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Putting Accuracy
Neal HatchJames Kuykendall
7/27/2006
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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
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Is There a Significance? General Factor Interaction (Basically 2FI)
Golfer Neal James Randall Jigg
Grade Uphill Downhill
Distance 6ft 12ft
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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
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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
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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
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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
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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
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Golfer - Neal
Novice Never played a full game (18) Should stick to putt-putt
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Golfer - James
Absolutely terrible putter Is terrible at golf and should
probably stop playing entirely
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Golfer - Jigg
Lifelong golfer Placed second in state senior year
in high school By far best putter in group
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Golfer - Randall
Played golf for approximately seven years
Excellent putter
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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
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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
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Strictly Interaction
We will be focusing on strictly interactions between factors and the accuracy, hole out, and lip out
No models were generated
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Analyzing Each Golfer
JamesNealRandallJigg
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Golfer - James
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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
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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
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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
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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
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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
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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
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Golfer - Randall
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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
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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
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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
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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
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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
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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
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Golfer - Jigg
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Analysis - Jigg
Percentage of Hole Outs 19/40 ~%50 accurate
No statistical interaction of grade and distance on accuracy with high Hole Out percentage
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Golfer - Neal
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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
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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
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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
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Other Factors Effecting Putts
Grass length Moisture Club type Grain – time of day
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Questions / Comments?