| thflame |
Hello All
Background information:
I am not proposing these changes to Pathfinder or any other system. I merely want people's feedback on these ideas for a separate system.
I am in the process of writing my own system, and since 3.5/Pathfinder are the closest things to what I'm looking for, I thought I'd start there for inspiration.
I have been playing pathfinder for about a year, and I played 3.5 since about 2008, so I know they general system pretty well.
For my system, I want as good of a ratio of "simple" to "simulationist" as possible. This effectively means, no unnecessary complications and minimal calculations during gameplay while offering a framework that supports doing just about anything you want.
Now, on to my, eh, questions/explanations, stuff:
I want to talk about how a character's core stats effect their "effectiveness" as a character in Pathfinder, and get input from people here on things they do and don't like about that aspect.
The most important "crunch" aspect is your character's stats and how they effect their abilities. In my system, I want to break down characters into Fluff (stuff that doesn't effect gameplay), Stats(what your core potential is), Skills(how well trained/educated you are in a particular area), and "Powers" (pretty much everything unique they can do).
In 3.PF, characters/creatures have a stats starting at 0 and going up, theoretically, indefinitely. A score of 10 is considered average and comes with a modifier of 0. From what I can tell, core stats are only used to calculate modifiers, which are used to determine your probability of success on a given check.
This is my first issue with the Pathfinder system. Aside from Feat prerequisites, odd numbers don't do much, if anything. A STR 13 guy isn't any more likely to succeed on a STR check than a STR 12 guy.
For my first question, are there any beneficial properties to having core stats work this way, or could this be worked around without much effect on the game?
My proposed implementation would be to just have Modifiers.
Next part, Since Pathfinder uses the 20 for checks, each point of modifier for a given check modifies your success rate by about 5%. Starting at a core stat value of 10, we have no bonus or penalty for that particular core stat. If we go down to 8 or 9, we have a 5% penalty to success. This continues down to a score of 1, where we have a 25% penalty to success. At 0, we immediately shift to a 100% failure, because we aren't allowed to roll checks with a 0 in a stat.
As an example, an easy DC is 10. A creature with a 1 in the respective stat, with no other modifiers, has a 30% chance of success (15 or better on a roll). Deal 1 point of damage to that stat, and now they are incapable of performing that check at all. It seems like there is a bit of a cliff here.
For my second question, should that "cliff" be there? Would people like to have a more even slope for characters who find themselves in dire straights or for exceptionally weak monsters?
My proposed implementation would be to add some more negative scaling before an effective "zero".
Finally, I find a problem with how stats "scale". An average human has a STR of 10. Someone twice as strong as that character would be 20, right?
How come, if these people were to have an arm wrestling match, the 10 STR guy has a 26.25% chance of winning? A 1 STR guy has a 11.25% chance of winning. A guy, with a Strength of 1/10th of the average human being, would have a 11.25% chance to beat a guy TWICE as strong as the average human. (I actually had a similar situation happen to a character of mine. My full orc fighter with 26 STR lost an arm wrestling match with a 15 STR Dwarf.)
Maybe, on the other hand, someone is NOT twice as strong as a human until they can achieve a DC twice as high as the average human could? In that case, it would take a STR 50 guy to be twice as strong as the average human. By that logic, the STR 1 guy is actually 3/4 as strong as the average human being. I feel like this system doesn't accurately portray a huge population of a theoretical fantasy world that way.
So, for my third question, is this a desirable outcome of the system? Should 1 STR creatures have a 11.25% chance of beating your 20 STR fighter in an arm wrestling match? Should you have to get a STR of 50 for mere average mortals to no be able to challenge your might?
My proposed implementation would be to either stretch out the spectrum or use a smaller die. On one hand, numbers would need to be fairly large, especially for creatures like dragons. On the other hand, we won't get to roll the d20 (it IS a lot of fun to roll) and we may remove degrees of success or failure that would otherwise be desirable.
So, what do you guys think?
| Serisan |
Typing on my phone, so very briefly...
You've hit on why stats are more than just modifiers in PF. It is the backbone of the system, affecting all other aspects of the game. I would recommend looking at other systems before settling on this model. My initial thought is to recommend a review of a capped stat system, a dice pool system, and a stat-divorced system. White Wolf has done dice pool for ages, while the Cypher system (Numenera) is awesome for stat-divorced. I helped co-author a capped system, but we never published.
