Resourceful Comparisons

March 11, 2008 at 1:32 pm (Game Balance, Game Design, Game Mechanics) (ammo, hit points, mana, time)

I have previously argued that a game will only be balanced if players’ capabilities are good at what they’re intended to be used for without usurping the functions of other capabilities.  In order to determine whether that’s the case, we need to consider the effectiveness (for the player) of taking each of several options in a given situation, and compare the usefulness of each.

One of the hardest parts of comparing the effectiveness of two player options–for example, turning invisible versus hurling a fireball–is often finding a common basis for comparison.  Let’s face it, in terms of their immediate effects, those probably accomplish completely different things.  They probably synergize in different and complicated ways with a whole host of different circumstances and strategies, so we don’t do them justice if we consider simply swapping in one for the other in an otherwise identical strategy, and their effects on the game’s final outcome are probably (intentionally) virtually impossible to predict in the general case.  We’re comparing the proverbial apples to oranges.  Where do we even begin?

Resources

As usual, there’s no silver bullet, but one widely-applicable strategy is to abstract the game state as a set of resources, by which I mean quantifiable assets that can be expended to change the course of the game.  For example, ammunition is a resource–you can use it up in order to fire your weapon, which is one of the ways you can affect the game’s outcome.  “Mana” (or energy, power, etc.) often serves a similar role in fantasy-themed games.

Hit points are a resource; they allow you to not die when you suffer damage.

Game money is a common resource; it’s often used to obtain other resources or paid in order to accomplish actions like securing a safe place to rest, bribing in-game characters, etc.

Perhaps most importantly, time is a resource–sometimes in-game time and real time are separate resources.  There’s generally a limit to how many things you can do at once, and/or how long it takes to complete an action (and if the game limits the amount of real time you can spend doing something, it’s a resource you use up while you’re observing, thinking, planning, etc.).  Often there are game actions that only cost you time, and no other resource.

The set of resources can vary a lot from game to game, and sometimes there’s more than one way to abstract a single game into different piles of resources.

But once you’ve made this abstraction, you can express a lot of the things that happen in the game as conversions between different resources.  For example, maybe a healing spell looks something like this:

Healing Palm:  Converts 25 mana (spell cost) and 1 round of your time (casting time) into 100 hit points (spell’s effect)

A fireball reduces enemy resources (hit points) at a cost of your own (mana, casting time).  A teleport spell uses up mana (spell cost) but saves time (the time of traveling to the destination by conventional means).  Taking a defensive stance might cost time (that could have been spent attacking, for example) but conserve hit points when you get attacked.

Of course, not everything can be easily expressed as resources, but this abstraction still often allows for a more simplified comparison.  Even if an action has a weird effect that’s hard to quantify, you can usually express its cost (or opportunity cost) in terms of resources, and then at least you only have a wacky unknown on one side of the scale.

Duty Cycles: Refreshing Resources

Once you’ve identified some resources, you should figure out how and when each of them is limited.  Ask yourself:  how do I get more?  What happens if I run out?

In the classic RPG, at the end of an adventure, the party goes back to town, stays at an inn, and emerges bright and fresh the next morning, with all of their health, spell points, etc. restored to them.  If this is the primary way you recover after fighting, then those resources basically need to last you until the next town–at which point any extra you may have remaining doesn’t matter.  Many other games have a similar expectation that you “refresh” all of your resources in some regular cycle.

But not all resources necessarily refresh on the same time scale.  If you’re in the middle of a battle, your time is probably tightly budgeted, and every second you spend casting a healing spell or rooting through your inventory for a potion is giving your opponent “free” attacks against you–but between battles, you may be able to change your equipment, rearrange your inventory, and cast as many spells as you want without worrying about how much time it takes.  If you’re trekking through the wilderness, you may be able to recover some resources by sleeping in your tent every night–but if you run out of supplies (food, potions, etc.) you can’t get any more until you reach a center of commerce.

The different schedules for refreshing resources are extremely important, because they’ll usually tell you exactly where to make a distinction in your analysis between “short-term” and “long-term,” and they’ll tell you which variables are strategically important in each timeframe.  If your mana gets reset every hour but you slowly build up victory points over the length of the whole game, that already speaks volumes about how to strategize in the game.

Converting Resources

Once you’ve abstracted a lot of your game choices into resources, you’ll want to try to ensure that the usefulness of each resource is fairly consistent.  You should start by looking at two things:

1)  The efficiency with which one resource can be transformed into another (for example, turning mana into health with a healing spell).

