Disc Golf – Is a Hyzer Shot Easier
than an Anhyzer Shot?
David R. Gibson, Brian Ring
November 14, 2012
Math 2620 C
1.0 Introduction and Problem Statement
Brief statement of what you are studying and what your preliminary belief is about the difference in the two
populations is.
This report considers the accuracy of disc golfers as they play two different holes. Both holes are heavily wooded
and similar in length; however, one hole requires curve to the right and the other requires a curve to the left. A disc
golfer will tee off and when the disc lands, we will record the distance to the basket. The closer to the basket, the
more accurate the shot. We suspect that disc golfers will be less accurate with the hole that requires a curve to the
right.
In the sections that follow we provide some background information on disc golf, explain our experimental setup,
detail our sampling plan, summarize the data descriptively, and provide a summary of our findings.
2.0 Background
Provide any background information required to understand your study. Define terms as necessary.
Disc golf is a sport that is played in a manner similar to ball
golf except that the player throws a disc (similar to a Frisbee)
instead of hitting a ball. A player starts by throwing his disc
from the tee pad counting how many throws it takes to get
the disc in the basket. The objective is to make the least
number of throws possible to get the disc in the basket. The
figure on the right shows a player putting. If she is
successful, the disc will catch in the chains and drop into the
basket. The middle figure on the right shows a player teeing
off.
Source: http://mainetoday.com/uncategorized/swing-tossputt-great-maine-spots-for-mini-golf-disc-golf-batting-cages/
There are many types of throws in disc golf. One of the most
common is the backhand throw. This is similar to the way
many people would throw a Frisbee when they use their
right hand, carrying the disc from the left side of their body
out in front of them and releasing the Frisbee. The backhand
through in disc golf is illustrated in the figure on the right.
There, we see the player doing a run-up (called an X-step). In
the second from the left image we see the right arm pulled
back. He propels his arm forward and releases the disc when
his arm is in front.
Source: http://laurabenish.blogspot.com/
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Variations in the arm angle and disc angle (see figure on right) at
release control whether the disc flies relatively straight, curves to
the left, or curves to the right (see figure on the far right). For a
right-handed, backhand throw, there is a strong tendency for the
disc to fade to the left at the end of a stable (flat) throw (see
figure on right). Thus, it is easier for a right-handed player to
curve the disc to the left due to a technique called hyzer where
the disc is tilted down upon release. Curving the disc to the right
uses a technique called anhyzer and is generally harder to execute
(for a right-handed player) due to the natural tendency of the disc to fade to the left.
Source (figure on right): http://www.cloud9discgolf.com/Innova_Disc_Guide_s/10.htm
Source (figure on far right): http://www.dgcoursereview.com/forums/showthread.php?t=80082
3.0 Experimental Setup
Provide any details on the experimental procedures you will use. In later sections you will define the populations you
will study and provide a sampling plan. So, don’t do that here. In some sense, this section is background information
for your sampling plan.
We will collect our data at Freedom Park Disc Golf Course in Valdosta, GA. We will use holes 7 and 12. The layout for
each hole is shown below. We will consider players teeing off from the White tee (Amateur tee) and throwing
towards the basket in the “A” (close) position. Hole 7 requires a throw that curves to the right as it navigates a
corridor of trees. Hole 12 is similar except that it requires a throw that curves to the left. Both holes are similar in
length (156 feet and 176 feet, respectively) and easily within reach of almost all players provided the corridor of
trees is navigated properly.
Notice that there is a “Mando” on hole 12. This means, that in official play, the thrown disc must go around the right
side of the tree shown. However, in casual play, most people do not follow this rule and just play from where ever
the disc lands. In our data collection, we will ignore this rule as well so as to make the comparison more fair.
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The straight-line (Euclidean) distance of each throw to the
center of the basket will be recorded. We will use a Keson 100 ft.
Nylon Coated Steel Tape Measure as shown on the right with
units in feet, inches, and 1/8th inches. We will round all distances
to the nearest inch.
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4.0 Populations
Carefully define the two populations you are studying.
We consider two populations where both populations have these characteristics:




Male members of the Facebook group, Valdosta Disc Golf
Have been playing disc golf from 1-3 years
Consider themselves amateurs
Primarily use a right-hand backhanded throw.
Including the characteristics above, we define the two populations:


Population 1 – Hole 7 tee shots
Population 2 – Hole 12 tee shots
5.0 Sampling Plan
Provide all details of your sampling plan: who, what, when, where, how. Discuss any situations that could arise that
will disrupt your plan and how you will deal with these.
The participants for the study were chosen by sending an email to all men who are members of the Disc Golf
Valdosta Facebook site. We excluded women from the study because there are very few and we didn’t think we
could get enough so that we had an equal number of men and women participants. In the email, we told them
about our study asked if they wanted to participate. The email is shown below:
We are taking a course in statistics (Math 2620) at Valdosta State University. As a part of that course,
we are conducting an experiment to compare the accuracy between two different holes on the course
to see which hole is “harder”. If you are chosen for the experiment, we will ask you to make your
standard throw from the tee of one of the holes. If you are interested, please respond to these
questions:





Have you been playing disc golf for 1-3 years?