Each of these offers very different challenges and benefits. Understanding them all will provide better perspective on for your review of d20 stats.
| Bob Bob Bob |
There are a few bits and pieces in the rules that use actual stat instead of modifier. Holding Your Breath and Carrying Capacity off the top of my head. Feat requirements are also supposed to use odd stats, though that was to give them more value (since they knew they otherwise didn't have much point).
But whether it's necessary or not depends on what you replace it with. They all have upsides and downsides. If you used the system we have now, using modifier instead of score, point buy becomes much harder and things like the every four levels stat boost just aren't possible (as well as the stat books and anything that gives an odd-numbered bonus). There couldn't be incremental change that didn't actually give a bonus. That kind of system would spike harder and plateau longer (gain a big boost, then not change anything for a while).
0 is also a failure condition for HP (well, plus Con score) and the condition is way more severe (death). Since a 0 in a stat represents "you no longer can use this stat" it makes perfect sense that a 0 Dex means you're helpless and a 0 Wis means you're brain dead. What would the alternative be? If you've been drained to 0 Str, it means you literally can't exert Str. What's the "first" condition you get before you hit helpless, flopping around?
So, 20 Str is actually more like four times as much Str as 10 (by carrying capacity) and Str over 20 is times four as much for every +10 score (+5 modifier). So 30 Str is 16x as much as 10 Str. 40 Str is 64x as much, etc. (not including size and legs).
However, anything that requires a roll is automatically being left up to "luck". If they don't want to risk the result they can take 10. That leaves a 30 Str person unable to lose against the average Joe on his best day instead of requiring Str 50. Because that's also part of the point. It takes an average Joe on his best possible roll, at the absolute peak of his concentration and muscle control, against someone rolling badly (not paying attention, not actually pushing, fell for a feint, etc.). The underdog winning is a fairly common trope, and for good reason. While it doesn't happen nearly as often as TV/movies would have you believe, it does happen. The 90 lbs weakling winning because Burly McMuscles' elbow slipped on some water while staring at the waitress sounds like an acceptable outcome.
| thflame |
I DO want stats to be the backbone of my system, however. (I already have a lot of ideas about how stuff will work, I just need to iron out the details of the base system so I know how to balance my other mechanics.)
I have looked at other systems like GURPS, Shadowrun, Rolemaster, and FATE. Pathfinder is still the closest to what I want, by far. I like the "check" system of 3.PF, I just want that die roll to fall in a range of values that is reasonable for the current situation. (My 26 STR orc character doesn't lose an arm wrestling match with a 10 STR commoner 16.5% of the time.)
| thflame |
There are a few bits and pieces in the rules that use actual stat instead of modifier. Holding Your Breath and Carrying Capacity off the top of my head. Feat requirements are also supposed to use odd stats, though that was to give them more value (since they knew they otherwise didn't have much point).
Thanks for pointing that out. I overlooked carry cap and hold breath. I guess my only issue here is that such things aren't used more often to justify them taking up space on my sheet. These things could easily be changed to run off of modifiers.
But whether it's necessary or not depends on what you replace it with. They all have upsides and downsides. If you used the system we have now, using modifier instead of score, point buy becomes much harder and things like the every four levels stat boost just aren't possible (as well as the stat books and anything that gives an odd-numbered bonus).
Yeah, that's why I'm not just home-brewing a tweak to Pathfinder. That would be a nightmare.
There couldn't be incremental change that didn't actually give a bonus. That kind of system would spike harder and plateau longer (gain a big boost, then not change anything for a while).
I actually like the idea of a system where each incremental bonus gives you stuff. I hate dead stat points. When I point buy, I like to have odd numbers, so when I get stat boosts, they DO something. In order to keep this under control, I'd like to minimize the amount of boost you get from these points.
0 is also a failure condition for HP (well, plus Con score) and the condition is way more severe (death). Since a 0 in a stat represents "you no longer can use this stat" it makes perfect sense that a 0 Dex means you're helpless and a 0 Wis means you're brain dead. What would the alternative be? If you've been drained to 0 Str, it means you literally can't exert Str. What's the "first" condition you get before you hit helpless, flopping around?
