Concept Driven Character Creation

I spent a long time pondering how best to present the process of creating a character in Explore; simple practical steps that would allow you to quickly create a character you were happy with. Although it seems simple enough - allocate the bonuses to your attributes and spend points on skills - they are interlinked decisions. Of particular importance is this: the first time you create a character it should be an opportunity to learn how the game works, it should not be necessary to first gain an in-depth knowledge of the rules to make sensible decisions.

In the end I realised that not only did I have three fundamentally different approaches to creating a character - further it is actually desirable to have different methods. None of these is a "better method" than the others, and I like all three for different reasons.

Method A: Attribute First

This is the "purest" method. You create a raw, untrained character that matches your concept, and then develop them with skills you feel appropriate.

Choose three attributes which describe your character well (e.g. "tall", "athletic", "intuitive" ) and three which the opposite describes your character well (e.g. "slight", "poor memory", no "soul").

This should be a reasonable start for a description of your character.

Put a bonus of 2 in the attributes which described your character well, 0 in those where the opposite was true, and 1 in the remainder.

For example the character described above gets:

Height	2	Dexterity	1	Intuition	2
Build	0	Coordination	1	Memory	0
Athletic	2	Quickness	1	Empathy	1
Toughness	1	Perception	1	Soul	0

From this fill in you character sheet to see what bonuses your character has in different skills. This should confirm that your character has a natural advantage in the skills and saves you would expect from your character description. If not, then revisit your choices (or fix the rules!)

In our example we have:
+4: Muscle:Kill, Muscle:Lift, Melee, Unarmed, Thrown, Bows, [Parry], Muscle:Acrobatics, Muscle:Run, Thief, Scout, [Artefacts]
+3: [Body], Muscle:Sprint, Wilderness, Ride, [Directed Spells], [Observation], Language, Lore, [Detect Magic]
+2: Healer, [Psychic Attack], Music, Art, Dancing, [Runes], Craft
+1: [Psychic Defence]

Note for purposes of spending points on skills note that you don't spend points on the items in [brackets] - these are skills you get for free. Also note the various Muscle: items are all aspects of a single skill "Muscle" - you spend points on Muscle and then decide which aspects of Muscle to improve (power, speed or acrobatics).

Next, as your character, choose what skills you want to learn. You may want to improve weak areas, or concentrate on things you're naturally good at.

Our character has a clear non-magical inclination. They have quite a broad range of skills at +4, and looking at their +4 in kills and bows but only +3 in body decide to concentrate not on straight-up combat but a more sneaky approach, taking as main skills scout, bows, & muscle (for kill).

Method C: Class First

This is the most traditional method and the easiest to understand. You select a standard character class which comes with a standard set of abilities, and advice on how to distribute the attribute bonuses.

Select a class you wish to play. Each class advises which attributes are important for that class, and which are unimportant. Put your 2s in three of the important attributes, 0s in three of the unimportant attributes.

For example, a Warrior's primary focus is Melee fighting. Hence their primary four skills are Melee, Kill, Parry, and Body. All four are of equal importance and use attributes CQI, HBA, CQA, HBT. Height, Build, Athletics, Coordination and Quickness all give bonuses to two skills. Intuition helps with Observation, and Toughness helps with Psychic Defence - both also key skills for a warrior. Hence the description of the Warrior class lists as important attributes Height, Build, Toughness, Athletics, Coordination, Quickness, and Intuition.

In contrast Dexterity, Memory, Empathy and Soul give bonuses to few useful skills, so these are listed as the least important attributes.

We choose Height, Build, and Quickness to be +2, and Dexterity, Memory and Empathy to be 0; the rest are 0.

When the character sheet is completed this gives us: (with relevant skills for a Warrior in bold).
+5: Muscle:Kill, Body, Muscle:Lift, Muscle:Sprint
+4: Melee, Unarmed, [Parry], Muscle:Run, Muscle:Acrobatics, Dancing
+3: Ride, Scout, Bows, Thrown, [Detect Magic], [Directed Spells]
+2: [Observation], [Psychic Defence], Thief, Wilderness, Art, Lore, [Psychic Attack], [Runes]
+1: Music, Language, Healer

Method S: Skills First

This is the most complicated method, one which is focused on getting the best bonuses for your character.

