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Lesson 3: Player Equality and
Fairness (ii)
Third year course in Quality Assurance and Game Balance
Bachelor Degree in Video Game Design and Production
Third term, April 2019 Dr. Marc Miquel Ribé
BALANCE TYPE 2:
“BALANCE IS TO ENSURE PLAYER EQUALITY AND
FAIRNESS”
player-(game)-player
This second type of balance, when it fails, it does affect ”Sustained Uncertainty”.
Equality and Fairness
Equality can only create ‘fairness’ if everyone starts from the same place.
In online multiplayer games, some players may have not acquired the skills in order to
compete; then giving them specific tools (noobtubes in CoD) helps making the game
fair. Many games aim at equality, though… because they do start at the same time.
Ensuring equality and fairness in games are similar problems that require balancing.
• What is the most classic way in games to guarantee player fairness?
• Symmetry
Historically, most competitive games have been, more or less, "symmetrical" games --
games like chess or go, where each player starts out with exactly the same powers at
his fingertips. This is nice, because at least the powers are balanced between the two
players. A symmetrical game is a balanced game in terms of player equality.
[http://www.gamasutra.com/view/feature/134768/understanding_balance_in_video_.php?print=1]
• Asymmetry
The idea of games with symmetrical forces has largely fallen out of favour in the era
of video games and modern tabletop games.
After all… symmetry can be boring, and unrealistic in life.
“Symmetry is artificial”.
Street Fighter 2 (1991)
Cash n’ Guns (2005) Some games are asymmetrical in terms of
characters’ actions, and some are
symmetrical in terms of actions but
asymmetrical with an ‘extra skill’.
Symmetry is absolute, but asymmetry not.
[http://www.gamasutra.com/view/feature/131699/designers_notebook_a_symmetry_.php]
“It is also possible, and often desirable, to give opponents different resources and
abilities. If you do, be aware that you have a significant balancing task ahead of you!
Here are some of the reasons you might create an asymmetrical game:
1. To simulate a real-world situation. If the point of your game is to simulate the
battle between Axis and Allied forces during World War II, a symmetrical game
does not make sense, since the real-world conflict was not symmetrical.
2. To give players another way to explore the gamespace. Exploration is one of the
great pleasures of gameplay. Players often enjoy exploring the possibilities of
playing the same game with different powers and resources.
3. Personalization. Different players bring different skills to a game — if you give the
players a choice of powers and resources that best matches their own skills, it
makes them feel powerful — they have been able to shape the game to
emphasize the thing they are best at.
4. To level the playing field difficulty. Sometimes, your opponents have radically
different skill levels. This is especially true if you have opponents that are
computer controlled. Consider the game of Pac Man. It would be more
symmetrical if there were just one ghost chasing Pac Man, not four.
5. To create interesting situations. In the infinite space of all the games that can be
created, many more of them are asymmetrical than are symmetrical. Pitting
asymmetrical forces against each other can often be interesting and thought pro-
voking for the players, since it is not always obvious what the right strategies will
be to win the game.”
Schell (2009; p. 202)
Asymmetry can be fun when there is an element of ‘role-
playing’…and fun does not rely only on mechanics.
But…and there is always one but: it comes with the risk of
turning the game unequal and unfair.
Interesting board game discussion: [https://boardgamegeek.com/thread/636692/game-balance-symmetry-vs-
asymmetry]
BALANCE TYPE 2:
“BALANCE IS TO ENSURE PLAYER EQUALITY
AND FAIRNESS”
player-(game)-player
• This Lesson is about “managing well“ asymmetries
to both make the game interesting (i.e. sustaining
the uncertainty) and fair.
• We need to allow everyone to win “in its own way”.
Overview of the Lesson
In this lesson we will see the next topics:
1. Temporary asymmetry: first-move advantage
2. Character asymmetry according to its power definition
3. Character asymmetry according to its physical characteristics
4. Group characters’ inner asymmetry
5. Multiplayer group characters and gameplay asymmetries
6. Character asymmetry in persistent worlds-based games
In games, it is necessary to keep player equality, otherwise people do not want to
compete. These are some of the different techniques to do it.
In this Lesson we will see six game design aspects in order to guarantee player
equality depending on the game and playing mode.
1. Temporary asymmetry: first-mover advantage
PROBLEM:
In turn-based games, someone must start playing first and this may give her some
advantage.
This is a well-known problem which exceeds board games or any sort of games. Also
in business, there exists the discussion whether the first-mover obtains a greater
position in the market. Check it out:
[https://en.wikipedia.org/wiki/First-mover_advantage]
Even in football there exists the discussion…
QUESTION: Why do Champions league playoffs are unbalanced?
• Why do goals from visiting teams count double also in the overtime? This is
unbalanced by definition – it is unbalanced in absolute terms.
For example, the first game ends 0-0. The second game ends 0-0 and this clearly gives
advantage to the visitor team. Or, 1-2 and 1-2, 3-2 and 3-2…
This may be unfair as the visitor has this one kind of advantage, plus being at home
during the first game.
• Also, UEFA is proposing changing the order for each team’s penalty kicks. Why?
Because according to a research study (by Ignacio Palacios-Huerta y José
Apesteguia from London School of Economics and Universitat Pompeu Fabra), the
team which starts has a 21% more probabilities of winning than the other team,
which may be explained by psychological pressure. They analyzed 2900 penalty
kicks in 270 games between 1970 and 2008, and they concluded it is unbalanced
because of the outcome (outcome balance).
• The traditional ABAB model would change into ABBA (similar to the tie break in
tennis). The new sequence would alternate the one that starts to throw in each
block and, according to the UEFA explains, would be done as
follows: ABBAABBAAB... If all five pitches are equal, the sequence BAAB... will be
followed until there is a fault.
[http://www.marca.com/futbol/2017/05/05/590c11cdca4741e3028b45fa.html]
QUESTION: So are penalty kicks?
SOLUTION(S):
There are many different possible solutions. The main conclusion is that the solution
must be specific to the kind of game.
Interesting discussion: [https://en.wikipedia.org/wiki/First-move_advantage_in_chess]
QUESTION: Why does not Monopoly provide a move to compensate the first-player
advantage?
In chess, only the weakest pieces on the board,
pawns or knights, can move on the first turn,
and they cannot move very far or establish a
dominant position. The asymmetry of going
first is considered very low, so for practical
purposes chess is a symmetric game. However,
some data show that whites win 5% more of
the time.
A possible solution for chess is to ask both
players to “secretly write down the first move”
and then play it.
“There are a few common techniques for compensating the first-turn advantage:
• Rotate who the first player is. In a four-player game, for example, after each
complete round (where every player has a turn), rotate the starting player to the
left for the next round. In this way, the player who goes first on this round will
go last on the next round. (When I was growing up, my game group used a pencil to
mark the first player, so we dubbed this the “Pencil of Power” technique.)
• Give the disadvantaged players some extra resources. For example, if the objective
of the game is to score the most points by the end of the game, give each player a
different number of points to start the game, with the last player having slightly
more points to compensate for the disadvantage of going last.
• Reduce the effectiveness of early turns for the first players. In a card game, maybe
players typically draw four cards at the start of their turn. You could modify this so
that the first player only gets to draw one card, the next player draws two, and so
on until all players are drawing four.
• For very short games, play a series of games where each player gets to go first
once. This is common with card games, where a complete game is played in a series
of hands.”
Schreiber (gamedesignconcepts.wordpress.org)
VIDEO: First Move Advantage - How to Balance Turn-Based Games - Extra Credits
[https://www.youtube.com/watch?v=TRHdIScOMWQ]
In GO, they have raised the number of
free points given to the second player
several times.
In HearthStone some players prefer being
second because they consider extra cards
as a more important advantage.
