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Gaming Theory

Explains theory behind game design and analyzes choices made in modern MMORPGs.

Author: GamingTheory

#3 - BPS, DvBpRP, and BE-Margin

Posted by GamingTheory Saturday July 26 2014 at 7:56PM
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Last time, we discussed how playing a video game can be likened to learning to play an instrument [specifically, this piano].  When players first start, they progress very rapidly, but that learning curve starts to plateau as a player's skill increases.  MMOs are a genre where players can often reach a "skill cap" and be effectively doing everything their character can, from a physical gaming perspective [pressing all the right buttons at the right time], relatively easily... at least, no game currently requires the dedication to a series of button-presses that Ravel's J'eux Deau does.

As players increase skill in the game, they consume content faster.  If you know all the fastest ways to move around, and have used specific keyboard macros to make those movements fit your hand, it just makes sense that you will reach a target area of the world faster than someone who is, as some may say derogatively, a "Keyboard Turner".  This means that as players grow more skilled at a game, but the game does not throw greater physical challenges at them, then developers must produce content at an increasingly rapid rate to keep up with the increased fluency of skilled players.  In certain cases, this leads to unsustainable demand, where skilled players can consume content on orders of magnitude faster than it can be produced, and those players represent a large majority of the game's playerbase.


This time, we'll talk a little bit about how we can keep track of what buttons players are pushing, how often they are pushing them, and then we will examine how that might impact design decisions.


BpS - Buttons per Second

A fairly obvious acronym and statistic, BPS stands for "Buttons Per Second" and is a statistic many developers watch fairly closely.  The most obvious representation of this comes in one of two forms; either a "global cooldown" or a "cast limit". 

Global Cooldowns: Games with Global Cooldown systems allow players to only use one skill for each pre-labeled time limit.  The most familiar of these is likely WoW's 1.5 second GCD, but numbers range from .5 seconds (some Korean 2D MMOs) to 2.5 seconds (FFXIV).  Too much lower than .5 seconds, and lag becomes a strong component of gameplay.  Too much higher than 1 second, and players grow bored.  Think again of a piano.  If you have access to one, try pressing only one key every 2.5 seconds.  It is not going to be a very interesting listening experience.  Games with the Global Cooldown system tend to exclude movement from their restrictions.

In Global Cooldown systems, the formula for ideal player BPS is generally ideal BPS = c+Expected Movement Buttons, where c is calculated by [GCD*c=1].

Time-Capping Systems: Game with Time-Capping (or Cast Limit) systems put a cap on the amount of buttons a player can press in a given span of time [usually one second].  Many FPS games use this system... if a player holds down a "Fire" key, then depending upon gun scores or player statistics, the player fires a certain number of bullets or deals a certain amount of damage in a second.  Obviously, if a player could hold down a key and immediately empty a 200-round clip, there become strong balance issues to a game.  Some fantasy-themed MMOs cap player actions at 2 or 3 or 4 actions a second.  These caps may include movement actions [so if you fire off three arrows at a boss, you may be unable to use the dodge button until the current second has finished and a new second begins, awarding you three new actions].

In Time-capped systems where movement is included, the simple formula is ideal BPS = Cap.

((**There is a current argument being made by certain developers that good players should, at certain times, choose not to hit a button, and allow resources to regenerate or other gameplay mechanics to occur.  Currently, I would suggest that while a well-placed rest may be a designed part of musical piece, having each measure in 4/4 time filled with two notes and a half rest makes for an exceedingly boring piece of music... something you might expect players to graduate from within their first few months of being introduced to an instrument.))


DvBpRP - Diverse Buttons per Repeat Press

This horrible acronym [seriously, just say the words] is an attempt to quantify the player's need to press many different buttons before returning to an initial button.  Diverse Buttons per Repeat Press is calculated by [AVG Buttons pressed before Initial Button Pressed again (per sequence)] - 1, and hopefully repeated for at least three different sequences of tasks.


DPS Rotation, no Procs: Self-Buff Short (1), Mob Debuff Long (2), Mob Debuff Short (3), Builder 1  (4), Builder 2 (5), Builder 3 (6), Finisher 1 (7), repeat.  BPS = 6.

