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# Best Court Area Shot Locations for Basketball Players

 ✓ Paper Type: Free Assignment ✓ Study Level: University / Undergraduate ✓ Wordcount: 3439 words ✓ Published: 11th Oct 2021

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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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

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