d20 or 3d10? A skill improvement system question

[John Blaz]

Hey Forgers! It's me again (you know the guy that posts an idea for a new system about once a month). Anyway, I have an idea for a Swords & Sorcery, Conan-esque type of game.

It's a standard d20 Roll under Stat + Skill system thus far.
The stats are Strength, Toughness, Agility, Dexterity, Intellect, Focus, Empathy, Perception and Willpower. (probably going to narrow stats down later)

Now I had an idea on a way to let characters increase skills "Elder Scrolls style", that is if you want to get better at swordfighting, you'd better start swinging that thing. I want the skills to have a higher cap than the attributes, because as the skill's rise, so do the stats. Example: after raising X amount of Strength related skills (Melee, Jump, Swords), the character's Strength would increase slightly. Whenever a character uses a skill and rolls higher than their current skill level on a d20, but still succeeds at using the skill, they get 1 XP towards that skill. After acquiring X amount of XP, the skill rises by 1. This way, skills are fairly easy to upgrade early on, but as you get better it becomes harder and harder to possibly learn more about the skill.

Example: Grognar has a Sword skill of 7 and a Strength of 3. To successfully hit something he needs to roll a 10 or below. To gain an XP towards his Sword skill, he needs to roll between an 8 and a 10.

My initial idea was to make skills each cost maybe 5 or 10 XP to upgrade. For every 5 skills upgraded, the stat related to it goes up one point.
Now I am thinking that characters could choose X Primary skills that only cost 3 XP to upgrade, Y Secondaries that cost 5, and everything else would be Minor and cost 10 XP.

The problem is, because stats are constant and apply to many different skills, I wanted them to be harder to improve than skills (as you can see), but for my improvement system to work in its current state, I need skills to be able to reach 20 (to account for the d20). At the same time, I want stats to have a enough room where a starting character can get some use out of them (say maybe 3-6 starting out) but still have room for improvement. Would this system work if I made stats go up to 10 and skills to 20, but instead of a d20 I used a 3d10 roll?

[Selene Tan]

On a d20, the chance of earning skill XP will go up as the attribute increases regardless of Skill, until Stat + Skill is greater than 20, at which point the chance of XP will decrease as Skill increases.

When trying to rolling a number greater than Skill but less than or equal to Stat+Skill, you're basically trying to roll a number within a range equal to the value of Stat. e.g. Grognar with his 3 Strength has 3 possible numbers where he'll gain skill XP. (8, 9, and 10 in your example.) On a d20 every number is as likely as every other number, so he'll always have a 3/20 chance for Sword XP until his Strength goes up to 4. However, when Stat+Skill is greater than 20, the fact that you can't roll higher than 20 on a d20 cuts off the range of XP-earning numbers, so the probability of skill XP will go down with every increase in Skill.  e.g. if the range would be 19, 20, 21, 22, but only 19 and 20 are possible to roll on a d20, there will only be a 2/20 chance of gaining skill XP rather than 4/20.

With 3d10, the further a number is from the average (16.5), the less likely it is to come up. I'd have to do some analysis to see how the increased range for greater Stat values interacts with the diminishing probabilities of higher-than-average numbers. Depending on the starting values, 3d10 might be closer to what you want.

[MacLeod]

It might be better if the Xp required was always the same... but the Skill category (Primary, Secondary, Minor) would determine how often the Skill gained Xp.

So you could say that the Xp requirement is 5. Primary Skills gain 1 Xp on a 1, 2 and 3. Secondary Skills gain 1 Xp on a 1 and 2. Minor Skills gain 1 Xp on a 1. You could also have some free floating Xp that can be allocated to a Skill via paid training. This unallocated Xp could be generated by defeating foes, completing quests or as rewards for role playing.

If you used a D100, you could make it more interesting I think... wider range of numbers makes it easier to add bonuses to a Skill without it getting out of hand. You could make it so that each Skill regardless of category has a 15% chance of gaining 1 Xp. However, based on the Category it gains either 3, 2 or 1. So a d00d with Athletics 5 [Minor] would still be outshone by a guy with Athletics 5 [Primary].

[John Blaz]

On a d20, the chance of earning skill XP will go up as the attribute increases regardless of Skill, until Stat + Skill is greater than 20, at which point the chance of XP will decrease as Skill increases.