Do you play 2-4 times per month, on average?
Do you consider yourself an “amateur” at disc golf?
Do you commonly use a right-hand, back-hand throw (if selected for the experiment, you will
be asked to use this throw on a hole?
Are you available to from 9am-11am on Saturday, September 22 or Saturday, September 29?
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22 people responded “yes” to all five questions. 17 of these were available on both dates. From these 22, we
randomly selected 8 participants for Saturday, September 22 and 8 participants for Saturday, September 29. We
sent another email to the individuals chosen for the experiment asking them to show up on the designated date. We
did not tell them which hole they would be throwing from.
The sampling plan is shown below:
Saturday, September 22, 9am-11am
1. Read Introduction and Instructions*
2. Warm-up – participants warm-up in any way they choose including stretching, putting, or driving.
3. Walk participants to Hole 7
4. Repeat 5 times:
a. A person is selected at random and they make their throw. Repeat until all 8 have thrown once.
b. Each person finds their disc
c. The investigators measure the distance for each throw.
Saturday, September 29, 9am-11am
 Same as September 22 except we will use Hole 12
Several situations could arise to disrupt our sampling plan:
1. One of the 8 people chosen does not show up – In this case we will simply rotate through the people that
showed up until a total of 40 throws have been made. Thus, some participants may have one more throw
than some others.
2. Rain – In this case we will reschedule
3. A group playing a round of disc golf needs to play the hole we are using – We will continue the current
rotation of players throwing, take our measurements, and then let the group play through. Then, we will
continue with the rotation.
6.0 Insurance of a Simple Random Sample
Discuss how your sampling plan ensures a simple random sample.
The following conditions must be met to have a simple random sample
1. Each item in the sample comes from the same population. Provided that the respondents to our email
responded truthfully on all conditions (e.g. that they have been playing 1-3 years, etc) then this criterion has
been met.
2. Each item in the sample is independent of the others. This criterion is not fully met for several reasons.
First, each participant will be throwing 5 times and so their distances to the basket will necessarily be
dependent upon one another. Second, players can be influenced by other players’ throws. For instance, one
player may be more accurate by throwing a “high” hzyer shot and others may try to emulate that.
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3. Each member of the population has an equal chance to be in the sample. This criterion has been meet
because all male members of the Facebook group were contacted about participation.
7.0 Data Collection
Provide any information about the actual data collection.
The data collection went fairly smoothly. One thing we had not thought out very well was how to measure straight
line distance when there were trees and or bushes/undergrowth in the path from the disc to the basket. For the
case of undergrowth that was not too tall, we simply held the tape measure up off the ground. In a few cases, trees
prevented us from accurately measuring the straight-line distance. In these cases we measured the distance to the
tree, roughly estimated the diameter of the tree, and then continued with the tape on the other side of the tree.
8.0 Analysis
Analyze your data as thoroughly as possible using numerical descriptive statistics, histograms, boxplots, and z-scores.
Focus should be on the center of the data, the spread of the data, and skewness of the data. You should compare the
two samples as much as possible as opposed to simply listing facts about the samples in isolation.
6.1 Introduction
Figure 1 shows a scatter plot of the throws for each hole. Most of the throws for Hole 7 (blue circles), which requires
a right curve, are to the left of the basket and in front of it. This suggests that throws are landing along the rightcurved corridor leading to the basket. We see a similar result for Hole 12 (green triangles), which requires a left
curve, most of the throws are landing along the left-curved corridor leading to the basket. However, in the case of
Hole 12, the throws appear to be closer to the basket.
7
25
20
15
10
Hole 7
Hole 12
Basket
5
0
-5
Y (feet)
-10
-15
-20
-25
-30
-35
-40
-45
-50
-55
-35 -30 -25 -20 -15 -10
-5
0
5
10
15
X (feet)
Figure 1 – Scatter plot of throws.
8
20
25
30
35
6.2 Numerical Descriptive Statistics
The numerical descriptive statistics are shown in Table 1 below.
Descriptive Statistics: Hole 7, Hole 12
Variable
Hole 7
Hole 12
N
40
40
Mean
26.13
18.12
StDev
14.71
8.76
Minimum
0.97
1.69
Q1
14.46
12.68
Median
26.54
18.71
Q3
39.61
24.76
Maximum
53.36
32.75
Range
52.39
31.06
IQR
26.15
12.07
Table 1 – Numerical descriptive statistics
Central Tendency of Data
The numerical descriptive statistics shown in Table 1 reveal that the Hole 12 throws are about 31% closer to
the basket than the Hole 7 throws which amounts to about an 8 foot advantage.
18.12 − 26.13
∗ 100% = −30.6%
26.13
Variability of the Data
The Hole 12 throws have about 40% less variability than the Hole 7 throws as measured by the standard
deviation.