The impact of first-turn advantage is greater in developed resource games like
HearthStone or Magic than in static resource games like Checkers or Chess.
Two more conclusions:
• The impact of first-turn advantage is greater when the players are
professionals. They really know how to look for the ‘edge’.
• In real-time based games like League of Legends which have turn-based
phases, it also matters. The “pick” and “ban” phase of the game.
[http://www.riftherald.com/competitive/2017/1/5/14180256/pro-lol-pick-ban-format-new-bans]
[http://www.riftherald.com/competitive/2017/1/5/14180256/pro-lol-pick-ban-format-new-bans]
The first three bans and six picks of the new system will function like the old: three
bans per team, back and forth, before a snake draft starting with blue side. Midway
through red side’s second pick rotation, however, the two teams will ban two more
champions each, starting with red side. Then the second phase of picking finishes off
the draft in the same snake format.
Blue is benefited for being the first to ban and the first choice in Pick phase 1, but
red is benefited for being the first to choose twice in a row, and being the first to
ban in Phase 2 and the first to pick in the last phase.
Blue: 2 advantage moves (one of them being first-turn) / Red: 3 advantage moves
League of Legends Pick and Ban Phase
2. Character asymmetry by its power definition
PROBLEM:
When asymmetry implies more power in a single aspect, there is no player equality
and the game is simply boring.
The problem goes like this:
“If A beats B, and B beats C, then A beats C.”
Why would someone choose B (or C)?
This results in useless characters.
Besides, transitive relationship are not always realistic.
This relates to the fundamental balancing law:
“Everything and everyone needs a counter”. How can we do it?
Transitive relationship
SOLUTION:
We need to create an intransitive relationship, one of those in which everything is
related as a counter of something else.
An intransitive relationship can only appear in asymmetry, but asymmetry by itself
does not guarantee it.
What is the most classic example?
Rock, Paper and Scissors is its literal implementation.
• Each choice has an equal chance of winning.
• We do not know the other player’s move.
What is the best strategy in RPS?
Choosing is random? right? Sure?
It is a “one-player-one-move-game” that is totally balanced!
It becomes a psychological game in which there is no dominant player.
Intransitive relationship
“The solution to Rock-Paper-Scissors is a ratio of 1:1:1, meaning that you should
throw about as many of each type as any other. If you threw more of one type
than the others (say, for example, you favoured Paper), your opponent could
throw the thing that beats your preferred throw (Scissors) more often, which lets
them win slightly more than average. So in general, the “solution” to RPS is to
throw each symbol with equal frequency in the long term.”
r p s
R 0 -1 1
P 1 0 -1
S -1 1 0
The payoff (prize) from each option is equal.
• Payoff for R = 0r + (-1)p + 1s = s-p
• Payoff for P = 1r + 0p + (-1)s = r-s
• Payoff for S = (-1)r + 1p + 0s = p-r
Let’s go back to our equations. Rock-Paper-Scissors is
a symmetric zero-sum game, so:
R = P = S = 0.
Since the opponent must select exactly one throw, we
also know the probabilities of their throw add up to
100%:
r + p + s = 1
R = 0 = s-p, therefore p=s
P = 0 = r-s, therefore r=s
S = 0 = p-r, therefore p=r
r+p+s = r+r+r = 1,
therefore r=1/3
Since r=p=s, p=1/3, s=1/3
Schreiber (gamebalanceconcepts.wordpress.org)
Solving RPS with Unequal Prizes (Payoff)
Suppose we made a rules change: every win with Rock counts as two wins instead
of one. Then we would have a different solution where the ratios would be
uneven.
We then use this to construct our three payoff equations:
R = 2s-p P = r-s S = p-2r
Again, the game is zero-sum and symmetric,
and both us and our opponent must choose
exactly one throw, so we still have:
r+p+s = 1
Again we solve:
R = 0 = 2s-p, therefore 2s = p
P = 0 = r-s, therefore r = s
S = 0 = p-2r, therefore 2r = p
r+p+s = r+2r+r = 1,
therefore r=1/4
r=s, therefore s=1/4
2r=p, therefore p=1/2
r p s
R 0 -1 2
P 1 0 -1
S -1 1 0
“This is an answer you’d be unlikely to
come up with on your own without doing
the math, but in retrospect it makes
sense: since Scissors is such a risky play,
players are less likely to choose it. If you
know your opponent is not likely to play
Scissors, Paper is more likely to either
draw or win, so it is actually Paper (and
not Rock) that is played more
frequently.”
A more powerful character does not
imply the best choice in all occasions.
It can slip out of hands, but you get the idea…
Intransitive relationships ensure player fairness.
Example: How does Pokémon relate to this?
• Mainly, Pokémon types form an intransitive relationship with each other.
• At the same time, Pokémon levels form a transitive relationship.
Here is the ‘secret’ damage formula!
• Level is the level of the attacking Pokémon.
• A is the effective Attack stat of the attacking Pokémon if the used move is a physical
move, or the effective Special Attack stat of the attacking Pokémon if the used move
is a special move (ignoring allGen. II/negativeGen. III+ stat stages for a critical hit).
• D is the effective Defense stat of the target if the used move is a physical move or
a special move that uses the target's Defense stat, or the effective Special Defense
of the target if the used move is an other special move (ignoring
allGen. II/positiveGen. III+ stat stages for a critical hit).
• Power is the effective power of the used move.
Type: Super effective, not very effective, or not effective.
[http://bulbapedia.bulbagarden.net/wiki/Damage]
Always provide a counter… How do we balance characters?
In both symmetrical and asymmetrical games we need to take care of two aspects:
1. There is no dominant strategy for a character. We can see that by studying the
payoff for each attack and by calculating the cost-benefit ratio.
2. Most importantly and fundamental, characters create or are defined as an
intransitive relationship in the entire game. This is even more key than aspect 1.
By the way, this is very common in turn-based games.
Character’s attributes are ‘permanent objects’,
while characters’ moves can be seen as
’temporary attributes’.
Depending on each character attributes, we
can see some of them can become a ‘dominant
strategy’… which is the third type of balance.
We are going to study them in the next Lesson.
3. Character asymmetry in physics
PROBLEM:
We have a game in with no special ‘character type’ to guarantee an intransitive
relationship by definition like in Pokémon. At the same time, the game is with real-
time action, and this changes everything. The problem is there is always a player who
is the best.
We need to build an intransitive relationship as a result of the characters’ attributes.
What should we do?
• In a fighting game, this would raise some questions such as: “how much damage
can I inflict with a throw in a game?”, then we could calculate, taking into account
the probability of success and the damage (i.e. calculating the Expected Value for
each attack type).
• Then, we could create a matrix of payoffs for each character’s physics attribute and
abilities (actions), taking into account costs and benefits against each other
character… and voilà… then maybe we could see an intransitive relationship.
Too difficult? Perhaps…
SOLUTION:
As said, creating a mathematical model in order to see if there is an intransitive
relationship and understand the ‘absolute balance’ may be expensive. The best option
is to playtest and to measure the ‘perceived balance’. Hence, tweak, playtest, tweak.
We will need to do a lot of playtesting and trust it!
We need a lot of data, since it can become a very subjective topic (just check Twitter,
everyone has an option on what is powerful and what is weak).
• What can we tweak?
- Character size
- Hitboxes
- Speed performance
- Attack damage
- Attack spread
- …
We can buff (increase the power) or nerf (decrease the power) for each character’s
attacks and characters until we obtain the desired intransitive relationship.
QUESTION: Once we know what characteristics to tweak, what is best strategy to
balance a move or character: buffing or nerfing?
Analysis: What Makes a Move Overpowered?
[https://www.youtube.com/watch?v=uQnfm911Xoc]
Active Frames are the ones in which an attack can make damage (Benefit)
The other two are necessary but undesired (Costs).