I have no issue with 0 being a failure point. I have an issue with the difference between a 1 and a 0 being a 75% drop in effectiveness, when previously, every 2 points granted you a 5% change.
So, 20 Str is actually more like four times as much Str as 10 (by carrying capacity) and Str over 20 is times four as much for every +10 score (+5 modifier). So 30 Str is 16x as much as 10 Str. 40 Str is 64x as much, etc. (not including size and legs).
That makes thing worse. If 20 STR is 4x as strong as 10, then a guy 4x as strong as Joe Average loses to him in a contest of strength 26.25% of the time.
The 30 STR guy (16x as strong) loses 11.25% of the time.
40 STR guy (64x as strong) loses 1.5% of the time. (Ignoring nat 1 as an auto fail)
However, anything that requires a roll is automatically being left up to "luck". If they don't want to risk the result they can take 10. That leaves a 30 Str person unable to lose against the average Joe on his best day instead of requiring Str 50. Because that's also part of the point. It takes an average Joe on his best possible roll, at the absolute peak of his concentration and muscle control, against someone rolling badly (not paying attention, not actually pushing, fell...
This is true, but sometimes (RAW) you aren't allowed to take 10. I suppose, as a DM, I could rule that Joe Average just loses by default, but Joe Average might be a PC. It's one thing to show Joe that it is impossible, RAW. It's another to go against RAW, and screw Joe over, because RAW is dumb. (Though, if that was my only problem with Pathfinder, I'd homebrew it anyway.)
It also doesn't help 20 STR guy very much. He now loses 20% of the time.
On this front, I have toyed with doing something like doubling all DCs, then allowing players to add their FULL respective stat to Skill Checks instead of their modifiers, as a homebrew solution.
| Bob Bob Bob |
Sure, but those "dead" points exist for a reason. A point buy that can only do modifiers has values of -2, 2, 5, 10, and 17. What's a standard point buy under that system? And if you're rolling them, same problem. Do you do 2d3-1? d6-1? Or do you round off a 3d6? The "dead" points pad the gap and spread the numbers out. It also plays much nicer with ability damage/drain, as poisons can occasionally do no damage (1 damage on an odd stat) and lowering the dice will increase damage (since 5 damage (1d6) twice is -5 modifier, but -3 modifier (1d3) twice is -6).
...I don't think you understand what I mean by failure point. At 0 it stops working. Yes, it decreases incrementally until then, but at some point it just flat out breaks. That's what happens at -Con HP, that's what happens at 0 in a stat. If you're saying it falls off too fast then increase what "average" is (or in your case, change the lowest negative modifier). You can also not have a lowest modifier, but then you need an exponential curve of weakness (can only lift a teaspoon, can only lift a leaf, etc.) and it's probably going to get wacky. For something simple like Strength, there's an obvious failure point (when you can no longer support yourself). For others it's more complicated, but the general idea is the same.
I can beat people stronger than me quite easily. It's called judo. Fake outs, messing with your opponent, stuff like that can all help a weaker person win at arm-wrestling. They only have to push their opponent hard enough to hit the table, it doesn't matter if the other person could have come back with a little more room if they hit the table. It's like a race. Whoever crosses the finish line first wins, regardless of how close the other guy is or whether they're faster. There's a very specific limited range you're measuring in.
You can ban taking 10 if you want, but that doesn't change the fact it's an option, and one which entirely negates the Str 30 person's chance of losing. If I'm doing a performance with a band I can choose to do it like practice (take 10) or try to be showy (roll) and possibly do really good (20) or fail spectacularly (1). If the Str 30 guy decides to be all tricky and the Str 10 guy decides to push with all their strength right from the start, yes, the Str 30 guy can lose. That's what take 10 is designed to prevent. Trained experts tripping over their shoelaces.
| Rub-Eta |
As an example, an easy DC is 10. A creature with a 1 in the respective stat, with no other modifiers, has a 30% chance of success (15 or better on a roll). Deal 1 point of damage to that stat, and now they are incapable of performing that check at all. It seems like there is a bit of a cliff here.