Select two or three key skills you want your character to be good at, then place the +2 bonuses in your attributes one at a time, selecting them to maximise your key skills, filling in these bonuses against the relevant skills. When you have placed all your +2 bonuses, place your +1s to complete your key skills, and then use the remaining +1s to ensure a balanced character, or place your 0s in attributes you won't benefit from. In this method you often switch around where your bonuses are several times to create the character you desire.

For example we want our character to be good at Scout, Bows and Muscle:Kill. (Bows to hit the target, Kill for the strength to shoot a strong bow). That means the key attributes are CPI, DPI, and HBA. We only have three +2s to spread out, so we put them in Perception, Intuition (both shared with Scout and Bows) and save one for Muscle:Kill. Since Athletics gives us a bonus also on Parry we put our last +2 there. To keep a good bonus in each of these four skills we don't want to then put a 0 in HBCDQ - which only leaves Toughness, Memory, Empathy and Soul. We don't want Body of less than 3 (the average) so opt to put the zeros in MES.

This gives the following bonuses:

+5: Bows, Scout, Thief, Thrown
+4: Muscle:Kill, [Parry], [Observation], Melee, Wilderness, Unarmed, Muscle:Lift, Muscle:Acrobatics, Muscle:Sprint, Muscle:Run, [Psychic Attack], [Detect Magic], Lore
+3: [Body], Healer, Art
+2: Ride, [Directed Spells], [Runes], Dancing, Language
+1: [Psychic Defence], Music

We buy rank 3 in Bows, Scout and Muscle (3*4=12 points), rank 2 in Melee (2 points), and rank 1 in Thief and Wilderness (total 16 points = level 1).
We don't bother spending any points on Thrown, despite our natural ability in it.
We get some of the skills in brackets for free - we get rank 1 in Body and Psychic Defence (as we're 16 points = level 1), rank 4 in Parry (for the 10 points spent on Bows, Muscle and Melee), rank 3 in Observation (for the 6 points spent on Scout, Thief and Wilderness).
We don't get any ranks in Runes, Detect Magic, Psychic Attack or Directed Spells as we've not spent points on spells.

We also get some points to spend on the "secondary skills" - Lore, Art, Dancing, Language, Music. These should probably be in another font to show they're different.

Note that this character has no +6s and no +0s - it is not what you would expect from a Min/Max character optimisation. Also they have ended up with a weak spot - only a +1 in Psychic Defence. There is no "best" allocation of points - which should mean you avoid cookie cutter characters despite the lack of random attribute generation.

Summary

As you can see, both Attributes or Class first are simple enough systems. Make some simple decisions and copy the numbers on to the character sheet and you're done.

The Skills first system requires you to understand the system, so is difficult to explain directly, but once you have done either of the other two systems a couple of times you should understand how the system works and anyone could do Skills first. I find that after I have created a character via this method I tinker a bit with swapping attributes about to get the best fit, and I think that's probably helped by having a trivial spreadsheet (or online form) so you can quickly play around with different choices and see the effect.

For the completed rules I'm planning on one chapter being entirely about creating class based characters using the Class first Method (i.e. a step by step creation process), then a second about creating skill based characters starting with the Attributes first Method, then a brief explanation about the Skills first Method.

Probably that's the next thing I should be working on - the two chapters on creating a character in a logical order.

Attributes and Related Skills

So, here it is - my new attribute system that I'm sad to say has taken me the last five months to get into shape.

Overview

Attributes are broad brush bonuses to represent aspects of your character to give consistent characters. Aspects of your character which you role play (problem solving, personality / conversations) are not covered by attributes, nor are physical attractiveness or luck.

Each attribute is a bonus of 0,1,2 and three attributes bonuses apply to each skill, giving each skill a bonus between 0 and 6.