Let me tell you a story. The man who broke basketball was George Mikan from Lakers
in the sixties, a very tall player who was blocking every attempt from the other teams.
• First, the reaction was to play keep-away from the other team until the time ran
out. It worked and the Pistols beat the Lakers 19-19 (lowest scoring in NBA)… until
the “Shot Clock” was introduced to speed the games.
Why would they make a rule such as the Clock to ‘buff’ Mikan?
Because not only balancing matters but the spectacle itself too (fun to watch different
strategies).
The point is: buffing can be more effective than nerfing, and you may perceive in your
playtesting that you are making the game more fun to play.
A game can be symmetrical or asymmetrical and balanced in terms of power but
boring… We want to see diverse characters and movesets. If we achieve this purpose
more easily by buffing, it is great! One thing is to balance, the other is to provide
uniqueness and variety. Do not kill the game variety to balance for player equality.
Analysis: Why We Should Buff More Than Nerf Core-A Gaming Core-A Gaming
[https://www.youtube.com/watch?v=bsC8io4w1sY]
Think about it: nobody wants others to nerf
their character. It feels like a “loss”, and this is
a depressing feeling. Therefore, if you nerf a
character to balance it with another,… it may
result in a bad feeling for the existing
community.
Please, watch it!
What was the final solution for Mikan and basketball in general?
Create more possible strategies for the other players!
They created a strategy to sum points for smaller players (3 point line). They said: “we
will give the smaller player a chance to score and open up the defence to make the
game more enjoyable to fans”.
Mikan agreed and even supported this new rule.
PROBLEM:
The scenario can make a character more asymmetric than others. Scenarios provide
implicit strategies in their characteristics. Where is the limit between both?
SOLUTION:
As said, you can define a ‘main’ scenario in which competition should be fair for the
entire group of characters. Then, you can provide other scenarios which may be unfair
but interesting. Or you can provide a ‘random’ feature to select the scenario.
https://www.ssbwiki.com/Tournament_rulesets_(SSB4)#Banned_Stages
• As an extremely large stage, it is
banned in all serious tournaments in
every game it is featured in because its
size and build provides opportunities
for what is perceived broken camping
and stalling.
• The stage is almost always banned in
competitive settings because it is
possible to walk off into the blast line,
which allows for camping and easy
KOs, especially via chain grabs.
TRUST THE PLAYERS AND GIVE THEM CHOICES!
Forbidden in tournaments
PROBLEM:
Still, we are not sure we balance well the characters: playtesting in a closed
environment is not as reliable as real-market and championships. Perhaps some
characters are great for solo playing, but become quite useless when testing them in a
real competition.
We want all characters being actually played. We do not want just to buff the weaker
ones. How can we know which are the most overpowered characters (those that
players should take to win in a competition)?
Tiers lists (created through voting and feedback).
0) God tier (no character should be in this tier, if they
are, you are forced to play them to be competitive).
1) Top tier (don't be afraid to put your favorite
characters here. Being top tier does not necessarily
mean any nerfs are needed).
2) Middle tier (pretty good, not quite as good as top).
3) Bottom tier (I can still win with them, but it's hard).
4) Garbage tier (no one should be in this. Not
reasonable to play this character at all.)
[https://www.ssbwiki.com/tier_list]
Talking at GDC 2015's eSports Summit, Alexander Jaffe tells us: you could use the ‘tiers
lists’, the ‘win rate’, and the play frequency to guess which player to choose.
• Tiers lists tell us a lot about players’ perceived balanced, but they happen to be very
influenced by the ‘play frequency’ of each player. In the end, players who come across
the same characters get frustrated by them… We do not know the absolute balance.
• Character Win Rate is an important source of information. But it does not tell us
about asymmetry, how it is constructed,…We do not know the absolute balance.
Alexander Jaffe. Metagame Balance For eSports & Fighting Games [https://www.youtube.com/watch?v=miu3ldl-nY4]
Balancing Multiplayer Games. David Sirlin [http://www.sirlin.net/s/GDC-2009-sirlin-handout6.pdf]
How to Pick a Character [https://www.youtube.com/watch?v=AGHGEttNjyo]
SOLUTION:
Let’s use the meta-game data that is being generated in competitions to understand
optimal character selection. Then we can re-balance and improve other characters.
Matchup Charts can be created by real-data or just approximations. They are like Win
Rate but each character against each character.
We cannot just ‘sum’ each line of a character to know which one is the best! This is too
simplistic because it is a sort of average… we are omitting that this is forming an
intransitive relationship (remember the second example of Rock-Paper-Scissors, the rock
was not the best option even though it meant winning 2x).
Jaffe tells us that more or less the table (the matchup charts with the win rates) looks
like an intransitive relationship. Then we can use it to calculate (with a linear program
similar to solving the equations with RPS) how frequently I should play a character in a
competition.
Similarly, in this example, he explains how the Starcraft win-rate of Terran against
Protoss is 59% and against Zerg is 56%. Play frequency for the Terran should be 36%
(larger than the third we obtained in Rock-Paper-Scissors).
This is the frequency that we should play each character to win in long-term! (not the 1/3 of RPS)
This is much useful to understand balance than the tier lists.
Using the linear algorithm with the matchup table provides us this ”play rate”
(play frequency) that we should play each character to win. It also provides the
players that nobody would need to choose (and we need to buff).
If we do the same using the matchup chart of Smash Bros Brawl...
We find that Metaknight is super overpowered. It has to be played at least 55% of the time in any
strong community if you want to win in the long run (e.g. a competition with many matches).
4. Group characters and inner asymmetry
PROBLEM:
We do not have only one character, but a race or group of characters. There is the
possibility of creating just stronger units, and we know transitive relationships are
boring and predictive.
SOLUTION:
Every type of unit in a real-time strategy game should be unique in some way and not
just a more powerful (but otherwise identical) version of another unit. This design
principle is called orthogonal unit differentiation and was introduced by designer
Harvey Smith at the 2003 Game Developers’ Conference.
Each unit is best in a specific dimension (attribute).
• The more unique dimensions and orthogonality, the more different challenges we
can create for these group characters.
• A group of units (e.g. a strategy-game race) form an intransitive relationship
among them, but they should also form one against an hypothetical group of units
from the other team.
In Orthogonal Unit Differentiation the underlying intransitive relationship may be
defined by ”types” (Pokémon-like) but it is usually created by the physics attributes of
each unit (Clash Royale-like).
It may exist in very different sort of games... Even in cooperative games such as Team
Fortress II. Each character has a different move.
How did they create races in Warcraft III? A conversation with Rob Pardo
GDW: Game balancing always seems to involve tuning system variables numbers up
and down. Sounds like with WarCraft III you guys thought really big early in the project
and then tuned some numbers downward as you went along.
RP: That’s right. Early on we brainstormed tons of cool ideas. We have lots of sharp,
creative people here so we come up with way more ideas than we could ever put in a
game. Then the designer’s job over the next year or two years (however long the dev
cycle is before the beta) is to hone all those ideas. Some we have to get rid of, some
we have to modify, and some become a cornerstone of the gameplay.
One of our mantras—we have lots of mantras around here—is “concentrating the
coolness”. With Warcraft III, for example, we could’ve blown out to 20 or 30 units per
race if we wanted to, but we wanted each unit to be meaningful. And we wanted to
make sure each race had a unique feel. So even though every race has flying units
and worker units they still all do things in different ways.
Full interview in Fullerton (2014; p. 301)
In strategy games such as Warcraft or Starcraft, there is an important point to take
into account…Units are both characters and strategies at the same time!
Most important, building these units carries approximately equivalent costs, in terms of
raw materials needed: A Zerg, a Protoss, and a Terran each must use similar amounts of
resources to build units that provide equivalent fighting power.
