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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.?] writes:
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