Related Skills

Attribute bonuses tell you something specific about the character, and have little or no overlap. In contrast, because related skills share some (or all) attributes, related skills have similar bonuses.

The following diagram shows which skills share two or more attributes, and hence which have similar bonuses:

For example, Thown and Scout share all three attributes, so share a box. These skills have the same bonus.
Healer, Bows, Thief and Art all share (Manual) Dexterity and Perception, so are joined by lines going to a circle marked "DP". These skills have bonus within 2 points of each other. (I'm amused that Artists and Thieves are closely related!)

This diagram allows you to not only to spot related skills, but to spot skills that should be related (but aren't) or skills that are related (but shouldn't be). This allowed me to spot flaws in the system and hence refine it. Note that all skills are related to at least one other skill.

This is an evolution of the previous system where Kill & Lift were linked to Body because the first pair using STR whereas Body used CON which was a linked attribute. If I drew a related skill diagram for the previous system however it would be extremely sparse and simplistic.

The Attributes

Height (Tall/Short)

Being taller also makes you heavier and thus stronger and resilient.

Build (Broad/Slight)
Being broad makes you heavier and thus stronger and resilient.

Athletic
This makes you stronger, but not heavier, thus improving your power-to-weight ratio.

Toughness
Includes endurance / stamina, and resilience to damage or poison.

Dexterity
This is manual dexterity - coordinated finger and hand movements.

Coordination
The ability to move the body smoothly in a controlled fashion. It includes balance, hand-eye co-ordination, and proprioception.

Quickness
The ability to make the body respond and move quickly (but not necessarily with any power behind it).

Perception
The ability to notice things with the senses - for example judge how far it is to the tree, or how windy it is, or to notice a damp patch on the floor - but not to infer anything from them.

Intuition
The ability to make inferences without conscious logical thought - for example to draw conclusions from your perceptions as to what is important.

Memory
The ability to learn and recall knowledge. Note that most skills require you to remember things - memory only helps skills which require large amounts of memorising.

Empathy
The ability to understand and interpret the feelings of others. It has a supernatural side, similar to sensing someone's aura.

Soul
This is both the artistic soul, and the magical soul.

Attribute Bonuses

Which attributes apply to each skill and save is described below, along with an explanation of why the attribute applies. This should clarify further what the attributes mean.

Note that two combinations of attributes are repeated several times:

- Coordination + Quickness combined form overall Agility.

- All ranged attacks (thrown / bows / directed spells) use  Perception (for sensing the target), and Intuition (for judgements such as the distance to the target)

Note that in some cases the attribute helps in learning the skill which thus indirectly helps in performing the activity. Similarly if the attribute mostly helps then that positive reinforcement helps you improve at the skill which makes you better in general.

Runes
Soul (to sense the magic in the runes), Memory (to remember Rune Lore), Intuition (to apply the rune lore).

Detect Magic
Soul (to sense the magical aura), Perception (to sense the physical manifestations of the magic), Intuition (to sift through the sensory information and determine what is magical).

Dancing
Soul (for artistic performance), Coordination and Quickness (for overall agility).

Art (Painting / Sculpture)
Soul (for artistic ability), Perception (for seeing the world), Dexterity (for handling the tools).

Music (by Instrument)
Soul (for artistic performance), Empathy (for a performance with feeling), Dexterity (to play fast / complex music).

Lore (by Subject)
Memory (to remember the lore), Perception (to examine things - both when learning and when applying the lore), Intuition (to apply the lore).

Language

Memory (to remember the words/grammar etc), Intuition (to apply it in unfamiliar situations, to improve), Empathy (picking up emotional signals helps communication).

Observation
Perception (to notice things), Intuition (to sift through what you notice to spot relevant things or draw inferences), Memory (to remember what things should look like and thus spot inconsistencies, or simply to recall prior hiding places).

Directed Spells
Soul (for controlling the magic), Perception + Intuition (for ranged attack).

