Home > Articles

  • Print
  • + Share This
This chapter is from the book

This chapter is from the book

Determining the Granularity for Numbers

After you come up with attributes for game objects, you need to assign numbers to the attributes. Because you are making up all the attributes and numbers for your game, technically you could use any numbers you want. The granularity of the numbers you use can have a dramatic impact on how a player perceives the game. The following sections provide some to help you determine the granularity of your numbers.

Numbers Should Relate to Probability

Numbers should have a visible impact on the game. The larger the possible outcome of a random event, the larger the corresponding numbers of the game must be. For example, if a character has 10 HP, it doesn’t matter if the character receives 11 damage or 5,000 damage, as either one will be a one-hit kill. Say that you know a character is rolling 1D6 (a single six-sided die) for damage, and you always want the character to survive at least three hits. In this case, the minimum hit point value would be 111.

Let’s consider backgammon as an example. (Do a search for “official backgammon rules” if you need to familiarize yourself.) In backgammon, the maximum number of moves a piece can take at one time is 24. The maximum is 24 because even the largest roll possible can have a use and not be wasted. In addition, 24 is the number of spaces on the board (see Figure 11.1). The relationships between the number of needed movement spaces and the potential outcomes of the dice are intertwined. If you were to expand the board, you would likely need larger potential rolls to keep the game moving. Conversely, if you were to shrink the board, you would want to reduce the amount of possible movement.

Figure 11-1

Figure 11-1 Backgammon board

Some Numbers Need to Relate to Real-World Measurements

Some numbers, such as height, weight, and speed, are analogs of the real world. The scale of those numbers has already been decided for you. Even if it is better for your game to use three-digit numbers than to use smaller numbers, you can’t decide that every person in your game is going to be measured in hundreds of feet (or meters) in height. Players have incoming knowledge of fixed scales and expect you to play along with the real world. So, if being taller in your game is better, then you will need to adjust your scale. There are a few ways to do this:

  • Use a smaller unit of measurement so you get larger numbers.

  • Adjust your scale of numbers to fit a fixed attribute.

  • Convert the real-world scale to a game scale.

For example, you might list attributes for a basketball player as follows:

  • Example 1

  • Strength: 150

  • Height: 6 (feet)

  • Speed: 220

  • Dexterity: 180

This looks odd because the height attribute is a single digit, while the rest of the attributes are triple-digit numbers. In addition to looking odd, this would create the need to use fractions or decimals. Here’s another example of attributes for a basketball player:

  • Example 2

  • Strength: 150

  • Height: 182 (centimeters)

  • Speed: 220

  • Dexterity: 180

This scale is much better. All the attribute numbers are triple-digit numbers and within a similar range.

Here’s another example of attributes for a basketball player:

  • Example 3

  • Strength: 50

  • Height: 72 (inches)

  • Speed: 73

  • Dexterity: 60

This scale is also better than the first one. Changing to a more granular measurement of inches and switching all attributes to be two-digit numbers makes them line up nicely.

Now consider this final example of attributes for a basketball player:

  • Example 4

  • Strength: 150

  • Height: 165 (game units)

  • Speed: 220

  • Dexterity: 180

This scale also works because you have ditched reality and made your own scale that enables the attributes to all be three-digit numbers in a similar range. Making up your own units may lead to a bit of confusion as a player won’t initially know how to picture a height of 165 game units, but you can overcome this difficulty with art.

User Smaller Numbers for Easier Calculations

A player needs clear numbers for each individual calculation and for repeated calculations. If you are asking players to do calculations in their head in the game, then you need to limit the complexity of the numbers. Further, if you are asking players to do many calculations or frequently recurring calculations, you need to further restrict the complexity of those calculations. It is easiest for players to process simple numbers—that is, small whole numbers.

In very old games, attribute numbers are all very small. The number of pieces a player has, the faces of the dice, and total points for a game tend to be no more than two digits. Often they are single digits. Old games use small whole numbers to make the numbers easier for players to remember and use in calculations in their heads. The more frequently a player is required to do calculations, the simpler the calculations tend to be and the smaller the numbers involved are.