Cost / Benefit Ratio for each unit (although this is the third type of balance – Lesson 3)
“If you have a battlefield with say 10 or 20 units, then the hero could be realistically
balanced to them.“ Rob Pardo from Blizzard
5. Multiplayer group characters and gameplay asymmetries
PROBLEM:
How do we balance team asymmetry? One side may be stronger than the other.
Fable legends (Lionhead): Coop tactical RPG vs. Dungeon keeper strategy game
The story is that the game was cancelled… but it had many development challenges:
1. Two different gameplay to develop
2. Strategy game with Xbox controller
3. Balancing sides (the important one for us!)
The villain has four unit types
mapped to the four buttons.
Clever. But will four units be
interesting enough?
An interesting question for any game which involves asymmetric team sizes:
• Should we completely balance them with player equality? Should aim for a 50-50
win rate as an output balance? If so, when the villain wins, four heroes lose.
• The other way around seems OK… If we tweak the game to let heroes win, more
people wins. Do we make more people happy by letting them win at expenses of
the villain player? Is it fair? Is it commercial?
• If we boost villains power, we are giving an incentive to a more unusual side and
make a more hardcore experience.
Fable Legends - The Challenges of Asymmetric Multiplayer - Extra Credits
[https://www.youtube.com/watch?v=n2MTkotf-gk&t=309s]
Discussion about “one-vs-many” games.
[https://boardgamegeek.com/thread/1167572/dice-tower-354-asymmetrical-games]
SOLUTION:
Extra credits people and me have no
answer to the question for Fable games.
It depends on the game. Let’s see the
next example…
La Puta i la Ramoneta (Catalan Games, Marc
Miquel) is a card game of political fiction to
undo the tie between Catalonia and Spain.
In the game the pro-independence win
positive points for Catalan self-government
and culture, Spanish state wins negative
points (against Catalan self-government and
culture) and federalists want everything to
stay the same.
Should the game be balanced to guarantee
player equality for both the Spanish
government and the Catalan pro-
independence players? I think so.
In fact, playing the Spanish state side feels
like having more power and fun (with sort of
role-playing and imitation also) but it is not
easier to win.
Even though it may seem so, the game dynamics do not favour the federalist (tie
points) because the two extreme players divide the columns to play. The federalist
must negotiate much more and lie to others to win.
In a game with 1 Spanish state, 1 federalist and 1 pro-independence, the first has
always equal power (number of cards draw and played) than the others. Even more
pro-independence players join the game, the Spanish state has equal power.
Team and gameplay asymmetry: ‘fruity’ board games
Another way to balance team asymmetry or any asymmetry is to use different victory
conditions. Another way which adds to the previous is to use hidden identities.
This sort of balance state is named “fruity” (Schreiber, 2010) because each character
is sort of different. There is no way to model their opportunities and assess player
equality. In these cases, the only possible balance method is playtesting.
6. Character asymmetry in persistent worlds-based games
PROBLEM:
In a persistent world-based game, some characters are slightly stronger than others.
The community realizes that and starts picking them. What can we do?
Buff or nerf? Or just buff the worst (we said it was better)? Should we use data from
the meta-game to do that like Jaffe did?
SOLUTION:
To provide new characters which are stronger… and create a cyclical imbalance. The
game is always imbalanced, but in a new way.
Why should we do that? For two reasons:
1. The player experience is a community-based experience. We need to influence
the community and bring novelty. The community is the game.
2. We know that if we sell these new characters, we are going to get some revenue.
Perfect Imbalance - Why Unbalanced Design Creates Balanced Play - Extra Credits
[https://www.youtube.com/watch?v=e31OSVZF77w]
PROBLEM:
In a MMO, the community is the most important part of the game experience (which
is not introduced by the game designer).
How do we balance an MMO so it does not become dominated by one type of player?
Most importantly, how do you balance it so it persists and players keep playing (so we
sustain the uncertainty)?
SOLUTION:
Asymmetry is a natural thing in an ecosystem.
To think of the community as an ecosystem…
If one species disappears, the chain may be broken
and the rest end up disappearing…
How does this translate into online games?
Balancing an MMO Ecosystem - Getting a Mix of Player Types – Extra Credits
[https://www.youtube.com/watch?v=1drDuaQXm_U]
Remember Bartle’s Taxonomy? Killers, Achievers, Socializers and Explorers. This is the
ecosystem, and they do have slightly different goals (p.e. socializers prefer chatting
than being in the actual gameplay).
The online community shrinks and may end up disappearing.
There needs to be a specific proportion of each in equilibrium.
Here comes the paradox of player fairness-sustain uncertainty in MMO. To guarantee player
fairness, you need to provide different ways of winning, so all players can win their way, even
they lose from the other player perspective (they die).
So, you can allow player mass and gameplay inequalities to keep the ecosystem in equilibrium
and not decreasing. You are not just balancing the game, but the community. You are balancing
mechanics and community dynamics at the same time.
• If the game becomes dominated by socializers:
there is no one to compete with, etc.
• If the game becomes dominated by achievers: no
one to chat with, to play against, etc.
• If the game becomes dominated by killers: vicious
and bad for new players…
• …
Achievers may be the best “kills” a killer needs, explorers may be less bothered by
killers but help achievers increase by teaching them techniques, socializers are in a
feedback loop with themselves (the more there are, the more they talk) and may
be killed by killers, etc.
It is all about reaching equilibrium in the ecosystem in which there exists some
variety,… so killers do not break it all.
You do this through the mechanics and content you create.
You do not want equal player distribution among the player psychological types per
se, you only want the ecosystem to be in equilibrium.
Is it unfair? No, since each player psychological type enjoys (and somehow wins)
the game in a slightly different way.
No player type (and character) becomes totally dominant as long as there is a
community balance so each type can play.
Concluding remarks
1. Creating a fair competition is the most important type of
experience for a multiplayer game. When it is not possible,
uncertainty is lost. This relates to the first type of balance.
2. Symmetry creates player equality, but asymmetry is much more
realistic and interesting. Intransitive relationships are the way to
convert asymmetry into something fair in very different scenarios
(turn-based games, physics-based and real-time games, etc.).
3. In order to verify there is an intransitive relationship, sometimes
we need to balance taking into account output data rather than
modelling mathematically the game. Other times we just listen to
our instinct and playtesters perceptions of balance'. It's up to you!
The next lesson will be dedicated to Equivalent Strategies.
The golden rule of player/player balance
“A player should never be put in an unwinnable situation
through no fault of their own."
Rollings and Morris (2003, p. 139)
Game Balance Course Selected References
• Adams, E. (2014). Fundamentals of game design. Pearson Education. Chapter 11.
• Adams, E., & Dormans, J. (2012). Game mechanics: advanced game design. Chapter 8.
• Fields, T. (2014). Mobile & social game design: Monetization methods and mechanics. CRC
Press. Chapter 9.
• Fullerton, T. (2014). Game design workshop: a playcentric approach to creating innovative
games. CRC press. Chapter 10.
• Oxland, K. (2004). Gameplay and design. Pearson Education. Chapter 16.
• Schell, J. (2014). The Art of Game Design: A book of lenses. CRC Press. Chapters 10-11.
• Sylvester, T. (2013). Designing games: A guide to engineering experiences. " O'Reilly Media,
Inc.". Chapter 6.
• Rollings, A., & Morris, D. (2003). Game architecture and design: a new edition. Chapter 5.
• Selinker, M. (Ed.). (2011). The Kobold Guide to Board Game Design. Part 4.
• Schreiber, I. Game Design Concepts [https://gamedesignconcepts.wordpress.com] (Level 16).
• Schreiber, I. Game Balance Concepts [https://gamebalanceconcepts.wordpress.com].