Psychic Defence
Soul (for sensing the attack magically), Toughness (for resisting the attack physically), Memory (for resisting the attack mentally).

Psychic Attack
Soul (for controlling the magic), Perception (for sensing the target physically), Empathy (for sensing the target mentally).

Ride
Coordination and Quickness (for the required physical agility), Empathy (for connecting emotionally with the mount).

Healer
Perception (to correctly perceive the problem), Memory (to remember what to look for and what to do), Dexterity (to fix the problem).

Scout (Sneak / Hide)
Perception (to spot the squeaky floorboard), Intuition (to work out where to stand so you remain in shadow), and Coordination (to step over the squeaky floorboard carefully).

Thief (Pick lock / disarm trap / pick pockets)
Perception (to examine the trap/lock carefully), Intuition (to work out how to disarm this particular trap), and Dexterity (to disarm it with steady hands).

Wilderness (Navigate / track / survival / snares / forage)

Perception (to notice the tracks), Intuition (to judge where to look when the tracks vanish), Memory (to remember what animal makes those tracks). Wilderness is highly related to Observation but here the Memory bonus is recalling all the miscellaneous facts / sights / sounds / smells of the wilderness.

Run

Athletics (for power-to-weight ratio), Toughness (for endurance - being able to maintain the speed), Quickness (for speed of movement of limbs).

Sprint

Athletics (for power-to-weight ratio), Build (for muscle bulk for an explosive acceleration), Quickness (for speed of movement of limbs).

Acrobatics

Athletics (for power-to-weight ratio), Coordination + Quickness (for overall agility).

Parry / Dodge

Coordination + Quickness (for agility), Athletics either as per Acrobatics (for Dodge) or for blocking the blow (for Parry).

Bows

Perception + Intuition (for ranged attack), Dexterity (for accurate controlled releasing of the bow).

Thrown

Perception + Intuition (for ranged attack), Coordination (for accurate throwing motion).

Melee & Unarmed
Coordination + Quickness (for agility), Intuition (for selecting the best attack opportunity).

Body
Height + Build (for pure bulk), Toughness (for resistance to damage).

Kill & Lift
Height + Build (for strength from bulk), Athletics (for power-to-weight ratio).

Note that all attributes give a bonus to at least one offensive or defensive capability. Out of the four bonuses you can get in combat - on attack, damage, dodge, and body - attributes give bonuses to at most two of these.

Next post I'll talk about how you go about determining your attribute bonuses to shape the character you want.

Struggling with Attributes

Moving Away From The Big 6*3d6

In Explore I’ve gone through several iterations of attributes, moving further and further away from the traditional big six with 3d6.

Originally I started with the big six but wanted more balanced attributes without resorting to the usual solutions of escalating scores / point buy acrobatics / cookie-cutter stat arrays – I used this method to randomly generate six values 3-18 via 3d6 which always add up to 63 whilst keeping the same distribution as 3D6.

The next iteration was to replace the mental attributes (INT, WIS and CHR) with Memory and Intuition, so as to remove Logic and Personality attributes to make those issues purely down to roleplaying – and to split DEX into Agility and Reflexes.

Next I wanted some correlation between related stats. That’s tricky to resolve, but dropping the 3-18 and instead working only with the bonuses -3 to +3 made it possible. (It was a shame to lose the balanced 3D6 system though). I arranged the attributes in pairs – Strength/Constitution, Agility/Reflexes, Memory/Intuition – where the total sum of bonuses is 0, and each pair differs by no more than 2. Thus if you have STR 1 you cannot have a CON of -2 or -3. This was generated via rolling two D% and using this lookup table.

Using this system I then derived Height and Weight from the stats, which also gave me the consistency between the physical character and their stats.

This is the version I’ve used for the last two years. It works reasonably well, and creates varied, balanced and consistent characters. However when considering Climbing, which is about power-to-weight ratio, I encountered difficulties - when I put the numbers together something wasn't making sense. At this point I realised that if in the real world Height and Weight influence Strength, it would be simpler if it worked that way round in the game.