Think again about backgammon, for example. Players need to be able to calculate rolls and results in their heads, and complex systems of multiplication or addition would cause unneeded confusion. For each turn in backgammon, a player rolls 2D6 to determine how much movement their pieces get for that turn. A player gets double that movement with a roll of doubles. (Rolling double 6s, for example, allows the player to move a total of 24 spaces.) On every turn, the player uses the individual rolls of the dice, or adds together the rolls of two six-sided dice, and turns go by in a matter of seconds. Fortunately, adding together the rolls of two six-sided dice is a very easy calculation and does not slow the pace of the game. In addition, the results are all small numbers. The results also tie into the physical space of the game. The board contains only 24 spaces, so any more movement than that would be useless.

Let’s now consider scoring in the game spades. Spades has a rather sophisticated scoring system, where players guess their score at the beginning of the game and then, at the end of the game, compare their final results to their initial guess. They then use a scoring system to interpret their results and calculate the final score. This is a somewhat complex calculation, and players often use paper or a calculator to do the scoring—but it is only done once during a game. The numeric results are also much larger than in backgammon, with scores in the hundreds or even up over 1,000. Because this calculation occurs only once a game, it’s an event and can even build some tension as a game is calculated, but if it were done every turn, it would completely bog down the game.

Early and even many modern tabletop games and pen-and-paper RPGs continue to use attribute numbers in the single digits and low double digits. For example, a sample fifth edition Dungeons & Dragons character could start with the following attribute scores:

  • STR 10 DEX 13 CON 14 WIS 19 CHA 14

Note that all of these numbers are in the low two-digit range. Also, while this is a modern, fairly sophisticated game, it is working under the same limitations as backgammon in that the players are needing to do calculations in their head. Whereas in backgammon, players do calculations every few seconds, in an RPG they do calculations every few minutes.

As you can see from these examples, the less frequently calculations are made, the more complex they can be and the larger the numbers involved can be. When assigning numbers to attributes, you should think about how much calculation you expect your players to do in their heads. The more calculations, the smaller the numbers should be for attributes. The more frequent the calculations, the smaller and simpler the calculation and numbers must be.

Use Larger Numbers for More Granularity

If small numbers are easier for players to understand, why not use single-digit numbers for everything? Small numbers do not allow for much granularity or variety. Say that you are assigning strength to five fantasy characters. These are the five characters, and the feeling you want to convey through the strength attribute for each of them:

  • Human: Middle-of-the-road guy

  • Ogre: Much stronger than anyone else

  • Ork: Stronger than humans but significantly weaker than ogres

  • Goblin: Weakest by far, but not so weak that they can be ignored

  • Dwarf: Stronger than humans but notably weaker than orks

Here’s how you might turn these feelings into numbers if you want to constrain the numbers to 10 and below:

  • Human: Middle of the road leads you to choose the halfway point, which is 5.

  • Ogre: Because this is the strongest character, it is 10. Note that there is no longer room on the scale for stronger characters like dragons or giants. While this might be fine within the scope of your game, it does limit your ability to expand the game.

  • Ork: You might assign an ork a strength of 7 because an ork is much weaker than an ogre but is not that much stronger than a human.

  • Goblin: A goblin is the weakest character, so you assign it 2, but 2 might be too weak.

  • Dwarf: You are now stuck. If you assigned a dwarf 6, then this character would be stronger than a human but not notably weaker than an ork.

As you can see, even with just five characters and a few criteria, you start running out of space in the scale to properly translate your feelings about character strengths into numbers. As you add more characters and more criteria, the scale will get even more crowded, and characters will start to feel too similar. To fix this, it is tempting to make all the values considerably larger, allowing more granularity to work with.

Very Large Numbers Are Confusing

Given the problems discussed so far with small numbers, it might seem like a good idea to go to the opposite extreme in a computer game. If you were to use four- or five-digit numbers, you would have plenty of space to make a large variety without ever crowding your range. Further, given that the computer will be doing all the calculations, you don’t need to worry about players doing lots of math on big numbers, as they would need to do with a board game. But calculations are not limited to just what a player must do to make the game progress; they also tie in to how well the player can understand what is going on in the game. We humans are, in general, not designed to calculate large numbers in our heads. For example, try to calculate the final hit point score for each of the following scenarios in your head:

  • 5 hit points, taking 2 points of damage

  • 100 hit points, taking 27 points of damage

  • 34863298 hit points, taking 456321 points of damage

It’s clear that the smaller the numbers, the easier the calculations.

