The Atomic Theory of RPGs

Foreground: Image by slightly_different from Pixabay, editing and compositing by Mike;
Background: Bubble Chamber event captured Dec-16-1958 by the US Department Of Energy, courtesy the National Archives at College Park – Still Pictures, Public domain, via Wikimedia Commons; distorted and colorized by Mike.
When I studied Chemistry in Secondary School (which, when I started, was known more commonly as “High School”), we started with the Dalton Model of Atomic Structure, of atoms as fundamental units of matter that could not be subdivided, and then moved on to the Thompson “Plum Pudding” model.
In essence, this describes a negatively-charged pudding with positively-charged raisins floating in it.
We then moved on to the Bohr “Solar Atom” structure, before being presented with a glimpse of the more complex world that was still being deciphered at the time.
This approach was chosen because it established that everything we were being taught was a generalization and an approximation, a tool that was useful for understanding the essentials of Atomic structure as it pertained to chemical reactions.
My first year university course in the subject basically trod the same ground, though it covered it a lot faster.
Even today, the “Solar Atom” provides a gentle introduction to the chemical world, even though we know better – we know that electrons are quantum energy fields that collapse into particles when observed, particles that occupy energy states that match the ‘electron shells’ or ‘orbits’ of the Bohr model (noting that my understanding of these things is way out of date, and that I have simplified outrageously), and that quantum theory explains why the innermost shell can only hold 2 electrons (at most), and so on – all assumptions that simply had to be taken for granted by the simpler model.
I’ve always found it useful to occasionally strip and coalesce phenomena into its simplest possible structure, even though that structure is impossibly oversimplified. It then becomes possible to introduce the complications of reality, one at a time, and gain a greater understanding of why they are, and how they interrelate.
The other day, I idly wondered, ‘why not do that for RPGs and see what can be learned?’ – and so, this article was born.
The Atomic RPG
What is the absolute simplest RPG model that you can think of?
Try this: one stat, for how effective a character is. You state what you want to try and do, and roll against this stat, and if you succeed in the roll, your character succeeds in his action.
This is the “monotomic hydrogen” of RPGs. The stat is the solitary proton, the electron is the die roll (a virtual thing that actually exists in all possible results until you actually roll a die and read off a result), and the description of intended action are the electron shells that contain the die roll and give it significance.
Combat mechanics
Let’s think about combat with this ultra-simple RPG. There are all sorts of models that could be used, but perhaps the simplest is the one from the Hero System: You have the average result as a threshold of success, and the difference in “ability” (attacker minus defender) increases or decreases that threshold. Roll under the net threshold, and you succeed.
Hold up – we need some way of tracking damage, don’t we? The simplest possible mechanism is a fixed unit of damage, but increased sophistication and chance would result from using a die roll – say a d6. If you get hit, you lose a d6 in temporary reduction to your one and only stat.
That immediately produces an interesting and rare dynamic in which an initial failure can cascade through subsequent rounds until it results in victory; it literally gets progressively easier to win a fight. But luck can only go so far; if there’s a big enough differential between the combatant’s ability scores, luck has to start going your way over two or three or even more rounds or you quickly become shish kabob.
The Helium RPG
Helium adds a second proton and a second electron, and needs to add some neutrons to hold it all together. I’m leery of pushing the analogy too far, but let’s push on and see how we go.
Instead of one stat, we now have two, and some form of differentiation in definitions. The most obvious one is to separate the character’s abilities into physical and mental prowess. This lets us track these independently
At this point, if you were to add both stats together, they would always have to total the same number, because we have no mechanism for variation. A character could be good physically, or good mentally, or some sort of compromise between the two.
So far, so good, but as soon as we do this, we need some guidelines for the GM to use in deciding which stat to use, and that’s our first Neutron.
We need to think about Smart vs Smart contests, and relegate our previous “combat” structure to Brawn vs Brawn contests. Each of these needs to be defined, and we have to think about the resulting damage and what it means. There has to be an analysis of Smart vs Brawn, and if that can ever happen, and what it means. Those complexities are the second Neutron – essential mechanics to hold the whole thing together and control the interactions.
The complexity of our model has suddenly shot way up.
Atomic Number Rising
The number of protons in an Atom defines its Atomic Number. this is a convenient indexing of elements, it doesn’t mean much more than that – at first glance.
But each positive charge in the nucleus needs to be balanced by a negative charge, and so we add more electrons, and have to start worrying about how they pack, and energy being pumped in to increase an electron’s ‘orbit’, which it then yields as a photon. And an interesting pattern begins to emerge.
