# Game numbers and meaning

Each game has it's own "maximum number". One question that comes into mind every time I play a(nother) game is how are these maximums determined and how do these affect gameplay? To explain, here's some rough references from games and anime.

# Numbers on Levels

One instance is the "level cap". In some games, it's 100 - which I can easily understand to be like percentage. But other games have weird level caps. I remember Fallout (3?) having a level cap of 30. The anime Log Horizon has a level cap of 90 (and increased to 100 after "the apocalypse"). Ragnarok Online once had 99, then increased (to 120?) for Renewal servers.

# Numbers on Attributes

Another instance is attributes (Strength, Agility, Intelligence etc.). Ragnarok Online starts you at 5 a piece and level up in small increments. Skyrim starts you at ~15-25 depending on race. In the anime Sword Art Online, they have this scale of 1000.

# Numbers on Damage

Then there's attack power. In Yu-Gi-Oh card game, the attack power comes in the thousands. MTG on the other hand is as small as 0-10, with the 1-6 range as very common numbers. DotA damage starts <100 and reach as high as 2000 on critical strikes.

# Exceeding caps

Then there's this Skyrim mod that makes you level up in excess of the cap. Why would they make something like that? Is there something beyond the level cap that the regular game doesn't address? Is the system not enough?

In summary, here's my questions:

• How are these scales and maximums determined? Is there some magical formula or a generic guideline (like from a game)?

• How does these number affect overall gameplay? I mean I can have a 100-scale that does the same thing as 1000-scale or 10000-scale. But why do they opt for these numbers? Why go for smaller ones or the insanely huge ones?

• Why is there a level cap? And what does it mean when the level cap is broken or increased?

• What’s in a number? that which we call a four By any other number would work as well! Commented Nov 2, 2014 at 6:56

I'm going through your questions one by one.

How are these scales and maximums determined? Is there some magical formula or a generic guideline (like from a game)?

No, there is no magic formula whatsoever. The only rule of thumb is that people usually like round numbers. That is why there are so many games with max lvl 100 (or 99) and not max lvl 639. Beyond that, how the maximum is decided depends on several gameplay elements, such as how the character power progresses, the half life of your players, playtesting sessions, etc.

To elaborate a little bit, usually you plan how long you expect players to play to reach cap level. It shouldn't be the same say for a casual 1 player RPG than for a hardcore MMORPG, so the caps and how hard it is to reach it has to be adjusted accordingly.

How does these number affect overall gameplay? I mean I can have a 100-scale that does the same thing as 1000-scale or 10000-scale. But why do they opt for these numbers? Why go for smaller ones or the insanely huge ones?

It affects the progression of the game. You can multiply damage by 100 and enemy life by 100 and get the same power ratio, but the progression would be different.

It is not the same if you start a game dealing 10 damage and at endgame you deal 100, than if you deal 100.000. On the second case your progression is much more dramatic than in the first. Again, this depends on what kind of experience you want to provide with your game. You want advance players to wipe the floor with newbies assess or to have a smaller, more reasonable gap? Do you want players feel like going from crap to god or a more flat progression?

Why is there a level cap? And what does it mean when the level cap is broken or increased?

Probably the first reason in computer games is because there is a limit on what you can represent in a computer. This is particularly poignant in early RPGs where some stats were represented as bytes, and thus their maximum value was 255 (never though this maximum value was odd?). But there are also gameplay implications. For one, many people like progression towards a goal. That is why reaching a level cap is satisfying. The second, more obvious, is because you want to limit player power. You don't want players to get infinitely powerful in an online game to promote competition, and even in single player games, you want player to be confronted with challenging enemy encounters (and dynamic enemy leveling not always cut it).

Final notes

Actually your question is a little bit skewed because it assumes that leveling systems with caps is the most common practice. However there are lots of alternatives, including limitless leveling system, or progression systems that don't rely on levels at all. For a more informed reading, I would recommend the Wikipedia article on Experience points.