The takeaway is that you need to find the right amount of granularity for your game. In general, you want to use numbers that are just large enough to accommodate all needed variety but no larger than absolutely necessary.

Humans Hate Decimals and Fractions, but Computers Don’t Mind Them

It is exceedingly rare, outside of educational math games, to ever show a player a decimal score or a fraction. It’s not that they aren’t valid numbers, but people just don’t like seeing or (worse) calculating them. Games typically show players only whole numbers.

However, behind the scenes, computers have absolutely no problem calculating decimals. This means you can feel free to use as many decimal places as you want for computer calculations as long as you can present whole (rounded) numbers to the player in a way that is not confusing.

Numbering Example

Figure 11.2 provides an example in which each column presents a pair of values: one for Attribute A and one for Attribute B. In each pair, the ratio of A to B is the same: 94%. Because each pair has the same ratio, for a computer, they would all work exactly the same way. However, players would be able to comprehend some of these numbers easily and others with great difficulty. If the players are going to see the numbers, you should use just the two-digit numbers, if possible, or the three-digit ones.

Figure 11-2

Figure 11-2 Number granularity example

  • + Share This
  • 🔖 Save To Your Account

InformIT Promotional Mailings & Special Offers

I would like to receive exclusive offers and hear about products from InformIT and its family of brands. I can unsubscribe at any time.


Pearson Education, Inc., 221 River Street, Hoboken, New Jersey 07030, (Pearson) presents this site to provide information about products and services that can be purchased through this site.

This privacy notice provides an overview of our commitment to privacy and describes how we collect, protect, use and share personal information collected through this site. Please note that other Pearson websites and online products and services have their own separate privacy policies.

Collection and Use of Information

To conduct business and deliver products and services, Pearson collects and uses personal information in several ways in connection with this site, including:

Questions and Inquiries

For inquiries and questions, we collect the inquiry or question, together with name, contact details (email address, phone number and mailing address) and any other additional information voluntarily submitted to us through a Contact Us form or an email. We use this information to address the inquiry and respond to the question.

Online Store

For orders and purchases placed through our online store on this site, we collect order details, name, institution name and address (if applicable), email address, phone number, shipping and billing addresses, credit/debit card information, shipping options and any instructions. We use this information to complete transactions, fulfill orders, communicate with individuals placing orders or visiting the online store, and for related purposes.


Pearson may offer opportunities to provide feedback or participate in surveys, including surveys evaluating Pearson products, services or sites. Participation is voluntary. Pearson collects information requested in the survey questions and uses the information to evaluate, support, maintain and improve products, services or sites, develop new products and services, conduct educational research and for other purposes specified in the survey.

Contests and Drawings

Occasionally, we may sponsor a contest or drawing. Participation is optional. Pearson collects name, contact information and other information specified on the entry form for the contest or drawing to conduct the contest or drawing. Pearson may collect additional personal information from the winners of a contest or drawing in order to award the prize and for tax reporting purposes, as required by law.


If you have elected to receive email newsletters or promotional mailings and special offers but want to unsubscribe, simply email information@informit.com.

Service Announcements

On rare occasions it is necessary to send out a strictly service related announcement. For instance, if our service is temporarily suspended for maintenance we might send users an email. Generally, users may not opt-out of these communications, though they can deactivate their account information. However, these communications are not promotional in nature.

Customer Service

We communicate with users on a regular basis to provide requested services and in regard to issues relating to their account we reply via email or phone in accordance with the users' wishes when a user submits their information through our Contact Us form.

Other Collection and Use of Information

Application and System Logs

Pearson automatically collects log data to help ensure the delivery, availability and security of this site. Log data may include technical information about how a user or visitor connected to this site, such as browser type, type of computer/device, operating system, internet service provider and IP address. We use this information for support purposes and to monitor the health of the site, identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents and appropriately scale computing resources.

