Trial Chart

Trial #	Angle Measure	Max Height	Y or N
1	57.75	12.14	Y
2	56.2	12.9	Y
3	58.7	12.73	N
4	59.34	12.3	N
5	71.38	14.3	Y
6	52	11.7	N
7	58	12.26	Y
8	56.54	12	N
9	58.55	11.52	N
10	60.1	13.18	N
11	58.81	12.9	N
12	52.22	11.45	Y
13	64.24	13.13	Y
14	56.19	12.6	Y
15	57.1	11.9	Y
16	60.1	12.4	Y
17	60.4	12	N
18	59.74	12.6	N
19	56.1	11.9	Y
20	57.15	11.7	N
21	59.79	12.77	N
22	61.3	13.2	N
23	68.4	14.82	N
24	55.2	12.25	N
25	53.7	11.4	N
26	55.7	11.8	N
27	53.6	11.36	N
28	55.5	11.9	Y
29	62.5	13	N
30	52	11.3	N
31	53.58	12.1	Y
32	54.25	12.3	Y
33	67.38	14.7	Y
34	62.13	12.8	N
35	67.85	14.8	Y
36	56.2	11.8	Y
37	59.3	12	N
38	52.42	11.6	Y
39	62.5	13.5	Y
40	50.1	11.7	N
41	56.3	12.5	Y
42	49	11.8	N
43	47.61	11.5	N
44	47.52	11.4	N
45	50	12.1	Y
46	56.31	12.9	N
47	55	12.4	Y
48	57.2	12	N
49	54.5	11.8	Y
50	54	12.4	Y

Week 4

This week I began my experiment! I took 50 free throws and recorded every one. I put them into LoggerPro and found the angle and the max height. I LoggerPro-ed every single one of the fifty shots and put them into something like the following:

Green Line = Scale of 10 ft

Yellow lines = Origin

Week 3--Experiment basics

Credit

For this experiment, I would like to model the above diagram. Experimenting with different angles. I will measure using logger pro.

Given my height of 6'3, what launch angle is the best. Technically speaking, if I throw the ball straight up in the air with the right left-to-right distance it has the best chance of going in because of the greater surface area of the hoop opening. The shorter the arc, the less chance it has of going in because if the ball had eyes, it would "see" a smaller opening on the hoop.

Basic (informal) Procedure
Record multiple free throw attempts of various angles and corresponding speeds.
Use logger pro to track the distance and angle speed of each shot.
Chart what angle-range works best.

1. Record multiple free-throw attempts of all different angles.
2. divide the one video into multiple smaller videos.
3. Open each video in Logger Pro.
4. Place a horizontal line at the height of the center of the ball at the release point.
5. Play dot-to-dot on Logger Pro. The first few dots should be linear. Draw a solid line--the "line of best fit" of the first few dots.


1. Record multiple free-throw attempts of all different angles.
2. Separate the video into multiple segments. Each segment being one shot.
3. Put the video into Logger Pro
4. Set the Origin at the ball when I am in set position--Where I am beginning my upward motion.
5. Set the Scale. The obvious, easy way to do this is put 10 feet from the rim to the ground.
6. Play dot-to-dot for 10 frames. Find the linear regression of that segment. One way to do this is to put the cursor over the 10th dot and look at the coordinates in the top right corner. Plug those "triangle side lengths" into this angle calculator to find the shooting angle.
7. Calculate the arc height. Click the ruler with the arrow next to it and make a line segment from the top of the arc to the ground. Note: This will not work unless you do step 5.
8. Make a table of all of the values

Week 2

Physics of Basketball
Over the course of this period, I basically researched the physics of taking a free throw.
I discussed this topic with some of my friends but they all basically said the same thing: The angle and the power of the shot must correlate in order for the basketball to go in.

• Free Throws
• Statistics show that the taller a player is, the lower his percentage is. 
• Some Backspin is recommended.
• Don't aim at the center of the hoop, but rather about 5 centimeters more towards the backboard. 
• Angles shoot be between 50 and 55. 
• The hoop is twice the diameter of a basketball so there is some room for error. 
• The height of the arc should be about as high as the top of the backboard. 
• Dr. Tom Amberry holds the world record for most consecutive free throws made. He made 2750 CONSECUTIVE FREE THROWS AT AGE 72 AND ONLY STOPPED BECAUSE THE GYM WAS CLOSING FOR THE NIGHT. yea.
• http://freethrow.com/ lists "Free throw shooting" as one of Dr. Amberry's hobbies after he retired from podiatry. 
• He did this in a gym. This does not test the mental confidence that a player in the NCAA Championship game in the last minute has. 

• 
• https://news.ncsu.edu/2009/11/161mkfreethrow/
• 
  

This is the equation that explains how to find the proper angle of a free throw

For this experiment I want to figure out why even the best basketball players miss a good amount of free throws. I want to figure out what they must do to improve their percentage.

Week 1--Research

The Physics of Basketball by John J. Fontanella

I chose this book because I was looking to do something related to basketball or baseball (the two easiest sports to analyze and replicate for this project).

Physics all over basketball, beyond just shooting.

Shooting--The angle of launch, trajectory, etc.

Experiment--arc of a shot
The arc of the basketball depends on the velocity and angle of the shot.

Experiment--Height of the bounce depends on velocity and angle of dribble.

Experiment--Heat depends on the number of dribbles experienced by the basketball.

The necessary power is dependent on the angle and vice versa.


In general, the greater the distance between the shooter and the hoop, the greater the necessary force.

credit

The closer you are to the hoop, the greater the shooting angle will be. If you are right under the hoop you are going to be shooting almost straight up.
There isn't one magical angle, however. Many angles work just fine, just not as efficiently.

Many angles work. The higher the angle the better the chances of the ball going through the hoop.
credit 

http://www.secretsofshooting.com/the-physics-of-shooting/

credit

Athletes can use muscle memory in practice but in a game it gets much harder. NBA MVP candidate Steph Curry made 94 out of 100 three-pointers in practice, 77 of which found the net consecutively. In games, however, he averages only 44% from the three-point line. The biggest reason for this is the fact that Curry had to shoot from different angles, distances, etc..


Free throws are the only thing in basketball that are the same all the time. Three-pointers, layups, and jump shots are always different, but free throws is always only the shooter and the basket.

Adjust to the height of the shooter. Wilt Chamberlain finished with 51.1% FT