...With 3d10, the further a number is from the average (16.5), the less likely it is to come up. I'd have to do some analysis to see how the increased range for greater Stat values interacts with the diminishing probabilities of higher-than-average numbers. Depending on the starting values, 3d10 might be closer to what you want.

I hadn't thought of that Selene, good observation. I would love to see what an analysis of the 3d10 version would show.

It might be better if the Xp required was always the same... but the Skill category (Primary, Secondary, Minor) would determine how often the Skill gained Xp.

...If you used a D100, you could make it more interesting I think... wider range of numbers makes it easier to add bonuses to a Skill without it getting out of hand. You could make it so that each Skill regardless of category has a 15% chance of gaining 1 Xp. However, based on the Category it gains either 3, 2 or 1. So a d00d with Athletics 5 [Minor] would still be outshone by a guy with Athletics 5 [Primary].

I had considered making the stat govern how quickly the skill can improve, but I never ran with it. I've also thought about using d100 for the wide range, but for adding in difficulty modifiers and all, I think I want to stay with smaller numbers. Same reason I had wanted to stick with using a d20, just less dice rolling, and as little math as possible.

[Selene Tan]

I got the chance to play around with the numbers for a bit and put up the results as a spreadsheet on Google Docs. The first sheet is the probabilities for D20 rolls, the second one for 3D10. (The third is kind of a scratch-sheet, so you can ignore it.)

Generally, the probability of gaining skill XP is lower with the 3d10. There are some Stat/Skill combinations where it's higher for 3d10, but the highest probability, 29.4%, is much lower than the highest probability with the d20 -- 50%. It still has the effect where higher Stats make it more likely to gain XP. Also, the chance of gaining skill XP is pretty bad at low Skill values -- at Skill 3 / Stat 2 there's a measly 0.3% chance of gaining XP. The probability goes up as Skill rises, peaks at 15-16, and starts falling. So it's looking like "Roll between Skill and Stat+Skill to gain XP" won't get you the results you want.

One neat solution I've seen for gaining XP via skill rolls is that you gain XP only when you fail the roll. So characters with low Skill ratings will fail a lot but gain XP quickly, and the XP gain will slow as their Skill increases. It also makes it less likely that players will try to roll for everything just to get XP, assuming failure always has consequences.

Another possibility is to have a flat chance to gain XP (e.g. 1 on a d20), but make the amount of XP required to level the Skill depend on the current Skill level. XP Required = (New Skill Level) x (Constant Multiplier) is the simplest formula of this type. You can swap New Skill Level for Current Skill Level and have the same general progression.

If you want Stats to govern how quickly Skills improve, they'll have to influence the probability of gaining XP, the amount of XP required to gain a skill level, or both. It's a little easier to think about the growth rate if Stats only influence one of those two things.

[zmobie]

You probably already know this, but...

With 3d10, the possible die rolls are (1,1,1), (1,1,2), (1,1,3), (1,1,4)...... (2,3,4), (2,3,5), (2,3,6)..... (0,0,8,),(0,0,9), (0,0,0). The dots are where there are a lot of other possibilities.

The odds of getting any one of these combinations is 1 in 10³

10 possibilities, 3 different slots = 1000 combinations.

Now, the reason why you get a bell curve when you add up the numbers is because there are multiple ways for your 3 dice combination to get certain numbers.

For an easy example, how many ways can you get a 3.

there is 1 way to get a 3 on the triplet (1,1,1). There are still 1000 possibilities for rolls, and that means the chance that you will get a 3 is 1 in 1000 or .1%

How many ways can you get a 4? (2,1,1), (1,2,1), or (1,1,2).

That is 3 different ways out of 1000 possibilities or .3%

How many ways can you get a 15? (0,1,4), (0,2,3), (0,3,2), (0,4,1), (9,5,1), (9,4,2), (9,3,3), (9,2,4), (9,1,5).... as you can see, there are a TON. Meaning there will be a very high percentage that you will end up with a mean value for your dice total.

The more dice you roll, the more centered your bell curve will be, and therefore the more predictable your rolls are. You don't need to do any more analysis of this 3 dice system to know that you can't count on your players rolling a 3 or a 30. Numbers between 8 and 22 are going to show up most often. With this information you could make a system that relies on rolling between 8 and 22, but punishes anything under 8 and rewards anything over 22. With this dice system, however, your game becomes more deterministic. The more dice you roll and sum, the more predictable everything in your game will be. If this is what you are going for, then the more dice the merrier. If you want some determinism, but still want to have some chance, I'd go down to 2d10 (or 12, or whatever you like).

