There is a field of study called Game Theory which is essentially problem solving with win-case solutions.  Mathematics have a single correct answer for any given problem (be it a range or a value) yet real-world problems have so many interconnecting systems that you aren’t looking for an answer, you’re looking for a result.  For example, if we raise the purchase price of rice (which is supplied by 2 companies, world-wide) by 10%, what impact does it have on the world?

Moving specifically into the game sphere, the concept of inter-connecting mechanics has been seen for quite some time.  Oregon Trail had a few variables, Ultima 4 and beyond and most RPGs have elements that impact others, all along a chain.  Being oblivious to these mechanics isn’t detrimental if your focus is on the story/adventure and not so much on success.  I could build an Engineer in Mass Effect and still finish the game, even though a Soldier is obviously the superior power choice.  This “face” of the game allows players easy access without having to worry about the technical details.  Blizzard does this fairly well with their mantra of “easy to learn, difficult to master”.

One of the earlier games we learn to play is checkers.  A simple enough concepts, where movements are limited and the rules are simple.  You could teach a 5 year old to play and they would do reasonably well.  Give the same game to a 30 year old, with a penchant for strategy and you find yourself in a complex mathematical game.  There is suddenly a method to the madness.  Expand that up to Chess, where a 10 year old should be able to play.  Grandmasters of the game have the ability to play through hundreds of strategies in their minds, in a fraction of a second.  Put them up against a rookie and they will win but not without a lot of head scratching, wondering just what their opponent is trying to do.

That reminds me of a story where masters were asked to quickly look at a board with a game that had started, then replicate it on another.  Since they saw strategies instead of pieces, it was easy to replicate.  Have kids set up the pieces and suddenly the master’s were unable to replicate the boards – since strategies were removed.

Game mechanics are somewhat similar.  Street Fighter is notorious for pattern combat.  Seeing high level players compete, with fraction-of-a-second reflexes makes it seem amazing but what they don’t tell you is that they have the movesets memorized.  Guile has 3-4 attack patterns and if you can defend against those, you can defend against the best players.  The recent Batman: Arkham City has a flow to its combat system that makes it feel like a dance.  Once you get that pattern down, with a few variants, it’s really hard to die, even on the hardest difficulty.

MMORPGs are down the same vein.  You can level without strategy or pattern and even at max level, you can complete a lot of content by just button mashing.  If you want to execute the top tier content, you need to understand the mechanics (or have someone explain them to you) and then perfect your dance.  PvE content is somewhat flexible in this domain, since the numbers are stacked in your favor.  With 25 players, only 10 or so need to play optimally to succeed.  Heroic content needs 20 people.  PvP content however, is merciless.  WoW 3v3 arenas are dominated by the RMP (Rogue, Mage, Paladin) builds for a reason.  They offer huge burst damage, the best healer survival options and multiple control abilities.  Being able to lock down players completely for 10 seconds or more is simply masterful.  Waiting until the last second to interrupt that heal, means more damage dealt.  This is why E-Sports is so entertaining to those who want to learn the systems and seems completely fanatical to outsiders.

The best Starcraft players hover around 250 actions per minute (APM).  That’s 5 different actions, per second.  A starting player is closer to 50, making a pro 500% more effective at time management than a beginner.  Both are having fun, both have the same opportunity to compete, just on different platforms.

WoW’s LFR system lets casual players experience raid content and the heroic system allows the hardcore raiders to do so as well, with additional rewards.  CoD’s matchmaking system will let the rookie players play together and the pros on their own matches, ensuring a fairly even skill field at any given time.  SWTOR currently only provides a challenge to the casual market, limiting their potential userbase.  EvE is the complete opposite, putting up a large barrier to new players.

The mark of a good game, that meets multiple demographics, allows people to play a simple game if they want and provides them with appropriate rewards while allowing a more in-depth strategy to develop for those who want it.

A spider web you say?  Yes, it’s relevant.  Continuing on the theme of power, we’ve seen how it works and how it’s distributed.  Now it’s time to see how it interacts with other game systems – hence the web.

In most RPGs you will have some sort of customization option, be it feats in tabletop games or talents in MMOs.  This provides an extra set of variables of power and a flavor option for players.  It would be unbalanced if a character could play defensively, do as much damage as another character and also be a great healer – all at the same time.  Games use these systems to “slot” you into a specific role and balance you around it.  Of course, there’s always the illusion of choice.  With WoW and SWTOR, if you’re in a specific role for your class, you’re going to have to select 75% of the same things as everyone else.  Great for devs and if you think you had a choice, great for you.  In games like Rift or any sandbox game, devs have to balance against an imaginary baseline and ensure that all possible variables can reach that baseline.  Lots of work!  That’s why in those games, you rarely have multiple choices for tanking or healing characters – or at least their play is practically identical.

