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I was curious as to what amateur and professional game designers here think about the statistical success rate players think/feel they should have for an appropriately leveled obstacle to overcome with a dice roll. This applies moreso to RPGs than tabletop games given the disclaimers. Do you do a statistical analysis of a dice mechanic you're planning on using to look at the hard numbers or do you go more by feel/anecdotal testing? Or both? If you do look at the hard numbers, what % chance of success do you aim for with an easy, average, and hard difficulty appropriately leveled for the player character by whatever method you're using for advancement (if any)? For example, are you aiming for the average player character to have a roughly 50% chance at succeeding in an "easy" test or higher than that? What about an average player with an average difficulty test? Mix maxed character build vs a difficult test?

I recently discovered the anydice.com website (great utility!) and jumped head first down the rabbit hole of statistics, banging my head along the sides due to my limited knowledge of both the science and proper coding. Regardless, the numbers were illuminating and I discovered the actual success rate for the average dice pool in a d6 system I've been playing around with was noticeably lower than I expected and had to adjust upwards. I haven't tested it out in actual play but I've been shooting for around a 66% chance for a minmaxed starting character to succeed at an average test within their niche (i.e. a ranger using his or her bow) just using the naked character sheet (before adding any environmental or situational modifiers that may increase that) and the average player character succeeding about the same percentage on one difficulty level lower (easy).

Great question.

I am not a heavy "Crunch" kinda guy, but I have been playing wargames and RPGs long enough to have a bit of a feel for success rates.

Therefore, I operate much more by feel and test than I probably should.

 Easy E wrote:
Great question.

I am not a heavy "Crunch" kinda guy, but I have been playing wargames and RPGs long enough to have a bit of a feel for success rates.

Therefore, I operate much more by feel and test than I probably should.

I traditionally have done the same (though my efforts have at most culminated in a few house rules articles published on my blog and nothing more official). I saw the site referenced in a video and checked it out as I never actually "did the math" on my relatively simple d6 system tweaks. I was about 15% off in my napkin math calculations/expectations and though that the "average" roll would result in a 50-60% chance of success vs an average difficulty. I remember reading years ago that FFG subtly modified the dice results in favor of attackers over defenders in X-Wing so as to give the impression that your attacks did something most of the time (even if it was only a single point of damage). I probably played 50+ games of X-wing and never actually counted up the faces on the attack and defense dice but rather just assumed they were identical except for the icons. I wanted to also be above the expected 50% but wasn't sure if 60-65% would feel like too sure of a bet so I made this thread.

I want to know the actual odds. When I built out Conqueror, a huge part of the exercise was to make the percentages work. GW seriously fudged the numbers, and I wanted people to know what they were dealing with.

I then pegged the point values to the values I got with the result that - this is going to shock some folks - the higher points value unit will generally win against the lower points value one.

Consistently. As in: bank on it. I think a lot of the fun and "mystery" of GW games was that the point were arbitrary, so people went into battle without a clear idea of who will win. My game is drearily predictable. Unless you turn a flank or have some serious boss character (which is reflected in points!) the higher point value will almost always do the job because of how the dice will go.

Commissar von Toussaint wrote:
I want to know the actual odds. When I built out Conqueror, a huge part of the exercise was to make the percentages work. GW seriously fudged the numbers, and I wanted people to know what they were dealing with.

I then pegged the point values to the values I got with the result that - this is going to shock some folks - the higher points value unit will generally win against the lower points value one.

Consistently. As in: bank on it. I think a lot of the fun and "mystery" of GW games was that the point were arbitrary, so people went into battle without a clear idea of who will win. My game is drearily predictable. Unless you turn a flank or have some serious boss character (which is reflected in points!) the higher point value will almost always do the job because of how the dice will go.

Was/is GW really that beer and pretzels or is that more of a reference to early/80's Warhammer Fantasy? I've only been looking at success percentages since I'm talking about an RPG and don't necessarily have to "balance" much with a rules light system. Does your Conqueror system have non-easily defined or quantifiable aspects that the dice statistical calculator can't take into effect? How much of a difference in % chance do you expect with points cost increases?

 warboss wrote:
Was/is GW really that beer and pretzels or is that more of a reference to early/80's Warhammer Fantasy? I've only been looking at success percentages since I'm talking about an RPG and don't necessarily have to "balance" much with a rules light system. Does your Conqueror system have non-easily defined or quantifiable aspects that the dice statistical calculator can't take into effect? How much of a difference in % chance do you expect with points cost increases?

