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In generic terms, what makes something, regardless of what game it's being used in, over powered?

I hear the term a lot, and while I can recognize it when I see it in-play (often due to someone breaking a rule, in my experience) I have difficulty identifying exactly Why it's over powered.

Speaking in pathfinder terms here, a character that can deal 500 damage in one turn at level 1 is obviously over powered. I've only known stuff like that to happen when rules are being broken, the character in question was completely home-made, or occasionally when systems (read, splat-books) that had never been meant to be used/tested together, get used together.

For bonus points: Can anyone think of a good, non-game-specific definition to define something being over-powered? Preferably a definition that does not need an example to be explained.

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It might be worthwhile to expand this to include the term "broken," which is frequently used to describe the extremes of over-and-under-power, but is in fact slightly different. –  KRyan Feb 17 '13 at 16:20
    
I don't think you can define 'over-powered' outside of the context of a 'game'. Any usable definition of 'over-powered' relies on the concept of 'balance', which is impractical outside that context. Things are simply 'more effective' or 'more powerful', when measured against their intention. I may have missed the point of the for bonus points part. –  Zachary Yates Feb 17 '13 at 22:00
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@ZacharyYates he means "not specific to a particular game" not "not specifically in the field of games" –  KRyan Feb 18 '13 at 2:20
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I always imagined overpowered as bringing a single-action rifle to a small-arms show, and broken being bringing a briefcase full of explosives to a knife fight: One of them has obvious advantages with obvious drawbacks. The other doesn't even bother participating in the play concept and is just present to make explosions. If you prefer in terms of playground brawls, overpowered is bringing your own bully. Broken is bringing Bruce Lee. –  B.A. Thomas Feb 20 '13 at 13:09
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7 Answers

up vote 34 down vote accepted

Definitions:

  • Group: everyone wanting to build a character to a roughly similiar set of requirements.
  • Everyone: A set of 1 or more players with sufficient system expertise who communicate in some codified way, e.g. through a forum or around a game table.

Thesis:

  • An option is overpowered if, when presented as a choice, it will always be chosen by members of a group.
  • An option is balanced if, when presented as a choice, if will be chosen sometimes, due to its ability to fulfil requirements.
  • An option is underpowered if, when presented as a choice, it will always be ignored by the group.

Some discussion:

Balance is always a function of what choices players make within the context of the game. Given that choices are a function of given requirements, items are only commensurate within a group of similar requirements. Something that is overpowered for combat monkies may be universally ignored by the socialites. That split makes the discussion of balance between the two groups incommensurate. For most purposes though, most universal options in a game (like feats) can be discussed from the perspective of every character playing in the game. Only in rare cases where you have significant specialization of character can there be multiple groups within the same game.

This also serves to regulate objective/subjective things as well as "real" and "perceived" power. The players of a game are the only thing that matter (in general, as the rules are a social contract that can be set aside at the decision of the players). And their opinions are the exposed semiotic representation of their model of the game. Therefore, by looking only at their opinions, you can gauge the overpoweredeness of an option.

The level of effort one can put in to seeking different opinions varies. If you have sufficient system mastery to build characters for other people to arbitrary requirements, you may judge your own views of overpowered by seeing what options are present in what proportion of characters you build. System mastery, as awareness of options and their consequences, has a large impact in the perception of "overpowered" options: you can't push the I Win button if you don't see it flashing red in front of you.

Whether you decide to address people of different system mastery is a function of your chosen "research methodology." And is immaterial to the question, only to its applicability over large groups. The perception of overpowered is fundamentally subjective, and therefore relies in human perception of the mechanical-theoretical rules-space. It is, however, possible to generalize objective measurements for some systems if some goal-achievement models are present in those systems. (A build in 4e is considered overpowered by the community if it can kill one or more standard creatures of equal level per round.) That is abstracting the value system of the community to an objective and generalizable level.

Quoth lisardggY:

Let's run a test on your model to see how productive it is. Let's say I bring a new splatbook to the table and someone asks about a new class in it "is it overpowered?". Can this question be answered? Must the splatbook - and the new class - be an option for a while before it can be deemed over/underpowered? Must it be used in that particular group, or are we looking at rate of adoption across that particular's game userbase. Can that be measured? Aren't we ignoring the favorable bias earlier options will have over later ones?