These talent choices might include bonuses to your power stats or new skills and through this comes additional power weights.  If all of a sudden your talents give you 10% critical chance, then it becomes less powerful (in a diminishing returns system) to have it on your gear.  If you have a powerful spell that only triggers after a critical hit, then it becomes even more attractive to stack on your gear.  These trigger effects (or procs) can reach huge damage potential for characters and unbalance the game.  If you get a boost of power every crit and your chance is 10%, it’s almost a 10% power boost.  If you have a 50% crit chance, then it’s a 50% power boost.  Developers counter this with hidden caps, so that a given item can only proc a certain amount of times per minute (PPM).  WoW Rogue poisons are a good example of this as is TOR’s Sage skill set.

An artificial limit, diminishing returns and stats through talents give developers more knobs to fiddle with to try and balance characters.  If there was but one path to power, any change would be massive in scope and near impossible to test to ensure other characters were not affected.  With more options to fiddle with, you can target specific activities of a given class and get smaller changes.

The final item I want to discuss here is resources.  In all games you have hit points – a measure of when you live or die.  The other stat is for your power moves, be it energy, mana, rage or what have you.  Hit points are affected by the power moves hitting you (attacks or heals) and aren’t so important other than as a safety cushion for errors.  Power though, has a huge impact on performance.  If you’re out of mana, you can’t do anything.

In many games, DPS characters have auto-attack abilities with their weapons and don’t require power.  Magical ranged characters have this as well but the damage is usually pitiful (wands mostly).  Regardless, these abilities take the full impact of your power stats and have no adverse effects.  In fact, for some characters in some games, this might be one of the major sources of your damage.  This should be the same for all characters in a game though – otherwise it becomes a balancing nightmare.

In a power system, power stats have a significant impact on your damage potential.  If you cast more often (through speed boosts), you go through your power reserves more quickly.       Sometimes the speed boost will impact your damage over time attacks, providing an extra boost of damage.  These systems have “magic numbers” to target, if that damage is significant.

In a variable power system (mage mana), where you can increase your power reserves, the power drain can be compensated for, to a degree.  In a closed power system (rogue energy), this means that you will reach a point where you will be staring at your screen waiting for more power.  In some systems, there is a rhythm to the power balance (out/in) that allows you to perform specific chains of attacks and keep neutral.  If you increase the speed of those attacks and don’t increase the power regeneration rate, then you change the rhythm and break rotations.  Rotations mean you can look at the game instead of your keyboard, waiting for things to become available. The game is more fun.

Let’s look at WoW’s Rogue, a character with a fixed power pool.  They have auto-attacks that take full benefit from power stats.  Their damage over time attacks gain benefit from power stats as well.  Their energy regeneration rate is also affected by their speed rating.  This provides a system with a rotation, at any given power stat rating, and a fallback damage option (auto-attacks) when things go really wrong.

Now let’s look at SWTOR’s Imperial Agent, another character with a fixed power pool.  There is no auto-attack, so if you want to deal damage, you have to press a button and skip over a power move.  Damage over time attacks gain a benefit from all power stats but speed.  Power regeneration rate is not affected by speed, so the more you have, the less abilities you can use over a period of time, even though they might activate quicker.  This means you usually want to avoid all forms of speed boost.

Rift has rogues and warriors with fixed energy systems but they avoided adding any speed mechanic to their game.  It makes it easier to balance, even with less customization.

In the end, the more power stats you have and the more variables there are on your given character path, the more the need for simulation becomes apparent.  Years ago, you could estimate the power potential of a character in WoW with a simple spreadsheet as the mechanics were simple.  Today, you need a simulation tool to get an idea of your power potential.  Rift, with a lack of speed mechanic, simplifies this a lot since you can figure out damage potential fairly easily.  This is of course offset by the fact that you have hundreds of possible character possibilities.  TOR has a complicated power stat set (power, force/tech, main stat, crit, surge, accuracy, alacrity) but 2 of them are useless for 90% of the playerbase.  This makes modelling very simply and you can find spreadsheets telling you exactly what works best.

When it comes down to it, the choice of game mechanics is up to you.  WoW uses a simple to learn hard to master approach, Rift provides an extra layer of choice for players and TOR really just let’s you play without worrying about numbers at all.  Options are plentiful.

