Most
of the time The Designer's Notebook is full of opinionated jottings about
creativity, storytelling, or the social effects of interactive entertainment
- in other words, blue sky. Every now and then, though, I feel compelled
to write something abstruse and technical about game design, something that's
more of a how-to than a why-to or a why-not-to. This is one of those times.
This month I'm going to talk about the effect that positive feedback has
on game balance.
What Is Positive
Feedback?
When we speak of feedback in everyday life, we're usually referring to that
horrible shriek that happens whenever the microphone in a public-address
system gets too close to the speakers. The mic picks up whatever's coming
out of the speakers and tries to amplify it again. More generally, feedback
occurs whenever the output of any system is "fed back" into it
as some kind of an input. What happens with the microphone and the amplifier
is an example of positive feedback - a situation that tends to amplify the
output of the system.
Positive feedback plays an important role in game design, although you don't
hear many designers talking about it. It can gravely harm a game if improperly
implemented, but it also has significant benefits. It's an element of game
design that every designer needs to understand and learn to use.
Before I go into how it works, though, let's look for a minute at the way
games are won and lost. When you happen across two friends playing a game,
what's the first thing you say? "Who's winning?" of course. That's
not always an easy question to answer. Some games have a metric that determines
who's ahead at any given time; others don't. In ping-pong, for example,
it's obvious: whoever has the most points is winning. In chess, it's less
clear because the victory condition - checkmating the king - is not defined
in terms of accumulating points. You can very generally say that whoever
has taken the most pieces is winning, but it's perfectly possible to win
at chess with fewer pieces than your opponent has.
In game design, positive feedback can be defined as occurring whenever one
useful achievement makes subsequent achievements easier. In other words,
whenever someone gains something in a game, it gets easier to make further
gains. If the role of positive feedback in a game is too great, then whoever
first obtains the slightest lead in the game is guaranteed to win, because
they just keep getting farther and farther ahead. This makes it sound as
if positive feedback is always undesirable, but it isn't; it's just a question
of employing it properly.
Positive feedback appears mostly in games in which the victory condition
is defined in numeric terms, and throughout the game you're working to achieve
that victory condition by accumulating something. In Monopoly, for example,
it's money. Obtaining money in Monopoly allows you to buy and improve properties,
which makes it possible to obtain more money. Positive feedback can also
appear in games in which a numeric advantage of some kind helps to achieve
a non-numeric victory condition. Although the victory condition in chess
is non-numeric, it does generally help to have more pieces than your opponent.
Balance Graphs
So what are some of the effects of positive feedback on games? I think it
will help to look at something I'm calling a balance graph, although there's
probably a different name for it in formal game theory. I've included several
of them below. A balance graph plots the progress of a zero-sum two-player
game. Time is represented on the horizontal axis. The vertical axis indicates
who's ahead by some numeric metric, usually the difference in points scored
by the two players. If player A is ahead, the number is above zero; if player
B is ahead, it's below zero. At the left edge of the graph, the beginning
of the game, the players are even at zero. Dotted lines at the top and the
bottom of the graph indicate the victory condition for either player A or
B.
My first balance graph represents a simple sprint foot race in which player
A is a faster runner than player B. A immediately goes ahead and remains
ahead for the duration of the race. Straightforward races have no positive
feedback. Gaining the lead does not make it easier to retain or increase
the lead. (In fact, there's psychological evidence to suggest that the opposite
is true: runners try harder if there's someone slightly ahead of them. When
Roger Bannister was training to break the four-minute mile, he ran with
pacesetters who ran in front of him. This phenomenon has also been observed
in racehorses and sled dogs. However, it isn't part of the rules of the
game, which is what we're concerned with here.)
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Figure 1 |
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The next graph is an example of an unbalanced, i.e. unfair, game - whether
or not it includes positive feedback. Assuming that A and B are of equal
skill and there is no element of chance involved, something about the rules
is giving A an advantage, such that she takes the lead and maintains it
throughout a very short game.
