Dice Mechanics

Linear Distribution (Single dice, or unrelated sequential dice)

D20/D30/D%/Polyhedral 

1. Polyhedra: Uses d4-d12, and sometimes d20, more rarely d14, d16, d18. 
2. True20 : D20 used for all rolls Ex: True 20
3. D20 & polyhedra: D20 used to check successes, other dice use for success magnitude (most D20)
4. Roll+X: Any of the above, but add a fixed number to the roll.
5. Criticals: As above, but 1 is always a failure, a 20 is always a success. Ex: DnD 4e
6. D100: Use two D10 to determine a percent score. Ex: GURPS

NON-LINEAR (Dice-sum, dice-pool, and 'fat tails')

DICE-SUM (Normal Distribution)

1. xDx: Roll between 2-5 dice, sum the result. D6 and D10 are by far the most common.
2. xDx+x: As above, but add a fixed number to the roll. Ex: Green Ronin AGE system.
3. xDx+Dx: As above, but add a non-standard die to the roll. Ex: Monsters & Magic uses Roll+dX, with the base roll being 3d6. 
4. xDx&Dx: Sum a pool of dice to determine success or failure, and then roll a second die to determine the degree of success or failure. Ex: Chivalry and Sorcery. 
5. FUDGE: Roll 4d6, sum after using the conversion that 1-2=-1, 3-4=0, 5-6 = 1. ( FUDGE dice are almost necessary)
6. Attributes: Roll 2d6 or 3d6: The median value counts as a zero. The next great value (or pair of greater values for 3d6) counts as a +1, so that that the range is -5 to +5.
7. Flux: Two different colour dice (D6) are rolled, one positive, one negative - the lowest value is taken or if the same =0. Yields results -5 to +5. Ex: Traveler 5
8. Opposed Rolls: Rather than a fixed DC, defense is also rolled, and subtracted from the attack roll to determine success. Ties may be treated as partial successes. Ex: Mayhem

DICEPOOL (Binomial or Negative Binomial Distribution)

1. Success: Roll a number of dice; a die that rolls a certain number or greater counts as a success. D6 and D10 are most common. Typically between half and one third of numbers count as a success. 
1. Count: As per 'Success', but the count of successes matter.
2. Exploding dice: A dice-sum system where the highest value of die triggers the addition of another die of the same type: ie, rolling a 6 on a d6 means another d6 is rolled. 
3. Failure: Every natural 1 has negative consequences.
4. Mixed Pool: A dicepool that contains a variety of different dice.
2. Keep: Roll a number of dice, keep the one with the highest value, treating that as the outcome of the roll.
1. Keep Two: As per Keep, but keep the two highest dice and sum them. 
2. Keep+Count: Take the highest value from a pool, add +1 for other 'success'
3. Keep+Match: Take the highest value from a pool, add +1 for every dice also equal to that value. Ex: Heavy Gear, Pod 9.
4. Wild Dice: Roll two polyhedral dice, one default, one defined by a skill or attribute, and take the higher. Ex: Savage Worlds. 
1. Advantage: Roll 2d20, take the better or the worse. Ex: DnD 5e

ERRATIC DISTRIBUTIONS

1. STEP/RANK: At each rank, the dice rolled changes so as to represent an improvement in the median roll. Ie 1d10->1d12->2d6->d8+d6. Ex: Earthdawn.
2. One Roll Engine (ORE): A dicepool system where values in the pool are grouped into sets; the value is called the 'height', the number in the set is called the 'width'.

