Determining the best mid range shot location for left handed shooters through the statistics of professional basketball players
Introduction
This IA was heavily inspired through this quote by the greatest basketball player of all time known as Michael Jordan.
“Obstacles don’t have to stop you. If you run into a wall, don’t turn around and give up. Figure out how to climb it, go through it, or work around it.” Michael Jordan
This quote by Michael really resonated within me as I am considered short in the sport of basketball being a 5’4 male. Through my IA I am attempting to use statistics to find areas of the basketball court where I may have an advantage when it comes to scoring and playing defence in order to make up for my lack of size.
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For my IA I decided to investigate the sport of basketball which I am extremely passionate about. I have been playing basketball for fun since birth and have been playing organized basketball for the past 4 years of my life. Through my years of experience in the sport of basketball I am able to distinguish the connection between basketball and mathematics. Through my Internal Assessment I aim to determine if mathematical statistics and probability can be utilised in order to give me personally an advantage. These specific advantages being knowing the areas opponents are more likely to score from and where in theory I may have an advantage when it comes to scoring. Being a 5’4 male I am considered an undersized basketball player thus causing my game to rely heavily on my defensive ability in the midrange and my fade away jumper as well as precise catch and shoot ability. Through this IA my aim is to determine the areas on the court different sized opponents would be able to score on me at the highest percentage from thus showing to me the areas my defence would need to be much more aggressive and tight compared to other areas of the basketball floor. In addition to this I have taken the statistics of the best strictly left handed shooters in the NBA at each of the 4 height ranges I have created. The reason for this is because I myself am a left handed shooter and the statistics will be able to more clearly represent me as a basketball player compared to if I was to use right handed players who are considered a majority in the NBA. By analysing the probability of my opponents and I making a mid range shot at each of the 5 mid range locations I will be able to develop my game by knowing where I have a higher probability of scoring and where I would need to play better defensively.
In order to begin my investigation I gathered data on the midrange shot % of the best left handed players currently in the NBA at the 5 main midrange locations. By utilising the statistics of the best left handed NBA players at each of the 4 height ranges I will be able to analyse the statistics and know what aspects I can improve if I were competing against the best of the best. After gathering the data from various websites I determined the average shot % along with the population standard deviation of each of the 4 height ranges and 5 midrange shot locations. Next I determined the average shot % for each of the 4 height ranges at each of the 5 midrange shot locations. Finally by using the regression equation I am able to determine the probability that I myself as a 165cm tall left handed male am able to score a mid range shot from each of the 5 shot locations. This would theoretically tell me the areas I should aim to shoot from and where I may need more practice in order to develop my skills as a basketball player.
Fig 1. Diagram of an NBA court displaying all of the labeled 5 main mid range shot locations
Raw Data Table
Table 1. The Mid-Range Field Goal % was gathered for 3 NBA players for 4 varying heights. The 3 NBA players chosen at each height are considered the “best players at their respective heights, in order to reflect the statistics of basketball players at the most competitive level.
|
Height (cm) |
NBA Player |
Mid-Range Shot % Long Right Corner |
Mid-Range Shot % Long Right Elbow |
Mid-Range Shot % Long Straight |
Mid-Range Shot % Long Left Elbow |
Mid-Range Shot % Long Left Corner |
|
183 - 191 |
John Wall |
35.3 |
38.6 |
33.6 |
34.3 |
33.7 |
|
De’aaron fox |
25.0 |
41.8 |
28.9 |
43.9 |
38.2 |
|
|
Mike Conley |
35.7 |
39.2 |
41.9 |
42.0 |
42.0 |
|
|
193 - 201 |
James Harden |
38.8 |
36.1 |
39.4 |
38.1 |
37.1 |
|
D’Angelo Russel |
46.0 |
38.6 |
46.2 |
42.7 |
32.7 |
|
|
Shai Gilgeous Alexander |
33.3 |
52.1 |
52.5 |
40.6 |
66.7 |
|
|
203 - 211 |
Marvin Bagely III |
40.0 |
42.1 |
57.1 |
23.1 |
30.0 |
|
Domantas Sabonis |
30.0 |
34.7 |
43.9 |
43.8 |
42.1 |
|
|
Julius Randle |
20.7 |
30.9 |
32.2 |
38.7 |
23.8 |
|
|
213 - 221 |
Ivica Zubac |
100 |
50.0 |
52.6 |
41.7 |
33.3 |
|
Joel Embiid |
21.1 |
53.2 |
38.3 |
41.5 |
40.7 |
|
|
Kristaps Porzingis |
45.6 |
36.5 |
46.5 |
36.9 |
41.5 |
Calculations for the Average Shot % for Each Height
In order to determine what height had the NBA players with the best Mid-Range shooters I calculated the average Mid-Range shot % for each of the 4 height ranges.
