(+)Changing From a DC Ladder to a Success Ladder

[doctorbadwolf]

@pemerton Okay, I really appreciate the help, here. I know how to use anydice to get the raw data but I just go full himbo for some reason when I try to turn it into useful information. I mean I exaggerate, I built the old dice system by running numbers, but kinda like making a slick looking character sheet by beating my head against excel for hundreds of hours over the course of dozens of iterations, sometimes asking for help is really the better way!


So, one last question (I think), if you’re willing: how much smoother is the distribution with d6s? How about with a d12 and d6 rank dice?

I started with d10’s originally because it’s was d100+d10 rank dice, which is roughly the same as d20+ 1 point per rank, but curvier. So I’m not married to d10s, but they aren’t part of the game’s identity in my head. Especially since all attacks also function in d10’s, the idea being you only ever need up to 6 d10s to play the game. Obviously d6s are more common to have that many of, but we can also commission specialty dice sets with the Fir Bolg (of myth, big folk who spoke the first mortal language, and have a knack for linguistic, riddles, and throwing stuff) sigil for the game on the 10!

 

[pemerton]

So, one last question (I think), if you’re willing: how much smoother is the distribution with d6s? How about with a d12 and d6 rank dice?

Can you explain what you mean by "smoother" in this context?

My combinatorics and probability stops at an upper high school level, so I'm not doing anything very sophisticated: just calculating (with a bit of help from Anydice for the bigger numbers) the likelihoods of various results. I'm pretty sure it will be possible to set up d6-based thresholds that produce much the same spread of probabilities. But I think you already know that, and hence my question above.

 

[doctorbadwolf]

Can you explain what you mean by "smoother" in this context?

My combinatorics and probability stops at an upper high school level, so I'm not doing anything very sophisticated: just calculating (with a bit of help from Anydice for the bigger numbers) the likelihoods of various results. I'm pretty sure it will be possible to set up d6-based thresholds that produce much the same spread of probabilities. But I think you already know that, and hence my question above.

My understanding is basically that bigger dice will “swing” more than smaller dice, but I’m not sure if that is true. Perhaps a “rounder” or “less steep” bell curve? I’ll try to do some anydice work tomorrow to find answers.

Basically I’m curious if the change in success chance per additional rank will be less extreme with a smaller die size? IOW, will the difference from 1 die to 2 die be less of a jump with smaller dice?

 

[pemerton]

It depends where you set your boundaries.

Using d10s (and just repeating/consolidating from above):

If you set Total Failure as 7 or less, that will be 70% of 1-die rolls, about 20% of 2-dice rolls, less than 10% of 3-dice rolls, fewer than 1 in 200 4-dice rolls (but a bit more than 1 in 300), and about 1 in 5,000 5-dice rolls.

If you set Mitigated Success at 15+, that will be about 20% of 2-dice rolls, nearly 65% of 3-dice rolls, and about 90% of 4-dice rolls.

If you set Total Success at 20+, that will be 1% of 2-dice rolls, around 28% of 3-dice rolls, a bit more than 65% of 4-dice rolls, and close to 90% of 5-dice rolls.​

You can get a similar spread with d6s:

If you set Total Failure as 4 or less, that will be two-thirds of 1-die rolls, one-sixth of 2-dice rolls, and a bit less than 2% of 3-dice rolls. It's fewer than 1 in 1,000 4-dice rolls, and impossible for 5-dice rolls.

If you set it at 5 or less instead, that will be a bit over 80% of 1-die rolls, close to 30% of 2-dice rolls, less than 5% of 3-dice rolls, fewer than 1 in 200 4-dice rolls (but a bit more than 1 in 300), and fewer than 1 in 8,000 5-dice rolls.

If you set Mitigated Success at 10+, that will be one-sixth of 2-dice rolls, a bit over 60% of 3-dice rolls, and about 90% of 4-dice rolls.

If you set Total Success at 13+, that will be impossible with fewer than 3 dice, around 26% of 3-dice rolls, around 66% of 4-dice rolls, and just over 90% of 5-dice rolls.​

So I think changing from d10 to d6 has the effect of making it impossible rather than just extremely unlikely to get full success with 2 dice; also pushes the rate of Mitigated Success down a little bit for 2-dice rolls; and forces a choice about whether you want Total Failure to be a bit less likely, or a bit more likely, for one or two dice.

 

[doctorbadwolf]

It depends where you set your boundaries.

