Identity Relationship Linear Relationship An identity relationship - PDF document

8/5/2014 Zach Laster University of Helsinki  We talked previously on how values interrelate. Now we’ll  Relationships between numbers can be either look at some concrete examples and forms of two-way or one-way. relationships.  Generally these relationships are in reference  Numbers in games don’t mean anything alone. They need to converting one resource to another some form of comparison points (context) to become meaningful.  We can convert 1000 gp into the item above, for  If an item costs 1000 gp, is it worth a lot? instance.  What if a ship has 12 move a turn? Is it fast?  We can get 10000 gp from running a dungeon.  We only know whether something is good or bad based  We can spend 1000 gp for 10 HP on its relationship to other things.  etc  If smelting a block of iron costs 200 smelt, and coal provides 1000, we know something about how smelting works.  When determining game balance, we often try  If we frequently get bags of 10000 gp in a game, obviously the to tie all of the resources in a game back to a 1000 gp item isn’t really that valuable. single resource. This helps us determine how  If the world is thousands of tiles in size, 12 move won’t feel very fast; but we still don’t know how it compares against other move various things compare. speeds! Identity Relationship Linear Relationship  An identity relationship is where two numbers  A linear relationship is like the identity move together in exactly the same way. relationship, except it scales.  As one increases, the other increases by an identical  We can have a 1-to-12 relationship, for amount. example.  They can start at different values, and other things can act upon them  If I can get 10 HP for 1000 gp , that’s a 1 -100  Not quite the same as having a copy of the value relationship.  If you consider the example of food from ○ This assumes there are no progressive deals, Ultima III: Exodus, we can get food from gold like 20 HP for 1750 gp … That’s not a linear as a one-way identity relationship. Food then relationship at that point, obviously. decreases over time. 1

8/5/2014 Triangular Relationship Exponential Relationship (Polygonal)  Exponential numbers get big FAST  When we want something like the exponential relationship, just not as huge, we often go for triangle  Basically, this relationship is when you want to stair relationships. something to scale very rapidly, like buying skill points or stats in a system where the next one is  For each step on the one side, we increase the other more valuable than the first. by one more than it was increased last time.  1, 3, 6, 10, 15, 21…  Stat points in D&D 3.5 are a great example (gp for the magic items).  This probably looks really familiar  Same for gp costs on a number of magic item properties,  D&D 3.5 uses this as the XP requirement for leveling actually  Each level requires the previous level times 1000 XP  Often accomplished by doubling. more than they had to get to that level  Typically, we don’t bother with anything more than ○ 0, 1000, 3000, 6000, 10000… etc doubling. Tripling makes things almost prohibitively  We can actually use other shapes as well. expensive, in practice, or far too powerful. Formulaic Relationship Systems of Relationships  There is no reason you can’t create more  Since we typically have more than two customized relationships between numbers in a game which relate, we numbers. wind up with a network of numbers  Some numbers just might be lots more or less which interrelate. valuable  The difference between almost one-shotting  If we can convert 3 blue gems into a red something and actually doing so is HUGE gem, and 4 red gems into a green one,  If none of the standard relationships work we can obviously convert 12 blue gems for your case, make one up. You can build into a green gem indirectly. it from the standard ones, as an aid.  If these relationships are two-way, then a  The only key is to understand how the single green gem can get us 12 blue gems. relationship will impact everything else!  Constructing this network can help tip us  We can also get an idea of what the off to issues in our relationships. central resource in our game is.  I can get 100 gp from donating blood, and I lose  The above one was probably HP, given 10 HP for doing this. (1HP → 10gp) there are probably other relationships I nthe  I can heal myself for 10 HP using 5 MP (1MP → 2HP) game which affect HP directly (damage)  Most of the time, the game’s win or loss  I can buy a MP potion (5MP) for 50gp (10gp → 5MP) condition will be tied to this resource  1HP → 10gp → 5MP → 10HP → 100gp  You lose if you run out of HP ○ Whoops  Feedback loops aren’t inherently bad,  If it isn’t perhaps you should move it, or though, as we’ll see. redirect some of the relationships 2

8/5/2014  We’ve mentioned feedback loops, like the  Usually, these loops are controlled in the manner of diminishing returns. blood donation one before.  Killing Monsters results in XP (HP →XP)  Actually, most games use these loops. They  XP produces level ups ( XP→Level ) aren’t really bad.  Levels increase damage and such ( Level→damage )  The one given was bad because donating blood  Which makes us better at killing stuff probably isn’t something we wanted to  We’d be stuck in a loop (we are, actually, but…) incentivize like that. If it was, though, we’ve except killing that monster tends to become less done it. effective after a while.  Usually the loop looks more like:  We need more XP to get that next level ○ Kill monster ( HP→gp ) buy more stuff  The monster stops providing as much XP as it did before. (gp →damage ) kill more monsters (less HP→gp )  The combination is brutal. We need more, and we get less than before. It’s like a drug addition. (Actually, a lot like, ○ So feedback loops can also produce a but that’s another story.) progression, if they are controlled properly. Progression can also be tied to the resources, such as buying  maps or keys using gold to allow us to access new areas, or buying item blueprints or better items.  Often, gold is a related resource to HP, so really we are kind of spending HP In some cases, we can’t actually use all of the resource we  have Once you’ve bought all the stuff you want with gold, what’s it good for  aside from healing?  We can also bias costs to make certain things more or less cost effective, making them more valuable in terms of HP than other things of a similar price.  Incentivize particular items or spells.  Make higher tier things less effective by cost, but still more effective, slowing progression When looking at these relationships, we should also consider  how time is affected (it’s almost always a resource).  Now that we can compare things fairly well, what do we  When balancing things, we generally want our do with it? costs and benefits on an element to balance  The previous set dealt mostly in resources. Now we’ll look out at things from the perspective of costs and benefits.  Of course there might be a general bias towards  A cost is anything which can be considered a drawback or benefits, but that’s a design decision limitation.  We can still tie these back to the resources  Spending gold, using an action, expending a charge, unit caps, etc. fairly well, most of the time, but the only  The item has a limited number of uses, only works under certain important part be that they compare to each conditions, etc. other.  A benefit, then, is anything which improves out position  Note that some benefits come with costs.  Increases our health/damage/power  Makes the other guy more squishy  A weapon that deals double damage to orcs is really  Cool powers cool against orcs, but the benefit doesn’t apply most of the time (unless you are mostly fighting orcs) 3