Get documents about "Putting Accuracy
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Document Sample
Putting Accuracy
Neal Hatch
James 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 Plot Residuals vs. Run
Accuracy
4.20
2.40
Studentized Residuals
0.60
-1.20
-3.00
1 54 107 160
Run Number
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 15 1433.487 3.058431 0.0003
Golfer 3361.65 3 1120.55 2.390762 0.0712 very close
Grade 8122.5 1 8122.5 17.32985 < 0.0001 significant
Distance 3478.225 1 3478.225 7.421005 0.0072 significant
Golfer/Grade 2902.85 3 967.6167 2.064469 0.1076
Golfer/Distance 2076.025 3 692.0083 1.476442 0.2235
Distance/Grade 24.025 1 24.025 0.051259 0.8212
ABC 1537.025 3 512.3417 1.093112 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 One Factor Plot DESIGN-EXPERT Plot One Factor Plot
Accuracy 168 Accuracy 168
X = C: Distance X = C: Distance
Design Points Design Points
126 126
Actual Factors Actual Factors
A: Golf er = Neal A: Golf er = James
B: Grade = Downhill B: Grade = Downhill
Accuracy
Accuracy
84
84
42
42
0 2 5
0
6 12
6 12
DESIGN-EXPERT Plot One Factor Plot DESIGN-EXPERT Plot One Factor Plot
C: Distance Accuracy 168
C: Distance Accuracy 168
X = C: Distance
X = C: Distance
Design Points
Design Points
126
Actual Factors 126
A: Golf er = Randall Actual Factors
B: Grade = Downhill A: Golf er = Jigg
B: Grade = Downhill
Accuracy
Accuracy
84
84
42
42
0 3 4 0 5 5
6 12 6 12
C: Distance C: Distance
Uphill 6 and 12 foot putts for
each golfer
DESIGN-EXPERT Plot One Factor Plot DESIGN-EXPERT Plot One Factor Plot
Accuracy 168
Accuracy 168
X = C: Distance
X = C: Distance
Design Points
126 Design Points
Actual Factors 126
A: Golf er = Neal Actual Factors
B: Grade = Uphill A: Golf er = James
B: Grade = Uphill
Accuracy
Accuracy
84
84
42
42
3
0 2
0 5
6 12
6 12
DESIGN-EXPERT Plot One Factor Plot
DESIGN-EXPERT Plot One Factor Plot
Accuracy 168
C: Distance Accuracy 168
C: Distance X = C: Distance
X = C: Distance
Design Points
Design Points
125.484
126 Actual Factors
Actual Factors A: Golf er = Jigg
A: Golf er = Randall B: Grade = Uphill
B: Grade = Uphill
Accuracy
Accuracy
82.9679
84
40.4519
42
2
2
-2.06414 5 4
0 4
6 12 6 12
C: Distance C: Distance
6 foot downhill and uphill
putts for each golfer
DESIGN-EXPERT Plot One Factor Plot DESIGN-EXPERT Plot One Factor Plot
Accuracy 168 Accuracy 168
X = B: Grade X = B: Grade
Design Points Design Points
126 126
Actual Factors Actual Factors
A: Golf er = Neal A: Golf er = James
C: Distance = 6 C: Distance = 6
Accuracy
Accuracy
84 84
42 42
3 2
0 2 0 5
Uphill Downhill Uphill Downhill
DESIGN-EXPERT Plot One Factor Plot
B: Grade DESIGN-EXPERT Plot One Factor Plot B: Grade
Accuracy 168
Accuracy 168
X = B: Grade
X = B: Grade
Design Points
Design Points 125.484
126 Actual Factors
Actual Factors A: Golf er = Jigg
A: Golf er = Randall C: Distance = 6
C: Distance = 6
Accuracy
Accuracy
82.9679
84
40.4519
42
-2.06414 5 5
0 4 3
Uphill Downhill Uphill Downhill
B: Grade B: Grade
12 foot downhill and uphill
putts for each golfer
DESIGN-EXPERT Plot One Factor Plot DESIGN-EXPERT Plot One Factor Plot
Accuracy 168 Accuracy 168
X = B: Grade X = B: Grade
Design Points Design Points
126 126
Actual Factors Actual Factors