I began work on Conqueror when word arrived that 6th edition WHFB was going to be superseded by a new edition. To that point, I had assumed GW was using an iterative process to produce a final, finished game design. Once I realized that "churn" was the goal, I decided to bail out on WHFB and create my own design that I intended to be permanent.

One of the design goals was to make stats meaningful, removing the need for so many special rules. A key focal point was elves vs goblins. GW elves could not defeat an equivalent points value of goblins without special rules. This struck me as a design failure. The stats seemed widely divergent, but upon crunching the numbers, higher WS was only marginally important. The GW trinity of WS, S/T and Save forced results into a narrow range in the center of the probability curve.

Conqueror made skill the paramount value, and combined toughness with armor. The result was a much broader range of combat values, eliminating the need for special rules to obtain an "intuitive" result. That is to say, elves thrashed goblins, no special rules needed.

This opened up design space for special rules to feel more fluffy rather than correct design deficiencies.

The points were built around these results, and the calculations to make your own units (or duplicate the sample ones) are in the rulebook. Put simply, a unit that costs 2x as much as its opponent will inflict (on average) 2x as many casualties.

To put it another way: I show my math.

Commissar von Toussaint wrote:
Conqueror made skill the paramount value, and combined toughness with armor. The result was a much broader range of combat values, eliminating the need for special rules to obtain an "intuitive" result. That is to say, elves thrashed goblins, no special rules needed.

This opened up design space for special rules to feel more fluffy rather than correct design deficiencies.

The points were built around these results, and the calculations to make your own units (or duplicate the sample ones) are in the rulebook. Put simply, a unit that costs 2x as much as its opponent will inflict (on average) 2x as many casualties.

To put it another way: I show my math.

I've always been a fan of systems that include the rules to make custom units and it was a key feature for me of the old VOR system. So no special rules at all and instead you rely completely on the stat block?

 warboss wrote:
I've always been a fan of systems that include the rules to make custom units and it was a key feature for me of the old VOR system. So no special rules at all and instead you rely completely on the stat block?

No, I do use special rules, but they're keyed into specific game functions. For example, when a unit takes a certain level of casualties, it is "shaken," and suffers a permanent -1 morale modifier. However, some units are "unshaken," so they ignore their losses for morale purposes. This allows one to create "horde" units with low morale but also low sensitivity for losses.

Units that barely pass a morale check become "disordered," and now carry a -1 morale modifier until they can rally. "Orderly" units ignore this rule. "Obedient" units always pass morale and leadership checks; units with The Horror impose a -2 morale penalty on their opponents; "Summoned" units don't check morale, but lose wounds based on how badly they lost the combat.

Combine all three and you have the rules for "Undead."

I also have units that get bonuses when they charge, but I suggest balancing these powers, so you could have a unit that's ferocious on the attack but has low morale, so if you withstand the charge, they scatter.

Basically I took WHFB and filled out the gaps, creating units GW never bothered to build because their system operated in such a narrow range of probability.

Because the points values are so accurate, tactics become more important. The standard deviations in a GW game meant that characters and magic were more important than troop type; here it's the reverse. Thus if you want to win, a flanking attack or an assist by flyers is necessary. Characters help, but their leadership function is just as important as combat power.

(I have a special rule called "swarming" that allows units to dogpile solitary characters.)

Anyhow, there's a transparency in the numbers. I don't think there's a single re-roll option. Re-rolls play havoc with perceived probability, which is why GW is addicted to them.

I calculate success odds in games which I find satisfying myself in the genre I'm going for, then try to match those odds in my ruleset.

 lord_blackfang wrote:
I calculate success odds in games which I find satisfying myself in the genre I'm going for, then try to match those odds in my ruleset.

One of the core questions I had to resolve in designing Conqueror was how I wanted to handle a combat between elves and goblins. This was the "test case" of the melee combat system. Warhammer (in)famously had to throw several thumbs on the scale to make the fluff work because stats alone could not do the trick. For a smaller force of elves to beat goblins, goblins needed to fear elves. Elves with spears got an extra rank. Indeed, every elf unit got a special rule so that they could cope with the superior numbers (and lower points values) of goblins.

What I did was start with what I felt was a good "kill ration" for elves vs goblins and then I quantified that in the points system. This was a lengthy and iterative process and went through several changes in formula until I was able to get a number that represented the "expected value" of the dice.

This is why weapons aren't just a flat upgrade; some of them are multipliers because bringing twice as many weapons to bear (spears, pikes, 2nd hand weapon) is[b] a multiplier.

