Saturday, January 16, 2016

A Million Points of Damage, Part 1: RPGs, Math & RNG

While some games hide the variables under their hood to preserve immersion or avoid confusion, some like to show off their numbers. I'd like to look at how different games handle the way they present these numbers to the player and why, starting with a few older RPGs. 

Some games wear their numbers on their sleeves, and RPGs are a common example. After all, strategy is an important part of any RPG.

Take classic Square-Enix RPGs, for example.  The damage dealt, the damage received and various stats are visible to the player in battle. Have a look at Chrono Trigger:

It's quite common for turn-based RPGs like this to boast rather high numbers. Characters may hit other characters for hundreds, thousands or tens of thousands points of damage. But then there are RPGs that are incredibly modest with their variables - take Paper Mario, for example.

It's easy to dismiss this difference in design because Paper Mario was designed for a younger audience, as demonstrated by its visual style emulating a children's book. But I would argue there's a little bit more to it than that.

Consider one of turn-based RPGs common criticisms - repetition. Fighting the exact same enemy with the exact same moves using the exact same party; that gets old after a while. Of course, game designers have known this from the start, and this is how RPGs and RNG became bedfellows. Now, RNG simply stands for 'random number generator.' This may sound weird at first, but think about how often RPGs rely on a roll of the dice. From random encounters to critical hits, there's a lot of chance involved. To get back to the point, random numbers eliminate repetition to some degree. You're never quite sure which enemy or enemies you'll run into, never quite sure how much damage you'll deal or receive and so on.

So, why the big numbers? I believe one reason is because they allow for more flexible RNG. Note that the aforementioned Paper Mario, which uses tiny numbers, also employs no random numbers for the damage dealt and received. How could it? Were you to attack an enemy with 3 HP, using a base attack of 2, a random element would make a huge difference, because a single point of damage would. The game would rely far too much on luck. But allowing a few dozen points of variation against an enemy with thousands of HP adds a level of surprise that doesn't undermine strategy or skill, while still allowing you to just barely make or miss that last hit on the boss.

Of course, RNG is really just one facet of complex mathematics. I've claimed that RPGs are forthcoming with their numbers, but in reality, they only show you the end result of a few numbers that went through a dozen formulae. RPGs need to consider a character's attack power, the type of attack, the enemy's defense and many more things, and calculate a number based on that. Using only small numbers, those results would be robbed of all elegance; that 10 % buff a piece of armour gave, for example, will mean a lot more for a 1000 damage equip than a 1 damage equip, even if they have equal strengh within the context of their own game. As such, having big numbers behind the scenes has its advantages. A great example of an RPG franchise that is amazingly complex, yet pretends to be simple, is Pokémon. Take, for example, how the game calculates whether or not you catch a Pokémon.

source: Bulbapedia

But all of this only shows the advantage of using big numbers behind the scenes, not why some RPGs present these numbers to the player. That still boils down to a level of unpredictability, as I mentioned before.

However, is that all? Using numbers in the hundreds or thousands should provide plenty of variance if it was just about the RNG and maths. Why is it, then, that some turn-based RPGs use numbers that are much, much higher

To answer that question,we have to cover two things: Progression and spectacle. If you start the game dealing 1 damage, and you knock the final boss down with a 100 000 damage hit, you're going to feel incredibly empowered. You could've built from 1 to 10 damage, and if the game scaled at the same rate, it would've worked much the same as if the numbers would be higher. But it wouldn't feel the same, because the jump from 10 to 100 000 is so much greater than the jump from 1 to 10. Mechanically, it's completely arbitrary, but larger numbers allow for this greater sense of progress and have a way of looking spectacular. If your character spends a whole minute on a cutscene preparing the greatest attack you've ever seen, doesn't it feel like a dud if they deal 10 damage, even if that is a lot in the context of the game? Especially if there are spectators observing you playing, who have no way to contextualize the numbers, although that's a topic in and of itself.

So there you have it! The reason why turn-based RPGs have a fondness for large numbers is that they're flexible enough to use with RNG and complex mathematics, as well as the fact that they allow for a great sense of progress and spectacle.

That's my 2,458,948 cents, but it's entirely possible I'm wrong. Please feel free to respond! I'm planning to make 'A Million Points of Damage' into a series where I explore the transparency of variables in other genres and games as well, and your feedback is going to be an important part of how it develops. Have a great day, and I'll see you in the next one! 


  1. To your point about progress, I think a distinction should be made between just "progress" and "quantifiable progress." Compare the progress you observe in the 16-bit era RPGs as you describe here versus the progress you see in games such as fighting games (PvE), beat-em ups, or From Software games like Dark Souls. Unlike with RPGs, you measure your progress in these games by a matter of how well you perform in any given situation. Having numbers attached to an attack, as done in RPGs, allows a gamer to quantify their progress rather than relying on some unseen skill-based mechanic.

    1. Austin, thanks for your response!

      You're correct, and I'm actually hoping to go into how fighting games and beat-em ups use these numbers as well.

  2. I know this is an old post but this is something that I as a wishful-hope-to-be-game-designer have though about. While larger and increasing number do give a sense or progress and empowerment this can also have the effect of becoming pointless if no restraint is used while computing these values. For example in game where the damage goes to 100'000s or to millions RNG becomes meaningless, there is no excitement when scoring a particularly devastating hit as your mind truncates the value to 312k in both cases of 312'000 and 312'725, this empowerment can also be affected by simple things such as assigning a different color or size to the damage value depending on where on the RNG scale it lands. 27 in small white text next to 31 in an alarming orange and large numbers is much less impactful even though vs. a 40 HP foe the effect is essentially the same.

    1. Hey! Always nice to see people with ambitions. If you dedicate yourself to it, I'm sure you'll get into game design.

      Indeed, there are potential dangers to using ridiculously high numbers. In my experience, people pay a lot more attention to the numbers in RPGs that have smaller, more consistent numbers like Darkest Dungeon or Paper Mario.

      And as you say, presentation is a major part of the impact, which plays into the empowerment angle. There's something to be said for the concept of "game feel," though it isn't really considered a science.

      Thanks a lot for posting a response. Your contribution to the discussion is much appreciated.