This is absolutely a question for a specific research methodology. While my answer provides a framework and basic heuristics, it doesn't provide a research methodology. In general though, we cannot answer based on bringing a new splatbook to the table without looking at a community's experiences with a new splatbook. On the other hand, if it is possible to evaluate builds quickly with high system mastery, the way to do it is to say "okay, we care about balance. Let's make some builds for requirement X and see how often it shows up."

In terms of bringing a book to the group, this has a number of implications. First, yes, it's impossible to judge a book in a single night. Many things that are broken are broken because of their synergies. Making a ruling on something based on a first night hunch does not have a large enough sample. The lesson to learn from this is that new books should always be evaluated consistently. I'd recommend an option in the group's social contact to say "Look, new books are fine, but you get a penalty-free retcon of your character if it turns out that [we/a larger community] seem to feel its overpowered."

With that said, if your group builds 10-15 characters around a theme of the option presented and contrasts them with characters without the option but to the same requirements, it should be possible to get an intuitive feel for the option. But this takes work, and many people are unwilling to do it.

Again quoth lisardggY:

Your model can only describe a given element's power level for a game with an active and chatty community. It assumes, a prior[i], that an element's power level can't be determined in the context of its mechanics, only by its side effects.

Not quite. An active and chatty community will serve to make more people aware of more options and homogenize the system mastery as effective combinations are communicated.

The evidence we can see from optimization discussions is that no character element ever acts alone. Beyond that, we cannot create a rubric for mechanics without an understanding of desirable end points. We can do that both as game-creator and as game-reader. This model of mechanical-theoretical outcomes is ontologically neutral, it is not up to the game to assert which outcomes are desirable, it is up to the ontological imposition by the social contract of the specific gaming group. With that said, popular games like 4e generally strongly influence that social contract, but even by looking at answers to the querent we see that there are huge philosophical differences.

Therefore, as a way to normalize this across all game systems, we must go with subjective-perception of specific people, especially as "fairness" is operationalized differently between groups.

You may determine the overpowereness of an option as it impacts on your group's social contract by looking at its frequency of choice in the community that you care about. You may then evaluate that frequency of choice against metrics that you prefer, like "fairness" or "enjoyment" or "fulfilment" and consider if the frequency of choice serves to validate or undermine those metrics. If the frequency of choice is no longer a choice, the option is overpowered because it is warping the rest of your choices, instead of presenting a valid way to perform mechanical-practical or narrative building to requirements.

Quoth Zach:

All this game-theory is quite complex, and not exactly easy for a youngster like me to follow without some difficulty.

Let's start with the theoretical breakdown (numbered points used to assist in questions in comments):

  1. Games exist by virtue of a set of one or more gamers playing them.
  2. "Playing" is a very broad term covering any sort of ludic activity around the game, be it participating in a community looking at elaborations of the rules or imagining a story with the help of the rules or acting out your own power fantasy in a setting suggested in the rules.
  3. Therefore, the text, in order to be used, must be interpreted by the specific community using it at the time.
  4. Something can only be overpowered in the context of the community that is using it at the time. Other communities have different readings and value assignments that change the nature of the thing read.
  5. To generalize across all systems, an appeal to the statistics underlying the rules of a specific game cannot and should not be made: those statistics exist only through the interaction of players.
  6. A method, therefore, is needed to assess the subjective opinions of a community.
  7. The simplest method is to count the frequency of a choice made.
  8. Given: A group has more fun when not everyone makes the same choice, due to the increase in options, possibilities, and future choices.
  9. Therefore, we do not want the frequency of a choice made to outweigh (significantly) the frequency of other choices.
  10. A choice made mandatory by its historical frequency is no choice.
  11. A choice that becomes part of the game changes the game in unpredicted, and therefore undesirable ways. Usually this serves to shorten periods of ludic joy (combats become a very quick meatgrinder and people wonder ... "what next?")
  12. Therefore unusual frequency spikes are bad and be tagged with the negative label "overpowered."

Again quoth Zach:

I have only one issue with this; it suggests that certain overpowered options are simply required to be taken, within a certain group. Ex: If a group of optimizers is playing a game that focuses around combat, then the option everyone will take is building towards combat efficiency. Thus, combat-focused builds, by this theory, are overpowered within that group. However, as building a character that is not combat-focused would ultimately be a hindrance, and thus an option no one would take, then the only options would be under-powered builds, or overpowered builds.