Ok, so that’s the best picture I could come up with.

In the previous power post, I went over the various paths to acquire power, as a player.  This post will go over the developer’s mandate to control that path in order to provide game and player balance.

In a traditional start/end game, like Mass Effect, distributing the power is usually limited by two factors – time (experience) and content.  The longer you play, the more items you acquire, the better they are and the better your skill set becomes.  Some games give a carrot-on-a-stick effect to start the game, like God of War, where you have extraordinary power then lose it shortly after.  Still, as the game goes on, your experience and time played provides more power.  A developer can incrementally increase the power of enemies and map it along with your increases.  A game like Final Fantasy where you can “grind” levels to make content easier also provides a hardcore mode for players that want to complete the game at level 1.

The second part is tiered content.  Using Final Fantasy 13 as a great example of tiered content, the developers limit your power acquisition to chunks of gameplay.  No matter how much you grind in section 2, the developers have given you a minimum level of power to start and a maximum amount to end with.  The variance is also usually pretty small too. Any game that locks out zone X until you complete Y is artificially limiting your power.  That’s why games like Fallout and Skyrim can make some sections really easy and others impossible as an open game does not assume your power level – it gradually increases difficulty based on your power.  This requires more coding by the developer but less planning since they never have to guess at your power level.

In games with no end content, such as MMOs, balance is difficult.  A straight boost to a power stat (power, critical chance, critical multiplier, speed) means that an item from the lower levels can and will compete with a higher level one, unless you inflate it to higher levels.  WoW had trinkets that provided 2% critical chance in the lower levels.  For a higher level trinket to provide a better stat boost, it had to be 4% at the minimum.  Push this across 10 item slots and you have players with incredibly boosted stats.  Add in an expansion and now the items need to be 6% or more.  Power growth is uncontrolled.

Developers learned fairly quickly that you need to convert something into that base stat – hence ratings.  Ratings work under a formula that is based on your character’s level so that an item with 10 rating would give 2% crit at level 20 but only 0.1% at level 50.  As you increase levels, you also decrease the conversion ratio so that at any given level, a character should only have X amount of a base power stat.

Moving on a bit to more complicated matters – theorycrafting.  In games with multiple playstyles – ranged, melee, casting, tanking – certain stats are more interesting than others.  Some classes will prefer to stack critical rating, others speed boosts and to that end, will stack a single stat that provides a linear gain.  If I know that 100 crit rating gives me 1% crit, then I will stack 10,000 rating as it’s my most attractive stat.  From a balancing perspective, this means that the items that you design will have weights based on classes and some items will simply never be used.

Diminishing returns help with this issue somewhat as the more of a stat you stack, the less valuable it becomes.  If you’re familiar with a logarithmic scale, you can see that at a given point, a stat rating becomes less attractive than another.  Let’s say critical chance is your best stat, 2:1 compared to speed.  Once your critical rating stat gives half the rating it did at 0, then you can start putting points into speed rating.  This way, you still have the increased power from critical but the loss of power from the diminished returns is off-set by the increase in power from speed with has yet to have diminishing returns.

From a balance perspective, it’s also easier to balance diminishing returns as you’re effectively capping the possible value for a stat source. If critical rating is the only way to get critical chance, you could make it diminish completely at 30%.  If you have 1 or 2 more sources, diminish those as well so that the total possible in-game is 50%.  You know that the majority of people will be in the 35% range while the ultra players will be higher, 40-45%.  That’s much easier to balance than 10% vs. 80%.

Diablo 2’s magic find stat worked like this.  For basic items, it provided a linear return and for the best unique gear, it was a diminishing return.  So while you might always be gaining a better chance to find magic items, once you reached about 400 Magic Find, there was little benefit on stacking more of it if you were hunting uniques.

On the flipside, if you have hard caps on some stats, where once you reach a given point there is no more benefit, you’re essentially limiting your gear selection for players.  SWTOR for example had an original issue where Accuracy and Speed were completely worthless stats since you only needed a small amount to cap, yet 75% of all the high end gear had these two stats present.  With the game’s ability to swap stat packages around, high end players farmed a small set of gear (IA gloves mostly) for the Crit/Surge boosts, which were 3-8 times more valuable for every class.  This is poor design.  Changes were made in a patch to reduce the return on some stats and the next big patch, 1.2, should change the way stats are distributed across equipment.  Still, the stat system is flawed at its core in that game.