The second electron shell can hold 8 electrons, and if we add those (one at a time) to match the increasing atomic number, we get the basic structures of Lithium, Beryllium, Boron, Carbon, Nitrogen, Oxygen, Fluorine, and Neon. The third shell can also hold eight electrons, and that gives us Sodium, Magnesium, Aluminium, Silicon, Phosphorous, Sulfur, Chlorine, and Argon.
Whoops – except that this third shell can actually hold 18 electrons, but there are configurations involving electrons in the fourth shell that are more stable. So the next two elements, Potassium and Calcium, both add their extras into that fourth layer. Once there’s a pair of electrons there, the next bunch of elements all add to the third layer again, until it gets up to 16. When we add one more after that, to take us to 17, one of the outermost 2 electrons finds its way into the third shell, so that the pattern runs 2/8/16/2, 2/8/18/1, 2/8/18/2, 2/8/18/3, and so on. Things continue on from there until we get to 2/8/18/8, Argon.
If you line the elements up in a table so that the number of vacant spots in the outermost shells line up, clear patterns of chemical properties begin to show up. In fact, this table structure was first noted from those patterns of properties, and later explained by electron configurations. So strong are these patterns that they were successfully used to predict then-unknown elements and their properties – chemists then went looking for, and found, these hitherto-unknown elements. The number of empty spots also matters – a lot – to the chemical reactions that these elements prefer to undergo.
When you align the elements according to these patterns of electron configurations and similarity of properties, the resulting table is something most of us will find familiar – the Periodic Table of the Elements.

Image by User:Double sharp, based on File:Simple Periodic Table Chart-en.svg by User:Offnfopt – Own work, CC BY-SA 4.0, Link, background added by Mike. Click on this image for a larger version in a new tab.
The above depiction shows the elements up to Atomic Number 118, and all of them have been either found in nature or synthesized in an atomic laboratory. Wikipedia’s article (from which it derives) has an excellent description of the structure of the table, which I don’t think I can improve on:
The table is divided into four roughly rectangular areas called blocks. The rows of the table are called periods, and the columns are called groups. Elements from the same column group of the periodic table show similar chemical characteristics. Trends run through the periodic table, with nonmetallic character (keeping their own electrons) increasing from left to right across a period, and from down to up across a group, and metallic character (surrendering electrons to other atoms) increasing in the opposite direction. The underlying reason for these trends is electron configurations of atoms.
I would add that there are also trends down groups concerning melting points, boiling points, electrical conductivity, densities, and more.
The RPG Analogy
We can subdivide our two stats as much as we want. It’s common, for example, to subdivide the mental stat into two or three, one dealing with learned knowledge and the capacity to learn more, and the other either representing spirit, willpower & determination, or wisdom, or empathy; and it’s common for the ‘brawn’ stat to be subdivided into measures of strength, physical health and robustness, dexterity and/or agility and/or nimbleness, and possibly a third branch dealing with attractiveness. Some systems add still more stats.
If we accept the analogy that the simplest breakup (brawn and brain) corresponds to the innermost electron shell, then all these stats represent additional electrons in a new, outer layer. Most RPGs have six or seven such sub-stats.
This shows exactly why these additional stats are defined – they are all parameters whose values differentiate one simulated individual from another. They enable an individual to be better than average in one respect while being poorer in a counter-balancing other respect.
That’s a very pernicious concept; once it is accepted, any area in which it is not the case suddenly comes under sharp scrutiny.
Species, Archetype, and Class
The second and third items in the heading are different words for essentially the same concept, but just so that we’re all on the same page, let’s toss out some broad definitions:
Species –
Genetic traits and abilities, even in a world that doesn’t understand genetics. Fundamental properties deriving from what a being is, not what they have studied / learned.
Archetype –
A profession or occupational description and the suite of standard capabilities that are assumed to come with it, in the most general sense. Often employed in discussions of the most general manner to describe the traits common to all who are exemplars of the archetype.
Class –
Some game systems codify archetypes into specific character classes. Pretty much everything said of archetypes can be applied to character classes and vice-versa.
With that out of the way, let’s fit them into our atomic model. Conceptually, this can be done in several different ways, but given that specific expertises and abilities are defined by these choices as ways of simulating the overarching characteristic, that makes them most analogous to ‘just another stat’ in our model.
For example, a species of “Elf” will carry with it certain assumptions that distinguish it from all other species. Those assumptions – the ‘species profile’ – will find expression through the game mechanics as abilities and traits unique to an “Elf”. The same is true of a character class, such as “Wizard”, or an archetype such as “Muscle-man” (more often referred to by the generic term “Brick”).
The Skills Story
Right now, the knowledge stat (or whatever is serving in that capacity) defines the character’s capabilities in every sphere of knowledge. His strength stat (or whatever is serving in that respect) defines the character’s capabilities in every type of physical act, save those in which some other stat (Acrobatics, Dexterity, or whatever) is a more accurate choice. Normally, anything involving speed of reflexes, speed of motion, or finesse of motion, comes under that umbrella rather than raw strength, for example, and so on.
