Interactive fiction equation 2

Interactive fiction equation 2

21 January 2007

by Mike Rozak

Discuss on www.mXac.net/forums

This is a second instalment to my Interactive fiction equation article. If you haven't read it yet, then do so now, or you'll be completely lost.

Note: Throughout this document I make a lot of simplifying assumptions about the equation and its terms. In the long run, many (or most) of these assumptions may prove to be wrong.

Summary

The final equation I came up with last time was:

Writing a more-specific E(c)

In my last article, I glossed over the equation for E(c), and just provided a verbal explanation about how it described the enjoyment that a player got from the consequences of a choice, c.

Here's an actual equation for E(c):

E(c) = (Ec + kx (Ec - Exc)) · kw

The terms are:

• 
  Ec is a vector that describes what kind of experience the player gets, such as how many explosions there are, what kind of love triangle is created, how good the eye candy is, etc.
  
• 
  Exc is a vector describing the kind of experience the user expected to get from his choice.
  
• 
  kx is player-specific constant indicating how annoyed the player will be when they don't get exactly what they expect. If this is close to 0, then the player takes whatever comes their way and enjoys it. If kx is higher (such as 1.0), then the player gets annoyed when they don't get what want.

  kx could actually be turned into a function that differentiates between positive and negative arguments. Used as a scaling factor, kx causes players to be just as happy when they get more than they expected, as they are unhappy when they get less than they expected. Some players, optimists and risktakers, are affected less by negative unexpected outcomes than positive ones, while pessimists and risk-adverse players are affected more by the negative outcomes than the positive ones. As a simplifying assumption, though, I'll leave kx a constant.

  
  
• 
  kw is a vector that indicates how much the player likes a given experience. For example: Some players really like explosions, while others like love triangles more.
  

A player's enjoyment of a choice is affected by the consequences of the choice, Ec, what the player thought the consequences would be, Exc, and the player's personality, kx and kw.

The new E(c) presents some interesting (and obvious) conclusions:

• 
  The better that an author can predict the player's expectations of a choice, the better that the author can produce an experience that the player will enjoy. This is where a prescient author would prove useful, or at least some really good AI to predict the player's expectation of the choice.
  
• 
  The author shouldn't give the player exactly what they expect, but more. See We don't always get what we want. When players get more, they get an extra boost from kx (Ec - Exc). Of course, when players get less, this same equation works against the author.
  
• 
  Marketing and the early game experience should only attract players with similar kw. In other words, market the game as having lots of explosions, lots of love triangles, or great special effects, so that players self-select.
  
• 
  Likewise, marketing and the early game experience should attract players with similar Exc. This is a bit more subtle than kw though, and I'm not sure how to do it.
  
• 
  Authors should try to influence players into expecting certain events to happen, so that players' Exc will be known. Foreshadowing is one technique.
  
• 
  Players with high kx will be upset if they don't get what they expect. They're the equivalent to "Type A personalities". Low kx players accept whatever comes their way. I suspect there is a correlation with Bartle's player types: Achievers and killers are high kx, while explorers and socialisers are low kx. (I don't think the models match exactly though.)

  I mentioned the possibility of turning kx into a function, so that optimists and risk takers could be differentiated from pessimists and risk-adverse players. Risk takers would be attracted to the more uncertain world of PvP combat and socialisation because player-to-player interaction causes Ec to be difficult to predict. Conversely, risk-adverse players would be attracted to PvE combat and exploring because Ec is much more predictable.

  Another interesting prediction is that risk-adverse players (who like predictable Ec's), should prefer games with no (or little) randomness. PvE MMORPGs comply: Though they generate random numbers for damage and to-hit rolls, MMORPG combat requires so many blows to kill an enemy that the randomness is mostly eliminated from the system. Combat is (I'm exaggerating here) a matter of watching your hit-point slider drop vs. your enemy's hit-point slider, and predicting which one will hit zero first, very predictable.

  Raph Koster's book, A Theory of Fun, claims that games are simplified versions of reality, which I believe too. A simplified version of reality is inherently more predictable; therefore, people who are game players probably have high kx.

  
  

However, this time around, I have an equation:

The new terms are:

• 
  Exc' is a vector describing the player's expectations of what "should" happen when they choose their first (rejected) choice.
  