[John Blaz]

One neat solution I've seen for gaining XP via skill rolls is that you gain XP only when you fail the roll. So characters with low Skill ratings will fail a lot but gain XP quickly, and the XP gain will slow as their Skill increases. It also makes it less likely that players will try to roll for everything just to get XP, assuming failure always has consequences.

Another possibility is to have a flat chance to gain XP (e.g. 1 on a d20), but make the amount of XP required to level the Skill depend on the current Skill level. XP Required = (New Skill Level) x (Constant Multiplier) is the simplest formula of this type. You can swap New Skill Level for Current Skill Level and have the same general progression.

If you want Stats to govern how quickly Skills improve, they'll have to influence the probability of gaining XP, the amount of XP required to gain a skill level, or both. It's a little easier to think about the growth rate if Stats only influence one of those two things.

Thanks for the input Selene. I think I am going to play around with having the stats stay pretty much static throughout the game, but they determine the range for gaining XP.

[Egonblaidd]

I was going for a similar idea in my heartbreaker, but I warn you it's rather complex (to be performed regularly, that is).

First off, resolutions are a d100 roll.  Attributes are FIXED after character creation, so it's important to get good attributes for the skill you plan on using.  Skills, on the other hand, can increase WITHOUT LIMIT.  The formula that makes this possible is a little more complex than normal, so I mandate that the base chance of success be written on the character sheet, and only changed when a skill increases.  Difficulty modifiers would be like +/- 10% etc. a la WFRP.   The base chance of success is (attribute * skill) / ((attribute * skill) + X), where X is some constant.  I actually have it vary from skill to skill and call it the "learning curve" of the skill, but 50 is average.  So if you have an attribute of 7 and a skill of 6, your base chance of success is (7 * 6) / ((7 * 6) + 50) = 45.7%.  If you had an attribute of 7 and a skill of 100, your base chance of success would be (7 * 100) / ((7 * 100) + 50) = 93.3%.  So even with a skill of 100 (which is really high) you still have a 6.67% chance of failure.  Attribute tests are (attribute^2) / (attribute^2 + 50), so an attribute of 7 gives about a 50% base chance of success.

Now, when a skill is attempted the degree of success is noted.  An Intelligence test (or Cunning, depending on the skill, I have both in my system) follows the skill test, modified inversely by the degree of success.  So if you make your roll by 20, then the Intelligence test is at a -20% difficulty.  If you fail by 20, the Intelligence test is at a +20% difficulty.  So failing makes it easier.  If the Intelligence test is passed, that skill gains a skill point.  When ten skill points are accumulated on the same skill, that skill increases one level.  As skill increases, your chance of success with that skill increases.  This means your average degree of success is higher, which makes the follow-up Intelligence test harder, which means it is on average less likely that your skill will increase.  Obviously, a higher Intelligence increases the "soft cap" for skills by making them easier to level up.  If your base chance of success with a skill is 90%, you will on average have 40 degrees of success.  If your base chance of success for Intelligence tests is lower than 40%, then on average you won't have a chance to raise your skill, while if your base chance was 50%, you'd have on average a 10% chance to increase your skill.

Like I said, the math is a little convoluted, and the mechanics are somewhat tedious to be performed on a regular basis, so I've been considering some alternatives.  However, I am pretty happy with the probabilities and such.  Perhaps you could use some variation of this type of system.

[John Blaz]

I think I'm going to try this:

The stats go up to 5. Whenever the d20 skill roll equals the stat or lower, the character gains XP for that skill. Since there are about 15 Broad skills with around 70 Narrow skills beneath them (ie: Broad = Survival, Narrow = Find Water), I figure the characters could start with 2 Focus skills (10 XP), 5 Primaries (6 XP) and 5 Secondaries (3 XP). All other skills are considered Minor (1 XP).

Task resolution is 1d20 < or = Broad skill + Narrow skill + modifiers
I was thinking of having the Broad skills go up to 5, and the Narrow skills go to 15. Maybe for each10 skill ranks gained under the narrow skills, the Broad goes up by 1 (so gaining 3 points in Swords, 5 in Maces and 2 in Unarmed would raise the Melee broad skill by 1). This has the same effect as my original idea of having the Stats rise along with the skills, but allows me to use the Stats primarily for determining XP and such. Then again, I might do away with Broad skills, not sure yet.