Yes, but there's a crucial point. Choices that everyone makes are no longer choices. Therefore, that group will, when looked at from the perspective of outsiders with different "menus" of choices will certainly be overpowered. It is quite likely, however, that within the group, there will be a normal distribution of choices within the set they consider allowable. And that that group would consider unusually high choices within their reading of the game to be overpowered from their own perspective.

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Sorry for the wall-o-academiese (+15 versus will to remain sane (save ends). This question pushed my theory buttons. Please edit to translate the most egregious bits. –  Brian Ballsun-Stanton Feb 17 '13 at 6:06
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That is the first time I've seen the word "semiotic" in use since I read What Video Games Have To Teach Us About Learning And Literacy. Bravo on that stunning breakdown of a complicated topic. –  DuckTapeal Feb 17 '13 at 6:27
    
It is, thanks. But it brings up other questions. Your model can only describe a given element's power level for a game with an active and chatty community. It assumes, a priory, that an element's power level can't be determined in the context of its mechanics, only by its side effects. –  lisardggY Feb 17 '13 at 8:51
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@lisardggY That may actually be true in practical terms. There is a point at which a system is sufficiently complex that its option permutations can't be mapped within a useful span of time (say, before the heat death of the universe). In such systems, only observation of emergent patterns is useful in a practical time span. I suspect that many complex RPGs are equally complicated as Go, and Go (unlike chess) can't be trivially mapped in a useful timeframe. –  SevenSidedDie Feb 17 '13 at 9:30
    
@Zach tried to break it down. Any specific questions? –  Brian Ballsun-Stanton Feb 20 '13 at 11:02
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While I appreciate Brian Ballsun-Stanton's explanation in so far as it cites the concepts of Game Theory that arose in the 1930s and '40s to explain rational decision-making in economic systems, I believe that it fails to capture the emotional thrust imbued in the notion of "Overpowered." Games Theory is primarily concerned with dominating strategies - that is, the better choice to make.

The problem with the notion of something that is Overpowered is not that it is the better choice, but the magnitude of difference between that choice and other choices. Moreover, if it were merely a better choice, something being Overpowered would be a good thing and everyone would take it. However, most people use the term Overpowered in a negative sense: suggesting that the Overpowered thing should be removed from the game.

Games Theory would suggest that most people would want to be Overpowered and would therefore want Overpowered as an option within the game. This does not correlate with the reality that most people want Overpowered options removed from games.

Therefore, I believe a much earlier principle better explains the notion of Overpowered, the theory of Justice espoused by Ancient Greek Sophists, though perhaps best worded by John Rawls in his essay Justice as Fairness.

Justice is thought of as a pact between rational egoists, the stability of which is dependent on a balance of power and a similarity of circumstances.

Players of a game expect a similar sense of justice to prevail within the game environment. Indeed, saying something is Overpowered is a subset of saying it is unfair. Fairness, therefore, seems to be the primary principle leading to the negative connotations behind Overpowered.

In order to be fun, a game must have a certain degree of stability, balance of power, and similarity of circumstance, just as John Rawls identifies as cornerstones of Justice. The basic principle in most Role-Playing Games is the expectation that all players will be able to create characters by following the standard rules of roughly equal power.

"Roughly equal power" is a difficult concept to define. If one character rolls 1d8 damage and another rolls 1d10 damage, is that roughly equal? What if it's 1d6 and 1d12? 1d4 and 2d6? All of these are damage dice that show up in weapons in D&D 4th edition, and all of these are considered roughly equal, at least in so far as the character dealing 2d6 isn't considered Overpowered by the character dealing 1d4.

On the other hand, a character rolling 100d12 damage would be labeled as Overpowered. There is therefore some unknown tolerance factor that we have to assume exists but cannot strictly define; this also means that we cannot strictly define whether an element is Overpowered. Instead, we merely know that, for any element that violates the tolerance threshold, that element is Overpowered.

The tolerance factor will vary both by game system and by player, further obfuscating the nature of Overpowered. Something might feel Overpowered to one person but not feel Overpowered to another, or something that is generally considered Overpowered in one game system might not be Overpowered when similarly presented in another system.