• Romero, B. & Schreiber, I. (2017). Game Balance. CRC Press. (Not available yet)
• Extra material: Asymmetric Play - Can One Game Cater to Many Playstyles? - Extra Credits
[https://www.youtube.com/watch?v=SQhxtfKH1f8]

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Game Balance 3: Player Equality and Fairness

  • 1. Lesson 3: Player Equality and Fairness (ii) Third year course in Quality Assurance and Game Balance Bachelor Degree in Video Game Design and Production Third term, April 2019 Dr. Marc Miquel Ribé
  • 2. BALANCE TYPE 2: “BALANCE IS TO ENSURE PLAYER EQUALITY AND FAIRNESS” player-(game)-player This second type of balance, when it fails, it does affect ”Sustained Uncertainty”.
  • 3. Equality and Fairness Equality can only create ‘fairness’ if everyone starts from the same place. In online multiplayer games, some players may have not acquired the skills in order to compete; then giving them specific tools (noobtubes in CoD) helps making the game fair. Many games aim at equality, though… because they do start at the same time. Ensuring equality and fairness in games are similar problems that require balancing. • What is the most classic way in games to guarantee player fairness?
  • 4. • Symmetry Historically, most competitive games have been, more or less, "symmetrical" games -- games like chess or go, where each player starts out with exactly the same powers at his fingertips. This is nice, because at least the powers are balanced between the two players. A symmetrical game is a balanced game in terms of player equality. [http://www.gamasutra.com/view/feature/134768/understanding_balance_in_video_.php?print=1]
  • 5. • Asymmetry The idea of games with symmetrical forces has largely fallen out of favour in the era of video games and modern tabletop games. After all… symmetry can be boring, and unrealistic in life. “Symmetry is artificial”. Street Fighter 2 (1991) Cash n’ Guns (2005) Some games are asymmetrical in terms of characters’ actions, and some are symmetrical in terms of actions but asymmetrical with an ‘extra skill’. Symmetry is absolute, but asymmetry not. [http://www.gamasutra.com/view/feature/131699/designers_notebook_a_symmetry_.php]
  • 6. “It is also possible, and often desirable, to give opponents different resources and abilities. If you do, be aware that you have a significant balancing task ahead of you! Here are some of the reasons you might create an asymmetrical game: 1. To simulate a real-world situation. If the point of your game is to simulate the battle between Axis and Allied forces during World War II, a symmetrical game does not make sense, since the real-world conflict was not symmetrical. 2. To give players another way to explore the gamespace. Exploration is one of the great pleasures of gameplay. Players often enjoy exploring the possibilities of playing the same game with different powers and resources. 3. Personalization. Different players bring different skills to a game — if you give the players a choice of powers and resources that best matches their own skills, it makes them feel powerful — they have been able to shape the game to emphasize the thing they are best at. 4. To level the playing field difficulty. Sometimes, your opponents have radically different skill levels. This is especially true if you have opponents that are computer controlled. Consider the game of Pac Man. It would be more symmetrical if there were just one ghost chasing Pac Man, not four. 5. To create interesting situations. In the infinite space of all the games that can be created, many more of them are asymmetrical than are symmetrical. Pitting asymmetrical forces against each other can often be interesting and thought pro- voking for the players, since it is not always obvious what the right strategies will be to win the game.” Schell (2009; p. 202)
  • 7. Asymmetry can be fun when there is an element of ‘role- playing’…and fun does not rely only on mechanics. But…and there is always one but: it comes with the risk of turning the game unequal and unfair. Interesting board game discussion: [https://boardgamegeek.com/thread/636692/game-balance-symmetry-vs- asymmetry]
  • 8. BALANCE TYPE 2: “BALANCE IS TO ENSURE PLAYER EQUALITY AND FAIRNESS” player-(game)-player • This Lesson is about “managing well“ asymmetries to both make the game interesting (i.e. sustaining the uncertainty) and fair. • We need to allow everyone to win “in its own way”.
  • 9. Overview of the Lesson In this lesson we will see the next topics: 1. Temporary asymmetry: first-move advantage 2. Character asymmetry according to its power definition 3. Character asymmetry according to its physical characteristics 4. Group characters’ inner asymmetry 5. Multiplayer group characters and gameplay asymmetries 6. Character asymmetry in persistent worlds-based games In games, it is necessary to keep player equality, otherwise people do not want to compete. These are some of the different techniques to do it. In this Lesson we will see six game design aspects in order to guarantee player equality depending on the game and playing mode.
  • 10. 1. Temporary asymmetry: first-mover advantage PROBLEM: In turn-based games, someone must start playing first and this may give her some advantage. This is a well-known problem which exceeds board games or any sort of games. Also in business, there exists the discussion whether the first-mover obtains a greater position in the market. Check it out: [https://en.wikipedia.org/wiki/First-mover_advantage] Even in football there exists the discussion… QUESTION: Why do Champions league playoffs are unbalanced?
  • 11. • Why do goals from visiting teams count double also in the overtime? This is unbalanced by definition – it is unbalanced in absolute terms. For example, the first game ends 0-0. The second game ends 0-0 and this clearly gives advantage to the visitor team. Or, 1-2 and 1-2, 3-2 and 3-2… This may be unfair as the visitor has this one kind of advantage, plus being at home during the first game.
  • 12. • Also, UEFA is proposing changing the order for each team’s penalty kicks. Why? Because according to a research study (by Ignacio Palacios-Huerta y José Apesteguia from London School of Economics and Universitat Pompeu Fabra), the team which starts has a 21% more probabilities of winning than the other team, which may be explained by psychological pressure. They analyzed 2900 penalty kicks in 270 games between 1970 and 2008, and they concluded it is unbalanced because of the outcome (outcome balance). • The traditional ABAB model would change into ABBA (similar to the tie break in tennis). The new sequence would alternate the one that starts to throw in each block and, according to the UEFA explains, would be done as follows: ABBAABBAAB... If all five pitches are equal, the sequence BAAB... will be followed until there is a fault. [http://www.marca.com/futbol/2017/05/05/590c11cdca4741e3028b45fa.html] QUESTION: So are penalty kicks?
  • 13. SOLUTION(S): There are many different possible solutions. The main conclusion is that the solution must be specific to the kind of game. Interesting discussion: [https://en.wikipedia.org/wiki/First-move_advantage_in_chess] QUESTION: Why does not Monopoly provide a move to compensate the first-player advantage? In chess, only the weakest pieces on the board, pawns or knights, can move on the first turn, and they cannot move very far or establish a dominant position. The asymmetry of going first is considered very low, so for practical purposes chess is a symmetric game. However, some data show that whites win 5% more of the time. A possible solution for chess is to ask both players to “secretly write down the first move” and then play it.
  • 14. “There are a few common techniques for compensating the first-turn advantage: • Rotate who the first player is. In a four-player game, for example, after each complete round (where every player has a turn), rotate the starting player to the left for the next round. In this way, the player who goes first on this round will go last on the next round. (When I was growing up, my game group used a pencil to mark the first player, so we dubbed this the “Pencil of Power” technique.) • Give the disadvantaged players some extra resources. For example, if the objective of the game is to score the most points by the end of the game, give each player a different number of points to start the game, with the last player having slightly more points to compensate for the disadvantage of going last. • Reduce the effectiveness of early turns for the first players. In a card game, maybe players typically draw four cards at the start of their turn. You could modify this so that the first player only gets to draw one card, the next player draws two, and so on until all players are drawing four. • For very short games, play a series of games where each player gets to go first once. This is common with card games, where a complete game is played in a series of hands.” Schreiber (gamedesignconcepts.wordpress.org)
  • 15. VIDEO: First Move Advantage - How to Balance Turn-Based Games - Extra Credits [https://www.youtube.com/watch?v=TRHdIScOMWQ] In GO, they have raised the number of free points given to the second player several times. In HearthStone some players prefer being second because they consider extra cards as a more important advantage. The impact of first-turn advantage is greater in developed resource games like HearthStone or Magic than in static resource games like Checkers or Chess.