As soon as you differentiate statistics into multiple parameters, this becomes not only hypocritical but counterproductive. That’s because the purpose of our simulation has shifted – rather than being an abstract representation, we are now engaged in attempting to simulate a more rounded individual in the form of the designated parameters of the game system.
The obvious solution is to implement some sort of skills system in which no individual can possibly know it all. But this brings in a whole new group of assumptions about how the mechanics will work, and at this point we have minimal guidance on which to base solutions.
Fortunately, that minimal guidance is directly relevant and easily analogous. We defined an attack as the value of an offensive characteristic plus an average roll less the defensive characteristic of the target, because that was the simplest way of integrating all those elements. All we need to do is determine some analogous values and a basic set of game mechanics pops out the other side.
A skill use is the value of that skill plus an average roll less the difficulty of the task being attempted.
But this represents a further refinement again of the purpose of the game mechanics – we have just shifted from attempting to simulate a rounded individual through designated character parameters, to attempting to simulate a rounded but flawed and incomplete individual through designated character parameters.
Attack Rolls & Defensive Capability
Individuals don’t remain static. They get better at some things with training and education, they get better at most things with practice and experience, and they get worse at many things as they age and become more infirm – but might also get worse as their physical condition changes.
That’s inherent in the very concept of Skills. And it forces a reappraisal of some of the things that we had thought settled. In particular, our combat mechanics.
Attack Rolls
It no longer seems reasonable that a character’s attack roll remains static throughout his or her lifetime. If you can improve skills through education and training, you can improve other parameters. In particular, attack rolls and the character’s defensive capability.
Attack Rolls, first. If we uncouple these from direct relationship with the value of a stat, we can treat different weapons, or classes of weapons, as skills, and we can increase or decrease these independently of the root parameter measurement. It’s not just how strong you are, anymore; now it’s about how well you use that Strength.
That means that your attack roll can and should start considerably depreciated, and increase with time and expertise to become considerably better than the raw stat alone.
Defensive Capability
Next, defensive capability. Should that keep pace with the improving attack capability? This is not quite as simple a question as it first appears; the PCs are supposed to be exceptional individuals, and a player has invested some degree of effort in creating one of them. That always argues yes, in fact it argues that defensive capability should slowly outstrip the offensive ability.
But if you do that, the PCs will find it harder to succeed against anyone even a little bit better than they are, which makes adventures more fraught.
What’s more, because there will be multiple attempted attacks in any combat, any small imbalance will be geometrically magnified.
Single Attacks vs Maneuver Chains
And that brings in yet another consideration: does an attack roll represent a single blow (which will make combats last a long time) or is there some sort of time compression involved, with each attack representing an entire string of maneuvers?
Balancing these disparate considerations is most easily accomplished by divorcing the capacity for absorbing damage from being directly tied to the representative parameters. Assuming that time compression is mandated for playability reasons, we need to apply whatever the compression factor is to the capacity to absorb damage, either by deflecting it with defensive capabilities or by creating a semi-independent measure of this parameter – hit points.
The Hero system uses the “one action, one roll, deductions from damage done, no time compression” approach. D&D uses the “one roll, one string of actions, with time compression” approach, and compensates by increasing hit points with each progression in overall capability. Instead of deducting damage from most attacks, it also applies compression to the value of an individual hit point so that damage represents a cumulative impact of one or more successful blows, and applies a generous layer of abstraction.
It should now be noted that while we have an allowance for adverse or beneficial circumstances in our skill use, there is no such allowance in the combat mechanism. It’s easy enough to implement one, simply by applying a modifier to the attack roll.
Weapon Differentiation
But that opens the door to a new concept: weapon differentiation. Not all weapons are alike – some may strike more easily but more slowly; others my strike more heavily but compromise one or both of these parameters. These considerations can easily be addressed now that we have abstracted damage capacity, because that lets us abstract the damage done, as well. In fact, we can inflate or compress scales of hit points as desired to land us in a sweet spot in terms of weapon differentiation.
The latter is far easier to balance, but the actual choice doesn’t matter too much in this broad analysis.
What is more important is that a choice – weapon employed – brings with it a set of specifics within the game mechanics. Depending on the degree of abstraction in the game mechanics, there may be only one or two of these, or there may be a half-a-dozen or more.
Again, the specifics are just values that are held by the variables that go into character description within the game mechanics; so these are “protons’ within our RPG ‘solar atom’ just like anything else, and the mechanics that interpret the values are the corresponding neutrons, while the mechanism of actually collapsing a set of theoretical interpretations into a specific value are analogous to electrons in our model.