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Figure 2 |
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In Figure 3 we have a stalemate, a game that goes on forever with neither
player able to assume a commanding lead. This is a game that's too balanced:
neither player is able to achieve victory. The children's card game War
is a good example of this kind of game: it's all luck, no skill, and no
positive feedback, so it can go on for hours. This illustrates why positive
feedback is a useful thing: it helps to prevent stalemates. Once a player
assumes enough of a lead, the advantage that positive feedback confers guarantees
that he will win.
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Figure 3 |
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Figure 4 illustrates a game that's balanced, but positive feedback sets
in too soon, producing a fair but very short game. B gains a slight advantage,
then A retakes a slight lead, then B again, then A takes a longer lead and
promptly wins the game.
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Figure 4 |
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The ideal game, in my opinion, starts off even and balanced, but slowly
becomes unbalanced over time until one player inevitably wins - preferably
the better player! Figure 5 shows one example, although in this case player
B struggles on valiantly for quite a while.
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Figure 5 |
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Once a player's lead becomes commanding, the game shouldn't take too long
to finish. This is one of the (very few) problems with Monopoly. From the
time that it becomes clear that one player must win until he has actually
bankrupted all the other players is usually half an hour or more. The other
players just have to sit and wait through their slow slide into oblivion.
Positive Feedback in Games
So let's look at some examples of games with and without positive feedback.
As I mentioned before, races and most other athletic competitions don't
have positive feedback - at least, not designed into the rules. Scoring
points in basketball doesn't make it any easier to score further points.
Nor do most card games: cribbage or rummy, for example. On the other hand,
war games definitely do have positive feedback, especially if the victory
condition is simply to wipe out all the other player's units. Destroying
an enemy unit confers an advantage to the player who does it. The unit no
longer there to fight back, so it's easier to destroy the next unit, and
so on.
Another genre of computer game that has positive feedback is single-player
role-playing games. You start off with poor weapons; you kill some monsters;
you get some treasure, and you use it to buy better weapons. The better
weapons enable you to kill more monsters, you get more treasure, you buy
still better weapons, and so on.
Positive feedback needn't have a direct influence on the path to victory;
it can appear in other areas of a game as well. While I was at Bullfrog
Productions, I was lead designer on a new game (never published, alas) called
Genesis: The Hand of God. Genesis was a god game in the spirit of Bullfrog's
original Populous, in which you could affect the weather of a landscape
with divine power, drawing on mana generated by your simulated worshippers
to do so. One of our innovations was that there were several different types
of mana, depending on the nature of the landscape in which your worshippers
lived. For example, if they lived in a wet area, you got a lot of water
mana, which you could use to make rain. Of course we realized immediately
that this was a positive feedback loop: the more water you had, the more
water you could get. On the other hand if your people lived in a desert,
it was very difficult to make rain because they were producing very little
water mana.
In the end we concluded that this wasn't a problem for the game. Making
rain in a wet area made it wetter, but so what? If you made it rain all
the time you would drown your own people, and there was no benefit in that.
We also thought that making the desert bloom shouldn't be too easy at first,
but once you got it started, it should get easier. Although it was positive
feedback, it didn't endanger the balance of the game because it didn't confer
a direct advantage over your opponents.
Controlling
Positive Feedback
So far I've looked at both the benefits and the dangers of positive feedback.
The benefit of it is that it prevents stalemates, helping games to come
to an end. The danger is that it will unbalance a game too quickly and bring
it to an end too soon. So how can we limit positive feedback? There are
several ways.
Use Negative Feedback
Negative feedback is the opposite of positive feedback; it's an effect that
tends to diminish, rather than amplify, the output of a system. A good example
of using negative feedback to control positive feedback is the way that
the player draft works in American professional football. In general, a
team that wins a lot is going to have more money than a team that loses
a lot. A winning team could use that money to outbid other teams to hire
the best new players graduating from college. The best teams get more money,
which enables them to hire the best players, and so they continue to win.
Poor teams can only afford poor players, so they continue to lose - a clear
case of positive feedback.
In order to prevent this, and try to balance the strength of all the teams,
the National Football League introduced a drafting system. New players can't
simply auction themselves to the highest bidder; rather, the teams take
turns to choose players from those available, and most importantly, the
worst teams choose first. This means that the worst teams get first choice
of the best players, and the quality of the teams is evened out somewhat.