  • 16. Two more conclusions: • The impact of first-turn advantage is greater when the players are professionals. They really know how to look for the ‘edge’. • In real-time based games like League of Legends which have turn-based phases, it also matters. The “pick” and “ban” phase of the game. [http://www.riftherald.com/competitive/2017/1/5/14180256/pro-lol-pick-ban-format-new-bans]
  • 17. [http://www.riftherald.com/competitive/2017/1/5/14180256/pro-lol-pick-ban-format-new-bans] The first three bans and six picks of the new system will function like the old: three bans per team, back and forth, before a snake draft starting with blue side. Midway through red side’s second pick rotation, however, the two teams will ban two more champions each, starting with red side. Then the second phase of picking finishes off the draft in the same snake format. Blue is benefited for being the first to ban and the first choice in Pick phase 1, but red is benefited for being the first to choose twice in a row, and being the first to ban in Phase 2 and the first to pick in the last phase. Blue: 2 advantage moves (one of them being first-turn) / Red: 3 advantage moves League of Legends Pick and Ban Phase
  • 18. 2. Character asymmetry by its power definition PROBLEM: When asymmetry implies more power in a single aspect, there is no player equality and the game is simply boring. The problem goes like this: “If A beats B, and B beats C, then A beats C.” Why would someone choose B (or C)? This results in useless characters. Besides, transitive relationship are not always realistic. This relates to the fundamental balancing law: “Everything and everyone needs a counter”. How can we do it? Transitive relationship
  • 19. SOLUTION: We need to create an intransitive relationship, one of those in which everything is related as a counter of something else. An intransitive relationship can only appear in asymmetry, but asymmetry by itself does not guarantee it. What is the most classic example? Rock, Paper and Scissors is its literal implementation. • Each choice has an equal chance of winning. • We do not know the other player’s move. What is the best strategy in RPS? Choosing is random? right? Sure? It is a “one-player-one-move-game” that is totally balanced! It becomes a psychological game in which there is no dominant player. Intransitive relationship
  • 20. “The solution to Rock-Paper-Scissors is a ratio of 1:1:1, meaning that you should throw about as many of each type as any other. If you threw more of one type than the others (say, for example, you favoured Paper), your opponent could throw the thing that beats your preferred throw (Scissors) more often, which lets them win slightly more than average. So in general, the “solution” to RPS is to throw each symbol with equal frequency in the long term.” r p s R 0 -1 1 P 1 0 -1 S -1 1 0 The payoff (prize) from each option is equal. • Payoff for R = 0r + (-1)p + 1s = s-p • Payoff for P = 1r + 0p + (-1)s = r-s • Payoff for S = (-1)r + 1p + 0s = p-r Let’s go back to our equations. Rock-Paper-Scissors is a symmetric zero-sum game, so: R = P = S = 0. Since the opponent must select exactly one throw, we also know the probabilities of their throw add up to 100%: r + p + s = 1 R = 0 = s-p, therefore p=s P = 0 = r-s, therefore r=s S = 0 = p-r, therefore p=r r+p+s = r+r+r = 1, therefore r=1/3 Since r=p=s, p=1/3, s=1/3 Schreiber (gamebalanceconcepts.wordpress.org)
  • 21. Solving RPS with Unequal Prizes (Payoff) Suppose we made a rules change: every win with Rock counts as two wins instead of one. Then we would have a different solution where the ratios would be uneven. We then use this to construct our three payoff equations: R = 2s-p P = r-s S = p-2r Again, the game is zero-sum and symmetric, and both us and our opponent must choose exactly one throw, so we still have: r+p+s = 1 Again we solve: R = 0 = 2s-p, therefore 2s = p P = 0 = r-s, therefore r = s S = 0 = p-2r, therefore 2r = p r+p+s = r+2r+r = 1, therefore r=1/4 r=s, therefore s=1/4 2r=p, therefore p=1/2 r p s R 0 -1 2 P 1 0 -1 S -1 1 0 “This is an answer you’d be unlikely to come up with on your own without doing the math, but in retrospect it makes sense: since Scissors is such a risky play, players are less likely to choose it. If you know your opponent is not likely to play Scissors, Paper is more likely to either draw or win, so it is actually Paper (and not Rock) that is played more frequently.” A more powerful character does not imply the best choice in all occasions.
  • 22. It can slip out of hands, but you get the idea… Intransitive relationships ensure player fairness.
  • 23. Example: How does Pokémon relate to this? • Mainly, Pokémon types form an intransitive relationship with each other. • At the same time, Pokémon levels form a transitive relationship.
  • 24. Here is the ‘secret’ damage formula! • Level is the level of the attacking Pokémon. • A is the effective Attack stat of the attacking Pokémon if the used move is a physical move, or the effective Special Attack stat of the attacking Pokémon if the used move is a special move (ignoring allGen. II/negativeGen. III+ stat stages for a critical hit). • D is the effective Defense stat of the target if the used move is a physical move or a special move that uses the target's Defense stat, or the effective Special Defense of the target if the used move is an other special move (ignoring allGen. II/positiveGen. III+ stat stages for a critical hit). • Power is the effective power of the used move. Type: Super effective, not very effective, or not effective. [http://bulbapedia.bulbagarden.net/wiki/Damage]
  • 25. Always provide a counter… How do we balance characters? In both symmetrical and asymmetrical games we need to take care of two aspects: 1. There is no dominant strategy for a character. We can see that by studying the payoff for each attack and by calculating the cost-benefit ratio. 2. Most importantly and fundamental, characters create or are defined as an intransitive relationship in the entire game. This is even more key than aspect 1. By the way, this is very common in turn-based games. Character’s attributes are ‘permanent objects’, while characters’ moves can be seen as ’temporary attributes’. Depending on each character attributes, we can see some of them can become a ‘dominant strategy’… which is the third type of balance. We are going to study them in the next Lesson.
  • 26. 3. Character asymmetry in physics PROBLEM: We have a game in with no special ‘character type’ to guarantee an intransitive relationship by definition like in Pokémon. At the same time, the game is with real- time action, and this changes everything. The problem is there is always a player who is the best. We need to build an intransitive relationship as a result of the characters’ attributes. What should we do? • In a fighting game, this would raise some questions such as: “how much damage can I inflict with a throw in a game?”, then we could calculate, taking into account the probability of success and the damage (i.e. calculating the Expected Value for each attack type). • Then, we could create a matrix of payoffs for each character’s physics attribute and abilities (actions), taking into account costs and benefits against each other character… and voilà… then maybe we could see an intransitive relationship. Too difficult? Perhaps…
  • 27. SOLUTION: As said, creating a mathematical model in order to see if there is an intransitive relationship and understand the ‘absolute balance’ may be expensive. The best option is to playtest and to measure the ‘perceived balance’. Hence, tweak, playtest, tweak. We will need to do a lot of playtesting and trust it! We need a lot of data, since it can become a very subjective topic (just check Twitter, everyone has an option on what is powerful and what is weak). • What can we tweak? - Character size - Hitboxes - Speed performance - Attack damage - Attack spread - … We can buff (increase the power) or nerf (decrease the power) for each character’s attacks and characters until we obtain the desired intransitive relationship.
  • 28. QUESTION: Once we know what characteristics to tweak, what is best strategy to balance a move or character: buffing or nerfing? Analysis: What Makes a Move Overpowered? [https://www.youtube.com/watch?v=uQnfm911Xoc] Active Frames are the ones in which an attack can make damage (Benefit) The other two are necessary but undesired (Costs).