Using d10s (and just repeating/consolidating from above):

If you set Total Failure as 7 or less, that will be 70% of 1-die rolls, about 20% of 2-dice rolls, less than 10% of 3-dice rolls, fewer than 1 in 200 4-dice rolls (but a bit more than 1 in 300), and about 1 in 5,000 5-dice rolls.​

​

If you set Mitigated Success at 15+, that will be about 20% of 2-dice rolls, nearly 65% of 3-dice rolls, and about 90% of 4-dice rolls.​

​

If you set Total Success at 20+, that will be 1% of 2-dice rolls, around 28% of 3-dice rolls, a bit more than 65% of 4-dice rolls, and close to 90% of 5-dice rolls.​

You can get a similar spread with d6s:

If you set Total Failure as 4 or less, that will be two-thirds of 1-die rolls, one-sixth of 2-dice rolls, and a bit less than 2% of 3-dice rolls. It's fewer than 1 in 1,000 4-dice rolls, and impossible for 5-dice rolls.​

​

If you set it at 5 or less instead, that will be a bit over 80% of 1-die rolls, close to 30% of 2-dice rolls, less than 5% of 3-dice rolls, fewer than 1 in 200 4-dice rolls (but a bit more than 1 in 300), and fewer than 1 in 8,000 5-dice rolls.​

​

If you set Mitigated Success at 10+, that will be one-sixth of 2-dice rolls, a bit over 60% of 3-dice rolls, and about 90% of 4-dice rolls.​

​

If you set Total Success at 13+, that will be impossible with fewer than 3 dice, around 26% of 3-dice rolls, around 66% of 4-dice rolls, and just over 90% of 5-dice rolls.​

So I think changing from d10 to d6 has the effect of making it impossible rather than just extremely unlikely to get full success with 2 dice; also pushes the rate of Mitigated Success down a little bit for 2-dice rolls; and forces a choice about whether you want Total Failure to be a bit less likely, or a bit more likely, for one or two dice.

Huh. Thank you.

It looks like d6s require shorter "bands" of results, as well. That could be a good or bad thing, as a style choice. A very short ladder works very well for pbta games, but those games don't tend to feature much numerical/statistical improvement over time.

The spread you have there works pretty well. 1 die only happens when you are unskilled at a thing, or have 1 rank and a penalty (or more ranks and a severe penalty, but that is probably going to be rare). 2 dice is 1 rank, so the lowest that total success could be would be 12, I think. That results in 99% total success at 5 ranks.

Of course, rolling nothing but 1's and 2's happens. I've seen it happen when someone casts fireball in dnd, when rolling for stats, etc, enough to not discount it. Part of the reason I chose rank dice rather than rank bonuses is that you always have the ability to totally fail. Thing is, at 5 ranks, total failure has to be 6 or less for that to even be possible, and that would make it literally impossible when unskilled.

Okay, yeah, I think that d10's work better than d6's. Since I don't work for a few hours yet, I'm going to tinker with things like d12+d6 rank dice, just for fun. It feels pretty good in The One Ring, but the One Ring also has special pips on the d12 and the d6s that mess with probabilities.

 

[doctorbadwolf]

Before I map out the percentages, now that you've helped me grok the sort of field of play, here, the reason I'm considering d12+d6 is that by making the "Action Die" and the "Rank Dice" separate types, I can more easily do stuff like say, "when you make a skill check that deals damage, mitigates damage, heals, etc, the result of your Action Die is the number used for that effect." Rather than asking for a second roll. Could even do things like, "Your damage/healing/whatever is equal to you Action Die. For each level of success you achieved, you can add 1 rank die from the roll of your choice." Doing so could allow for active defense to be a roll where your result on the success ladder reduced the dice pool of the effect you're defending against, rather than subtracting a number. It just opens up a lot of stuff I could playtest and tinker with to make the system dynamic without increasing complexity in unfun ways.

Spoiler: Mitigated Failure

1d12
7+ is 50%
8+ is 41%
9+ is 33%
10+ is 25%

1d12+1d6
7+ is 79%
8+ is 71%
9+ is 62.5%
10+ is 54%

1d12+2d6
7+ 95%
8+ 91% (similar in feel to all d10s, so far)
9+ 87%
10+ is 81% (this puts it closer to the d6s)

1d12+3d6
7+ 99%
8+ 98.6%
9+ 97%
10+ 95%

Any difference no longer matters, in terms of getting past total failure. Anywhere from 8-10 feels good here.

Spoiler: Mitigated Success

1d12
11+ is 16.6%
12+ is 8.33%
13+ is impossible

1d12+1d6
11+ is 46%
12+ is 37.5%
13+ is 29%
14+ is 21%
15+ is 14%

1d12+2d6
11+ is 74%
12+ is 66%
13+ is 58%
14+ is 50%
15+ is 42%

1d12+3d6
11+ is 92%
12+ is 88%
13+ is 82.6%
14+ is 76.5%
15+ is 69.5%

1d12+4d6
11+ is 98%
12+ is 97%
13+ is 95%
14+ is 84%
15+ is 88.5%

1d12+5d6
11+ is 99.77%
12+ is 99.5%
13+ is 99%
14+ is 98%
15+ is 97%

Spoiler: Total Success

1d12
cannot be achieved untrained or without some sort of help or bonus.