|
μ=xn μ =35.3+38.6+33.6+34.3+33.7+25.0+41.8+28.9+43.9+38.2+35.7+39.2+41.9+42.0+42.0 15 μ ≈ 36.9
|
Figure 1: Sample calculation calculating the average long mid range shot % for shooters between 183 cm and 191 cm
Calculations for the Population Standard Deviation of Shot % for Each Height
By also calculating the population standard deviation of shot % for each height I would be able to find out how consistent of a shooter the NBA players were at each of the 4 height ranges. The population standard deviation was used because it takes into account all of the data points within a sample rather than using the sample standard deviation which only takes into account certain data points within a data set.
|
σ= σ= σ ≈ 5.15 |
Figure 1: Sample calculation calculating the population standard deviation for long mid range shots shot by shooters between 183 cm and 191 cm
Table 2: The average mid range shot % and standard deviation for left handed professional NBA players from ranging heights
|
Height (cm) |
Average Mid Range Shot % |
Standard Deviation |
|
182.88 - 191 |
36.9 |
5.15 |
|
193.04 - 200.66 |
42.7 |
8.62 |
|
203.2 - 210.82 |
35.5 |
9.40 |
|
213.36 - 220.98 |
45.3 |
16.6 |
Fig 1. A histogram displaying the average mid range shot % for each of the 4 different height ranges
By analysing both the table and graph it is evident that the height range with the best mid range shooting % is the 213.36cm-220.98cm height range. However this is also the height range with the highest standard deviation.
Calculating Average Shot % for Each Location
In order to determine the areas on the court I would have the best chance of making a midrange jumper I determined the average shot % for each of the 5 mid range locations on the court. This data also tells me the areas where my opponents would have a higher chance to score, forcing me to play heavier, much more aggressive defence in those locations.
|
μ =35.3+25.0+35.7+38.8+46.0+33.3+40.0+30.0+20.7+100+21.1+45.6 12 μ ≈ 39.3 |
Figure x: Sample calculation calculating the average long mid range shot % at the right corner
Calculating the Population Standard Deviation of Shot % for Each Location
The population standard deviation of shot % for each of the 5 locations was calculated in order to determine where shots taken were the most consistently scored.
|
σ= σ ≈ 20.0 |
Figure x: Sample calculation calculating the population standard deviation for long mid range shots taken at the right corner
Table 3:
|
Shot Location |
Average Mid Range Shot % |
Standard Deviation |
|
Long Right Corner |
39.3 |
20.0 |
|
Long Right Elbow |
41.2 |
6.80 |
|
Long Straight |
42.8 |
8.39 |
|
Long Left Elbow |
38.9 |
5.52 |
|
Long Left Corner |
38.5 |
10.0 |
Fig 2. A bar graph displaying the average mid range shot % for each of the 5 different mid range shot locations.
By analysing both the table and graph it is evident that the height range with the best mid range shooting % is the 213.36cm-220.98cm height range. However this is also the height range with the highest standard deviation.
Calculating Average Shot % by Height For Each Location
One sentence explaining why you calculated this
|
μ =35.3+25.0+35.7 3 μ ≈ 32.0 |
Figure x: Sample calculation calculating the average long right corner shot % for shooters between 183 cm and 191 cm
Table 4:
|
Height (cm) |
Average Shot % Long Right Corner |
Average Shot % Long Right Elbow |
Average Shot % Long Straight |
Average Shot % Long Left Elbow |
Average Shot % Long Left Corner |
|
182.88 - 191 |
32.0 |
39.9 |
34.8 |
40.1 |
38.0 |
|
193.04 - 200.66 |
39.4 |
42.3 |
46.0 |
40.5 |
45.5 |
|
203.2 - 210.82 |
30.2 |
35.9 |
44.4 |
35.2 |
32.0 |
|
213.36 - 220.98 |
55.6 |
46.6 |
45.8 |
40.0 |
38.5 |
One sentence summarizing table
Calculating Probability of Making a Long Mid Range Shot for a basketball player who is 165cm Tall
This was done in order for me to understand where I myself as a 165cm tall male would theoretically have the best chance of the 5 shot locations to make a mid range shot. This would help me when I am deciding where to shoot from on the court in a 5v5 basketball game scenario.