I also made the combat more decisive by making it both "bloodier" and providing rules that caused morale to degrade. Contrast this with a Warhammer engagment where two units hit, a few models die, but it's mostly tallying up the combat score that settles it. Of course, if characters and magic get involved, they will absolutely matter more than the troops around them.

In Conqueror characters can tip the balance, but their primary use is to raise leadership. It's the troops that do the dirty work.

Obviously, dice mean luck matters, and you can get box cars or snake eyes and throw everything away, but the results generally lie in the middle.

 lord_blackfang wrote:
I calculate success odds in games which I find satisfying myself in the genre I'm going for, then try to match those odds in my ruleset.

Not to push my luck but what percentages are you looking for exactly for which level of difficulty? I've been looking at about 65-75% for an "expected" outcome with easy difficulty with base dice before adding in situational modifiers/rerolls, 50-60% for an average difficulty test, and 25-33% for a difficult test.


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Commissar von Toussaint wrote:

Because the points values are so accurate, tactics become more important. The standard deviations in a GW game meant that characters and magic were more important than troop type; here it's the reverse. Thus if you want to win, a flanking attack or an assist by flyers is necessary. Characters help, but their leadership function is just as important as combat power.

(I have a special rule called "swarming" that allows units to dogpile solitary characters.)

Anyhow, there's a transparency in the numbers. I don't think there's a single re-roll option. Re-rolls play havoc with perceived probability, which is why GW is addicted to them.

Obviously I haven't tried it let alone analyze it but what relative importance would you ascribe the stats/point values to the success rate versus the actual die roll? From the description you gave (and I appreciate the indepth response), it sounds like the randomness of the roll is less important than what you're bringing to the scenario in the baseline stats/point cost.


Automatically Appended Next Post:

Commissar von Toussaint wrote:

Obviously, dice mean luck matters, and you can get box cars or snake eyes and throw everything away, but the results generally lie in the middle.

I was a bit too early with my question regarding your prior post but this addresses it a bit. What range of dice rolls/percentage chances do you think matter in your system versus the points costs/stats?

 warboss wrote:

 lord_blackfang wrote:
I calculate success odds in games which I find satisfying myself in the genre I'm going for, then try to match those odds in my ruleset.

Not to push my luck but what percentages are you looking for exactly for which level of difficulty? I've been looking at about 65-75% for an "expected" outcome with easy difficulty with base dice before adding in situational modifiers/rerolls, 50-60% for an average difficulty test, and 25-33% for a difficult test.

I can't give you any precise numbers right now. Example, if I'm making a campaign skirmish I'll look at Necromunda and see the final odds of actually killing a person with one shot is, say, 8%. I'll try to match that within the framework of my own dice mechanic and stat range, whatever they may be.

Thanks for the quick reply. Fair enough. I was only thinking of one or two steps (just hit or hit and damage only) in your example rather than the final end result (removing a model from play).

 warboss wrote:
I was a bit too early with my question regarding your prior post but this addresses it a bit. What range of dice rolls/percentage chances do you think matter in your system versus the points costs/stats?

Since I use d6s, the maximum probability of a casualty is 83.333% (hit on a 2+, no save). The minimum is 2.777% (hit on a 6, save of 2+). If you look at the GW hit/wound/save matrix, it clips the range down considerably, with a maximum casualty result being only 69.444% (hit on a 2+, wound on a 2+, no save). It may be narrower; now that I think of it, WHFB's best "to hit" score may have been a 3+.

Basically, the GW system limits results to a narrow range, but uses wider point values, creating a situation where a model that costs two or three times as much in points cannot inflict comparable margins of damage in combat. Conqueror is much closer in those multipliers, so elves with spears (140 points) are reasonably likely kill twice as many goblins with hand weapons (70 points) than they lose.

There was a point where i did the hard crunch. Then there are only so many actual variations on the formulas. At this point i know within 3-4% the general success rates of anything going on and thats "close enough".

 Lance845 wrote:
There was a point where i did the hard crunch. Then there are only so many actual variations on the formulas. At this point i know within 3-4% the general success rates of anything going on and thats "close enough".

I think the odds should be transparent. I hate the way GW obscures them by having re-rolls and other mechanics to muddy the waters.

If gaming is a test of skill, the players should have a reasonable chance of estimating the consequences of their actions. Otherwise it's just random.

If your game is a test of skill, that sounds important.

If it is not a test of skill, perhaps a spectacle, or a story; than transparent crunch is less important.