DPS Rotation, with Procs: Self-Buff Short (1), Mob Debuff Long(2), PROC #1 (3), Mob Debuff Short (4), Builder 1 (5), PROC #2 (6), Builder #any (7), Finisher #1 (8), repeat.  BPS = 7

DPS Rotation, while moving: Self-Buff Short (1), Mob Debuff Long (2), Builder #1 (3), Builder #2 (4), Finisher #2(5). BPS = 4.  Repeat, replace Mob Debuff Long with Mob Debuff Short, replace Finisher #2 with Finisher #1, BPS = 4.

Three cases: (6 + 7 + 4)/3 = ~5.6 DvBpRP.

DPS is the obvious case for example purpose, and is indeed where this statistic gets far and away the most scrutiny.  However, other roles [support roles especially] tend to not be looked at quite so stringently, and thus suffer from much lower numbers [for example the pre-expac version of Rift's Chloromancer or Bard, which generally required putting up a few buffs and then hitting the same key over and over until the fight ended.]

As with BPS, higher DvBpRP generally increases the skill threshold.


Button Error Margin

Perhaps the most interesting statistic is Button Error Margin.  This is the amount of time a player has to hit a certain button before experiencing some negative effect [or the loss of opportunity for a positive effect].  The most obvious cases are player defensive abilities.  If an enemy is bearing down on you with a rapidly spinning up railgun, you have a certain window in which to either 1) defend, or 2) leave the area.

The most obvious issue with Button Error Margin is lag.  If a designed ability gives a player a one-second window to avoid the negative effect or gain the positive effect, but the player experiences a half-second of lag on average, that player is left with only a half-second in which to press the button.  Also consider that human reaction time that does NOT involve decision-making [so the user is aware of the desired action] still takes about .2 - .3 seconds [Click here to check YOUR score!].

The second obvious issue is what we mentioned during the BPS section; the restrictions games place upon the ability of players to use abilities.  If I have an ability that requires a one-second window, a player has a half-second of lag and a fairly fast .2 second reaction time, AND knows what is required of them, they STILL must match that .3 seconds of eligible button pressing with a time when they are not capped by a global cooldown or time-capped limit on inputs.


The Context

While all of this is fairly interesting, a BPS of 1.8 does not, in and of itself, dictate whether a game is "good" or "bad".  That is dictated by relative presence of risk and rewards, which is not something that can be determined by offline calculations or 1000-hour dummy-target tests.

For example, lets say I am a designer who has created a high-risk, high-reward system for the players in my game.  If they select a spec with a high BPS and DvBperRP, they have a effect-size of roughly 160% of what someone with a low BPS and DvBperRP spec has.  However, they also have a floor around 40% [playing poorly but still GCD capping, just making bad decisions that destroy the synergy of the spec], whereas the person with the 3-button rotation would be hard pressed to fall below 80% of their potential output.

This seems like solid design, and in truth, it probably is.  Players that like to theorycraft will complain that the slow spec is uselessly unplayable due to its low relative max potential, but that is only a concern if, and only if, players can reasonably be expected to operate at levels very close to theorycrafting potential.  If an encounter requires players to be constantly on the move, or situations happen where specs with "ramp-up" time [like most PK situations] cannot complete full cycles, then the second spec looks much more attractive.

In truth, probably the best middle line to walk is to make sure that there is a wide variety of choices available to the player, as well as a wide variety of requirements... and the rewards justify meaningful choices.   If the game is so slow that all players can accomplish the most difficult sequences [imagine playing an MMO on an 8-bit Nintendo Controller], then it will be impossible to distinguish player rewards based on this type of analysis.

The goal is not to hit certain numbers or avoid certain results of formulas.  Players are amazingly skilled and dedicated, and should not be underestimated.  If we put a difficult task into a game, some of them will accomplish it, even if that task is something that looks penned by Listz.  The goal is to get a good balance going of reward for the players that undertake those challenges.  They should have higher ceilings and lower floors.  They may level twice as fast or top the Kill/Death boards if they are a skilled player, but they may risk leveling at half the speed with ten times the deaths if they have yet to master the skills required of a demanding player choice.

1) Offer the player the choice

2) Reward the player if they accomplish the requirements of that choice

3) Parcel out rewards appropriate to the difficulties of the choice


What's the fastest game you've ever played?  What is the slowest?