Figure:
|
f(x) = 0.134x+13.1 f(?) ≈35.21% ∴ The probability of me as a 165cm tall basketball player making a long mid range shot is 35.21% |
Figure x: Extrapolating the long mid range shot % for a basketball player who is 165cm tall
Calculating Probability of Making a Long Mid Range Shot from Each Location for Someone who is 165cm Tall
The probability of making a Mid Range Shot from the long right corner for me who is 165 cm Tall was done in order for me to identify the probability I would have of making a mid range shot from the long right corner.
Long Right Corner
Figure:
|
f(x) = 0.595x-80.7 f(?) ≈17.475% ∴ The probability of a 165cm tall shooter making a shot from the long right corner is 17.475% |
Figure x: Extrapolating the long right corner shot % for a shooter who is 165 cm tall
Long Right Elbow
Figure:
|
f(x) = 0.0891x+23.2 f(?) ≈37.9015% ∴ The probability of a 165cm tall shooter making a shot from the long right elbow is 37.9015 % |
Figure x: Extrapolating the long right elbow shot % for a shooter who is 165 cm tall
Long Straight
Figure:
|
f(x) = 0.312x-20.1 f(?) ≈31.38% ∴ The probability of a 165cm tall shooter making a shot from the long straight is 31.38 % |
Figure x: Extrapolating the long straight shot % for a shooter who is 165 cm tall
Long Left Elbow
Figure:
|
f(x) = -0.136x+66.4 f(?) ≈43.96% ∴ The probability of a 165cm tall shooter making a shot from the long left elbow is 43.96 % |
Figure x: Extrapolating the long left elbow shot % for a shooter who is 165 cm tall
Long Left Corner
Figure:
|
f(x) = -0.189x+76.6 f(?) ≈45.415% ∴ The probability of a 165cm tall shooter making a shot from the long left corner is 45.415 % |
Figure x: Extrapolating the long left corner shot % for a shooter who is 165 cm tall
Add a sentence or two at the bottom here just saying that these calculations are not entirely accurate because of how low the R squared values are
Data doesn't fit trend line well because r square is low
Conclusion
Through the data collected a number of conclusions can be drawn. First off, through data collected it was determined that the height range with the best average mid range shot % is the 213.36 cm - 220.98 cm range (Refer to Table 2). The position traditionally played by the 213.36 cm - 220.98 cm height range is known as the center position. Centers today are usually skilled at close range shots and have an advantage when it comes to scoring mid range shots through their height and arm length. Most players who are not centers usually practice the 3pt shot while centers mainly focus on their mid range shot giving them an edge most of the time. Moving on, the mid range with the highest shooting % for left handed NBA players is the long straight shot, followed by the long right
References
https://www.ranker.com/list/best-current-nba-left-handed-players/ranker-nba
https://www.statmuse.com/nba/ask/john-wall-shot-chart-career
https://www.statmuse.com/nba/ask?q=de%27aaron+fox+shot+chart+career
https://www.statmuse.com/nba/ask/mike-conley-shot-chart-career
https://www.statmuse.com/nba/ask/james-harden-shot-chart-career
https://www.statmuse.com/nba/ask?q=d%27angelo+russel+shot+chart+career
https://www.statmuse.com/nba/ask?q=shai+gilgeous-alexander+shot+chart+career
https://www.statmuse.com/nba/ask/marvin-bagley-iii-shot-chart-career
https://www.statmuse.com/nba/ask/domantas-sabonis-shot-chart-career
https://www.statmuse.com/nba/ask/julius-randle-shot-chart-career
https://www.statmuse.com/nba/ask/ivica-zubac-shot-chart-career
https://www.statmuse.com/nba/ask/joel-embiid-shot-chart-career
https://www.statmuse.com/nba/ask/kristaps-porzingis-shot-chart-career
http://www.planetofsuccess.com/blog/2017/inspirational-basketball-quotes/
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