A cliff that I've almost never encountered. Your design should focus on more prevalent flaws to improve upon. Not corner cases while you open up for more prevalent flaws.
Finally, I find a problem with how stats "scale". An average human has a STR of 10. Someone twice as strong as that character would be 20, right?
No? 15 is twice as strong as 10. 20 is twice as strong as 15 (this is how the Str math functions in PF).
How does using only modifiers help this? Isn't 2 twice as strong as 1? That's a huge cliff.That makes thing worse. If 20 STR is 4x as strong as 10, then a guy 4x as strong as Joe Average loses to him in a contest of strength 26.25% of the time.
This is a problem in the check system, not the stats.
| thflame |
Sure, but those "dead" points exist for a reason. A point buy that can only do modifiers has values of -2, 2, 5, 10, and 17. What's a standard point buy under that system? And if you're rolling them, same problem. Do you do 2d3-1? d6-1? Or do you round off a 3d6? The "dead" points pad the gap and spread the numbers out. It also plays much nicer with ability damage/drain, as poisons can occasionally do no damage (1 damage on an odd stat) and lowering the dice will increase damage (since 5 damage (1d6) twice is -5 modifier, but -3 modifier (1d3) twice is -6).
I don't really want to deal with stat generation until I iron out a stat system. I'm fairly confident that I can come up with something that is balanced once I have a system in place. I'm leaning toward having large stat numbers that do fairly little on their own, so balancing should be easier, in theory.
...I don't think you understand what I mean by failure point. At 0 it stops working.
I get that. At a certain point you lack the Str/Dex to move, Con to live, Int to think, etc. I just think that we go from "disadvantaged"(25% more likely to fail) to "completely inept"(can't make a check) too quickly.
I can beat people stronger than me quite easily. It's called judo. Fake outs, messing with your opponent, stuff like that can all help a weaker person win at arm-wrestling.
Wouldn't those all fall under Skill Points/BAB/alternate skill checks? I plan to implement a skill system and allow players to work around the given problem.
A charismatic player can, given the option, perform a Bluff Check to catch the guy off guard for a small bonus.
Someone could take points in "arm wrestling" to represent learning and practicing a technique, for a small advantage.
They only have to push their opponent hard enough to hit the table, it doesn't matter if the other person could have come back with a little more room if they hit the table. It's like a race. Whoever crosses the finish line first wins, regardless of how close the other guy is or whether they're faster. There's a very specific limited range you're measuring in.
Yes, but that "very specific limited range" is 1-20. In order for your raw statistics to weigh in as much as the random chance, you'd need a stat 40 points higher. I don't even think that's possible between two characters of the same race.
You can ban taking 10 if you want, but that doesn't change the fact it's an option, and one which entirely negates the Str 30 person's chance of losing.
I didn't say I wanted to ban taking 10. I just pointed out that the rules say you can't always do that.
From the Core Rulebook, pg. 86: "When your character is not in immediate danger or distracted, you may choose to take 10."
Let's have another example. Joe Average (10 STR) and Hercules (30 STR guy) are in a hallway 10 feet high and 10 feet wide. There is a 1 foot thick stone slab separating them(Wheels make the weight a non issue). From each end of the hallway, a wall of spikes is coming. The spike won't stop until someone dies. The goal is to push the wall harder than your opponent does to push them back and have them killed first.
Because this is a life or death situation, Take 10 isn't an option. I'm okay with Herc losing because he rolled a 1 (Pulled a muscle, hand slipped, whatever) or Joe rolled a 20 (adrenaline spike, his god looked out for him, etc.) I'm not okay with Herc losing because he rolled an 8 and Joe rolled a 19.
| thflame |
thflame wrote:Finally, I find a problem with how stats "scale". An average human has a STR of 10. Someone twice as strong as that character would be 20, right?No? 15 is twice as strong as 10. 20 is twice as strong as 15 (this is how the Str math functions in PF).
How does using only modifiers help this? Isn't 2 twice as strong as 1? That's a huge cliff.
