Putting Accuracy

Neal HatchJames Kuykendall

7/27/2006

Why is Putting Important? Approximately 70% of a round of golf is

played within 100 yards of the green Par is the best score possible if a green

is three putted The easiest way to lower a handicap is

to improve putting “Drive for show, putt for dough” is an

often used phrase to depict how important putting is to the game of golf

Is There a Significance? General Factor Interaction (Basically 2FI)

Golfer Neal James Randall Jigg

Grade Uphill Downhill

Distance 6ft 12ft

Hypothesis Downhill putts are more difficult

because speed cannot be used to force the ball to hold the line

The further away from the hole the more difficult the putt

Looking for interactions rather than generating a model for accuracy, hole out and lip out

Equipment / Materials Practice Putting Range (Auburn

Links) 25’ Measuring Tape Medical Tape (Mark Distance) 3 Golf Clubs

Jigg – Odyssey 2 Ball Neal – Odyssey 2 Ball Randall – Scotty Cameron James – Wilson

Experimental Method

Putting Order Randomized Hole out was considered accuracy

of zero Distance was measured from

outside of hole to center of ball Design Expert software was used

to show interaction

Procedure

Following the randomized order, each putter attempts to the best of his ability to make the putt from varying distances and grade

Accuracy (in), Lip out, and Hole out were recorded for each run

Assumptions

All golfers will attempt to the best of their ability to make the putt rather than lag the ball close to the hole

No effect of different clubs

Golfer - Neal

Novice Never played a full game (18) Should stick to putt-putt

Golfer - James

Absolutely terrible putter Is terrible at golf and should

probably stop playing entirely

Golfer - Jigg

Lifelong golfer Placed second in state senior year

in high school By far best putter in group

Golfer - Randall

Played golf for approximately seven years

Excellent putter

Definition of Terms

Outlier T – identify extraneous data Cook’s Distance – identify highly

influential points ANOVA – Analysis of variables

(variance) Box Cox – plot to help determine

transformation

Determination of Significant Factors for the Group of Golfers

DESIGN-EXPERT PlotAccuracy

Run Number

Stud

entiz

ed R

esidu

als

Residuals vs. Run

-3.00

-1.20

0.60

2.40

4.20

1 54 107 160

Strictly Interaction

We will be focusing on strictly interactions between factors and the accuracy, hole out, and lip out

No models were generated

ANOVA- Determination of Interaction of factors for Accuracy

Response: Accuracy          

ANOVA for Selected Factorial Model            

Analysis of variance table [Partial sum of squares]            