Rawls has more to add on the notion of fairness that might help us better understand Overpowered:

Usually acting unfairly is not so much the breaking of a particular rule, even if the infraction is difficult to detect (cheating), but taking advantage of loop-holes or ambiguities in rules, availing oneself of unexpected or special circumstances which make it impossible to enforce them, insisting that the rules be enforced to one's advantage when they should be suspended, and more generally, acting contrary to the intention of a practice.

Emphasis added by me. If this hadn't been written in 1958, I'd be certain Rawls were referring specifically to D&D :)

The key issue here is the notion of the intention of rules of a game. This leads to the distinction of RAW (Rules As Written) and RAI (Rules As Intended). Often, something that is Overpowered follows RAW, but violates RAI; or so players complaining about the Overpowered thing might claim.

For example, in my lengthy discussion on A Brief History of Basic Attacks, I argue that overriding the Melee Basic Attack with at-will powers in D&D 4th Edition violates the intention of a Basic Attack being a Basic source of damage without the same level of crippling effects present in At-Will powers. A Fighter using Beast Switch as an MBA, interrupting an enemy's attack by sliding them away and knocking them prone and thereby cancelling out that attack, is considerably more powerful than simply dealing damage, and in violation of the intention of Combat Challenge's damage reprisal for ignoring the Fighter's mark.

However, this is merely one interpretation of the intention. Did the game designers intend for the Fighter to merely deal damage (as I claim, by comparing that mark reprisal to other damage-only effects like the Paladin's Divine Challenge or the Battlemind's Mind Spike), or did they intend for it to nullify the attack (as others claim, either by suggesting that building complexity is a feature of the game or by comparing it to Swaying Branches, which allows Wardens to forgo dealing damage to potentially nullify an enemy's attack by sliding it).

Both sets of arguments depend on how a player interprets the intention of the rules, and really this is at the core of the notion of Overpowered as well. The reason there is no way to come up with a self-contained definition of Overpowered that can be used to identify Overpowered things in any setting is that Overpowered is a subjective, rather than objective, property. It is as difficult to strictly understand as beauty: most people simply know it when they see it.


In conclusion, I would suggest the following answer:

Something is Overpowered if it violates the intention of the game system.

However, this is merely an objective short-hand for the subjective reality behind the notion, so it would be more completely defined as:

Something is Overpowered to you if you feel it violates the intention of the game system.


@SevenSidedDie asks:

How does this account for games like World of Synnibarr and RIFTS, that clearly contain overpowered things, but these things are congruent with the intentions of the system? Perhaps the it has something to do with balance not being part of the design intentions? If so, does this answer only apply if we first assume balance as a necessary good?

If the powers in RIFTS and other similar systems are intended by the game's designers to have a large variance in power, these powers are, by my definition, not overpowered. They are not OVER powerful because they are not powerful OVER the power intended for them to have. They may be "very" powerful or "too" powerful but, whatever they are, they aren't "overpowered."

The term "overpowered" carries a negative connotation: if something is overpowered it is, in some sense, bad. In my analysis, this badness comes from a violation of intended game balance. In order for violating the game balance to be bad, respecting the game balance must therefore be "good." Thus, in order for someone to be able to categorize a feature of a game as overpowered, they must also be assuming that balance in that game's system is good.

Thus, while I am not suggesting that every game system must be balanced or that every player must view balance as necessarily good, a player must view balance as a good in order to be able to discuss overpowered aspects of a system.

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But RPGs are not played solo, so I think that this is a less than useful definition. Perhaps "something is overpowered to your group if your group feels" would have made it a bit more broad and applicable. –  wraith808 Feb 17 '13 at 15:04
    
+1 oh snap Brian got out-theoried! –  mxyzplk Feb 17 '13 at 15:11
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No, @mxyzplk a different theoretical basis has been advanced. If this was academia, Soulrift and I would start sniping over the walls of journal articles. ... That actually sounds kinda fun... –  Brian Ballsun-Stanton Feb 17 '13 at 23:31
    
It has been a long time since I played RIFTS, but every time I did the GM took steps to make sure all the characters were roughly in the same "power band". Whether that was all extremely powerful or on the lower end, they were always at least comparable. –  TimothyAWiseman Feb 19 '13 at 17:49
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Let me chip in with the blue collar guy's answer to this question, drawn from experience not theory.