  • 29. Let me tell you a story. The man who broke basketball was George Mikan from Lakers in the sixties, a very tall player who was blocking every attempt from the other teams. • First, the reaction was to play keep-away from the other team until the time ran out. It worked and the Pistols beat the Lakers 19-19 (lowest scoring in NBA)… until the “Shot Clock” was introduced to speed the games.
  • 30. Why would they make a rule such as the Clock to ‘buff’ Mikan? Because not only balancing matters but the spectacle itself too (fun to watch different strategies). The point is: buffing can be more effective than nerfing, and you may perceive in your playtesting that you are making the game more fun to play. A game can be symmetrical or asymmetrical and balanced in terms of power but boring… We want to see diverse characters and movesets. If we achieve this purpose more easily by buffing, it is great! One thing is to balance, the other is to provide uniqueness and variety. Do not kill the game variety to balance for player equality. Analysis: Why We Should Buff More Than Nerf Core-A Gaming Core-A Gaming [https://www.youtube.com/watch?v=bsC8io4w1sY] Think about it: nobody wants others to nerf their character. It feels like a “loss”, and this is a depressing feeling. Therefore, if you nerf a character to balance it with another,… it may result in a bad feeling for the existing community. Please, watch it!
  • 31. What was the final solution for Mikan and basketball in general? Create more possible strategies for the other players! They created a strategy to sum points for smaller players (3 point line). They said: “we will give the smaller player a chance to score and open up the defence to make the game more enjoyable to fans”. Mikan agreed and even supported this new rule.
  • 32. PROBLEM: The scenario can make a character more asymmetric than others. Scenarios provide implicit strategies in their characteristics. Where is the limit between both? SOLUTION: As said, you can define a ‘main’ scenario in which competition should be fair for the entire group of characters. Then, you can provide other scenarios which may be unfair but interesting. Or you can provide a ‘random’ feature to select the scenario. https://www.ssbwiki.com/Tournament_rulesets_(SSB4)#Banned_Stages • As an extremely large stage, it is banned in all serious tournaments in every game it is featured in because its size and build provides opportunities for what is perceived broken camping and stalling. • The stage is almost always banned in competitive settings because it is possible to walk off into the blast line, which allows for camping and easy KOs, especially via chain grabs. TRUST THE PLAYERS AND GIVE THEM CHOICES! Forbidden in tournaments
  • 33. PROBLEM: Still, we are not sure we balance well the characters: playtesting in a closed environment is not as reliable as real-market and championships. Perhaps some characters are great for solo playing, but become quite useless when testing them in a real competition. We want all characters being actually played. We do not want just to buff the weaker ones. How can we know which are the most overpowered characters (those that players should take to win in a competition)? Tiers lists (created through voting and feedback). 0) God tier (no character should be in this tier, if they are, you are forced to play them to be competitive). 1) Top tier (don't be afraid to put your favorite characters here. Being top tier does not necessarily mean any nerfs are needed). 2) Middle tier (pretty good, not quite as good as top). 3) Bottom tier (I can still win with them, but it's hard). 4) Garbage tier (no one should be in this. Not reasonable to play this character at all.) [https://www.ssbwiki.com/tier_list]
  • 34. Talking at GDC 2015's eSports Summit, Alexander Jaffe tells us: you could use the ‘tiers lists’, the ‘win rate’, and the play frequency to guess which player to choose. • Tiers lists tell us a lot about players’ perceived balanced, but they happen to be very influenced by the ‘play frequency’ of each player. In the end, players who come across the same characters get frustrated by them… We do not know the absolute balance. • Character Win Rate is an important source of information. But it does not tell us about asymmetry, how it is constructed,…We do not know the absolute balance. Alexander Jaffe. Metagame Balance For eSports & Fighting Games [https://www.youtube.com/watch?v=miu3ldl-nY4] Balancing Multiplayer Games. David Sirlin [http://www.sirlin.net/s/GDC-2009-sirlin-handout6.pdf] How to Pick a Character [https://www.youtube.com/watch?v=AGHGEttNjyo]
  • 35. SOLUTION: Let’s use the meta-game data that is being generated in competitions to understand optimal character selection. Then we can re-balance and improve other characters. Matchup Charts can be created by real-data or just approximations. They are like Win Rate but each character against each character. We cannot just ‘sum’ each line of a character to know which one is the best! This is too simplistic because it is a sort of average… we are omitting that this is forming an intransitive relationship (remember the second example of Rock-Paper-Scissors, the rock was not the best option even though it meant winning 2x).
  • 36. Jaffe tells us that more or less the table (the matchup charts with the win rates) looks like an intransitive relationship. Then we can use it to calculate (with a linear program similar to solving the equations with RPS) how frequently I should play a character in a competition. Similarly, in this example, he explains how the Starcraft win-rate of Terran against Protoss is 59% and against Zerg is 56%. Play frequency for the Terran should be 36% (larger than the third we obtained in Rock-Paper-Scissors). This is the frequency that we should play each character to win in long-term! (not the 1/3 of RPS)
  • 37. This is much useful to understand balance than the tier lists. Using the linear algorithm with the matchup table provides us this ”play rate” (play frequency) that we should play each character to win. It also provides the players that nobody would need to choose (and we need to buff).
  • 38. If we do the same using the matchup chart of Smash Bros Brawl... We find that Metaknight is super overpowered. It has to be played at least 55% of the time in any strong community if you want to win in the long run (e.g. a competition with many matches).
  • 39. 4. Group characters and inner asymmetry PROBLEM: We do not have only one character, but a race or group of characters. There is the possibility of creating just stronger units, and we know transitive relationships are boring and predictive. SOLUTION: Every type of unit in a real-time strategy game should be unique in some way and not just a more powerful (but otherwise identical) version of another unit. This design principle is called orthogonal unit differentiation and was introduced by designer Harvey Smith at the 2003 Game Developers’ Conference. Each unit is best in a specific dimension (attribute). • The more unique dimensions and orthogonality, the more different challenges we can create for these group characters. • A group of units (e.g. a strategy-game race) form an intransitive relationship among them, but they should also form one against an hypothetical group of units from the other team.
  • 40. In Orthogonal Unit Differentiation the underlying intransitive relationship may be defined by ”types” (Pokémon-like) but it is usually created by the physics attributes of each unit (Clash Royale-like).
  • 41. It may exist in very different sort of games... Even in cooperative games such as Team Fortress II. Each character has a different move.
  • 42. How did they create races in Warcraft III? A conversation with Rob Pardo GDW: Game balancing always seems to involve tuning system variables numbers up and down. Sounds like with WarCraft III you guys thought really big early in the project and then tuned some numbers downward as you went along. RP: That’s right. Early on we brainstormed tons of cool ideas. We have lots of sharp, creative people here so we come up with way more ideas than we could ever put in a game. Then the designer’s job over the next year or two years (however long the dev cycle is before the beta) is to hone all those ideas. Some we have to get rid of, some we have to modify, and some become a cornerstone of the gameplay. One of our mantras—we have lots of mantras around here—is “concentrating the coolness”. With Warcraft III, for example, we could’ve blown out to 20 or 30 units per race if we wanted to, but we wanted each unit to be meaningful. And we wanted to make sure each race had a unique feel. So even though every race has flying units and worker units they still all do things in different ways. Full interview in Fullerton (2014; p. 301)
  • 43. In strategy games such as Warcraft or Starcraft, there is an important point to take into account…Units are both characters and strategies at the same time! Most important, building these units carries approximately equivalent costs, in terms of raw materials needed: A Zerg, a Protoss, and a Terran each must use similar amounts of resources to build units that provide equivalent fighting power. Cost / Benefit Ratio for each unit (although this is the third type of balance – Lesson 3) “If you have a battlefield with say 10 or 20 units, then the hero could be realistically balanced to them.“ Rob Pardo from Blizzard
  • 44. 5. Multiplayer group characters and gameplay asymmetries PROBLEM: How do we balance team asymmetry? One side may be stronger than the other. Fable legends (Lionhead): Coop tactical RPG vs. Dungeon keeper strategy game The story is that the game was cancelled… but it had many development challenges: 1. Two different gameplay to develop 2. Strategy game with Xbox controller 3. Balancing sides (the important one for us!) The villain has four unit types mapped to the four buttons. Clever. But will four units be interesting enough?