  Sum of   Mean F    

Source Squares DF Square Value Prob > F  

Model 21502.3 151433.48

73.05843

1 0.0003  

Golfer 3361.65 3 1120.552.39076

2 0.0712

very close

Grade 8122.5 1 8122.517.3298

5

< 0.0001

significant

Distance3478.22

5 13478.22

57.42100

5 0.0072significan

t

Golfer/Grade 2902.85 3967.616

72.06446

9 0.1076  

Golfer/Distance2076.02

5 3692.008

31.47644

2 0.2235  

Distance/Grade 24.025 1 24.0250.05125

9 0.8212  

ABC1537.02

5 3512.341

71.09311

2 0.3541  

Pure Error 67492.8 144 468.7      

Cor Total 88995.1 159        

Downhill putts at 6 and 12 feet for each golfer

DESIGN-EXPERT Plot

Accuracy X = C: Distance

Design Points

Actual FactorsA: Golf er = NealB: Grade = Downhill

C: Distance

Accu

racy

One Factor Plot

6 12

0

42

84

126

168

22 55555

DESIGN-EXPERT Plot

Accuracy X = C: Distance

Design Points

Actual FactorsA: Golf er = JamesB: Grade = Downhill

C: DistanceAc

cura

cy

One Factor Plot

6 12

0

42

84

126

168

DESIGN-EXPERT Plot

Accuracy X = C: Distance

Design Points

Actual FactorsA: Golf er = RandallB: Grade = Downhill

C: Distance

Accu

racy

One Factor Plot

6 12

0

42

84

126

168

333 4444

DESIGN-EXPERT Plot

Accuracy X = C: Distance

Design Points

Actual FactorsA: Golf er = JiggB: Grade = Downhill

C: DistanceAc

cura

cy

One Factor Plot

6 12

0

42

84

126

168

55555 55555

Uphill 6 and 12 foot putts for each golfer

DESIGN-EXPERT Plot

Accuracy X = C: Distance

Design Points

Actual FactorsA: Golf er = NealB: Grade = Uphill

C: Distance

Accu

racy

One Factor Plot

6 12

0

42

84

126

168

333

DESIGN-EXPERT Plot

Accuracy X = C: Distance

Design Points

Actual FactorsA: Golf er = JamesB: Grade = Uphill

C: Distance

Accu

racy

One Factor Plot

6 12

0

42

84

126

168

2

55555

2

DESIGN-EXPERT Plot

Accuracy X = C: Distance

Design Points

Actual FactorsA: Golf er = RandallB: Grade = Uphill

C: Distance

Accu

racy

One Factor Plot

6 12

0

42

84

126

168

4444

2222

DESIGN-EXPERT Plot

Accuracy X = C: Distance

Design Points

Actual FactorsA: Golf er = JiggB: Grade = Uphill

C: Distance

Accu

racy

One Factor Plot

6 12

-2.06414

40.4519

82.9679

125.484

168

55555 4444

6 foot downhill and uphill putts for each golfer

DESIGN-EXPERT Plot

Accuracy X = B: Grade

Design Points

Actual FactorsA: Golf er = NealC: Distance = 6

B: Grade

Accu

racy

One Factor Plot

Uphill Downhill

0

42

84

126

168

33322

DESIGN-EXPERT Plot

Accuracy X = B: Grade

Design Points

Actual FactorsA: Golf er = JamesC: Distance = 6

B: GradeAc

cura

cy

One Factor Plot

Uphill Downhill

0

42

84

126

168

2555552

DESIGN-EXPERT Plot

Accuracy X = B: Grade

Design Points

Actual FactorsA: Golf er = RandallC: Distance = 6

B: Grade

Accu

racy

One Factor Plot

Uphill Downhill

0

42

84

126

168

4444 333

DESIGN-EXPERT Plot

Accuracy X = B: Grade

Design Points

Actual FactorsA: Golf er = JiggC: Distance = 6

B: Grade

Accu

racy

One Factor Plot

Uphill Downhill

-2.06414

40.4519

82.9679

125.484

168

55555 55555

12 foot downhill and uphill putts for each golfer

DESIGN-EXPERT Plot

Accuracy X = B: Grade

Design Points

Actual FactorsA: Golf er = NealC: Distance = 12

B: Grade

Accu

racy

One Factor Plot

Uphill Downhill

0

42

84

126

168

55555

DESIGN-EXPERT Plot

Accuracy X = B: Grade

Design Points

Actual FactorsA: Golf er = JamesC: Distance = 12

B: GradeAc

cura

cy

One Factor Plot

Uphill Downhill

0

42

84

126

168

DESIGN-EXPERT Plot

Accuracy X = B: Grade

Design Points

Actual FactorsA: Golf er = RandallC: Distance = 12

B: Grade

Accu

racy

One Factor Plot

Uphill Downhill

0

42

84

126

168

2222

4444

DESIGN-EXPERT Plot

Accuracy X = B: Grade

Design Points

Actual FactorsA: Golf er = JiggC: Distance = 12

B: GradeAc

cura

cy

One Factor Plot

Uphill Downhill

0

42

84

126

168

4444 55555

DESIGN-EXPERT Plot

Accuracy X = A: Golf er

Design Points

Actual FactorsB: Grade = DownhillC: Distance = 6

A: Golfer

Accu

racy

One Factor Plot

Neal James Randall Jigg

0

42

84

126

168

22 333 55555

DESIGN-EXPERT Plot

Accuracy X = A: Golf er

Design Points

Actual FactorsB: Grade = DownhillC: Distance = 12

A: Golfer

Accu

racy

One Factor Plot

Neal James Randall Jigg

0

42

84

126

168

55555 4444 55555

DESIGN-EXPERT Plot

Accuracy X = A: Golf er

Design Points

Actual FactorsB: Grade = UphillC: Distance = 6

A: Golfer

Accu

racy

One Factor Plot

Neal James Randall J igg

-2.06973

40.4477

82.9651

125.483

168

333 2555552

4444 55555

DESIGN-EXPERT Plot

Accuracy X = A: Golf er

Design Points

Actual FactorsB: Grade = UphillC: Distance = 6

A: Golfer

Accu

racy

One Factor Plot

Neal James Randall J igg

-2.06973

40.4477

82.9651

125.483

168

333 2555552

4444 55555

ANOVA-Determination of Interaction of factors for Hole out

Response:

Hole Out          

ANOVA for Selected Factorial Model            

Analysis of variance table [Partial sum of squares]            

  Sum of   Mean F    

Source Squares DF Square Value Prob > F  

Model 5.775 15 0.3852.05333

3 0.0154  

Golfer 2.225 30.74166

73.95555

6 0.0096significan

t

Grade 0.1 1 0.10.53333

3 0.4664  

Distance 0.225 1 0.225 1.2 0.2752  

Golfer/Grade 1.55 30.51666

72.75555

6 0.0447significan

t

Golfer/Distance 0.625 30.20833

31.11111

1 0.3467  

Distance/Grade 0.9 1 0.9 4.8 0.0301significan

t

ABC 0.15 3 0.050.26666

7 0.8493  

Pure Error 27 144 0.1875      

Cor Total 32.775 159        

Comparison of number of hole outs

One Putts

02468

10121416

Uphill 6 Foot Downhill 6 Foot Uphill 12 Foot Downhill 12 Foot

Putt Type

Num

ber o

f hol

e ou

ts

One Putts

0

5

10

15

20

25

30

Downhill Uphill

Grade

Num

ber o

f hol

e ou

ts

ANOVA- Determination of Interaction of factors for Lip out

Response: Lip Out          

ANOVA for Selected Factorial Model            

Analysis of variance table [Partial sum of squares]            

  Sum of   Mean F    

Source Squares DF Square Value Prob > F  

Model 1.69375 15 0.112917 1.366387 0.1716  

Golfer 0.81875 3 0.272917 3.302521 0.0221  

Grade 0.05625 1 0.05625 0.680672 0.4107  

Distance 0.05625 1 0.05625 0.680672 0.4107  

Golfer/Grade 0.36875 3 0.122917 1.487395 0.2205  

Golfer/Distance 0.16875 3 0.05625 0.680672 0.5652  

Distance/Grade 0.05625 1 0.05625 0.680672 0.4107  

ABC 0.16875 3 0.05625 0.680672 0.5652  

Pure Error 11.9 144 0.082639      

Cor Total 13.59375 159        

Lip outs cont. Golfer was determined to be a factor,

although this is believed to stem from the fact that 2 golfers had 13 out of 15 lip outs

Lip outs are thought to have no correlation from any of the factors we tested

As Randall and Jigg were the better putters, there is a higher probability of their putts ending up near the hole

Analyzing Each Golfer

JamesNealRandallJigg

Golfer - James

ANOVA - JamesResponse: James' Accuracy      

ANOVA for Selected Factorial Model            

Analysis of variance table [Partial sum of squares]          

  Sum of   Mean F    

Source Squares DF Square Value Prob > F  

Model 10605.3392 3 3535.113 11.88796 < 0.0001 significant

Distance (A) 3532.91696 1 3532.917 11.88057 0.0015  

Grade (B) 6398.73801 1 6398.738 21.51782 < 0.0001  

Distance and Grade (AB) 907.790643 1 907.7906 3.052738 0.0896  

Pure Error 10110.5556 34 297.3693      

Cor Total 20715.8947 37        

Values of "Prob-F" less than 0.05 indicate model terms are significant      

Time-Based Effects - James

DESIGN-EXPERT PlotAccuracy

Run Number

Stu

dent

ized

Res

idua

ls

Residuals vs. Run

-3.00

-1.50

0.00

1.50

3.00

1 14 27 40

Outlier T - JamesDESIGN-EXPERT PlotAccuracy

Run Number

Out

lier T

Outlier T

-3.50

-1.75

0.00

1.75

3.50

1 14 27 40

Cook’s Distance - JamesDESIGN-EXPERT PlotAccuracy

Run Number

Cook

's Di

stan

ce

Cook's Distance

0.00

0.25

0.50

0.75

1.00

1 14 27 40

ANOVA - James

Response: James' Hole Out      

ANOVA for Selected Factorial Model            

Analysis of variance table [Partial sum of squares]          

  Sum of   Mean F    

Source Squares DF Square Value Prob > F  

Model 1.84210526 3 0.614035 8.350877 0.0003 significant

Distance (A) 0.59210526 1 0.592105 8.052632 0.0076  

Grade (B) 0.59210526 1 0.592105 8.052632 0.0076  

Distance and Grade (AB) 0.59210526 1 0.592105 8.052632 0.0076  

Pure Error 2.5 34 0.073529      

Cor Total 4.34210526 37        

Values of "Prob-F" less than 0.05 indicate model terms are significant      

Significance

Strong interaction of Grade and Distance on Accuracy for James

Strong interaction of Grade and Distance on Hole Out for James

No interaction of Grade and Distance on Lip Out for James

Golfer - Randall

ANOVA - RandallResponse: Randall's Accuracy      

ANOVA for Selected Factorial Model            

Analysis of variance table [Partial sum of squares]          

