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Formulae in Video Games
Tcheldor
Registered User regular
Registered User regular
Hey all,
I've been wondering for a while now, how do developers come up with the actual formulae they use to determine how the mechanics of a game work? These formulae, especially for things like JRPGs, are the key to balance and as companies like blizzard have demonstrated in the past, the numbers are really important to making a game fun.
I know we have many people who have worked in the game industry, developed their own games etc. on these boards, and I was wondering if they might be able to share some insight into this nitty gritty part of game development.
Additionally, I will say that one of the reasons I'm making this thread is because I'm in the early stages of working on a game, and this is one of the important roadblocks ahead.
I've been wondering for a while now, how do developers come up with the actual formulae they use to determine how the mechanics of a game work? These formulae, especially for things like JRPGs, are the key to balance and as companies like blizzard have demonstrated in the past, the numbers are really important to making a game fun.
I know we have many people who have worked in the game industry, developed their own games etc. on these boards, and I was wondering if they might be able to share some insight into this nitty gritty part of game development.
Additionally, I will say that one of the reasons I'm making this thread is because I'm in the early stages of working on a game, and this is one of the important roadblocks ahead.
League of Legends: Sorakanmyworld
FFXIV: Tchel Fay
Nintendo ID: Tortalius
Steam: Tortalius
Stream: twitch.tv/tortalius
FFXIV: Tchel Fay
Nintendo ID: Tortalius
Steam: Tortalius
Stream: twitch.tv/tortalius
Tcheldor on
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One way to create your own formulas in Excel is to start off by creating a table that has the general values you are looking for. Highlight the values and then insert in a line graph. Right-click directly on the line inside the graph and the select the 'add trendline' option. A window will appear that allows you to customize the graph line. Select the type of formula you want to create and then check the 'display Equation on chart' box at the bottom of the window. This will insert in a formula that most closely matches the values you used in creating the original chart. The formula can be pretty raw so you'll still want to touch it up to make sure it gives you what you are looking for.
The best advice is to build up your game logic step by step. For instance, if your game is based on level progression, then start off with the 'levels' table. Once you're satisfied with your level table, you can now use 'levels' as one of the base inputs for your next formula/table. Once you complete that table, you have now have created another base input you can utilize to create any future formulas/tables, and so on. My background is in developing MMOs, so some of this advice might not be applicable to you depending on the type of game you are planning to develop.
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Most just seem to let the QA guys let them know if something is out of wack.
As a general rule, the best thing you can possibly do is run test cases. Your intuition of how things should work will often be dramatically wrong.
For example, if you have a flat damage reduction armour system, you automatically make weapons with large damage ranges more effective than those with small damage ranges even if they have the same average damage.
Example:
I have 50 armour (reduce damage by 50)
I have two weapons that do on average 50 damage per strike. One does 1-99, the other does 50-50.
One does on average zero damage to this target. The other averages 12.5.
Just test everything. Also, make sure you keep control of scaling.
For example, if you have a magic system where the only stat which affects magic damage is a flat additive one, eg spellpower from WoW, then the damage output will scale linearly (assuming no other complications) with the amount of spellpower you put on items.
If, however, you give melee characters 3 stats: attack speed, critical strike, and attack power, then they will scale multiplicatively. Attack speed increases the value of attack power, crit increases the value of attack speed, etc etc. They will outscale the casters quite dramatically unless you carefully set up your ability system.
FFXIV: Tchel Fay
Nintendo ID: Tortalius
Steam: Tortalius
Stream: twitch.tv/tortalius
ironically, most RPGs overcorrect and end up making mages a billion times more powerful than melee characters. :P
Registered just for the Mass Effect threads | Steam: click ^^^ | Origin: curlyhairedboy
In the process of dealing with difficulty and stat systems within my own game at the moment.
Here's some long-winded insight into what I'm dealing with and how I plan to do it. It may sound unrelated to formula but it is all based on the perfection of difficulty and statistical formula that manage the game behind the scenes.
Games are the only media that have the ability to self-evaluate and evolve as they are played.
Relying on a fixed formula when every player is different is not good enough for me.
Spoilered for long. Mainly written because I have barely defined it myself.
The player wants to feel all-powerful, yet remains challenged. Either absolute end of the balance spectrum lies a very boring territory everyone wants to avoid. No challenge is simply tedium, too much is simply aggravating, finding the balance for each individual player is what I'm looking for.
The possible bad: Balancing ends up like oblivion, you're level 50 but so is everything else. Increasing the difficulty manually here just increases the length you spend hacking away at things.
The possible good: Each encounter requires thought, provides adequate rewards, and doesn't end before the player wants it to; everyone is a winner.
Many games are actually trying to do something along these lines; often with ugly results because they didn't properly stress test them or didn't understand certain play styles.
For my game, I'm hoping that ultimately I will end up with a player-regulated difficulty system that modifies the game through the players own decisions and gameplay actions, rather than offer a static choice that might prove under or overwhelming as the game continues. The game should scale only when a player challenges it to do so. A game with an emphasis on combat should never devolve into simply trading blows.
