Disc Golf Is a Hyzer Shot Easier Than an Anhyzer Shot?

Disc Golf – Is a Hyzer Shot Easier than an Anhyzer Shot?

David R. Gibson, Brian Ring

November 14, 2012

Math 2620 C

1.0Introduction 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.

2.0Background

Provide any background information required to understand your study. Define terms as necessary.

Source:

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:

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.

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):

Source (figure on far right):

3.0Experimental 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.

The straight-line (Euclidean) distance of each throw to the center of the basket will be recorded. We will use a Keson100 ft. Nylon Coated Steel Tape Measure as shown on the right with units in feet, inches, and 1/8thinches. We will round all distances to the nearest inch.

4.0Populations

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

5.0Sampling 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?

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:

1. A person is selected at random and they make their throw. Repeat until all 8 have thrown once.
2. Each person finds their disc
3. 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.

6.0Insurance 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.
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.

7.0Data 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.

8.0Analysis

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 right-curved 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.

Figure 1 – Scatter plot of throws.

6.2 Numerical Descriptive Statistics

The numerical descriptive statistics are shown in Table 1 below.

Descriptive Statistics: Hole 7, Hole 12
Variable N Mean StDev Minimum Q1 Median Q3 Maximum Range IQR
Hole 7 40 26.13 14.71 0.97 14.46 26.54 39.61 53.36 52.39 26.15
Hole 12 40 18.12 8.76 1.69 12.68 18.71 24.76 32.75 31.06 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.

Variability of the Data

The Hole 12 throws have about 40% less variability than the Hole 7 throws as measured by the standard deviation.

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.

6.3Histograms

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).

Figure 2 – Histogram for Hole 7 throws /
Figure 3 – Histogram for Hole 12 throws

6.4Boxplot

The boxplots are shown in Figure 4 below.

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.

6.5Z-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
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

9.0Summary 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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