Taking a step back I bit the bullet and stopped blogging the revised rules, and decided to allow myself to follow any train of thought without worrying about the consequences, to see what I could come up with. Not for the first time I was glad I don't have a Kickstarter to complete!

Sacred Cows

Freed up to consider anything this quickly lead to the germination of a new system, but finalising it to something I'm happy with has been something I’ve been wrestling with on and off for the last five months. As you’ll see, mechanically it is only a slight evolution of the previous system, but the approach is very different. In particular it keeps the key benefit of the previous system - closely related skills still have bonuses which can differ by no more than 2 - and doesn't require any alterations to the rest of the rules (aside from a couple of +3s added to target numbers). In fact, apart from making character creation simpler and more transparent, it doesn't really impact on gameplay.

In the process I’ve ended up with a lot more attributes – something which I’ve previously been quite opposed to – but the reasons behind my opposition to that have evaporated. In addition I’ve removed randomness from character generation – something I’ve had in since day one. Both of these were a bit of a sacred cow, but it was making character creation difficult.

My goals are:

• Attributes are broad brush bonuses to represent aspects of your character to give consistent characters.
• Aspects of your character which you role play (problem solving and conversations) are not covered by attributes.
• I want clarity of what an attribute bonus means – it should tell me something specific about the character.
• I would like you to be able to choose attribute bonuses based upon what you would like your character to be like - that is without having to make dissociated decisions* during character creation.
• There should be as small an overlap between attributes as possible.
• It should be reasonably clear which attributes should give bonuses to skills.
• I want to keep the same size range for bonuses to skills from attributes – seven steps from worst to best – as that has worked well so far.
• I want only bonuses not penalties – my group was particularly enthusiastic about this change, despite it being only psychological.
• It should be possible to excel at activities by having bonuses in different attributes. For example, you can be strong by being tall, or by being well built, or muscled.
• The skills which have similar bonuses due to taking bonuses from similar attributes should be plausible. For example, acrobatics should be strongly linked to dancing, but not to lock picking.

In some respects it now resembles Rolemaster – which was a surprise as I'm a refugee from Rolemaster – and Size is of course an attribute in Runequest. Nothing is new under the sun – but every journey is different. On the other hand it still strongly resembles the prior system - strongly related skills (those sharing two out of three attributes) can only defer by at most 2 - exactly as before - but this "related skills" concept is now quite wide-ranging.

In the next post I'll unveil the attributes and what skills they apply to, and illustrate with a nifty diagram how I found problems and refined them away (well, I like it anyway!).

*It is often claimed that all character creation is dissociated - what I mean by dissociated character creation is the common situation where you make a choice about an aspect of the character purely based upon the mechanical effectiveness of the choice in the game rules, rather than your character concept.

Fairness of Dice Modifiers and Advantage / Disadvantage

In discussions on Delta's post on Advantage and Disadvantage the question arose about the merits of percentage increases versus percentage point increases in probabilities and which is the more important consideration. I'm going to compare a few systems to see the effect of modifiers on the results and explain in the process why I place such importance on the proportional increase of probabilities. At the end I'll cover Advantage / Disadvantage and I'm surprised by the findings.

Comparing Linear and Bell Curves

Firstly I'll compare a linear system versus a bell-curve system and analyse what the differences are - so I'll choose D% for the linear system, and 3D6 for the bell-curve system.

If you need 51+ on the D% system, or 11+ on the 3D6 system, then in both cases you have a precisely 50% chance on success. It makes no difference to the outcome which system you used. In fact, for any target number you need on the 3D6 there is an almost exact equivalent target number on the D% system. Hence in this first analysis it makes no difference to the outcome - the only difference is:

The chance of making a target number is clear in a linear system, and obscure in a bell-curve system.