  Sum of   Mean F    

Source Squares DF Square Value Prob > F  

Model 1102.41323 1 1102.413 4.724546 0.0362 significant

Grade (B) 1102.41323 1 1102.413 4.724546 0.0362  

Residual 8633.48421 37 233.3374      

Lack of Fit 249.384211 2 124.6921 0.520536 0.5987 not significant

Pure Error 8384.1 35 239.5457      

Cor Total 9735.89744 38        

Values of "Prob-F" less than 0.05 indicate model terms are significant      

Time-Based Effects - Randall

DESIGN-EXPERT PlotAccuracy

Run Number

Stud

entiz

ed R

esidu

als

Residuals vs. Run

-3.00

-1.50

0.00

1.50

3.00

1 14 27 40

Outlier T - RandallDESIGN-EXPERT PlotAccuracy

Run Number

Out

lier T

Outlier T

-3.50

-1.75

0.00

1.75

3.50

1 14 27 40

Cook’s Distance - RandallDESIGN-EXPERT PlotAccuracy

Run Number

Cook

's Di

stan

ce

Cook's Distance

0.00

0.25

0.50

0.75

1.00

1 14 27 40

ANOVA - RandallResponse: Randall's Lip Out      

ANOVA for Selected Factorial Model            

Analysis of variance table [Partial sum of squares]          

  Sum of   Mean F    

Source Squares DF Square Value Prob > F  

Model 0.77962578 2 0.389813 3.265602 0.0497 significant

Distance (A) 0.40007112 1 0.400071 3.351539 0.0754  

Grade (B) 0.40007112 1 0.400071 3.351539 0.0754  

Residual 4.2972973 36 0.119369      

Lack of Fit 0.0972973 1 0.097297 0.810811 0.374 not significant

Pure Error 4.2 35 0.12      

Cor Total 5.07692308 38        

Values of "Prob-F" less than 0.05 indicate model terms are significant      

Significance - Randall

Strong interaction of Grade on Accuracy No interaction of Distance on Accuracy

Slight interaction of Grade and Distance on Lip Out

No significant interaction of Grade and Distance on Hole Out

Golfer - Jigg

Analysis - Jigg

Percentage of Hole Outs 19/40 ~%50 accurate

No statistical interaction of grade and distance on accuracy with high Hole Out percentage

Golfer - Neal

ANOVA – Accuracy

Response:

Neal's Accuracy        

ANOVA for Selected Factorial Model

Log Transform            

Analysis of variance table [Partial sum of squares]          

  Sum of   Mean F    

Source Squares DF Square Value Prob > F  

Model 2.41667213 3 0.805557 2.129208 0.1153 not significant

Distance (A) 0.0068631 1 0.006863 0.01814 0.8937  

Grade (B) 0.51684232 1 0.516842 1.366091 0.2509  

Grade and Distance (AB) 1.95866195 1 1.958662 5.177035 0.0295  

Pure Error 12.4851078 33 0.378337      

Cor Total 14.90178 36        

Values of "Prob-F" less than 0.05 indicate model terms are significant      

ANOVA - Hole Out

Response:

Neal's Hole Out        

ANOVA for Selected Factorial Model            

Analysis of variance table [Partial sum of squares]          

  Sum of   Mean F    

Source Squares DF Square Value Prob > F  

Model 1.93971471 3 0.646572 4.92705 0.0062 significant

Distance (A) 0.21020878 1 0.210209 1.601848 0.2145  

Grade (B) 1.28027247 1 1.280272 9.756021 0.0037  

Distance and Grade (AB) 0.57963553 1 0.579636 4.416979 0.0433  

Pure Error 4.33055556 33 0.131229      

Cor Total 6.27027027 36        

Values of "Prob-F" less than 0.05 indicate model terms are significant      

Significance Slight interaction of Distance /

Grade (AB) on Accuracy Made high percentage of 12ft

Downhill putts Strong interaction of Grade (B) and

Distance / Grade (AB) but not Distance (A) on Hole Out

No Lip Outs

Other Factors Effecting Putts

Grass length Moisture Club type Grain – time of day

Questions / Comments?