2)  The efficiency with which one resource can be substituted for another to accomplish a given effect (for example, using mana to make a more powerful attack versus taking an extra round to make two attacks).

By doing this, you can begin to build up a picture of the conversion rates between different resources (even if they can’t be freely converted all the time).  If a regular attack deals 100 damage, that suggests the time it costs you to make that attack is valued at around 100 damage.  If there’s also a special attack that deals 150 damage at the cost of 10 mana, that suggests a point of mana is considered around 5 times as valuable as a point of damage.  And so on.

These conversions generally won’t (and shouldn’t) be exactly the same across all actions; you get strategic depth by making some resources more valuable for some things and less valuable for others, and the game should probably be taxing the player some of his resources when he wants to perform an unusual conversion.

By varing the efficiency of different resources, you can establish which actions are “staples” (things that you do a lot, or when you don’t have any particular reason to do something else) and which are specialized tools that you use only when the circumstances require it.  For example, if the wizard is supposed to rely primarily on spells rather than physical attacks, his spells should be more efficient, giving him an incentive to switch to physical attacks only in unusual cases (like when he runs out of mana, or when an opponent is immune to magic).

You can also establish what positions you want to be in, and what positions you want to force your opponent to be in–for example, if your attacks deal more damage (for the same cost) when you stand on higher ground, then standing on higher ground is a tactical advantage, because it allows you to use one of your resource conversions (time into damage) more efficiently.

Many games have a resource hierarchy, where resource A can be converted into (or substituted for) resource B, but not the other way around.  This establishes that some resources are more valuable because of their flexibility (even though they might not be more efficient).

You should also look for resource conversion cycles–ways that you can convert one resource into something else, and then eventually back into the original resource; for example, sacrificing health for mana, and then using a healing spell.  You usually want to avoid having any cycles that generate resources from nothing (where you get back more than you put in), but remember that time is usually a limited resource, so even if you end up with more of the other resources than you started with, if you lost valuable time, it’s not really something for nothing.

Conversions between resources on different time scales are particularly important, and often signal some of the most important strategic trade-offs in a game.  For example, maybe you can spend some gold (a cumulative resource that has no maximum and never gets “refreshed”) in order to buy a potion that you can drink to restore health (a resource that gets automatically refilled every game day).  You’ll get back all your health anyway if you can just survive to the next day, and the same cannot be said for your coin, so this is a poor exchange–unless, of course, you aren’t going to survive to the next day without that potion.  The goal then becomes to survive using as few potions as possible, so that when a new day dawns and you have maximum health, you also have as much gold remaining as possible.

Conversions that go the other way (trading ephemeral resources for more permanent ones) are dangerous to have in a game, but sometimes workable.  The ideal way for the player to use those conversions is to trade all of his short-term resources for long-term ones right before they expire, which means the player effectively has the ability to generate long-term resources every refresh period, but that the amount generated depends on how well he manages the short-term resources.

This can lead to very bizarre strategies, especially when the number of refresh periods is variable–for example, in some CRPGs (Final Fantasy or Legend of Dragoon, for example) you can convert battle actions (a resource only relevant on battle timescales) into HP (a daily resource), so it makes perfect tactical sense to deliberately start lots of battles with weak enemies (or prolong battles after enemies have nearly been defeated) in order to maximize your longer-term resource.  This is counter-intuitive, and doesn’t make sense from the perspective of the game’s story, but that’s what the mechanics support.  This sort of conversion always raises red flags for me.

As for the rest…

You may recall, back at the start of this article, I used a comparison between a fireball and invisibility to begin this discussion, and the canny reader may be wondering exactly what resources could possibly represent invisibility.

Depending on the exact function of “invisibility” in the game, and the goals of the game, you may be able to abstract that as denying your opponent the use of certain actions (like targeting you with an attack), thus forcing them to do something less resource-efficient instead and/or saving you resources he might have taken away (like health).  Or maybe you can look at it as depriving your opponent of information, decreasing his ability to find the best use of his resources.  But in some games, you probably just aren’t going to be able to give it a rigorous representation in the resources abstraction.

But even if you can only analyze some parts of a game using resources, that still makes the analysis as a whole easier, by reducing the number of special cases you need to worry about.  It also gives you a nice measuring stick–even if you can’t precisely quantify the effects of a choice, you can compare it to other choices that you can quantify.  And the more of the game you can understand, the better an intuition you’ll develop about the remaining parts.