Of course, it's not that simple in practice; teams are allowed to trade
their positions in the selection order, and the quality of their play depends
a lot on the quality of the coaching, not to mention the other players already
on the team. But the principle is sound. The draft system helps to prevent
one team from establishing an unassailable position through positive feedback.
Be careful about negative feedback, however - if it's too strong, it can
produce stalemates or even wild swings in the lead, as Figure 6 illustrates.
In this example, being in the lead confers some kind of strong disadvantage
that causes the lead to flip to the other side and back again.
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Figure 6 |
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You often see this in turn-based multi-player party games for adults, in
which the object isn't really to reward skill, but to have a good time without
worrying too much about who's winning. Everybody gets to be in the lead
at some point, and the winner is mostly a matter of chance.
Limit the Benefits that Positive Feedback Provides
In chess, it's obviously helpful to remove your opponent's piece from the
board. But imagine what chess would be like if you could not merely remove
the piece, but turn it into one of your own. This would confer a much greater
benefit to taking an opposing piece, in other words, stronger positive feedback.
Chess games would be shorter. This actually happens in Japanese chess, which
is called shogi. A player who has removed an opposing piece from the board
may reintroduce it at a later point as one of his own (with certain restrictions).
This is why most real-time strategy games don't allow you to seize enemy
units and use them yourself, nor do they allow you to take over enemy production
facilities. If you could grab your opponent's factories and start turning
out units for your side, the game wouldn't last very long. They are limiting
the benefits that positive feedback provides.
In addition to the drafting process, pro football has other rules that help
to prevent the wealthiest teams from dominating all the others year after
year. One rule is the salary cap, which limits the total amount that each
team may pay all its players. No matter how much money a team has, it can't
spend more on salaries than the salary cap dictates. Another is a fixed
team size. No team can have more than 53 players during the regular playing
season, even if it can afford to. These artificial restrictions serve to
constrain the effects of positive feedback. In effect, they're making sure
that "money isn't everything."
Define Victory In Other Terms
As I mentioned earlier, the victory condition doesn't have to be defined
in terms directly influenced by positive feedback. In chess, victory is
defined in strategic rather than numeric terms. In real-time strategy games,
you can create missions in which victory must be achieved by stealth, or
by detecting a weakness in the enemy defenses, or by surviving for a certain
amount of time, or any number of other scenarios. One of the weaknesses
of RTS's at the moment is that too many of them depend on overwhelming the
enemy with sheer numbers - in effect, production efficiency - rather than
rewarding strategic skill. This leads to a "cannon-fodder" mentality
among players that is uncomfortably reminiscent of Field Marshal Haig at
the Somme. Let's hope they don't practice using those kinds of games at
West Point.
Ratchet Up the Difficulty Level to Compensate
This is exactly what role-playing games do. As I described above, there's
clear positive feedback in the character growth: winning battles enables
you to buy better weapons which enables you to win still more battles. If
you always faced the same kinds of opponents, you would quickly become invincible,
and the game wouldn't be much of a challenge. Therefore, as your character's
strength and ability grows, the game increases the toughness of your enemies
as well. The difficulty of winning each battle remains fairly constant (with
local variations) throughout the game.
Increase the Influence of Chance
This isn't the best way to reduce the effect of positive feedback, but it
does work. Monopoly does this to some extent. One bad roll of the dice can
set the leading player back significantly. Of course, it can hurt just as
much as it can help, unless you load the dice against the leading player
- and if you do that you'd better not tell them about it! Children's games
tend to rely on chance more than games for adults do. It helps to balance
out disparities in skill and allows the loser to blame bad luck rather than
himself (I don't necessarily endorse this, I merely note it).
Conclusion
Balancing a single-player computer game is a bit different from balancing
a multiplayer one. In a single-player game it isn't necessary to be "fair"
in quite the same way as it is in a multi-player game. The challenge in
single-player real-time strategy and role-playing games usually depends
more on the player's ignorance of what he's up against than the computer's
strategic or managerial skill - often because the computer doesn't have
much. But most RTS's are designed with multiplayer modes these days, and
in those cases it is necessary to balance them properly and make sure you're
being fair to each player, especially if they have asymmetric forces. In
multiplayer mode, positive feedback has an important role to play. Use it
wisely!
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