• Some other anecdotes relating to the limits of binary representations: Early versions of WoW kept track of all money internally using the smallest denomination (copper) and storing it in a 32-bit integer. Therefore, you could never have 429497 gold (2^32 copper) or more per character. Eventually they switched to a 64-bit int, but years later Blizzard was bitten by the Diablo III auction house's use of 32-bit integers; when exploited it caused massive inflation. In early versions of Kerbal Space Program, the huge world caused various hilarious failures due to loss of floating point precision. Commented Nov 2, 2014 at 7:29

How are these scales and maximums determined?

Mostly through painstaking developer & QA team iteration, also known as Blood, Sweat & Tears. Game balance grows geometrically more complex with each additional gameplay factor. See Combinatorial Game Theory. Custom formulae may also be used to ease the problem, but ultimately we rely on an iterative approach.

How does these number affect overall gameplay? I mean I can have a 100-scale that does the same thing as 1000-scale or 10000-scale. But why do they opt for these numbers? Why go for smaller ones or the insanely huge ones?

Because there needs to be a small, finite scale on which your (finite) team of devs / QAs can balance the game. Precisely balancing 1000 discrete levels is over 10 times more difficult than precisely balancing 100 discrete levels. All of this adds up to... blood, sweat & tears.

Why is there a level cap?

Cost-benefit analysis: Because if there weren't a cap, developers could sit there bleeding, sweating and crying indefinitely just in order to balance levels, which is hardly cost effective since most games are paid for upfront, one-off (if that, in view of piracy)... unless the developers have promised and are being paid for X new balanced levels per month. Balancing takes time.

And what does it mean when the level cap is broken or increased?

It is like voiding the warranty on your phone by jailbreaking it. Yes you still have that brand of phone, but you can no longer rely on the "safety" that the developers provided in the original, unmodified product. Hence, beyond the level limit, strange, unbalanced things will happen. See Fate, by the designer of Torchlight, where the character level cap is extremely high (199) and the dungeon levels are practically unbounded. Balance quickly goes out the window after the usual dungeon range (about 1-30 or so, within a range of 2^31-1 or 2 billion levels).

The Crux of the Matter

Producing game balance procedurally, i.e. without human QA, is a very difficult problem indeed, since gameplay itself is human-subjective... though I have no doubt that some innovators out there are at least attempting to develop such a system. So for now we do it manually, which takes time.

The amount of levels is often designed to meet the amount of creatures, areas , techniques / powers and other types of game content. Levels are a way to classify content and reward the player. You may need more when you have more content to offer; levels reflect the time the player spent in the game and are used to classify content as appropriate to players with a certain amount of experience (not xp) in that game.

If you have a very large amount of content, you would likely want to offer more levels. If you are following a certain RPG rule-book like D&D then it may not be so. Levels are also used to reward the player and keep them excited about the game. A lot of players enjoy leveling up and powering up their characters so if your target audience requires this stimuli, adding a lot of levels may seem like a good idea.

All and all, it's about the ux. Going to either extreme would interfere with the gameplay experience. Having only 2 levels, would make the players feel like they have achieved nothing for too long awhile and having 1000 levels, would make content too specific possibly, and also constantly disrupt the play when the character's attributes and powers need to be upgraded.

In general I advise not to think about levels but focus on content, character powers and such. Later on classifying the content and powers as appropriate for certain levels.

Levels can be summed up as a rate of progress.

To find your level cap or whatever break your game into 3 parts, the beginning, middle and end.

Find out how much attributes and skills you want in total at the end. Then balance out the middle so that everything works fine and then look at the numbers of encounters and their challenge to find the rate of progress. You also want the first few levels to be rewarding at the start so tweak until it works.

Damage and health numbers are completely arbitrary. It is only a question of precision. Games with very small numbers have bigger impact because of the scale of the damage. For example in a game with 34HP, 12 damage is immense but its the same as 3441HP and 1249 Damage the only thing you get is more number precision that doesn't go into rounding problems.

Ultimately it is about relationships between things and scale then anything else.