir - .20distance + e

The beta weights for the model are included in Table 3 and indicate as

putting increases one unit, the players finish increases by 311.12 units, holding

everything else constant. Interestingly only greens in regulation and putting were

significant in the model. Although driving distance and driving accuracy were not

significant in the model the inter-correlations suggest they are important factors.

Certainly, a player hitting more fairways will likely hit more greens in regulation.


Table 2 Means, Standard Deviations, and Inter-Correlations for the U.S. Open Backwards Regression (N = 27)

Variable M SD 1 2 3 4

U.S. Open Finish 28.19 20.51 -0.23 -0.1 -0.48** 0.2

Predictor Variables 1. Driving Accuracy 49.87 6.84 - -0.2 0.67** 0.41*

2. Driving Distance 285.83 13.22

- -0.04 0.02 3. Greens in Regulation 56.38 6.19

- 0.67**

4. Putting 1.64 0.06 -

* p < .05, ** p < .001

Table 3 Multiple Regression Analysis for the 2012 U.S. Open Championship (N = 27)

Variable B SEB β R2

Model 1

0.78 Driving Accuracy 0.6 0.42 0.2

Driving Distance -0.2 0.16 -0.13 Greens in Regulation -4.2 0.55 -1.27** Putting 311.12 42.84 0.97** Constant -218.71 72.39

Model 2

0.77 Driving Accuracy 0.72 0.41 0.24

Greens in Regulation -4.26 0.55 -1.29** Putting 308.66 43.28 0.96** Constant -273.841 57.7

* p < .05, ** p < .001


Results of the 2012 Masters Backwards Multiple Regression:

A backwards regression was again conducted to determine the most

influential factor for success in the 2012 Masters championship. Again, the four shot

making areas constitute the predictor variables. Assumptions were checked and

met. The means, standard deviations and inter-correlations can be found in Table 4.

The beta weights for all models are included in Table 5. The results of the

backwards regression unearthed a significant model for explaining player success,

F(3, 38) = 49.47, p < .001. Like the U.S. Open model, only putting (t = 10.19, p <

.001) and greens and regulation (t = -11.02, p < .001) were significant in the Masters

model. The adjusted R2 value was .78, which is a large effect size according to the

literature. The model that best explained player success in the Masters was:

Masters Finish = -154.86 – 2.45gir + .16accuracy + 196.95putting + e

Not surprisingly, only greens and regulation and putting were significant

contributors to the model. The beta weights suggest as putting increases by one

unit a players finish increases by 196.95, holding everything else constant.

Table 4 Means, Standard Deviations, and Inter-Correlations for the Masters Backwards Regresstion (N = 42)

Variable M SD 1 2 3 4

Masters Finish 25.93 17.1 -0.48** -0.29* -0.09 0.34* Predictor Variables

1. Greens in Regulation 63 7.17 - 0.33* 0.36* 0.57** 2. Driving Distance 280.58 6.57

- -0.31* 0.08

3. Driving Accuracy 72.24 8.53

- 0.21

4. Putting 1.64 0.08 -

* p < .05, ** p < .001


Table 5 Multiple Regression Analysis Summary for the 2012 Masters Championship (N = 42)

Variable B SEB β R2

Model 1

0.8 Greens in Regulation -2.46 0.26 -1.03**

Driving Distance 0.03 0.24 0.01 Driving Accuracy 0.17 0.28 0.09 Putting 197.31 19.84 0.91** Constant -162.7 75.55

Model 2

0.8

Greens in Regulation -2.45 0.22 -1.03** Driving Accuracy 0.16 0.16 0.08 Putting 196.95 19.34 0.91** Constant -154.86 27.45

Model 3

0.79

Greens in Regulation -2.38 0.212 -1** Putting 197.14 19.34 0.91** Constant -147.73 26.57

* p < .05, ** p < .001

2012 U.S. Open Discussion and Links to Literature: The explaining model for the U.S. Open included all four shot making areas,

F(4, 22) = 19.74, p < .001. Although only greens in regulation (t = -7.70, p < .001)

and putting (t = 7.26, p < .001) significantly contributed to the model. Meaning that

the small greens challenged players on their approach shots to the green. This was

expected, since the greens were reduced in preparation for the U.S. Open

championship (Belkin et al., 2012; Farris, 2012).