A rules option, character, gear, or other game element is "overpowered" if it gives you significantly more effectiveness than most other options in a way that impacts the fun of the game for its participants. As @Soulrift points out, the implication is that an overpowered option is undesirable due to being unfair and should be banned or "nerfed" (reduced in effectiveness) as a result, but it's not pure unfairness, it's unfairness that affects the fun of the game.

The term is often used in a couple different contexts.

  1. Trivially Overpowered: A rules option that gives you significantly more benefit than other elements with the same cost just on its face. So if a game has a bunch of abilities that cost you one slot or the same number of skill points or the same amount of in-game money, and most give you a certain kind of benefit (e.g. +2 to a weapon attack) but one gives you much more than that (e.g. a +4 to a weapon attack), the latter is then overpowered because it gives you more for the same cost. This kind of being overpowered is easily discernable from reading the rules BUT it may not actually result in practical imbalance in play. This kind of option might be banned or nerfed in order to maintain people's fun by not feeling like their choices are constrained to better "must-have" choices. Also this is the area where you get a lot of rules-theory arguments - often the compares are not as direct and there's a lot of judgment involved in what "better" means.
  2. Contextually Overpowered: Often discussions about being overpowered hinge on a specific context. A rules option might be overpowered in a certain kind of game - telepathy in an investigative/mystery driven game, for example. This kind of option might be banned or nerfed to maintain the narrative fun for everyone and not "spoiling"/short-circuiting the experience of the plot.
  3. Practically Overpowered: An option that in game allows any player to far outshine his compatriots - from "kill power" to spotlight time, anything that makes them a dominant force and other PCs seem like accessories in the dominant mode of the game - is practically overpowered. Often results from unforeseen combinations of options and contexts. This kind of option might be banned or nerfed in order to maintain the sense that everyone participating is contributing to the game in some equitable measure. It doesn't have to be in raw damage; different character types often have different kinds of contribution to a game, so different focuses don't usually trigger this, but if two characters have the same focus and one has some option or option combo that makes them greatly more effective, it affects the sense of participation of other players.

So when one asks Is a summoned tyrannosaurus overpowered? they are asking if that is a choice that is just plain always better than the other summoning choices - trivially overpowered, such that he should be constrained to always choosing that option. Vow of Poverty, overpowered or underpowered? is similar, with the added layer of "for monks" or other certain kinds of characters.

When one discusses Overpowered PCs (Gabe's Dilemma), one is talking about being contextually overpowered, to where it's hard to challenge them with meaningful plots.

And when one asks Is one of the characters in my group overpowered?, or my recent concern about my own PC outstripping both the opposition and other PCs, What to do when your character is just too good?, this is about being practically overpowered - does that character's contribution diminish those of his compatriots and lead to a loss of fun from the others in the group.

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I really like the links to different sorts of questions about overpower issues on this site. Those are great examples. –  KRyan Feb 17 '13 at 16:42
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Lots of good theory, here's my simple answer:

A game actor/mechanic is overpowered when it is both:

  1. Prolific in the sense that the majority of players use it.
  2. Detrimental to a player who does not use it.

The second point is the most important.

Take for instance a DnD 2.0 campaign I played 15 years ago (sorry it's been so long I can't remember all the details).

The DM had a couple of house rules, the overpowered one being that you could simply be ambidextrous if you said you were. That translated into a greatly reduced penalty for dual wielding, he also removed the penalty for having a medium sized weapon in your off hand.

Everyone in the campaign played some sort of multi-classed fighter, and dual wielded. (Except me, single class human fighter). The other players, despite being multi-classed leveled faster than me. They were able to sustain such high damage output that I rarely ever killed any monsters, so I got very little XP.

Other character progression problems aside, those particular house rules were overpowered. I think the same concept can be applied to any rule set.

Here's a neat allegory from Magic: http://boardgames.stackexchange.com/questions/4280/why-is-skullclamp-banned

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Something is Overpowered to you if you feel it violates the intention of the game system.