Balancing this is something of an art form and it's likely I may never get it perfect.
I will be scaling difficulty via increased statistics/group variation and allowing monsters to gain special prefixes/suffixes, similar to how Diablo 2 did elite and champion monsters.
You take an existing monster, slap a new color on it and give it the ability to spew fire. Of course, the harder the monster you defeat, the greater the reward.
I loved fighting these sort of variants personally, as you were unable to deal with them with ordinary filler methods, and you could put your character, items, and build to its fullest.
At the end of these battles, you also knew that good loot awaited.
I'm hoping to get it fine-tuned enough that the player will experience defeat at least once or twice each area but to never exceed a certain amount. Player activity would be recorded and everything would be tweaked slightly to their playstyle and try to maximize enjoyment.
The irony of this dynamic balancing is that the stats system the player is building on must become largely trivial; yet always maintain the illusion that it is of great importance and benefit to him. The actual formula I will be using in my game will be mostly of percentile nature because I can never let the stats really get out of hand without destroying balance. A party-building turn-based game should never be easy or include 'filler' battles, the fun of these games is building your party and seeing the fruition of your efforts.
As numbers get larger, the percentile for dealing damage gets slighter smaller. Damage ranges for each attack usually vary between 10% and 30% using a direct comparison between the players stats and the target.
For example:
1000 damage on a 500 defense target = 25% damage
1200 damage on a 500 defense target = 27% damage
1000 damage on a 750 defense target = 21% damage
1000 damage on a 1000 defense target = 18% damage
The player can continue to ramp up statistics but extreme stats can only take him/her so far, the reverse is also true; characters should never be killed in a single unpreventable attack.
As the players victory rate raises, so does the enemy stats and variety of rare abilities of the coming encounters, at the same time, item drop quality increases if the player continues to win. When the player begins to have real difficulty, the difficulty drops back slightly or they have the option of:
avoiding more dangerous encounters, finding the stairs upward, or improving their existing items via special dungeons.
The process repeats indefinitely.
I've barely even started working on this system, it's difficult to say if it will work the way I intend; the only thing you really need to remember has already been said... you must test it.
I've already built a grind game around this theory, but it is too small-scale for my current project to adopt.
Naturally, a system of this sort only works in the environment of my own game: A procedurally generated 2D world.
There is still a heck of a long way to go. PS: looking for artist/music/writing talent!
tl;dr
I let the player determine balance by monitoring their actions in the game.
Left4Dead is good example of this. It consistently pushes against your team, yet never becomes questionable.
Oblivion is a bad example of this. It just scales every enemy and equips it with items your level, taking nothing else into account.
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Flat damage reduction has that problem, but miss rate or percentage based mitigation are also fraught with potential issues.
For example, lets say as a tank I have 50% physical damage resistance base. If my armor adds 35%, and a buff that adds 10%, I'm not actually not getting a 45% increase in survivability, I'm getting a 1000% increase in survivability (It'll take ten times as much damage to kill me as base). Similarly, if mob base miss rate is 50%, and I have an ability that reduces it by 40%, I've increased survivability by 5 times.
City of Heroes had abilities formulated with this, and it really played havoc with things. In the early days of the game it was actually possible to get %100 buffed damage resistance as a tank and become immortal. It was eventually capped at 90%, but still a tank with 90% damage resist and enough defense to put enemy hit down to the 5% cap could take literally 100 times the damage of a undefended blaster even before inherant HP differences. D&D 3E also had a similar problem with AC where stacking bonuses from different sources could cap out enemies at 5% and make you literally 10x more survivable than a typical character before hp. The big problem also was you could end up with situations where a mere 1 point of AC could double survivability by taking you from a 1 in 10 hit rate to 1 in 20, wheras normally a point of ac was only worth about a 10% increase in survivability, moving you from being hit 50% of the time to 45% of the time.
I only wish every RPG would have spells with scaling damage/ratios
that's how the usual logic goes, but...
mages usually get ranged AoE nuke spells, which nearly instantly kill groups that melee fighters would have to chew through. in the end, mage classes wind up as the most efficient killers by far.
Registered just for the Mass Effect threads | Steam: click ^^^ | Origin: curlyhairedboy
indeed
my point was more that you should do examples to see how it actually works
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Trade-offs. DPS isn't everything.
Currently playing: GW2 and TSW
For most multiplicative effects, you need to use an asymptotic curve in order to map them to a linear benefit. So, to take the damage reduction example, you should probably first state it as an arbitrary numerical value, rather than a percentage, because it's going to be converted. Then, just map it to the function Y = X / (X + c), where Y is the actual damage reduction, X is the statistic, and c is a constant that controls the equation (simply enough, it's the statistic required to achieve 50% damage reduction). So, for example, assume we call things percentages to be confusing, and so set c to 100%.