Radioactivity
Before I get onto the subject of applying these theoretical concepts to practical purposes, there’s one more analogy that emerges as an extension to this model.
When an atomic nucleus grows too large, it becomes unstable, prone to shedding parts of itself as particles and – in the process – becoming some simpler element. We describe this property as ‘radioactivity’. Continue to add to the atomic mass and cataclysmic failure becomes not only possible but an eventual inevitability.
As a child, too smart perhaps for my own good, I formulated the proposition that since Iron was the end-point of all nuclear processes (an oversimplification), it could be suggested that every atom higher on the periodic table could be considered radioactive; it was just that the isotopes and elements that we consider ‘stable’ within this range have such lengthy decay rates that we don’t notice the decay.
I have no idea of the relationship between this premise and reality, and don’t care (for the purposes of this discussion); the point is that the same thing happens if rules systems become too complex. Arguably, my Zenith-3 rules lie some distance above the critical threshold, but by focusing attention on one subsystem at a time, the whole is just barely manageable. So it’s not the equivalent of Plutonium, or anything higher on the atomic table – but it might be Lead, or Mercury, or (my personal choice), Gold.
Why is all this important?
Aside from codifying the relationship between these elements of game mechanics as applied to actual play, there’s a symbolic relevance that should not be neglected.
The nucleus – the ‘proton elements’ and the ‘neutron infrastructure’ that supports them in matched pairs – define individual characters within a game system. The ‘electrons’ – again paired with the protons – represent the capacity of those character-defining elements to interact with anything else, and in particular, to interact with other characters.
This is the precise relationship of atomic structure within the chemical elements with the chemical reactions that make up the natural world. So this model – though it proved insufficient in chemistry – informs us as to some general principles in game design that are easily overlooked, and those have practical application.
Matched Pairs
You have to consider the characteristics that describe a character, including things like species and character class, as inseparably bound to a set of mechanics that interpret the traits of the specific values those characteristics can contain.
Because it’s our tendency to collect those interpretations and then sort and separate them into collective properties – putting all the weapons into a single table, for example – this truth can sometimes get obscured.
This obfuscation means that people think they can change one part of the game mechanics without impacting on characters and character balance. The reality shows that it is impossible to make such a change without fundamentally affecting actual characters, for good or ill. Those effects can be subtle, or grossly overt.
Similarly, you can’t change a characteristic without altering both the supporting game mechanics AND the way those mechanics interact with other characters and/or the reality external to the character.
I’ve lost count of the number of times I’ve seen game mechanics proposals that looked fine on paper, but that failed abysmally when put into actual practice. Some of these mistakes were mine – see, for example, My Biggest Mistakes: The Woes Of Piety and Magic – some belonged to others.
If you understand the relationship between these game design components, you can at least know where to start to look for unwanted consequences, and have at least a shot at understanding why the game mechanics of which you were so proud have collapsed into a screaming heap – and what to do about it.
The Door To Options
But that’s not the only, or even the most powerful application of this analogy, useful though it is; even more significant is this – it gathers under the one umbrella, all the ways in which characters can interact with anything external to them (including die rolls for things like understanding of the game world).
While, at first glance, it might seem that all these potential interactions are viable, the reality is that some combinations need to be forced into combination; they aren’t ‘natural’. Other combinations are more relevant, and describe some aspect of the game reality that you might find useful.
These can be obvious – STR vs STR, for example, or an Attack Role vs DEX to attempt to hit a character performing some acrobatic maneuver – or more subtle.
“He’s trying to grab me by the shoulders? I want to twist so that he gets a handful of cloak, enabling me to simply divest myself of it and roll to one side, but I want it to look accidental so that he doesn’t actively resist.”
You could simulate that as a DEX (motion) vs STR (grip), but that would be fairly obvious. If you want a motion to look accidental, it might be more appropriate to use CHAR (the perception of the character and their actions by others) vs STR (grip). You might decide not to go this way; but at least you will have considered the available alternatives, including those that might not have occurred to you otherwise.
This can be a way of taking the spotlight from one of the combat monsters and momentarily shifting it to a character that normally wouldn’t get such attention, simply by specifying that this is the avenue of advancing the plot that is preferred from a plot perspective.
Comprehension is the bonus
Ultimately, this analogy captures aspects of game design and function, calling attention to inobvious parts of the system, and giving the GM a greater range of options and a deeper understanding of the game system being used. That potentially makes you a better GM – not instantly, but the potential is there, if you work on it. This is a road map to such enlightenment, not a set of Cliff’s Notes.
And don’t forget how the functional purpose of the game mechanics changed as the contents became more complex. That gives you a tool for the analysis of new game systems that you might encounter ‘in the wild’.
You can’t ask a lot more of an abstract representation than all that!
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