Given that we're all using academic work, I think it is time to bring post-modernism1 out to play. Game systems appear to (some) readers to have a textual intentionality.2 If "over-poweredness" then is reliant on interpreting textual intentionality, then it is subject to textual methods of criticism. Conducting a hermeneutic of RPG systems to develop a concept of intentionality can produce a variety of valid readings—my Nethack Simulator is your Monty Hall. However, Brian's method of reading—system mastery of the synthetic hypertext of a rules system—leads to a dependably static reading of intentionality. A kind of legal hermeneuticism, a "rules lawyering." If Brian, or an optimisation forum, or Susan Q. Public were to optimise a rules function against a "canon" text for a game system, they would come to similar awarenesses of the intentionality of the game3 at a level preceding the authors' collective attempts to structure intentionality in the game. The authors never contemplated that you equip a kobold as a god, but their text clearly intends that you may. Susan Q. may analyse the mechanics of ro-sham-bo and discover, despite the attempts to produce an even power level, that people of one culture prefer rock 36% of the time. The living text of ro-sham-bo then displays its own intentional function, and any reader may duplicate that reading solidly.

The only issue here is that while power-levels are then readable in a shared manner by similar authors—that the majority of game function X produces 40 units, but game functions Y produce 60 units consistently—how do we ensure a consistent reading of whether Y is over-powered, or within the "intentionality" of the game itself? Through a similar, second reading of textual intentionality, this time structured around play-purposiveness rather than mechanical power. Is 2e reliably readable by multiple versed readers as a chance for ideally homosocial ideally male bonding over ornate wish fulfillments, a necessary meta-rule being that all players feel that they contribute meaningfully to standardised scenarios of opposed mechanical actions? We can then, system by system, evaluate the mechanical variance against the intentionality of play purposiveness in the text in its context. The play purposiveness need not be mechanical—if the text cries out for Mary Sue to save us all, then nobody will complain that Mary Sue saves us all, Mary Sue's mechanical capacities are not problematic unless she is underpowered.

Broken would then be a level worse, not merely a felt dissonance of mechanical representation and play purposivity, but rather a violation of social code elements of the game. To bring an overpowered character to situation is to improperly but permissibly distort play. To bring an underpowered character to situation is to improperly but permissibly distort play. To bring a broken character is to violate the meta-rules of play.

Brian's concept of requirements for play and mechanics4 is useful, it formalises the purpose of mechanics for an instantiation of a game. It produces a shared reading of the purpose of play and the purpose of the mechanics, and then allows for players to unbreak a broken system.

In relation to cases where readers believe that mechanics are overpowered without apparently violating the intentionality of a game system, I think that this is an imprecision, a metaphor against other games where such power disparities would be negative. In a sense there is a slippage between "true" overpowered mechanics, that violate the game as play, and "false" overpowered items, that appear to violate the game as play, but sola scriptorum do not. This is a case of precision in establishing the hermeneutic context, particularly through what I perceive as importing the metaphor of overpoweredness into an incorrect context. Mary Sue's headband is designed to save the Enterprise, and is an element of the contract of play of "Mary Sue saves the Enterprise." There's a great power disparity between Mary Sue's headband and Joe Player's headband, and we metaphorically describe Sue's headband as overpowered due to power disparities commonly being the result of power over the agreed game diversity of power states. Sue's headband is an agreed power for play.

(I suppose hostile readings of "Mary Sue saves the Enterprise" as a game that ought to be balanced mechanically are possible, but such hostility would be reading in bad faith.)

1 Of a kind, I'm using Jameson's concept of the hermeneutic of the text http://en.wikipedia.org/wiki/Fredric_Jameson#Narrative_and_history

2 For a broad meaning of text. The dance of spoken word and a semi-static agreed interpretive structure can be seen as textual.

3 Dependent on their interpretive skill.

4 Brian Ballsun-stanton, Samuel Russell (2012) Constrained Optimization in Dungeons and Dragons : A Theory of Requirements Generation for Effective Character Creation.

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Damn you :) Don't you know that referencing Hermenutics is the Pazuzu of academia? Now we're all suffering +45 verus Will attacks! You've doomed us all! –  Brian Ballsun-Stanton Feb 18 '13 at 1:44
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Definition: Let the range of power in a game be normalised around a Normal distribution of mean 0 and standard deviation of 1. An over (under) powered value is defined as anything that is greater than a certain number of standard deviations (to be determined by the reader, say 3-sigma) away form the mean. If the value is negative, is is under-powered. Otherwise, it is over powered.