  • 45. An interesting question for any game which involves asymmetric team sizes: • Should we completely balance them with player equality? Should aim for a 50-50 win rate as an output balance? If so, when the villain wins, four heroes lose. • The other way around seems OK… If we tweak the game to let heroes win, more people wins. Do we make more people happy by letting them win at expenses of the villain player? Is it fair? Is it commercial? • If we boost villains power, we are giving an incentive to a more unusual side and make a more hardcore experience. Fable Legends - The Challenges of Asymmetric Multiplayer - Extra Credits [https://www.youtube.com/watch?v=n2MTkotf-gk&t=309s] Discussion about “one-vs-many” games. [https://boardgamegeek.com/thread/1167572/dice-tower-354-asymmetrical-games] SOLUTION: Extra credits people and me have no answer to the question for Fable games. It depends on the game. Let’s see the next example…
  • 46. La Puta i la Ramoneta (Catalan Games, Marc Miquel) is a card game of political fiction to undo the tie between Catalonia and Spain. In the game the pro-independence win positive points for Catalan self-government and culture, Spanish state wins negative points (against Catalan self-government and culture) and federalists want everything to stay the same. Should the game be balanced to guarantee player equality for both the Spanish government and the Catalan pro- independence players? I think so. In fact, playing the Spanish state side feels like having more power and fun (with sort of role-playing and imitation also) but it is not easier to win.
  • 47. Even though it may seem so, the game dynamics do not favour the federalist (tie points) because the two extreme players divide the columns to play. The federalist must negotiate much more and lie to others to win. In a game with 1 Spanish state, 1 federalist and 1 pro-independence, the first has always equal power (number of cards draw and played) than the others. Even more pro-independence players join the game, the Spanish state has equal power.
  • 48. Team and gameplay asymmetry: ‘fruity’ board games Another way to balance team asymmetry or any asymmetry is to use different victory conditions. Another way which adds to the previous is to use hidden identities. This sort of balance state is named “fruity” (Schreiber, 2010) because each character is sort of different. There is no way to model their opportunities and assess player equality. In these cases, the only possible balance method is playtesting.
  • 49. 6. Character asymmetry in persistent worlds-based games PROBLEM: In a persistent world-based game, some characters are slightly stronger than others. The community realizes that and starts picking them. What can we do? Buff or nerf? Or just buff the worst (we said it was better)? Should we use data from the meta-game to do that like Jaffe did? SOLUTION: To provide new characters which are stronger… and create a cyclical imbalance. The game is always imbalanced, but in a new way. Why should we do that? For two reasons: 1. The player experience is a community-based experience. We need to influence the community and bring novelty. The community is the game. 2. We know that if we sell these new characters, we are going to get some revenue. Perfect Imbalance - Why Unbalanced Design Creates Balanced Play - Extra Credits [https://www.youtube.com/watch?v=e31OSVZF77w]
  • 50. PROBLEM: In a MMO, the community is the most important part of the game experience (which is not introduced by the game designer). How do we balance an MMO so it does not become dominated by one type of player? Most importantly, how do you balance it so it persists and players keep playing (so we sustain the uncertainty)? SOLUTION: Asymmetry is a natural thing in an ecosystem. To think of the community as an ecosystem… If one species disappears, the chain may be broken and the rest end up disappearing… How does this translate into online games? Balancing an MMO Ecosystem - Getting a Mix of Player Types – Extra Credits [https://www.youtube.com/watch?v=1drDuaQXm_U]
  • 51. Remember Bartle’s Taxonomy? Killers, Achievers, Socializers and Explorers. This is the ecosystem, and they do have slightly different goals (p.e. socializers prefer chatting than being in the actual gameplay). The online community shrinks and may end up disappearing. There needs to be a specific proportion of each in equilibrium. Here comes the paradox of player fairness-sustain uncertainty in MMO. To guarantee player fairness, you need to provide different ways of winning, so all players can win their way, even they lose from the other player perspective (they die). So, you can allow player mass and gameplay inequalities to keep the ecosystem in equilibrium and not decreasing. You are not just balancing the game, but the community. You are balancing mechanics and community dynamics at the same time. • If the game becomes dominated by socializers: there is no one to compete with, etc. • If the game becomes dominated by achievers: no one to chat with, to play against, etc. • If the game becomes dominated by killers: vicious and bad for new players… • …
  • 52. Achievers may be the best “kills” a killer needs, explorers may be less bothered by killers but help achievers increase by teaching them techniques, socializers are in a feedback loop with themselves (the more there are, the more they talk) and may be killed by killers, etc. It is all about reaching equilibrium in the ecosystem in which there exists some variety,… so killers do not break it all. You do this through the mechanics and content you create. You do not want equal player distribution among the player psychological types per se, you only want the ecosystem to be in equilibrium. Is it unfair? No, since each player psychological type enjoys (and somehow wins) the game in a slightly different way. No player type (and character) becomes totally dominant as long as there is a community balance so each type can play.
  • 53. Concluding remarks 1. Creating a fair competition is the most important type of experience for a multiplayer game. When it is not possible, uncertainty is lost. This relates to the first type of balance. 2. Symmetry creates player equality, but asymmetry is much more realistic and interesting. Intransitive relationships are the way to convert asymmetry into something fair in very different scenarios (turn-based games, physics-based and real-time games, etc.). 3. In order to verify there is an intransitive relationship, sometimes we need to balance taking into account output data rather than modelling mathematically the game. Other times we just listen to our instinct and playtesters perceptions of balance'. It's up to you! The next lesson will be dedicated to Equivalent Strategies.
  • 54. The golden rule of player/player balance “A player should never be put in an unwinnable situation through no fault of their own." Rollings and Morris (2003, p. 139)
  • 55. Game Balance Course Selected References • Adams, E. (2014). Fundamentals of game design. Pearson Education. Chapter 11. • Adams, E., & Dormans, J. (2012). Game mechanics: advanced game design. Chapter 8. • Fields, T. (2014). Mobile & social game design: Monetization methods and mechanics. CRC Press. Chapter 9. • Fullerton, T. (2014). Game design workshop: a playcentric approach to creating innovative games. CRC press. Chapter 10. • Oxland, K. (2004). Gameplay and design. Pearson Education. Chapter 16. • Schell, J. (2014). The Art of Game Design: A book of lenses. CRC Press. Chapters 10-11. • Sylvester, T. (2013). Designing games: A guide to engineering experiences. " O'Reilly Media, Inc.". Chapter 6. • Rollings, A., & Morris, D. (2003). Game architecture and design: a new edition. Chapter 5. • Selinker, M. (Ed.). (2011). The Kobold Guide to Board Game Design. Part 4. • Schreiber, I. Game Design Concepts [https://gamedesignconcepts.wordpress.com] (Level 16). • Schreiber, I. Game Balance Concepts [https://gamebalanceconcepts.wordpress.com]. • Romero, B. & Schreiber, I. (2017). Game Balance. CRC Press. (Not available yet) • Extra material: Asymmetric Play - Can One Game Cater to Many Playstyles? - Extra Credits [https://www.youtube.com/watch?v=SQhxtfKH1f8]