Do you prefer to play games where you are asked to press a few buttons rapidly, or a diverse set of buttons more leisurely?

Have you ever encountered a part of an MMO where your level of play was poorly matched to the rewards for the difficulty of the task?  What was your reaction?  [Change games, adjust character, start over, ignore, etc.?]

#2 - Player Skill Curves

Posted by GamingTheory Monday July 21 2014 at 9:42PM
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This is a keyboard.

Piano Keyboard

Full ones have 88 Keys [52 white keys and 36 black keys, but who is counting?] and this one has slightly fewer.  Still, it is a fairly standard keyboard, and can be about the equipment expected of most piano players.  If I am writing a piece of music for the piano, I can reasonably expect players to have access to this amount of equipment.

This is also a keyboard.

computer keyboard

It has an expected 108 Key-Commands in the standard system, and developers can expect gamers to have access to those 108 Inputs, as well as various combinations of them.  [Note that in the ASCII system there are not actually 108 physical keys... combinations of Shift tend to account for the other commands, like % or $ or &].


Using the first type of keyboard, with 88 keys, I can reasonably train a seven-year-old to press eight-to-ten of them in a given order, within about six months of their first encountering the tool.  Given three years, by the time that seven-year-old is ten, I can now expect him or her to be able to press 35 to 50 of the keys in a logical order, given a few weeks of practice, and including various combinations [chords].

Using the second type of keyboard, with 108 inputs, I can reasonably train a seven-year-old to press about 40 of them in the correct order, according to prompts on the screen, within six months.  Given three years of training, the student will be entering complex commands very rapidly across most of the 108 inputs, especially with consistent practice.

With adults, the learning curve tends to flatten.  While students are wildly different, if an adult has been playing a piano for about three years, I would expect them to be able to access all 88 keys at rates greater than 140 keys per minute [chords included].

So, here is my question... how many of you have been "playing" MMOs for longer than three years?


I use this roundabout example to get developers to think about what is physically happening when a player is playing a game.  Forget the big dragon breathing fire or the space-age missile launcher [which is really just a re-skinned fire-breathing dragon].  What is the player actually DOING?

The player is pushing buttons on a keyboard.

Here's the connection to the music example:  If you have been playing music for three years, but are still only allowed by your instructor to play songs with 5 - 10 notes [thumbs on Middle C!], HOW BORED ARE YOU?

As a player participates in MMOs, they become better at MMOing.  Of course, players learn at different rates and like different things, but all in all, they gain some knowledge and skills the more they play.  The problem becomes that very few games offer a skill curve that allows players to reasonably excel.  In your first MMO, this was likely accomplished through the leveling process.  You started out with only a few buttons to press, and gained more and more as your character leveled up.  Hopefully, if the experience was good one, the developers also put in reasonable challenges [harder sheet music] to encourage you to use more of those buttons.  If done well, the result is that you learned without being bored, and got much better at the game.  You may not have noticed it, but you probably type faster, and with fewer errors.  Credit MMOs.

Now, as a long-time player, you clear those skill hurdles much faster.  You probably do not even need the leveling process to guide you through them, or at least would appreciate it if you had access to a full range of skills sooner.  Those early levels can be brutally boring now, which is probably a marked difference from your first game, when they were FASCINATING!  The truth is that the levels have not really changed... you still have few skills and a very limited scope of available activities.  But as a player, you are ready to accept much greater challenges... if you can find them.


Player Learning and the Logarithmic Curve

Almost all human learning follows a logarithmic curve, where learning is graphed versus "experience" or "time spent on learning tasks".  It looks like this:

Basic Learning Curve: Log relationship between learning and time spent on learning tasks

When we first start learning something, we learn it very rapidly.  Think of a foreign language.  I could probably teach you 20 new words in a foreign language in less than an hour.  But in English, which you've likely been speaking for years and years if you are reading this blog... well, you probably don't learn 20 new words over the course of an entire month.  That's what the curve is saying.  At the start of a new learning situation, knowledge [and skill] is developed very rapidly.  Then, it starts to slow down.