Clearly, you need a large enough sample size for this to work -- as with all statistical methods. Your group of ten characters is not even close enough to get you some meaningful numbers. For example: If damage per combat round were you metric of power, you could get some statistics by taking all reasonable permutations of playable classes and skills and equipment and level and whatever your system has to influence combat then adding all appropriate entries for your bestiary.

Brian Ballsun-Stanton's answer is very game theoretic so I thought I'd add a statistical one.

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If you think of playing an RPG as a series of questions (How do you get past the guards, how do you kill the dread Lord Puppykicker, how do you talk sweet Lucina into eloping with you) then any time we already know the specific answer to an important question before it gets asked and we know that answer will not fail, that answer is probably overpowered. Pay particular attention to answers that get used more than once.

Most (not all, but most) games can be thought of as questions- usually from the DM (or local equivalent) to the players. The interesting stories that result from good play tend to be when the answers are not known, implying that multiple answers were roughly equally valid. If there are several equally valid answers, then those answers are not overpowered.

This applies to specific answers to questions. Thus, "Q. How do we deal with Lord Puppykicker? A. We kill him." isn't necessarily a problem, because killing is a generic answer. (That generic answer may be overpowered- In most editions of D&D, "I do magic to it" is a pretty overpowered answer, and in almost every RPG I've played, "We kill it" is a very overpowered solution. Your group may be alright with certain kinds of generic answers being overpowered. If you have a problem with the specific generic answer of "Kill it" then you probably have a separate issue. See how do i get my pcs to not be a bunch of murderous cretins for help.) "Q. How do you kill Puppykicker? A. Cast Broken Spell of Murdering on him." is an example of that spell being overpowered, because we probably knew that specific answer was going to be the answer when we asked the question.

This does not apply to unimportant questions. Lots of games take things for granted or decide that certain questions aren't interesting. "Q. How do we get to the village of Elvenhome? A. By walking." Walking is not overpowered- it's just an uninteresting question. "Q. How do we get the One Ring to Mordor? A. By handing it to a hobbit and sending him through Shelob the Giant Spider's lair." is an interesting question, and Cirith Ungol (The passage where the spider is hiding) is not overpowered because there were other roughly equal answers we could have given. (Just because an answer is good does not mean it's overpowered- other answers could have been as good. Just because an answer is terrible does not mean it is underpowered- other answers could have been as bad.)

If we do not know if an answer will work, then that answer is not overpowered. "Q. How do you kill the orc? A. Stab it with my Sword of Awesomeness!" is only overpowered if we know immediately that that answer will work. If it might miss, or if it might not kill the orc even if it hits, then it is not overpowered. (Ignore any case where part of the answer is "Then get really really lucky" such as plans that count on natural twenties, rolling more successes than you have dice, or other such examples.) It is still a good answer, there are other good answers, and this one may or may not work. Thus, it is not overpowered.

If something works perfectly, but could only work once, then it probably is not overpowered, but might be depending on how important the question is. "Q. How do you get in to the castle? A. Use the Scroll of Invisibility, which makes us invisible once" is probably okay, because that question was probably not extremely important, there was probably another way to answer the question, and that answer would only work once. On the other hand, "Q. How do you get in to the castle? A. Use the Ring of Invisibility, which makes us invisible as many times as we want" is probably a case of something being overpowered, because this answer will work perfectly to a lot of questions.

To summarize-

  • Is this answer specific? One particular tactic, weapon, or spell.

  • Is this answer a valid answer to important questions?

  • Are there several answers equally valid?

  • Do we know that this answer will work when used, or is there a reasonable chance it will fail?

  • Can this answer work on a large range of questions as many times as we need?

Anything that gets a yes on three of the five above questions is possibly overpowered.

Anything that gets a yes on four is probably overpowered.

Anything that gets a yes on all five is certainly overpowered.

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+1 for tying the overpoweredness of a Thing to the number and variety of situations that Thing is capable of overcoming, doing so in a way that is can be applied by any group, and for providing an easy-to-use mechanism for applying the metric to any game. –  GMJoe Feb 20 '13 at 7:14
    
I am... thoroughly out of my league academically. I've read Prof. Ballsun-Stanton's papers before so I thought I had a handle on the terminology, and I still needed to spend a few hours on simple wikipedia to follow some of the answers to this question. The fact that I went directly from simple wiki to giving my own answer is probably more than apparent. –  IgneusJotunn Feb 20 '13 at 14:17
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