Web Analytics

Pearson may use third party web trend analytical services, including Google Analytics, to collect visitor information, such as IP addresses, browser types, referring pages, pages visited and time spent on a particular site. While these analytical services collect and report information on an anonymous basis, they may use cookies to gather web trend information. The information gathered may enable Pearson (but not the third party web trend services) to link information with application and system log data. Pearson uses this information for system administration and to identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents, appropriately scale computing resources and otherwise support and deliver this site and its services.

Cookies and Related Technologies

This site uses cookies and similar technologies to personalize content, measure traffic patterns, control security, track use and access of information on this site, and provide interest-based messages and advertising. Users can manage and block the use of cookies through their browser. Disabling or blocking certain cookies may limit the functionality of this site.

Do Not Track

This site currently does not respond to Do Not Track signals.


Pearson uses appropriate physical, administrative and technical security measures to protect personal information from unauthorized access, use and disclosure.


This site is not directed to children under the age of 13.


Pearson may send or direct marketing communications to users, provided that

  • Pearson will not use personal information collected or processed as a K-12 school service provider for the purpose of directed or targeted advertising.
  • Such marketing is consistent with applicable law and Pearson's legal obligations.
  • Pearson will not knowingly direct or send marketing communications to an individual who has expressed a preference not to receive marketing.
  • Where required by applicable law, express or implied consent to marketing exists and has not been withdrawn.

Pearson may provide personal information to a third party service provider on a restricted basis to provide marketing solely on behalf of Pearson or an affiliate or customer for whom Pearson is a service provider. Marketing preferences may be changed at any time.

Correcting/Updating Personal Information

If a user's personally identifiable information changes (such as your postal address or email address), we provide a way to correct or update that user's personal data provided to us. This can be done on the Account page. If a user no longer desires our service and desires to delete his or her account, please contact us at customer-service@informit.com and we will process the deletion of a user's account.


Users can always make an informed choice as to whether they should proceed with certain services offered by InformIT. If you choose to remove yourself from our mailing list(s) simply visit the following page and uncheck any communication you no longer want to receive: www.informit.com/u.aspx.

Sale of Personal Information

Pearson does not rent or sell personal information in exchange for any payment of money.

While Pearson does not sell personal information, as defined in Nevada law, Nevada residents may email a request for no sale of their personal information to NevadaDesignatedRequest@pearson.com.

Supplemental Privacy Statement for California Residents

California residents should read our Supplemental privacy statement for California residents in conjunction with this Privacy Notice. The Supplemental privacy statement for California residents explains Pearson's commitment to comply with California law and applies to personal information of California residents collected in connection with this site and the Services.

Sharing and Disclosure

Pearson may disclose personal information, as follows:

  • As required by law.
  • With the consent of the individual (or their parent, if the individual is a minor)
  • In response to a subpoena, court order or legal process, to the extent permitted or required by law
  • To protect the security and safety of individuals, data, assets and systems, consistent with applicable law
  • In connection the sale, joint venture or other transfer of some or all of its company or assets, subject to the provisions of this Privacy Notice
  • To investigate or address actual or suspected fraud or other illegal activities
  • To exercise its legal rights, including enforcement of the Terms of Use for this site or another contract
  • To affiliated Pearson companies and other companies and organizations who perform work for Pearson and are obligated to protect the privacy of personal information consistent with this Privacy Notice
  • To a school, organization, company or government agency, where Pearson collects or processes the personal information in a school setting or on behalf of such organization, company or government agency.


This web site contains links to other sites. Please be aware that we are not responsible for the privacy practices of such other sites. We encourage our users to be aware when they leave our site and to read the privacy statements of each and every web site that collects Personal Information. This privacy statement applies solely to information collected by this web site.

Requests and Contact

Please contact us about this Privacy Notice or if you have any requests or questions relating to the privacy of your personal information.

Changes to this Privacy Notice

We may revise this Privacy Notice through an updated posting. We will identify the effective date of the revision in the posting. Often, updates are made to provide greater clarity or to comply with changes in regulatory requirements. If the updates involve material changes to the collection, protection, use or disclosure of Personal Information, Pearson will provide notice of the change through a conspicuous notice on this site or other appropriate way. Continued use of the site after the effective date of a posted revision evidences acceptance. Please contact us if you have questions or concerns about the Privacy Notice or any objection to any revisions.

Last Update: November 17, 2020