So where does this tie into games?  Well, if you are a piano teacher, you know that the average student quits after about two years.  That's when the learning curve really starts to "plateau"... they must spent a lot of time on learning tasks to gain any real new progress or knowledge.

Here's the connection to gaming:

As learning rate declines, so does interest based on novelty

As players learn more about the game and the gameworld, their interest starts to drop.  One can make a fairly convincing argument that the genuine interest a player has might be, in the current MMO release cycle, peaked BEFORE a game actually releases.  This puts developers at a severe disadvantage when trying to maintain interest via novelty [or having-new-things-to-discover].

What developers often tend to underutilize is exactly what we were discussing above; interest based on novelty tied to the physical aspects of the gaming system.  It is not a very uncommon story to hear players tell how "discovering a new spec/class/playstyle" re-ignited their interest in a particular game.  This is because they have essentially reset themselves to the left side of the curve, where they had lots to learn, and the rewards for doing so very large, compared to the high skill/learning level they had achieved on a different spec/character/playstyle.

As I said, developers do not tend to provide opportunities for players to really challenge themselves, physically, at a keyboard pressing buttons.  I noted in my last blog that there is currently no game in existence or development that seeks to market itself solely to non-novice players.  In essence, in the world of MMOs, we have hundreds of games that are "Piano For Beginners : Lesson Book #1", and nobody has ever published Lesson Book #2, Lesson Book #3, or even a decent recital piece.


Next time, I will discuss two statistics that attempt to quantify the physical experience of the player [their interaction with the keyboard, not the game world], and explain how a developer might use them to appeal to different playerbases.


Have you noticed your interest in a game decrease as your skill level in that game rises?  Tell us about your experience!

Have you ever "Mastered" an MMO [or a console/PC game], and if so, what kept you interested after you attained that very high skill level?

#1 - Balance

Posted by GamingTheory Sunday July 20 2014 at 12:10AM
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It does not take very long in the preview of a new game before someone corners a developer and asks about "Balance."  To many a dev, this may be the deer-in-the-headlights moment... if you have a pre-prepared answer, then it is your chance to [mix metaphors] and knock it out of the park.  If you don't... well, the sharks begin circling the deer.


So what is "Balance"?  When it is good, when is it bad, and how have games chosen to address it?  Most importantly, as is the focus of this blog, how does a developer's choice of a type of game balance impact YOUR enjoyment of the game?



Balance refers to the idea that players have similar capabilities as other players.  The most obvious form of disruptive balance is cheating; when players do something illegal to gain an advantage over others.  Of course, players are ALWAYS trying to gain an advantage over others!  You hid your mage behind that rock so my mage could not nuke him with a fireball!  That's gaining an advantage.  Balance refers to the tools developers have to control not the outcome, but the opportunity for players to compete with other players.


Well, if you have ever played a game with a cheater, or a little brother, you know that vastly imbalanced games are rarely enjoyable.  I have no interest in watching the New York Knicks play against the local junior high girl's basketball team, and that statement is only partially due to my lack of interest in the local junior high girl's basketball team.

From a developer standpoint, one attribute we always try and keep track of is PLAYER FRUSTRATION.  Player Frustration can be thought of as a scale that slowly rises as a player encounters challenges in the game, and is graphed versus enjoyment of the game.  As frustration rises, to a certain level, we call that "Challenge", and it is enjoyable.  However, after the frustration reaches certain levels, it begins to inversely correlate to enjoyment, eventually result in the player quitting the game.

Graph of Player Enjoyment vs. Player Frustration.  As frustration rises, so does enjoyment, until a peak, when frustration continues to rise and enjoyment decreases.


Since player perception of lack of balance is often reported by players as a primary cause of frustration, balance becomes an issue for the developer.


BALANCE SOLUTION #1 - A Level Playing Field [aka: Homogenization]

The oldest solution in the book is to try to give all players equal opportunity.  This is the common model in classless FPS games; theoretically, all players have access to the same equipment and options, and the only thing that differs is player skill.


- Player Perception: Players tend to think that they love this solution.  If players perceive the game to be balanced, then that hopefully limits some frustration they experience.  Developers are not always the strongest marketers of their games [and indeed, we have recently seen numerous faux pas when developers are thrust into the marketing role that have cost their games thousands, if not millions, of dollars], and having a solution like this lessens the burden upon the developer to convince players their solution is the right one.