"ORE (One Roll Engine) you roll a pool of 2-9 D10 and count matches. The number of matching dice is the width of the roll, and the number of the match is the height. A hard die is always 10, and a wiggle die have any number decided after the dice are rolled. For damage rolls, the width determines amount of damage, and the height determines hit locations. For most generic actions the width is the speed of the action and the height the quality. It is possible to get multiple matches in a single roll, which is how doing multiple actions in one round is handled. " - Jesper Anderson

TN & DC Alternates (Target Numbers, Difficulty Classes)

1. Roll Under: Roll under a fixed attribute, so that low roles are good, bonuses as negative numbers. EX: Advanced Dungeons and Dragons ('Whitebox', 2E) 
2. DC+X: Roll over a fixed attribute, so bonuses are positive numbers. Ex: DnD 3E, 3.5,4, 
3. Margin Triggers: A linear system where beating a DC by a certain number generates an additional effect, often a damage 'critical'. (Mayhem)
4. Risks/Raises: Before rolling, players may reduce their dice pool to obtain additional effects on a successful outcome.
5. TC based on the sum of several attributes

OUTCOMES
With a linear distribution, outcomes are fully random within a certain range; above that range, failure is inevitable. Below that range, success is inevitable. Dice-sum systems generate consistent bell-curves of which the median, minima and maxima are known. Estimating chances of success on a role is more difficult. Reference tables are necessary.  The effect of a +1 bonus is non-linear, but tends to 'auto-balance', as the value of a +1 is greater to the underdog. Dicepool systems where success is binary follow a binomial distribution. Systems that count successes follow a negative binomial distribution. Failure is always possible, although statistically unlikely. Including additional negative effects for 'natural 1;s' can be used to make failure more painful, or more common. Reference tables to estimate success are necessary. With large pools of dice, failures are rare, and large pools may (rarely) generate an awesomely large count of successes.

NOTABLE SYSTEMS

 Travis Casey

The horror RPG "Don't Look Back" uses this: Base roll is 3d6. If you have a bonus, you roll additional d6 equal to the bonus value to your roll, but only take the best three. If you have a penalty, roll additional d6 equal to the penalty value and take the worst three. Bonuses and penalties add together - e.g., a +2 bonus and -3 penalty become a -1 penalty.  Action value is the name for the degree of success. If i succeed by 5 i have a +5 action value. If i fail by 3 i have a -3 action value. In an opposed test, those with the highest positive action value win the contest.

Also note that the "d20/polyhedra" system you have there is used with many other games that don't use a d20 as the basic roll. A lot of old systems use a separate "damage die" in combat. A similar concept is also seen in 3rd edition Chivalry & Sorcery: you roll 2d10 to determine success/failure, and an additional d10 of a different color, which determines degree of success/failure. Green Ronin's "AGE" system uses 3d6, one of which is a different color. All three are added together, along with an attribute bonus, but one of the three is special and generates "stunt points" that can be used if you succeed.

Designing and RPG System

A lot of systems can be heavily modified to fit most goals, and making a new RPG system is a terrible first project for a new game designer, but I've found that I usually get great results by building a specific system toward a specific campaign or setting. It cuts out all the unnecessary content and ensures the mechanics serve the themes. Also, I end up with a complete and total understanding of the system which helps as the GM.

I wouldn't reccomend building new systems, especially gigantic sprawling ones, to most GMs - it's just not necessary and you don't get as much benefit from making players learn new rules as they do from learning about an exciting new world or cast of characters. However, I'm a game designer - and I've found a lot of the campaigns I want to create benefit from custom-designed content. 

Published systems often attempt to be catch-all, providing a broad and resilient experience for diverse settings, campaigns and so on. They can't afford to be as specifically tailored to exactly the setting and experience you want to run (if you have something less 'classic' in mind). The majority of them end up bloated with unnecessry classes or more general mechanics. In any case, RPGs are complicated enough that it's likely none will match your exact targeted experience perfectly. One skill check mechanic might be great for you, but their progression system might be emotionally dissonant.