A: Golf er = Neal A: Golf er = James
C: Distance = 12 C: Distance = 12
Accuracy
Accuracy
84 84
42 42
0 5 0
Uphill Downhill Uphill Downhill
DESIGN-EXPERT Plot One Factor Plot
B: Grade
DESIGN-EXPERT Plot One Factor Plot B: Grade Accuracy 168
Accuracy 168
X = B: Grade
X = B: Grade
Design Points
Design Points
126
126 Actual Factors
Actual Factors A: Golf er = Jigg
A: Golf er = Randall
C: Distance = 12
C: Distance = 12
Accuracy
Accuracy
84
84
42
42
2
2
0 4 0 4 5
Uphill Downhill Uphill Downhill
B: Grade
DESIGN-EXPERT Plot One Factor Plot DESIGN-EXPERT Plot One Factor Plot
Accuracy 168 Accuracy 168
X = A: Golf er X = A: Golf er
Design Points Design Points
126 126
Actual Factors Actual Factors
B: Grade = Downhill B: Grade = Downhill
C: Distance = 6 C: Distance = 12
Accuracy
Accuracy
84 84
42 42
0 2 3 5 0 5 4 5
Neal James Randall Jigg Neal James Randall Jigg
A: Golfer A: Golfer
DESIGN-EXPERT Plot One Factor Plot DESIGN-EXPERT Plot One Factor Plot
Accuracy 168 Accuracy 168
X = A: Golf er X = A: Golf er
Design Points Design Points
125.483 125.483
Actual Factors Actual Factors
B: Grade = Uphill B: Grade = Uphill
C: Distance = 6 C: Distance = 6
Accuracy
Accuracy
82.9651 82.9651
40.4477 40.4477
3 2 3 2
-2.06973 5 4 5 -2.06973 5 4 5
Neal James Randall Jigg Neal James Randall Jigg
A: Golfer A: Golfer
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 0.385 2.053333 0.0154
Golfer 2.225 3 0.741667 3.955556 0.0096 significant
Grade 0.1 1 0.1 0.533333 0.4664
Distance 0.225 1 0.225 1.2 0.2752
Golfer/Grade 1.55 3 0.516667 2.755556 0.0447 significant
Golfer/Distance 0.625 3 0.208333 1.111111 0.3467
Distance/Grade 0.9 1 0.9 4.8 0.0301 significant
ABC 0.15 3 0.05 0.266667 0.8493
Pure Error 27 144 0.1875
Cor Total 32.775 159
Comparison of number of hole
outs
One Putts One Putts
16 30
Number of hole outs
Number of hole outs
14 25
12
10 20
8 15
6 10
4
2 5
0 0
Uphill 6 Foot Downhill 6 Foot Uphill 12 Foot Downhill 12 Foot Downhill Uphill
Putt Type Grade
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
James
Neal
Randall
Jigg
Golfer - James
ANOVA - James
Response: 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 Plot Residuals vs. Run
Accuracy
3.00
1.50
Studentized Residuals
0.00
-1.50
-3.00
1 14 27 40
Run Number
Outlier T - James
DESIGN-EXPERT Plot Outlier T
Accuracy
3.50
1.75
Outlier T
0.00
-1.75
-3.50
1 14 27 40
Run Number
Cook’s Distance - James
DESIGN-EXPERT Plot Cook's Distance
Accuracy
1.00
0.75
Cook's Distance
0.50
0.25
0.00
1 14 27 40
Run Number
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 - Randall
Response: 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 Plot Residuals vs. Run
Accuracy
3.00
1.50
Studentized Residuals
0.00
-1.50
-3.00
1 14 27 40
Run Number
Outlier T - Randall
DESIGN-EXPERT Plot Outlier T
Accuracy
3.50
1.75
Outlier T
0.00
-1.75
-3.50
1 14 27 40
Run Number
Cook’s Distance - Randall
DESIGN-EXPERT Plot Cook's Distance
Accuracy
1.00
0.75
Cook's Distance
0.50
0.25
0.00
1 14 27 40
Run Number
ANOVA - Randall
Response: 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
Neal's
Response: 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
Neal's Hole
Response: 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?