- Developer Ease: "If we put something it, it has to be for everybody" is a fairly easy model of decision-making.  "Hey, here's my idea."  "Does it work for everybody?"  -> If yes, Implement.  If No, Do not Implement.  Those are the types of flowcharts that corporate higher-ups love to see.

- Simplicity: A sub-corollary to both the previous two, it is also important to realize that this solution is the most time-effective.  If developers are spread between multiple projects, or even multiple games, solutions like this are very effective.


- Boredom:  This con is so big, I am going to omit the other obvious ones.  It is likely that the largest reason for player attrition is boredom, so do everything you can to keep players from being bored.  Only the largest companies with millions of players are immune to boredom attrition


BALANCE SOLUTION #2 - Separate but Equal

This is the solution many readers are familiar with, because it is employed by modern WoW.  The idea here is that Balance exists by giving everybody a roughly even shot at success, with some slight tweaks to graphics/art or skill description to give the illusion of uniqueness.  GameDevs that use this system tend to start describing their skills by categories [Builders and Spenders, or DPS Cooldowns, or Survival Cooldowns, etc.].  Then, they give each class a slightly modified version of a set number of skills in those categories ["each class will get 2 DPS Cooldowns and 1 Survival Cooldown"] and make them different via art or small personal tweaks.


- Ease of Grouping: If MMORPGs are about the "MM", then this system makes it the easiest to participate in grouping behavior, because almost everybody brings the same things to the table.  Thus, it is a matter of picking players, instead of sorting them by class, specialization, equipment, etc.

- Ease of PvE Design: PvE design begins to look very homogenized, but it is very easy to do.  Things basically sort into "We expect the players to do THIS thing at THIS time, or else the players will lose."  There is very little guesswork in PvE design with this system, but also very little variety [no matter how I try and hide the damage-dealing ability from the Dragon, the solution is always "Player X hits Survival cooldown Y at Time Z... or the players lose."  If developers are pressed for time or interested in other aspects of their game, the simplicity of this type of encounter can make it easy to churn out vast amounts of content in very short amounts of time [usually limited only by how fast the art department can produce working skins of abilities and mobs to create a sense of uniqueness].

- Beginner-Friendly: There has yet to emerge a game solely created to target gamers with previous experience.  That means that everybody is concerned with the first-time player.  While there are market consequences and market gaps developing due to this blindspot by the major studios, the truth is that this system is incredibly beginner-friendly, and accountants love that.


- Difficult for Developers to "Get Right": The seeming lure of this system to developers is the idea that it will be "Easy" for them.  I have titled this category quite deliberately, and I highly encourage you to read the Brown V. Board Supreme Court decision.  Separate is INHERENTLY unequal.  Thus, devs walk an eggshell tightrope of trying to make everything equal...-ish.  Players will never really be happy on the equality claim, because they are not all strictly the same.  Players will never really be happy on the uniqueness claim, because they are all interchangeable parts.

- No Real Distinction Between Players: This issue effects some players more than others.  The obvious Pro to this is the increased ease of grouping... but this is the downside.  Since players are basically interchangeable parts, they often feel unappreciated or unnecessary.  Thus, why makes it easy to group players... but they have no reason to group YOU over any of a dozen or a hundred others, and grouping YOU gives no real benefit to the group as a whole?  This type of "shallow-grouping" may be the cost of "easy grouping".

- Elimination of Player Choice... and usually also Player Skill: These systems eliminate player choice in the interest of "Balance", and in doing so, create boredom.  Systems also tend to eliminate interest in players in "Rerolling" or trying out other classes, since all classes are basically the same.  Leveling-based games [like Ragnarok or Diablo I] die immediately in systems that discourage rerolling.

- The Balance "Razor Edge": Developers in this system are at the mercy of theorycrafters and simulations that say that there is one ideal way to play the game.  Since they have removed so many options for the players, if the players die, it is often perceived as the fault of the developers, and not something the players themselves and improve upon.  That is frustrating, because it creates an artificial "content wall" which immediately leads  to disbanded groups and boredom.