-Dan Felder

Goldilocks Systems

 People look for other systems because the existing systems are missing something. They are looking for a Goldilocks system. One that meets the needs of their playstyle. For me the system that did that for years was Hero. It is one of the best and most flexable point based RPGs out there. There's literally nothing you can't do with the system. It takes a lot of work to run the system because you have to make everything from parts. Though that is easier with many books with equipment, monsters, NPCs etc. It's still a big system that has some long standing issues that will never be fixed. This is due to the rabid fanbase that resists ANY change to the underlying system. So my choice is to labor on with the system and try to fix it with a ton of houserules, or to reengineer the system and make it more like the game I wish it was. Cut out the annoying stuff, fix what needs fixing. The thing that keeps stopping me is that the world needs another RP system like it needs another version of D&D (ie it doesn't).

-Jenevieve DeFer

"You need mechanics that support that experience"

Jeremy Forbing 

Elegant or clever game design are only relevant in service of a particular experience. Generic RPGs tend to be just that, generic. If you want a game to feel like a Hong Kong martial arts film, you need mechanics that support that experience. If you a system that simulates the deadly and horrific battles of World War I, you have to design towards that. The Marvel Heroic rules would be bad for Lovecraftian horror, but are great for playing superhero comics. How can we judge a mechanic without knowing what experience it is meant to create?

Arkham Horror and Bathtubs of D6

Matt Miller 

In Arkham, extra dice is always better. Every die in Arkham adds +1/3. But Arkham does a very nice job of limiting the dice you can add through the use of 'hands'. You only get two, and you you an only use two hands worth of spells/weapons* in a single attack.  In Arkham, things which do add piles of dice (withering, etc) also require a roll to activate, and include an additional cost. 

I recall some game that played with d10s. It made doing the mental math easy...but I think it was based on the ShadowRun style 'bathtubs of D6', where only a 1 counts as a success...which makes it worse than ShadowRun. ShadowRun, a 6d6 makes a success very likely. With a d10 system, you need 10d10. Making it a 1 or a 2 on a D10 doesn't alter it that much: 1/5 chance, vs a 1/6 on a d6--not worth the extra dice required. 

**Recalls to me, before the 'Christmas Tree' twinking out, there was a rule that players could only have one magic item.

Paen to Fate

Matt Miller

Mechanically, I'm really liking Fate of late. 4dF provides a very strong median tendency, while permitting sufficient variance to make things unpredictable. 

Rob Hicks 

The best thing about the fate die system is environmental or situational bonuses. You can creatively do just about anything to get the bonus, but you have to justify it through actions, environment and character history. It blends the strategic elements of the game with the storytelling.

Paul Goldstone 

Fate has extensive meta gaming that makes the game for me, players describing scenes, incidences etc to get mods. The end result being that if you have the skill you are more or less going to succeed. D20 for me has a huge amount of random, that doesn't cater to the if you have the skill you are most likey to succeed mechanic due to the wide possible variances. The arkham dice method for an RPG, when combined with a skill, offers the "have skill will succeed" mechanic which does seem to be popular of late. Its worth noting that ffg custom dice rpg have that, just with symbols over numbers, as does Mutant Chronicles to some extent (MC has a great system and is well worth looking at).

Nathan Dowdell 

IMHO, what makes Fate sing is the way that Aspects and the Fate Point economy turn a test from a pure risk consideration to a matter of cost - being able to spend after the fact, and suffer costs for success, changes the game dynamic hugely. Failure isn't the end, merely a chance to ask the question "how much is success worth to you?"

Matt Miller

You make an excellent point. The ability to 'burn' clue tokens in Arkham, AFTER a roll, is one of my favorite parts. It makes rolling slightly less visceral, but it still works: Clue Tokens are a representation of a generic advantage in understanding.

Damage Sizing

Matt Miller

In Netrunner, 7 points gets you victory, with points coming in packages of 1,2 or 3. Thus, any 'hit' after your second might be your last. Likewise, it might be 7 different successes. But it means that you start sweating every attack, because it might be your last. It's the same dynamic as playing with lv1 characters. In DnD, at lvl 1, max weapon being greater than max HP means a bad roll can end your character. But I think Netrunner strikes a good balance between 1st level DnD and the 'stacks of HP' problem.