I guess the statistical success rate of dice rolling is more important in some games than others.

Easy E wrote:If your game is a test of skill, that sounds important.

If it is not a test of skill, perhaps a spectacle, or a story; than transparent crunch is less important.

I guess the statistical success rate of dice rolling is more important in some games than others.

I definitely agree in general but in my case I'm fussing over it in regards to a rules light narrative RPG. If any genre would likely make it silly to obsess over it, I'd say it would probably be that one. I just want the narrative descriptions of the difficulty ("easy", "difficult", "average", etc) to actually correspond to the statistics whenever possible. Obviously, that depends on the exact number of dice rolled and the circumstance modifiers as well. Since I'm doing player facing rolls (a whole other thread to start if I don't find one already here!) for both traditional and solo play, it's a big deal for me personally since there won't be any behind the screen fudging.

Commissar von Toussaint wrote:
I think the odds should be transparent. I hate the way GW obscures them by having re-rolls and other mechanics to muddy the waters.

I don't know if you have any experience with the subgenre but how many mechanics would you consider to be too much/too muddy? I'm using a d6 dice pool so the actual statistics won't be readily available unless you're a vulcan or the Rain Man and that's before a reroll mechanic and some sort of "chaos" success/failure complication d6.

Lance845 wrote:There was a point where i did the hard crunch. Then there are only so many actual variations on the formulas. At this point i know within 3-4% the general success rates of anything going on and thats "close enough".

I'd say 3-4% is more than close enough! I'm shooting for general categories like average being 50-55% with just a simple die roll (before modifiers and/or rerolls are included).

 warboss wrote:
I don't know if you have any experience with the subgenre but how many mechanics would you consider to be too much/too muddy? I'm using a d6 dice pool so the actual statistics won't be readily available unless you're a vulcan or the Rain Man and that's before a reroll mechanic and some sort of "chaos" success/failure complication d6.

Back in the 80s, some board game designers expressed the belief that the combat results tables were too predictable, and tried to make it less transparent. One example of this was using to d6s to generate 36 potential results on a single table and then using slews of modifiers to shift them. The idea was supposedly to create uncertainty because generals shouldn't be able to figure out the odds, but what it did was make combat resolution extremely painful and involved.

A better solution was the stand-up pieces or fog of war systems (double blind comes to mind) where the odds are easy, but knowing the enemy's exact strength is hard.

In an RPG environment, this kind of fudging is even worse because your character should have an idea of what is within reach, just as you can look at a physical or mental challenge and decide your odds within a reasonable margin of error.

Commissar von Toussaint wrote:
In an RPG environment, this kind of fudging is even worse because your character should have an idea of what is within reach, just as you can look at a physical or mental challenge and decide your odds within a reasonable margin of error.

I actually agree and that's in part why I'm concerned with success rates (and the basis for starting this thread). I'm not trying to be crypic as things are still very much in flux but I do plan on publishing a small table with expected success rates similar to how Free League did with their Forbidden Lands game. These numbers don't apply to me but is rather just an example.

 warboss wrote:
I actually agree and that's in part why I'm concerned with success rates (and the basis for starting this thread). I'm not trying to be crypic as things are still very much in flux but I do plan on publishing a small table with expected success rates similar to how Free League did with their Forbidden Lands game. These numbers don't apply to me but is rather just an example.

I think is this why a lot of games use the straight percentiles or an easy to understand substitute, such as the dice pool. They provide a simple way to represent what the characters are good at and this in turn allows the players to better play the various roles they have chosen.

Something I like about the Storyteller system (Vampire, etc.) is that the degree of success shown by the dice can be played out in the story - one "barely makes the leap" as opposed to skipping effortlessly over the chasm. That adds a lot of flavor to the environment.

In wargaming (especially operational/strategic scale), the abstraction is much greater, so divisions and army corps are just knocked about and/or pushed back.

Something I've really come to appreciate in recent years is that in whatever you are doing, make the decisions of the players count and make the tests appropriate and meaningful. Don't bury them in dice rolling for everything, but instead (in the case of the RPG) focus on the story and setting or (in wargaming) the decisions that are appropriate to that level of command.

Commissar von Toussaint wrote:


Something I've really come to appreciate in recent years is that in whatever you are doing, make the decisions of the players count and make the tests appropriate and meaningful. Don't bury them in dice rolling for everything, but instead (in the case of the RPG) focus on the story and setting or (in wargaming) the decisions that are appropriate to that level of command.

So much this!