BALANCE SOLUTION #3 - Rock-Paper-Scissors

Perhaps the most viable long-term solution for a game reliant upon grouping, the idea here is that every player has both a complement and a counter.  Many older MMORPGs took this approach.  You would see a certain class, say a Bow-based ranged class like  a Ranger, be very strong against Mages, but at the same time, very weak against Warriors.  Warriors would be weak to Mages, and strong against Rangers.  Mages would be weak to Ranger, but strong against Warriors.


- Team Gameplay: This is the model that most encourage the "MM" in "MMORPG."  Truly strong players will quickly realize that they are not invincible in isolation, and will team up with other players to create a strong team.

- Avoids drawbacks of #1 and #2 above: Avoiding the obvious drawbacks [like the endless tweaking of the "Separate but Equal" system or the Boredom of the homogenized approach] is a strong pro in and of itself, simply due to the current supply/demand cycle of MMOs.  A truly rock/paper/scissors balanced MMO

- Natural tie from PvE to PvP: In both cases, it becomes fairly easy to accomplish objectives that encourage grouping, as well as ensure that all members of the group feel valuable.

- Class Diversity: This is the system that best allows for really unique abilities between classes, and great distinction among roles.  It is also the system that allows for the most character customization on the player side, and far less on the developer side.  Since players are naturally trumped by player or enemy abilities of different classes [in both PvE and PvP], we can give them really powerful and fun abilities without worrying too much about Balance. 

- Lack of Metagamey/Testing Arguments: This system never requires a developer to post about a .5% dps differential on target dummies between Spec A and Spec B, because that is not going to be the make-or-break of an encounter.  Getting your mages to line up and nuke the enemy archers when they appear is the important part, as is bringing along a mage that can do that.  Developers do not need to walk the "Balance Razor Edge" that they do in the Separate-but-Equal system.


- Solo Players: In MMOs that are solo games thinly disguised as MMOs [like the current WoW-endgame or the leveling portions of many quest-driven games], this system can be very frustrating.  Having to turn and run every time you see [Class X] just because you are [Class Y] can be an annoying experience.

- Organized Team Triumph: In systems like this, organization tends to trump player skill.  A group of mediocre players who are coordinated, on Vent, and brought the right class combinations will easily overpower disorganized group, often regardless of player skill.  To some developers, this actually goes in the "Pro" side, because again, it encourages interaction with others.  To accountants, this is a strong "Con", because players without a reliable formal group are the vast majority of current MMOers.


BALANCE SOLUTION #4 - Invest-to-Win

Now, I should distinguish that when I say "Invest-to-Win" I do not mean "Pay MONEY to Win".  The distinction is that this type of balance strategies knows and understands that the player who puts the most into the game will be the strongest.  Most often, this investment is in TIME.  Play more, get better stuff, be stronger.  The Balance factor becomes this: if you want to be stronger, then play more.  Many Korean/Eastern MMOs are accused of having these types of systems, but you will also see them in games like Diablo/TitanQuest, Spiral Knights, and most "Small Group" MMOs where there is seldom more than 4-10 players on a screen.


- Accountability: Some developers love a system where they cannot be faulted for player loss.  This is the exact opposite of the problem in the "Separate-but-Equal" system, where the developers can constantly be found to be at fault for incredibly minor issues.

- Logical: If you do something longer, you should be better at it, right?  It does make sense.

- Puts Progression in the Player's Hands: Many of the games that use these system have a fairly low "skill" threshold in two senses; first, the player literally only uses a few character skills [2 to 5 is pretty common], and second, the a "good" player does pretty much the same thing as a "bad" player.  That means that is a player wants to get better, they can play more, get better items, and become a better player.


- Lowered Value of Skill: The good things we get by putting progression in player's hands are often balanced out by the negatives of that same act.  Certain players pride themselves on being highly skilled, and when a highly skilled player cannot succeed at the same level as a player of lower skill, but greater investment, the highly skilled player becomes frustrated.

- Eliminates Low-Investment Players: Players who do not have available access to the currency of the progression system [be it time, money, or friends with Ditto safaris] tend to become frustrated and quit the game.



What other systems have you seen developers use to try and create a sense of Balance in their game?

Have you ever quit a game because of Balance?  What was the problem, and how could it have been addressed?

What was the best balanced game you have ever played, and why did it succeed so well?

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