The reasoning behind getting rid of the core stat number is that it is rarely used outside of calculating a modifier. It is an unnecessary complication in the rules (in my opinion). Outside of the few things it is used for, what would be the difference in having a STR score of "20", or having a STR score of "+5" You could even reverse derive carry weight and holding your breath and get pretty close to what you would already have. I don't know how many times I have had to explain how to derive your Modifier from your ability score.
Let's take something like ability damage. What's more simple:
You take 7 points of STR damage.
You take a -3 to STR checks.
thflame wrote:That makes thing worse. If 20 STR is 4x as strong as 10, then a guy 4x as strong as Joe Average loses to him in a contest of strength 26.25% of the time.This is a problem in the check system, not the stats.
Wouldn't that be a problem with Modifiers not being representative of your character's capabilities? If 15 STR character (+2) is twice as strong as 10 STR character (+0) then how come a 15 is only 10% more likely to succeed on a given STR Check than a 10?
For all other stats, stuff scales linearly. You can hold your breath for CON x 12 seconds. Each boost in modifier gives you 5% better chance of success. (Damage depends on weapon type, so its a bit random.)
| Bob Bob Bob |
As I said, if the dropoff is too fast just change the average. Make 20 Str a +0 modifier (or 30, or 40). That way the time to hit 0 is much longer and the dropoff less steep. If you're making a new system you can pick points like that.
Bonuses to arm-wrestling could fall under skills, or special ability checks, or whatever, but right now they're just part of the standard d20 roll. That's because the whole system is incredibly abstracted, because nobody gives a @#$% about arm-wrestling. Nobody is clamoring for "finer-grained arm-wrestling rules" (honestly, probably someone is, but not many). That being said, you just admitted that the stronger person doesn't always win, and you'd make ways for players without Strength (like Joe Average) to beat the much stronger person using other checks. So why is it a problem if they do it now? Why can't the 20 they rolled represent something like those checks, happened upon by luck?
...by "limited range" I don't mean anything to do with levels or stats. I mean that I'm faster than Usain Bolt*. *If I trip him first and we only measure the 10m right after that. For that 10m, I'm faster than Usain Bolt. It's not true any other time, or over a longer race, or outside of those conditions, but it doesn't matter. If our race is only 10m (and I'm allowed to trip him) then I win. Arm-wrestling only covers from the start to the table. Once someone gets pushed to the table, they lose, regardless of whether they could have won with more space.
Well, then clearly Hercules doesn't have 30 Str. Considering how easy it is for Pathfinder characters to hit that, that's probably right (can't even carry a ton). Maybe 40? As for Beefy McMuscles (30 Str), if the result comes down to a single roll (instead of more than one roll), it depends on a raw ability check (instead of, in the case of the wall, being a bull rush), if he has bad luck (rolls less than 10) and his opponent has good luck (rolls better than 10), then yes, I think he should lose. It's an incredibly contrived scenario in which the deck is wildly stacked against him and literally everything has to go wrong, and even then he only has an 11.25% chance to lose. Require more than one roll and that chance drops to 1.27%. Allow him to take 10 and he literally cannot lose.
| Majuba |
I for one don't see why arm-wrestling would be a check at all. Not everything needs to be a check (even excluding Take 10 stuff). It's more like a measurement than a feat of strength. You don't make a strength check to pick up 50 pounds - you see if you have the carrying capacity. You don't make a check to memorize a spell - you check if you have a high enough ability score (and level).
As for the spiked wall bit - Bob^3 has it right. If it's one check, then Joe Average got in a good shove that Herc wasn't expecting, and the spiked wall hits almost instantly. If there's time, Joe would have to be *very* lucky (i.e. determined in world) to survive.
| dragonhunterq |
Not really much into game design, so these are closer to idle thoughts than measured criticism.
Wouldn't that be a problem with Modifiers not being representative of your character's capabilities? If 15 STR character (+2) is twice as strong as 10 STR character (+0) then how come a 15 is only 10% more likely to succeed on a given STR Check than a 10?
In a word, playability.
To do what you seem to want you need to lose the dice. If you want the strength 20 guy to always beat the strength 1 guy the check system isn't going to work. You seem to want a digital result - compare stats if yours is higher you win.
Expanding the range of stats feels like it is going to be either unwieldy or invalidate the dice in the same way that a level 20 fighter full attacking a goblin might as well not roll.