However, the narrowing of the fairways seemed not to affect player success.

Since the driving accuracy skill area was not significant in the model, (t = 1.43, p =

.17). This was misleading because driving accuracy and greens in regulation are

significantly correlated, (r = .67, p < .001). Which makes sense because players


hitting from the fairway generally have more control over their approach shots, and

therefore hit the green in regulation with greater frequency. This is consistent with

the literature, in that greens in regulation and adjusted scoring average are

negatively correlated (Belkin et al., 1994). Overall, the adjusted R2 value of .74

indicates that 74% of the variance in player success can be explained by

performance in the four skill areas.

2012 Masters Discussion and Links to Literature The explaining model for the Masters included only putting (t = 10.19, p <

.001) and greens in regulation (t = -11.02, p < .001). This means that players who

were hitting greens in regulation and putting well, ended up performing well in the

Masters. Therefore the Masters discriminated players by these two skill areas.

Notice however that driving accuracy and greens in regulation were again

significantly correlated, (r = .36, p = .01).

The importance of hitting greens in regulation was logical considering the

weather conditions during the 2012 Masters. With 1.4 inches of rain dropping prior

to the tournament the greens were soft and receptive to approach shots (Greenberg,

2012). With the greens more receptive, players could miss fairways and still have a

legitimate chance at hitting the green in regulation. Wet greens tend to be more

forgiving to the ball’s approach angle and spin. Overall, the adjusted R2 value of .78

indicates that 78% of the variance in player success can be explained by

performance in two skill areas.


Future Research and Potential Methodologies Potential future research can look more in depth at how each major

tournament challenges players in each skill area. The number of skill areas

analyzed can be increased to better explain player success. The validity of the major

tournaments can be assessed using a more in depth knowledge of course slope

ratings. Potential methodologies include a principal axis factor analysis to validate

and reduce the number of shot making areas explaining player success.


References Belkin, D., Gansneder, B., Pickens, M., Rotella, R. and Striegel, D. (1994).

Predictability and Stability of Professional Golf Association Tour Statistics. Perceptual and Motor Skills, 78, 1775-1280.

Bolling, Jeff (2012). Finlen has Olympic fine-tuned for world’s best. Retrieved from

http://www.gcsaa.org/_common/templates/GcsaaNewsReleaseLayout.aspx?id=5641&LangType=1033

Farris, Kyle (2012). Olympic Club: What to Expect from the 2012 U.S. Open Venue. Retrieved from http://bleacherreport.com/articles/1203421-olympic-club-what- to-expect-from-the-2012-us-open-venue Greenberg, Chris (2012). Masters 2012: Augusta National to be Ready Despite Storm, Says Billy Payne. Retrieved from http://www.huffingtonpost.com/2012/04/04/ masters-2012-augusta-national-weather-conditions_n_1403383.html Klein, Bradley (2012). Olympic Club’s fairways a tough test. Retrieved From http://golfweek.com/news/2012/jun/10/olympic-clubs-fairways-tough-test/ Knuth, Dean (2010). How Tough is Augusta National? Retreived from http://www.golfdigest.com/golf-tours-news/golf-masters/2010-04/how-tough- augusta-knuth PGA Tour (2012). Retrieved 8 December 2012, from http://www.pgatour.com/ Quinn, R. J. (2006). Exploring Correlation Coefficients with Golf Statistics. Teaching

Statistics, 28: 10–13. Sachau, D., Andrews, L., Gibson, B. and DeNeui, D. (2009) Tournament Validity: Testing Golfer Competence. Measurement in Physical Education and Exercise Science, 13:1, 52-69. Schaap, R. (1974). Massacre at Winged Foot: The U.S. Open minute-by-minute. New

York: Random House. The Masters (2012). Tournament Statistics. Retrieved 8 December 2012, from

http://www.masters.com/en_US/index.html The U.S. Open (2012). Tournament Statistics. Retrieved 8 December 2012, from http://usga.usopen.com/

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RSEM 7110 Tournament Validity Paper - LinkedIn