8.76 − 14.71
∗ 100% = −40.4%
14.71
Similarly, the range and IQR show 39% and 54% less variability, respectively. This suggests that Hole 7, with
the required right curve is harder for most right-handed throwing back-hand to execute accurately.
Shape of the Distribution of the Data
The mean and median are similar in value for both holes suggesting symmetry in the data.
6.3 Histograms
The histograms for each hole are shown in Figures 2 and 3 below. Hole 7 throws appear to be right-skewed while
Hole 12 throws appear to be bell-shaped. The histograms also confirm that the variability is much larger for Hole 7
throws (range is about 60) compared to Hole 12 throws (range is about 35).
Histogram of Hole 7
Histogram of Hole 12
35
30
30
25
25
Percent
Percent
20
15
10
15
10
5
0
20
5
0
10
20
30
Distance (feet)
40
50
0
60
Figure 2 – Histogram for Hole 7 throws
0
7
14
21
Distance (feet)
Figure 3 – Histogram for Hole 12 throws
9
28
35
6.4 Boxplot
The boxplots are shown in Figure 4 below.
Boxplot of Hole 7, Hole 12
Hole 7
Hole 12
0
5
10
15
20
25
30
35
Distance (feet)
40
45
50
55
60
Figure 4 – Boxplot for Hole 7 and 12 throws
Central Tendency of Data
The median for Hole 7 appears to be about 7-8 feet larger than the median for Hole 12.
Variability of the Data
The variability is clearly larger for Hole 7.
Shape of the Distribution of the Data
The throws for both Holes appear to be fairly symmetric. For hole 7, this contradicts what we saw with the
histogram, but confirms our observation of symmetry using the numerical values of the mean and median
for each sample.
Outliers
No outliers are indicated for either sample.
Other Observations
 The closest 25% of throws for either hole are fairly close. 25% of Hole 7 throws are within about 14 feet
while 25% of Hole 12 throws are within about 13 feet.
 Approximately 25% of the throws for hole 7 are at least 40 feet from the basket where as none of the
hole 12 throws are further than about 32 feet.
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6.5 Z-scores
The distance from the basket for all throws is shown in the table below which is sorted from closest to furthest.
Beside each distance is the corresponding z-score. The z-scores do not indicate any outliers for either sample. The
closest throws have z-scores of -1.7 and -1.9 for holes 7 and 12 respectively. The furthest throws have z-scores of 1.9
and 1.7 for holes 7 and 12, respectively.
Table 2 – Data (sorted) and Z-scores for throws
Hole 7
Hole 12
Distance
Z-Score
Distance
Z-Score
1.0
-1.7
1.7
-1.9
1.6
-1.7
2.5
-1.8
5.8
-1.4
3.1
-1.7
5.9
-1.4
3.5
-1.7
8.5
-1.2
6.0
-1.4
10.1
-1.1
6.3
-1.4
11.4
-1.0
7.4
-1.2
12.7
-0.9
8.7
-1.1
12.9
-0.9
12.5
-0.6
14.2
-0.8
12.7
-0.6
15.2
-0.7
12.7
-0.6
15.6
-0.7
12.8
-0.6
16.4
-0.7
13.2
-0.6
17.6
-0.6
13.6
-0.5
18.2
-0.5
16.7
-0.2
18.3
-0.5
17.5
-0.1
18.6
-0.5
17.8
0.0
20.7
-0.4
18.3
0.0
21.9
-0.3
18.4
0.0
26.2
0.0
18.5
0.0
26.9
0.1
18.9
0.1
28.9
0.2
19.1
0.1
29.1
0.2
19.8
0.2
29.7
0.2
20.1
0.2
29.9
0.3
20.1
0.2
30.0
0.3
20.2
0.2
31.4
0.4
20.7
0.3
31.5
0.4
23.6
0.6
37.3
0.8
24.3
0.7
39.3
0.9
24.6
0.7
39.7
0.9
24.8
0.8
42.7
1.1
24.8
0.8
42.7
1.1
26.7
1.0
42.8
1.1
27.2
1.0
11
44.7
1.3
28.3
1.2
46.3
1.4
29.7
1.3
46.7
1.4
30.3
1.4
47.8
1.5
31.8
1.6
51.7
1.7
32.7
1.7
53.4
1.9
32.8
1.7
9.0 Summary and Conclusions
Summarize your findings and make some conclusions about your original question.
These sample results indicate that Hole 12 throws are closer, with its required left-curve (hyzer) is easier than Hole 7
with its required right-curve (anhyzer) as on average Hole 12 throws were 31% (8 feet) closer than the Hole 7
throws. Further, Hole 12 throws had much smaller variability (about 40%) than the Hole 7 throws also indicating that
Hole 12 is easier. Finally, both samples appeared to be somewhat symmetric, perhaps with a right-skew for Hole 7.
The results lend support to the claim that a hyzer shot is easier than an anhyzer shot for a right-handed player using
a back-hand throw.
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