Math in Game Development - Intervals & Charts/Plots (Chapter 2)

Chapter 2 of “Math in Game Development” will include more on how data is applicable in game development | Chapter 1

Lessons 3a - 3b are both plots, while 4a - 4b are charts, lesson 1a is about intervals.

Game developers try to use innovative and efficient techniques to calculate the state of their game. Developers get very diverse sets of data when it comes to retention, new players, and more. This tutorial will go over how to organize this data.

(1a) Vocabulary

Cluster - Data that are grouped closely together.
Frequency - How often-occurring a value is.
Gap - The numbers that have no data value.
Peak - The most frequently occurring values, or mode.
Symmetry - The left side of distribution looks like the right side.

The mathematical definitions for all words listed (except frequency) were received from Glencoe Math Course 1 Volume 2, page 891 (book)

(2a) Intervals & Charts/Plots - Intervals

An interval is two numbers and everything between them, like 1-5. An interval on a chart or plot must have an equal amount of numbers in between.

1-5 has 5 numbers included, 1, 2, 3, 4, 5. The next digit on the plot must be 6-10, 6, 7, 8, 9, 10. There cannot be an interval on a chart with different amount of numbers in between. In this demonstration, there must be 5 numbers included.

Intervals also include the numbers shown; for example 1-5 includes 1 and 5. However, if the question asks what numbers are between 1-5, 1 and 5 are excluded.

Intervals can help in game development, because developers get data so different and so diverse an exact digit wouldn’t give a clear overview. Intervals would be much more efficient in this case.

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(2a) Intervals & Charts/Plots - Line Plot

The line plot incorporates the frequency of a data set over anything else. By looking at a line plot, the mode is instantly calculated, and the median is easy to find.

Excuse my horrible drawing, but this is how a line plot looks. We can very easily see the mode is 90. To find the median, just start crossing out the stars to find the middle one, 91 is the median. A line plot is as simple as this.

A line plot is very helpful to find the frequency and the mode of a data set.

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(2b) Intervals & Charts/Plots - Box Plot

The box plot show the most important parts of the data, like q1 - q3, least and greatest numbers. However, a box plot does not show the frequency of a data set.

Excuse my bad drawing skills but this is a box plot.

“The box” is q1 - q3
The white lines close “the box”
The green represents Q1
The blue represents Q3
The black in “the box” represents the median
The black outside “the box” represents the highest and lower numbers

The frequency does not show in a box plot.

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(3a) Intervals & Charts/Plots - Histogram

A histogram is very similar to a bar graph.

Image credit: Histogram - Wikipedia
X-Axis: Arrivals/minute
Y-Axis: Frequency
A histogram uses intervals, and is “connected” to one-another, and is shaded in.

Mathematical definition: "A histogram is a type of bar graph used to display numerical data that have been organized into equal intervals.

The mathematical definition for “Histogram” was received from Glencoe Math Course 1 Volume 2, page 872

(3b) Intervals & Charts/Plots - Line Graph

A line graph is very simple. All the lines are connected, a line graph is easily interpreted. The line graph is very easy to read; to see decreasing/increasing data.

Image credit: How to Make Line Graphs in Excel | Smartsheet

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(4a) How is All This Data Applicable

The data retrieved from plots, charts, and graphs make it very easy to interpret a data set. How to make plots, charts, and graphs is by using the information discussed in Chapter 1. To have a very good understanding of your data, it is recommended to use:

  • line plot
  • box plot
  • histogram
  • line graph

Using all four of these tells you the frequency, q1 - q3, least and greatest number, intervals, data.


English is a second language to me, I am Italian. Apologies for any grammatical errors.


Can you give examples of specific data developers can plot and how it would benefit them?

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I indeed can.
A game developer decided to examine recent earnings from a new monetization strategy. This is what he earned (in USD, daily):

  • 90, 86, 90, 87, 88, 91

To plot this on a line graph:

Create a number bank and place a star or an “X” accordingly.

For a box plot:

Look for the Least number, the greatest number, the median, q1, and q3. The box (white lines in this example) is just to represent the q1 - q3.

How devs would benefit:

  • compare/contrast sales before the event
  • look for ways to improve
  • to see if there’s a pattern in the game’s analytics
  • looking how diverse the sales are through a plot

I explained it all in my examples shown with the illustration, but I hope this helped. :slight_smile:

Great stuff again!
Will you cover stuff like χ² Tests down the line?