If our "damage reduction" stat is 50%, then our function gives us 50% / (50% + 100%) = 1/3. So, we will take 2/3 damage, and it will take 50% longer to kill us. If our "damage reduction" stat is 100%, then we get 1/2, and it will take twice as long to kill us. A 50% increase in the stat increases the amount of time it takes us to die by 50% of the base value.
Naturally, players will be bothered by you calling this "damage reduction" when it's actually literally "survivability increase", but it's the simplest way of mapping things so that they scale linearly.
I hate that aproach, personally. I'd like _every_ point I invest in a character to be worthwhile throughout the character's lifespan, even if some points go towards situational abilities. Having to waste a certain amount of points on useless crap for the sole purpose of reaching something that is actually worthwhile is bad design. Diablo 2's skill trees eventually evolved to be (imho) the best example of how a skill tree should look/function. Very, very little there is absolutely worthless at the end of the day.
As opposed to, say, Titan Quest with abilities that literally do, add or prevent double digit damage when maxed in a game where you're dealing with thousands of points damage later on. Use percentages relative to your character level/difficulty, for the love of god.
Currently playing: GW2 and TSW
The point here isn't that you object to useless skills: you object to an investment in useless skills diminishing your endgame character, and there are ways to mitigate that: for example, allowing re-speccing, or giving free skills at certain low levels (which has its own advantages, in that it encourages experimentation). Maybe you see the existence of a skill as being an investment in itself: that low-level magic missile could have had a role in end-game, but it doesn't, and that's a waste? Why is it OK for skills to be situational... but early-game or mid-game doesn't count as a situation?
Obviously special effort needs to be spent on post-game, as a lot of time is generally spent there. But by focusing too hard on post-game balance, as if it's the only goal, you can either unbalance the early- to mid-game (something which post-game players generally don't care too much about, as that's an obstacle to overcome to reach the post-game) or you end up with a homogenous gameplay experience.
Actually, I don't play for postgame. I enjoy postgame, sure, but I create characters for the full spectrum of the game. As in, when I make a Dungeon Siege 2 character I make him with the intention of playing every difficulty. I don't build characters to have horrible, unenjoyable midgames just to enjoy super godlike endgames. That's for MMOs and shit, I don't put myself through that kind of torture when I'm playing by myself for myself.
I consider every point an investment, wether it be an attribute or a skill or a talent or whatever, and I totally understand that magic missile should rock at lower levels, but not at high level. What I'm asking is that, instead of magic missile being a 100% write-off later in the game, give it a synergy (like in Diablo 2) or maybe situational utility value in endgame (through clever design: maybe make magic missile light up areas, and thus could be used as a flare of sorts in endgame areas that are dark), or even just tertiary non-mechanical value (such as a qualifying for a special title since I put one point in every casting skill). Just don't make me look at that 1 point in magic missile when I'm level 79 and go 'God. What a waste'.
Obviously, if magic missile is an isolated skill (not required for anything else in a tree structure) then a respec fixed the problem easily. In vanilla Diablo 2 you ended up with a shitload of wasted points in prerequisite skills that contributed nothing past the intial few acts in the initial difficulty. That sucked rather fierce. Now? Now almost every synergizes or scales, plus you get character respecs. I admit freely to being a Diablo 2 fanboy though and thus my opinion may be slightly colored
Currently playing: GW2 and TSW
The issue here isn't obsoleted skills: it's forcing people to invest in obsoleted skills in order to get to better ones. Can't have no pudding 'til you've eaten all your veggies.
My way of doing this is basiclly what krapst78 said, pick a stat to be your grounding stat, level is the best measure of this as its the very defenition of linear. Then build up your system from there.
Now, it gets worse, you need to make sure to give aproperite multipliers, for example, a dot over 6 seconds should do a lot more then a burst spell on the same progression level. And thats saying nothing about a short front cone AoE vs a targetd AoE, a long range burst vs a short range burst that only works if you block first.
Basiclly you need to keep checks and balances, my way is to make all teir 1 skills of all classes first, then teir 2. I don't go class by class.
For the sake of my OP, my game is going to be turn based in a ye olde DQ or FF10, or Wizardy style, as again, it reduces variables and allows me to keep the player's power on a stricter leash.
I suppose I'll detail what I mean: I have a few major concepts: 1) HP/MP refills post EVERY battle, 2)AP determines what skills a character can use each turn. (Look at Arc Rise Fantasia for a good example of AP use, though I know they stole it from some other better game that I have yet to play).
I'm also going to limit character level growth via a story mechanism in each section while allowing the player to continue to gain new abilities. (Aiming for exp for power and Skill exp for skill points). This means that I can really control how strong the mobs will be vs the player.
FFXIV: Tchel Fay
Nintendo ID: Tortalius
Steam: Tortalius
Stream: twitch.tv/tortalius
This is all said as a player though, definately not a designer. Might not be a huge deal when balancing the game, but it makes a huge difference in how I play them.