In this first respect the bell-curve system has no advantage. However, people maintain that a bell-curve system is better because it more accurately models the real world, where things typically have normal distributions. In many things, such as the heights of humans, this is obviously true. But we're not actually considering the distribution of 100 arrows shot at a target, we're considering what proportion of them hit the target. Hence what matters is how we determine the target number for hitting the target. In both systems (linear and bell-curve) it is traditional to have a standard target number which is modified by bonuses or penalties for skill level and conditions. Hence the question becomes, when we give a bonus in the two different systems, is there a different effect?

Most obviously:

Any bonus/penalty in a linear system has a clear effect on the outcome in any given situation, it can be obscure in a bell-curve system.

That is, if you need 41+ on a D% to hit something, and due to a +10 bonus it is now 31+ you can clearly see that you had a 60% chance of hitting, and now you have a 70% chance of hitting. In comparison say you needed 13+ on 3D6, you get a +1 bonus and you now only need a 12+. That's a 25.9% chance of success changed into a 37.5% chance of success - hardly clear.

What is a fair bonus / penalty?

The next observation is that bonuses in the linear system always change the chance of success by a fixed number of percentage points. Is this an advantage in itself? The main consequence is the clarity of the system, which we have already covered - but I don't see any other inherent advantage to it. That may seem to be a contrary position, so I'll explain myself.

For example, in a game mixing skill and luck I offer both players a 5% chance to win the game outright before they play. I roll a D20 and on a 1 player A wins outright, on a 20 player B wins outright, else they play the game. In this case they'd both get the same chance of winning from the die roll. But if one player is great at the game, the other a novice, then the great player will not accept the offer as it reduces his chances of winning. It is an equal 5% for both sides, but that statement does not make it a fair proposition.

Just as the bell-curve's normal distribution doesn't inherently make it better, to see advantages / disadvantages of the systems we should examine what effect they have on the results in the game (and I see no other way of determining it).

Let us consider two opponents in combat. Some situational modifier comes into play which either gives both sides an advantage, or both sides a disadvantage. The opponents would consider it "fair" if it affected both sides equally. What do I mean by that? Do I mean it increases their chances of hitting by the same percentage points, or do I mean it improves them proportionally the same amount? What I mean is that the effect can be considered "fair" if it has no effect on the outcome of the contest. A "fair" effect is one which both sides could agree to before the contest, an unfair effect is one which would give one side an unfair advantage.

Given this definition, a fair effect is one which does not alter the ratio of the average damage per round for the two combatants. That is, an effect which doubles the average damage caused by one combatant should also double the average damage caused by the other combatant for it to be considered fair. This is the same as saying a fair effect on the chance to hit is one which does not alter the ratio of the chances to hit for the two combatants.

Are modifiers for D% or 3D6 fair?

Firstly lets consider 3D6:

Target Needed	% Chance Hit	% Chance with +1 bonus	Multiplier on average damage / rnd	% Chance with -1 penalty	Multiplier on average damage / rnd
3	100.0%	100.0%	1.00	99.5%	1.00
4	99.5%	100.0%	1.00	98.1%	0.99
5	98.1%	99.5%	1.01	95.4%	0.97
6	95.4%	98.1%	1.03	90.7%	0.95
7	90.7%	95.4%	1.05	83.8%	0.92
8	83.8%	90.7%	1.08	74.1%	0.88
9	74.1%	83.8%	1.13	62.5%	0.84
10	62.5%	74.1%	1.19	50.0%	0.80
11	50.0%	62.5%	1.25	37.5%	0.75
12	37.5%	50.0%	1.33	25.9%	0.69
13	25.9%	37.5%	1.45	16.2%	0.63
14	16.2%	25.9%	1.60	9.3%	0.57
15	9.3%	16.2%	1.75	4.6%	0.50
16	4.6%	9.3%	2.00	1.9%	0.40
17	1.9%	4.6%	2.50	0.5%	0.25
18	0.5%	1.9%	4.00	0.0%	0.00

So +1/-1 can either have little or no effect up to quadrupling / quartering the damage, and at the extremes the penalty means a hit becomes impossible (without special natural 18 = a hit rules).