Developers have an intricate balance to play if they have multiple paths to power.  The more you have, the more you have to make sure that all of them provide benefit to the player in a balanced fashion.  If one stat simply shines for everyone, expect game breaking situations (armor penetration in WoW is a good example).  Ratings and diminishing returns provide the mechanics that devs can use to balance stats between each other, between classes and across all levels of content.

Back to gaming!  The next few posts will go over the mechanics of RPGs, specifically the increase in power and the multiple paths that it can take.

Since the Pen and Paper (P&P) days, characters have faced adversity and through it, gotten stronger for the next challenge.  This is true in life, for the most part.  When computers came out, essentially large calculators, this process was shadowed somewhat by the adventure.  In today’s world, you can easily play any RPG game and ignore the behind-the-scenes calculations for power.  The game usually does a pretty good job of showing you what is an upgrade – in a linear fashion as well.  Only if you want to play at an elite level do you need to worry about min-maxing (a term that means minimizing your weakness while maximizing your power).

In this first post, I’ll look at the particular mechanics of that path and the various ways games get you to the top.

Power is gained through 3 main methods.  Acquiring new skills, more damage or more speed.  Certainly there is a mental aspect in performance but that’s for another post.  In RPGs would get new skills with new levels.  Batman doesn’t get his grapple gun for a while in his games, for example.  You get more damage either through numerical input from new equipment (better stats) or from leveling and improving the baseline of the skill you are using  (a level 60 backstab is stronger than a level 10).  More speed is really split into two sections: getting more efficient (the mental aspect) and accruing more numerical speed – usually through some haste metric.

The leveling aspect of power increase is linear, easily controlled and available to everyone.  At maximum level, every character should have access to their most powerful skills.  Some games in the past (Vanilla WoW, Everquest, etc…) made you hunt for these skills, giving players who had them a huge advantage over others.  In today’s game, that is gone.  EvE (and Glitch) is a little different in that the skills are available but time limits your ability to get them – you need to train for months.  From a developer’s standpoint, this is a fairly easy way to measure and control player power.  It also gives them points to balance classes.

Next is the increase in numerical power.  There are many variables here: level, attack power, critical chance, critical multiplier, base statistics, equipment.  Take a typical MMO.  Your fireball damage is based on the level of the skill, your intelligence modifier, your spell power boost, your chance of it hitting critically and the amount of damage that critical hit deals.  At lower ends of the numerical scale (say 100 damage) an increase of 10% overall damage is significant but not overly powerful.  At the higher end of the scale (say 100,000 damage) an increase of 10% damage is massive.  In WoW, characters can hit for that much or more and 99% of all characters in the game have less than 10% of that amount in hit points.  If you continue to add a linear amount of power, this soon gets out of control through compounding.

Compounding is where you continually add in percentages – just like a bank.  If I put in 100$ and it gains 5% every year then: year 1 = 105$ (100+5%), year 2=110.25$ (105+5%), year 3=115.76 (110.25+5%), etc…

If I say that each item adds 1% damage, people who have 60 items have an extraordinarily large advantage(81%) over those with 30 (35%), let alone 10 (10%).  Where someone should be 6 times more powerful, they are actually 8 times because your baseline increases continuously.

On top of that, since you have 5 or more variables that affect your power increase, it becomes increasingly difficult to manage and keep balanced.  If you were to make one method unattractive, people will go for another.  TOR has this problem where Critical Chance and Critical Multiplier are excessively powerful when compared to other methods.

The final increase is from speed.  The basic damage formula is called Damage Per Second (DPS).  If you’re able to get more attacks in per second, your overall damage will go up.  In shooting games, a fully automatic weapon will shoot more often than a sniper rifle but do less damage per hit.  Most of the time, the sniper rifle will have a higher DPS rating but the mechanics of the item make it hard to use consistently.  So let’s say the automatic hits for 20 damage every 0.5 seconds (40DPS) and the sniper rifle hits for 150 damage every 3 seconds (50 DPS).  If I were to increase the rate of fire by 10%, then the auto goes to 44DPS and the sniper to 55DPS.  It’s a linear gain for each but the sniper rifle gained more power overall.  Some games give a 50% boost to speed and in that instance, the sniper rifle gains 20DPS over the automatic.

You can see again how a compound gain of speed will benefit damage.  In many RPGs you reach a point where speed “caps” at a point where the game system can no longer handle the input (global cooldowns, energy, mana resources, etc…) but on the whole, more speed is good.

In the next post, I’ll go over how games balance these various power stats to ensure that people who have gone through a lot of hoops are more powerful than others but in a balanced fashion.  I’ll also go over how a complete lack of balance in some games puts an artificial barrier on gameplay.