• 
  ka is a constant that indicates how annoyed a player gets whenever they're told, "You can't do that", whether or not there was much expected difference between their first and second choices.
  
• 
  Xc' is a constant indicating how much the player expects the choice to work. Players will be more disappointed by "You can't do that" messages when an action works one place but not another.
  

A player's annoyance at getting a "You can't do that" message for their first choice, c', is equal to the difference in enjoyment between the expected experience for the first (failed) choice, c', and the expected experience for the second (accepted) choice, c. This difference is kx (Exc' - Exc) · kw. Add an additional constant, ka, that players experience whenever they're told "You can't do that", and scale by the player's expectations of actually being able to act, Xc'.

Some interesting observations:

• 
  (Exc' - Exc) · kw >= 0; which basically says, "Players choose the choice whose results they expect to enjoy the most." Which means that Exc' · kw >= Exc · kw.
  
• 
  If the author can control players' expectations of what choices are available, they can try to reduce Xc' to "zero", which prevents the player from being annoyed, or at least reduces the annoyance.

  I suspect that Xc' can never be reduced completely to zero (see below), since even if a player knows that a choice isn't available, they may still be annoyed at the author for not making it available.

  
  
• 
  If a player's second choice, c, has similar expected enjoyment to their first choice, c', then they won't be as annoyed by getting a "You can't do that" message. This might be handy, for example, with "one issue" players who only care about one type of experience, such as adrenalin or eye candy.
  
• 
  Players with a high ka don't like being told what to do.
  

This relationship between A(c, t) and A(c') allows me to produce a slightly better cutscene fudge-factor:

The new terms are:

• 
  Cd is a vector describing how much the cutscene's enjoyment differs from what the player expects (assuming that the player had a choice in the cutscene's direction). I could alternatively write Cd = (Exc' - Exc), which is an accumulation of (Exc' - Exc).
  
• 
  Xcs is a scaling factor, much like Xc'. It describes how annoyed a player gets despite the fact that they know they're not allowed to make choices during a cutscene.
  

A player's annoyance with a cutscene is a function of how much the cutscene's expected enjoyment diverges from the cutscene's expected enjoyment if the player could make choices during the cutscene, kx (Cd · kw), and how long the player has to sit around an not be allowed to make choices, ka t.

Some observations:

• 
  Even though players know they can't make choices during cutscenes, they still incur a scaling factor of Xcs. This means that the smallest possible value for Xc' is Xcs.
  
• 
  Players with high ka, who don't like being told what to do, will probably dislike cutscenes... unless the enjoyment from the cutscene is extra high.
  
• 
  In order to minimise (Cd · kw), long cutscenes might be procedural in nature, fine-tuning themselves to the player's guesstimated personalty. Basically, the cutscene would make innocuous choices for the player; as long as it got most of them right, the player wouldn't get too annoyed.

  For example: A common cutscene involves a short dialogue between a NPC and PC, with the PC responses being unimportant for the outcome of the scene, but necessary to prevent the NPC's "conversation" turning into a soliloquy. The current solution is to have the NPC speak, provide the PC with four slightly different responses that all have the same consequences, and repeat. This ends up presenting the player with a choice between four doors, all of which lead to the same room, which really annoys players when they find out. Using a guesstimate of the player's personality to select which of four responses will be used eliminates the need to offer false choices.

  
  

If I insert the new terms, I get:

E = d ( E(c) - P(y|d) A(c') - A(c, t) + ki ) I(d) P(d)

E = d (

- P(y|d) (kx (Exc' - Exc) · kw + ka) Xc'

- (kx (Cd · kw) + ka t) Xcs

+ ki

E = d (

- P(y|d) Xc' kx (Exc' · kw) + P(y|d) Xc' kx (Exc · kw) · kw - P(y|d) Xc' ka

- Xcs kx (Cd · kw) - Xcs ka t

+ ki

E = d (

+ (kx Ec - kx Exc - P(y|d) Xc' kx Exc' + P(y|d) Xc' kx Exc - Xcs kx Cd) · kw

- P(y|d) Xc' ka - Xcs ka t

+ ki

E = d (

+ kx (Ec - Exc - P(y|d) Xc' Exc' + P(y|d) Xc' Exc - Xcs Cd) · kw

- ka (P(y|d) Xc' + Xcs t)

+ ki

E = d (

+ kx (Ec - Exc - Xc' P(y|d) (Exc' - Exc) - Xcs Cd) · kw

- ka (Xc' P(y|d) + Xcs t)

+ ki

In English:

The enjoyment from a game is the sum over all decisions of the following factors, all scaled by how important the player thinks the decision is, along with the probability of encountering the decision.