In contrast we'll consider D% (with the targets chosen to match the previous table as closely as possible):

Target Needed	% Chance Hit	% Chance with +5 bonus	Multiplier on average damage / rnd	% Chance with -5 penalty	Multiplier on average damage / rnd
1	100.0%	100.0%	1.00	95.0%	0.95
2	99.0%	100.0%	1.01	94.0%	0.95
3	98.0%	100.0%	1.02	93.0%	0.95
6	95.0%	100.0%	1.05	90.0%	0.95
10	91.0%	96.0%	1.05	86.0%	0.95
17	84.0%	89.0%	1.06	79.0%	0.94
27	74.0%	79.0%	1.07	69.0%	0.93
39	62.0%	67.0%	1.08	57.0%	0.92
51	50.0%	55.0%	1.10	45.0%	0.90
64	37.0%	42.0%	1.14	32.0%	0.86
75	26.0%	31.0%	1.19	21.0%	0.81
85	16.0%	21.0%	1.31	11.0%	0.69
92	9.0%	14.0%	1.56	4.0%	0.44
96	5.0%	10.0%	2.00	0.0%	0.00
99	2.0%	7.0%	3.50	0.0%	0.00
100	1.0%	6.0%	6.00	0.0%	0.00

In both cases the values are reasonably consistent in the top half of the table, but the bottom half of the table is anomalous - towards the bottom end bonuses and penalties can have a disproportionate effect. The 3D6 system is not a clear winner with this measure of fairness. Thus we have seen:

Bonuses / penalties in a bell-curve system are not necessarily much "fairer" than those in a linear system.

We could choose a system on purpose so the bonuses / penalties are "fair", but clearly any closed system is going to have anomalies at the ends of the distribution where a bonus/penalty makes a result a certainty/impossibility OR ceases to have an effect. Hence:

Only an open-ended system can have "fair" bonuses/penalties throughout the range.

That doesn't mean all open-ended systems are "fair" - in fact many of them are quite wacky. (There can also be different non-modifier based systems that are "fair"). What would an open-ended fair system look like?

A Fair Open Dice System

The fairest system would be one where +1/-1 always modified your chance by a fixed proportion. You can do this easily, however there are other disadvantages of that as I always like to include a chance of failure. As a compromise I chose one where a +3 bonus halved your chance of failure (for failure<50%), or doubled your chance of success (for failure>50%). I approximated this with my open-dice system. (Note this is a bell-curve, but not a normal distribution). Here's the fairness test repeated for that system:

Target Needed	% Chance Hit	% Chance with +1 bonus	Multiplier on average damage / rnd	% Chance with -1 penalty	Multiplier on average damage / rnd
2	100%	100.0%	1.00	99.0%	0.99
3	99.0%	100%	1.01	97.0%	0.98
4	97.0%	99%	1.02	93.9%	0.97
5	94%	97%	1.03	89.8%	0.96
6	90%	94%	1.05	84.6%	0.94
7	85%	90%	1.06	78.3%	0.92
8	78%	85%	1.08	70.8%	0.90
9	71%	78%	1.11	62.3%	0.88
10	62%	71%	1.14	52.5%	0.84
11	52%	62%	1.19	43.5%	0.83
12	44%	52%	1.20	35.5%	0.82
13	35%	44%	1.23	28.2%	0.79
14	28%	35%	1.26	21.8%	0.77
15	22%	28%	1.29	16.3%	0.75
16	16%	22%	1.33	12.1%	0.74
17	12%	16%	1.35	8.6%	0.71
18	9%	12%	1.40	6.4%	0.74
19	6%	9%	1.35	5.2%	0.81
20	5%	6%	1.23	4.1%	0.80
21	4%	5%	1.25	3.3%	0.79
22	3.3%	4%	1.27	2.6%	0.79
23	2.6%	3%	1.27	2.0%	0.78
24	2.0%	3%	1.28	1.5%	0.76
25	1.5%	2%	1.32	1.2%	0.79
26	1.2%	2%	1.27	0.9%	0.77
27	0.9%	1%	1.29	0.7%	0.78
28	0.7%	1%	1.28	0.6%	0.85
29	0.6%	1%	1.17	0.5%	0.77
30	0.5%	1%	1.29	0.4%	0.79

Thus this system isn't completely "fair" but is a reasonable compromise. A +1 bonus can at most make you 40% better (and is generally between 20% and 40% better) and a -1 penalty can at most make you 29% worse (generally at least 20% worse). You could also come up with a different resolution system that better approximates my stated goal distribution.