1d12+1d6
16+ is 8.3%
17+ is 4%
18+ is 1.4%
19+ is impossible
20+ is impossible

1d12+2d6
16+ is 33.5%
17+ is 26%
18+ is 19%
19+ is 13%
20+ is 8%

1d12+3d6
16+ is 62%
17+ is 54%
18+ is 46%
19+ is 38%
20+ is 31%

1d12+4d6
16+ is 84%
17+ is 78%
18+ is 72%
19+ is 65%
20+ is 57.5%

1d12+5d6
16+ is 95%
17+ is 92.5%
18+ is 89%
19+ is 85%
20+ is 80%

Okay, so...I looked at a few progressions using those numbers, had to clarify my goals a little in terms of which steps on the ladder have shorter or longer bands of numbers, decided that the 80% chance of total success (20+) is about the highest I want total success to get, and I think that the following could work.

1-9 Total Failure.

10-15 Mitigated Failure. Highest possible result without a rank die. With 1 rank you'll get this 37.5% of the time, 3 ranks goes up to 87%, and masters sit at 99.5%. This is the Master's effective floor, though technically total failures will still happen every once in awhile.

16-19 Partial Success. Rare with 1 rank, impossible with none. 3 ranks is 62%, 4 ranks 84%, 5 ranks 95%. That feels good for being the halfway mark of the ladder, splitting failures and success.

Still might increase the size of both mixed results, tbh, but for now it's good enough to playtest.

20+ can't be got without 2 ranks and it's less than 10% then. 3 ranks is still only 30.5%, then about 58%, then about 80%. I wish I could keep the rest of the spread but not jump quite as high with 5 ranks, but I just can't find a way to do it with this model, and it takes a decent amount to get there.

At CharGen, you will likely only have 2 or 3 specialties at 3 ranks, and none higher than that. You'll be rolling 1d12+1 or +2 most often, meaning you'll mixed results the vast majority of the time, though at 1 rank you'll need to angle for a bonus more often.

You also have a few skills (and can never gain more) that are "Accurate", which means you reroll 1's. Obviously it behooves you to specialise in these, which is why they come from origin and archetype.

Also, again, you can spend an Attribute Point, which you start with 12-13 of, and you regain only some of per rest, to just increase a check by one step on the ladder. You don't want to do this too much, unless you don't mind not being able to use special abilities or mitigate incoming trauma, or push the scene in the direction you want, etc.

I think this feels really good. I'll playtest and report back soon.

 

[Argyle King]

You've stated that nothing else ever adds to the rolls.

Does anything subtract from the rolls? For example, would fog make a check to see something more sufficient?

 

[doctorbadwolf]

You've stated that nothing else ever adds to the rolls.

Does anything subtract from the rolls? For example, would fog make a check to see something more sufficient?

Penalties and bonuses exist in the form of +d or -d, rather than static modifiers. So, I guess it isn’t totally accurate to say nothing else ever adds to a roll. Well, not anymore. Before seeing the stats, I wasn’t sure if +/-d was a good idea. I had considered having a penalty reduce your ceiling by making you reroll max results on the die, or using basically advantage/disadvantage but only for the “Action Die”.

I may still use the adv/disad idea, but we will see what playtesting feels like.

Another way to go might be adding an extra die, and either dropping the highest or lowest rank die result.

 

[doctorbadwolf]

To sum up where I'm at now, 1d12 Action Die plus [rank]d6 rank dice. Success tiers at 10, 16, 20, total ranks from 1-5 (maybe 6, but a 6th rank is very diminished return. You're better off ranking up in related specialties and skills).

This makes it easier to keep straight ranks vs dice rolled, and allows the game to use the d12 Action Die to determine things like damage, as part of the roll.

It also might make the system I'm replacing the old Health system with work a little more smoothly, but that is a whole 'nother discussion.

 

[Argyle King]

Penalties and bonuses exist in the form of +d or -d, rather than static modifiers. So, I guess it isn’t totally accurate to say nothing else ever adds to a roll. Well, not anymore. Before seeing the stats, I wasn’t sure if +/-d was a good idea. I had considered having a penalty reduce your ceiling by making you reroll max results on the die, or using basically advantage/disadvantage but only for the “Action Die”.

I may still use the adv/disad idea, but we will see what playtesting feels like.

Another way to go might be adding an extra die, and either dropping the highest or lowest rank die result.

Are you familiar with FFG Star Wars?

Numerically, it handles things a lot differently than your system, but the idea of adding or subtracting dice is something that system uses.