• 
  How much enjoyment the player gets from the consequences of the choice, Ec · kw.
  
• 
  How annoyed the player gets when the outcome of the choice isn't what they expected, kx(Ec - Exc) · kw.
  
• 
  How annoyed the player gets when the outcome of their second (accepted) choice isn't as good as the outcome of their first (failed) choice, had the game allowed the first choice, kx Xc' P(y|d) (Exc' - Exc) · kw.
  
• 
  How annoyed the player gets when the resulting cutscene has produced a different outcome than they would have chosen if there were no cutscene, kx Xcs (Cd · kw).
  
• 
  How annoyed the player is at having their first choice rejected by the game, ka Xc' (P(y|d).
  
• 
  How annoyed the player is at having to sit through a long cutscene where they can't make any choices, ka Xcs t.
  
• 
  And finally, the extra immersion (which is good) that results from the player being able to make choices, ki.
  

Television, movies, and books can be thought of as a game with one long cutscene. With this assumption, the equation for linear fiction becomes:

E = d (

Ec · kw

+ kx (Ec - Exc - Xc' P(y|d) (Exc' - Exc) - Xcs Cd) · kw

- ka (Xc' P(y|d) + Xcs t)

+ ki

Xc' = Xcs, since Xc' can only go as low as Xcs. Basically, the player doesn't expect to make choices in linear fiction, but will still be slightly annoyed at the inability to do so.

ki = 0, since there are no choices.

E = (

+ kx(Ec - Exc - Xcs 1.0 (Exc' - Exc) - Xcs (Exc' - Exc)) · kw

- ka (Xcs1.0 + Xcs t)

+ 0

E =

+ kx ((Ec - Exc) - 2 Xcs (Exc' - Exc) ) · kw

- ka Xcs (1 + t)

Although this is a somewhat silly equation, it provides some useful conclusions:

• 
  The most important part of how much a player likes a TV show, movie, or book is based on how enjoyable the total experience was, Ec · kw.
  
• 
  This experience is hurt when the book (etc.) doesn't progress or end as expected, kx(Ec - Exc) · kw.
  
• 
  The experience is harmed when the characters in the story make choices that the player would not have chosen to do, 2 kx Xcs (Exc' - Exc) · kw. In other words, viewers don't like it when characters in horror movies do stupid things, like walking backwards, or splitting up so they're easier prey for the rampaging mass-murderer.
  
• 
  The longer the story is, the worse it is, ka Xcs (1 + t). (This is offset by the fact that longer stories can produce better Ec · kw).
  
• 
  Players with high kx will be affected more by (Ec - Exc) and (Exc' - Exc) than those with low kx. In terms of fandom, it means that players with high kx will be avid fans of some fiction and intensely dislike other works, while low kx people watch a variety of fiction.
  

• 
  A low (Ec - Exc) and low (Exc' - Exc) - They will have enjoyment preferences that are either common enough to attract enough authors to produce a stream of high quality entertainment, easily predicted enjoyment preferences, and/or preferences that are easy to satisfy in TV, movies, or books.
  
• 
  A low kx - Avid TV viewers are easy-going, instead being type-A personalities who like things to go their own way.
  
• 
  A low Xcs - When they're put in a straight-jacket and not allowed to make choices, TV viewers accept the restraint and don't squirm in their seats.
  
• 
  A low ka? - TV viewers don't get annoyed when they're told, "You can't do that." A low ka isn't necessary if the viewer has a low Xcs, or vice versa.

  Corollary: Dictators, who are fond of using intellectual straight jackets and telling people "You can't do that", don't like gamers because games resist control.

  
  
• 
  A low ki - TV viewers aren't immersed by making choices. Although the equation doesn't explicitly state this, the "real life" equation causes high ki people to be attracted away from TV.
  