How will you balance the system when low ability scores become more than a flaw, but an actual liability? or high ability scores become an automatic 'I win' if they can't be over come by someone with a lower stat? How do you balance encounters with such dramatic swings in the same group?
| thflame |
Not really much into game design, so these are closer to idle thoughts than measured criticism.
That's fine. It can't hurt.
To do what you seem to want you need to lose the dice. If you want the strength 20 guy to always beat the strength 1 guy the check system isn't going to work. You seem to want a digital result - compare stats if yours is higher you win.
Not at all. People in the same league with respect to an ability value should be able to compete. People weaker by orders of magnitude should need a nat 20 to out perform their opponent.
Expanding the range of stats feels like it is going to be either unwieldy or invalidate the dice in the same way that a level 20 fighter full attacking a goblin might as well not roll.
I am noticing that stats will likely be about twice as large and grant modifiers for each point.
If we are dealing with a situation where one guy is 4-8 times stronger, the only point of the dice roll should be to see if someone got a lucky (or unlucky roll).
I have no problem with a character who has specialized in being really good at one thing only being threatened in that area by other entities that have invested similar amounts in the same area.
How will you balance the system when low ability scores become more than a flaw, but an actual liability? or high ability scores become an automatic 'I win' if they can't be over come by someone with a lower stat? How do you balance encounters with such dramatic swings in the same group?
It's okay to have situations where some of the characters say, "I can't do that". It lets the other characters shine. Characters are also more than welcome to try something else more in line with their skill sets.
It's also okay to have characters that are so skilled in one area that they "can't" fail. They specialized that way, they should be rewarded when that comes up. (There will always be bigger fish, however.)
| Bob Bob Bob |
Well, we've been basing our concept of Strength on carrying capacity. What if we base it on checks? We'll take Joe Average (Str 10) and figure out who needs to oppose him. Joe Average succeeds on d20>=1-20 checks...52.5% of the time. So literally no amount of Strength would be twice as much. Okay, so now we include DC 21, and Joe only succeeds 50% of the time. "Twice as much success" would be +20 modifier, or 50 Strength. So 50 Strength is "twice as strong" as Joe Average, only using DCs from 1-21. Let's go up to a nice round point, 25. So include all DCs up to 25. 42% success for Joe, what's our other person need? +12 mod, or 34 Str to succeed 84.4% of the time. And taken to the logical extreme, DCs from 1-1000. Joe gets 1.05% success. For more than 2.1% success we need +11 mod, or 32 Str. So I guess it does flatten out relatively quickly (1-25 and 1-1000 being +1 apart). Probably 1-∞ is still +11, at most +10 mod.
That being said, by measuring successes of ability checks, 32 Strength is only twice as strong as 10 Strength. By carrying capacity, it's 20x as strong. Which is right? If you reduce carrying capacity to match the checks, several larger monsters should literally collapse under their own weight (they won't because the rules don't include their own weight). But they might collapse under the weight of their gear. Heck, they might not be able to move their children. Fire Giants (31 Str) weigh 5,000 to 9,000 lbs as adults. Under the new system, they'd have a max load of 400 lbs. Average human toddler is 20 lbs, even if we assume average adult is 200 lbs the smallest Fire Giant toddler is 500 lbs. We can look at elephants (200/12000) which brings giant babies in at ~100 lbs, but that raises several questions about their biology.
If you do the reverse, and make it so 15 Strength (twice as much carrying capacity) succeeds twice as often (we'll say +10 modifier), does that modifier only apply to raw ability checks? Because if it applies to attack rolls, armor is going to become worthless. And the scaling is different. In order to succeed 4 times as often as Joe Average you need at least a +31 modifier. So 20 Strength would give you a +31 to attacks? Would 20 Dex give you a +31 to AC? And the scaling keeps going. Want to be 8 times as strong as Joe (Str 25)? You need at least +71 modifier. If a first level Orc Barbarian can hit a +71 anything, I think your system has go very, very wrong.