Is this fairness an advantage that outweighs the loss of clarity of the linear system? That's entirely subjective - but there are other advantages of this approach.

For example I've previously noted that if you double the distance to a target, then it presents one quarter the size target to the archer, hence it is reasonable beyond a certain range for 2* distance to equate to 1/4 the probability of hitting or a -6 modifier.

Another question is whether you want the modifiers to be fair or not!

Fairness of Advantage / Disadvantage Mechanic

Now modifiers are not the only way of giving people bonuses - one currently popular method is the Advantage / Disadvantage system of 5th edition. How "fair" is this?

Target Needed	% Chance Hit	% Chance with advantage	Multiplier on average damage / rnd	% Chance with disadvantage	Multiplier on average damage / rnd
1	100.0%	100.0%	1.00	100.0%	1.00
2	99.0%	100.0%	1.01	98.0%	0.99
3	98.0%	100.0%	1.02	96.0%	0.98
6	95.0%	99.8%	1.05	90.3%	0.95
10	91.0%	99.2%	1.09	82.8%	0.91
17	84.0%	97.4%	1.16	70.6%	0.84
27	74.0%	93.2%	1.26	54.8%	0.74
39	62.0%	85.6%	1.38	38.4%	0.62
51	50.0%	75.0%	1.50	25.0%	0.50
64	37.0%	60.3%	1.63	13.7%	0.37
75	26.0%	45.2%	1.74	6.8%	0.26
85	16.0%	29.4%	1.84	2.6%	0.16
92	9.0%	17.2%	1.91	0.8%	0.09
96	5.0%	9.8%	1.95	0.3%	0.05
99	2.0%	4.0%	1.98	0.0%	0.02
100	1.0%	2.0%	1.99	0.0%	0.01

We can see that at the bottom end the advantage system roughly doubles the chance of success. As you get to the top the effect switches to halving your chance of failure, but it rapidly reduces that towards zero. Apart from the top end it equates quite closely to a +3 in my open dice system, and is similarly fair. Hence, rather surprisingly, neither side in a combat would have much to complain at if both sides got advantage on all rolls - those with a low chance to hit might have doubled their chance to hit, but those with a high chance to hit would have almost eliminated their chance of missing.

In contrast the disadvantage system roughly doubles the chance of failure in the top half, but in the bottom half the chance of success dwindles almost to nothing. So although there is no cliff to fall off at the bottom (it never reaches zero) it is far from "fair". Disadvantage is a slight issue for people who are mostly successful, but is dire for people that are unlikely to succeed.

I think it's quite surprising that advantage and disadvantage have such different effects.

To clarify this: as a simple example, is it better for you to be given advantage - or your opponent to be given disadvantage? Consider A hits 1/4 of the time, B hits 3/4 of the time:

Combatant	Standard chance to hit	With Advantage	With Disadvantage
A	1/4	7/16	1/16
B	3/4	15/16	9/16

Note there's not much difference between the two choices for A. Initially B is hitting 3 times as often, and their choice is to change that to 1.71 times as often (A gets adv) or 2.25 times as often (B gets disadv). It's slightly better for them to get advantage.

In contrast for A they are initially hitting B 3 times as often and their choice is to change that to 3.75 times as often (B gets adv), or to 12 times as often (A gets disadv).

It's not intuitive to me that one choice is so much better than the other for B. In fact it's always better to place advantage/disadvantage on the person whose least likely to hit - A puts advantage on themselves, B puts disadvantage on A.

Of course, this may be the effect that you're looking for!