Using the same equation to describe real life, I get:

E = d (

Ec · kw

+ kx (Ec - Exc - Xc' P(y|d) (Exc' - Exc) - Xcs Cd) · kw

- ka (Xc' P(y|d) + Xcs t)

+ ki

t = 0, since real life doesn't have any non-interactive cutscenes.

E = d (

Ec · kw

+ kx(Ec - Exc - Xc' 0 (Exc' - Exc) - Xcs 0) · kw

- ka (Xc' 0 + Xcs 0)

+ ki

E = d (

+ kx (Ec - Exc) · kw

+ ki

) I(d) P(d)

• 
  People like real life based on how well it their decisions turn out, Ec · kw.
  
• 
  They get annoyed when the consequences of their choices don't meet their expectations, kx(Ec - Exc) · kw, especially if they're a "Type A personality" that must get their way, kx.
  
• 
  People who are immersed by making choices like real life even more.
  

• 
  (Ec · kw) is high - Real life is meeting their needs. Conversely, people that want to be Napoleon, or wish to fly to mars, aren't having their needs met by real life, so they're unhappy with it. To use a less extreme example, people who aren't doing well in real life (poverty being one indicator) tend tend to gravitate towards TV or games.
  
• 
  (Ec - Exc) is high - People's expectations of real life are being met. This is slightly different than meeting people's needs; if you think that you should be able to invent a perpetual motion machine, you'll be sorely disappointed with real life, whether or not your other needs are being met.
  
• 
  Low kx - Even if real life isn't meeting expectations, many people are easy-going and don't care. However, if someone is a "Type A personality", wanting to have control over reality, but reality isn't meeting their expectations, then they won't like real life.
  
• 
  High ki - People who are immersed by making choices like real life.
  

People that enjoy real life, live in real life. People that enjoy TV (and movies and books) spend their time watching TV. The rest are often drawn to computer games, some of them to interactive fiction.

Therefore, a successful interactive fiction title/game should target the following personalities:

• 
  People whose needs cannot be met in real life or though stories. In both cases, their real-life (Ec · kw) and story (Ec · kw), should be low. One obvious stereotype that meets this requirement is teenagers, who want to be independent from their parents. They can't yet be independent in real life, and linear stories are a poor substitutes for experimenting with adult-style choices.
  
• 
  People whose expectations aren't being met in real life, with a low (Ec - Exc). The Sims is a perfect example: Can't have an idyllic family in real life? Create one on the computer.
  
• 
  People who know what they want but aren't achieving it in real life, and who aren't happy unless they get it, with a high kx. In the real world, there can be only one Napoleon, but virtual worlds can support many Napoleons.
  
• 
  People who are immersed by making choices, with a high ki. These people will also be attracted to real life, unless real life has other limitations.
  
• 
  People who take the road less-travelled and don't like being told what to (or not to) do; they have a high ka. Conversely, these same people get frustrated with games because game physics doesn't allow them to do everything they want to do. They will tend to stick to reality unless they have other reasons for playing a game.
  
• 
  People who don't like sitting through long cutscenes (aka: movies); they have a high Xcs. These people are also attracted to reality.

  Corollary: If a game can't produce long cutscenes that are as well written and with as much eye candy as movies, then the game either shouldn't have them, or it should significantly shorten them. Even if the long cutscenes are movie-quality, the market for interactive-movie games is so small that the financial investment would provide a higher return elsewhere.

  
  

• 
  Want fantasy, or at least something that they can't do in real life.
  
• 
  They want to interact with that fantasy. A book isn't good enough.
  
• 
  They are probably "Type A personalities" who will whinge on the forums when things don't go their way... Things may not be going their way in real life either, but whingeing to politicians and God (or their preferred deity) is even less fruitful.

  Corollary: They are avid Star Trek, Star Wars, or Lord of the Rings fans who avoid fiction that falls outside their limited interests.

  
  
• 
  They want to make lots of choices. First, they will want a variety of armours to choose from, from leather to plate. Then they will want armour for individual body parts.
  
• 
  They will whinge that they don't have enough choices in the game. They will ask to be able to paint their armour a solid colour. Once they have that feature, they will want to paint pictures on their armour. Once they have that, they will want embossed armour, or the ability to put flashing lights on it.
  
• 
  They don't like long cutscenes. However, those gamers that aren't true hard-core will love cutscenes and ask why they aren't included.