| Khudzlin |
I don't understand how you get fractional percentage points for single d20 rolls. You should get multiples of 5%. Joe Average succeeds a DC20 check 55% of the time (10-20), and a DC25 30% of the time (15-20). Now if you were doing opposed checks (d20+mod vs d20+mod), you'd get multiple of 0.25% (since there are 400 possible pairs of d20 rolls). So let's try by defining "twice as strong" as "succeeds twice as often in an opposed STR check". This means the stronger creature should win 2 out of 3 times (and the weaker the other 1 out of 3). The mod difference that achieves that is 3 (it's not exact, but it's the closest we can get). 4x as strong (80% success on opposed STR checks) happens with a mod difference of 5. This meshes with carrying capacity.
| Bob Bob Bob |
...Joe Average succeeds at a DC 20 check 5% of the time, as he has 10 Str (+0 modifier) and is thus rolling just a d20. My comparison was not for opposed Strength checks. It was the combined successes of all possible d20 rolls versus DC 1, DC 2, DC 3, up to DC 20 (and then 21, 25, and 1000) versus their failures. With every possible roll against every DC from 1-1000 (to be practical, more like 1-50) Str 32 will succeed twice as often as Str 10. That was the arbitrary criteria I chose. If you want to choose differently (opposed checks) you can.
That being said, your numbers are wrong. You're either rounding very heavily or not taking into account ties (4.25% of the time on your first example). If you want the higher Str to win (instead of tie or win) at least twice as often (instead of approximately), you need at least a +4 (30% v 66% instead of 34% v 61.75%). Your numbers do work for d20<=d20+3. The next comparison is just flat out wrong though, +5 mod gives you 26.25% v 70% (73.75% with ties). That's approximately triple, not quadruple. For a full comparison (no ties, at least 4x) you need +8 (16.5% v 80.5%), though +7 might be an acceptable rounding (19.5% v 77.25%). The (d20<=d20+X) version needs at least a 6, more like a 7. Here's how I do it. You ignore the 1s (they're the ties).
| Khudzlin |
Okay, I messed up with DC 20. The problem with your metric, however, is that it assumes a uniform distribution of DCs across the chosen range (an assumption which isn't borne out in play). There is a problem with opposed checks, however, and it's that ties are not taken into account (the only similar case where ties are taken into account is initiative checks - in which ties go to the highest modifier). I gave the ties to the stronger character (as in initiative), which gives* 264/400 for +3, 295/400 for +5 and 309/400 for +6 (so the +5 was a bit arbitrary, but it seemed closer). Anyway, going with opposed checks leads to the same kind of progression as carrying capacity (a set difference in ability score means a set ratio for success probability).
* I used exact probabilities: 1d20 - 1d20 is equivalent to 2d20 - 21, and it's easy to calculate probabilities for adding 2 identical dice (with n sides, an extreme result is 1/n^2 and each step toward the average increases the probability by that much)
| Bob Bob Bob |
Okay, I messed up with DC 20. The problem with your metric, however, is that it assumes a uniform distribution of DCs across the chosen range (an assumption which isn't borne out in play).Whose play? Mine? Yours? I already said the criteria was arbitrary. If I wanted to make a generalized set of DCs, what do I use? Every Strength check possibly allowed in every AP, weighted by sales numbers? Seriously, how do I generate "average" sets of DCs? That's why I just went with the set of all possible ones.
I could There is a problem with opposed checks, however, and it's that ties are not taken into account (the only similar case where ties are taken into account is initiative checks - in which ties go to the highest modifier). I gave the ties to the stronger character (as in initiative), which gives* 264/400 for +3, 295/400 for +5 and 309/400 for +6 (so the +5 was a bit arbitrary, but it seemed closer). Anyway, going with opposed checks leads to the same kind of progression as carrying capacity (a set difference in ability score means a set ratio for success probability).
* I used exact probabilities: 1d20 - 1d20 is equivalent to 2d20 - 21, and it's easy to calculate probabilities for adding 2 identical dice (with n sides, an extreme result is 1/n^2 and each step toward the average increases the probability by that much)
...300/400 is three times as successful, not four. You want 320/400 for an actual 4x success. Your numbers also don't extend. +10 mod (16 times as strong as +0) is 11.25% v 88.75% (~8 times as successful) using d20<=d20+10. Saying "it matches the carrying capacity numbers" means nothing if you don't include the "for Strengths at most 6 points apart".