On Stat Checks and d20s

[EDM Neo]

Something that's always bugged me is how variable a d20 roll is. Now, sometimes, this is fine; when performing an activity that actually would have highly variable results, it works great, but for other things... sometimes not so much.

For example, lots of people play arm wrestling as a simple strength check. d20+strength modifier versus d20+strength modifier. This works fine if two people are mostly evenly matched... but it gives unrealistic results when dealing with individuals who are unevenly matched. If you pit an 18 strength barbarian and an 8 strength wizard against each other, the barbarian will win most of the matches... but not quite all. The wizard has a non-negligible chance, a fair one, even, of soundly defeating the barbarian.

I think this article does a better job of explaining this then I can, but basically... 10 is the human average in each stat (strength, dexterity, constitution, intelligence, wisdom, charisma). It's not a bad score, it's a perfectly average one. A 12 or 14 is above average, but still within the limits of normality, just as an 8 is slightly below average, but not horri-badly so. But, once you get higher then that, you're getting outside the normal human limits.

A few exceptional people have existed that push 18ish, but they're legendary figures, the Olympic gold medalists and Einsteins and Gandhis... really not at all something that comes along every day. Barring outside interference, a real life skinny wimpy will never be able to beat an Olympic strongman in an arm wrestling contest. If he ever -can-, it won't be nearly as often as the d20+strength modifier rolls would indicate.

d20s do a fine job of portraying things realistically when you're dealing with reasonably decided upon DCs, and with most skill checks, especially when you account for various PnP things that our NWN dicebags don't portray, like the option to take 10 in some situations, or various circumstancial modifiers... but they aren't perfect for everything.

I think sometimes people should consider rolling a smaller dice and adding their ability modifier to it, rather then a full d20. For example, for the arm wrestling contest, opposed rolls of 1d4 or 1d6+strength+circumstantial modifiers. This way a lot of the variance is eliminated, which in some situations, is much more realistic. I'm not at all suggesting lower dice completely replace d20s... in many situations, they work just fine, and further, using bigger dice allow for some degree of "fairness." In certain environments, like a friendly competition between PCs, the chance of the puny wizard out-wrestling the hulking barbarian can sometimes be fun.

In summary... the variance resulting from using d20s is often a good thing, but when dealing with something that it'd be unrealistic or un-fun for there to be too much variance, it doesn't hurt to consider using a smaller dice like a d4 or a d6 once in a while.

Any thoughts?

Disclaimer: the above is just my opinion, feel free to disagree or ignore it as you will... I'm not at all talking authoratively on the matter.

*minor edit for typos*

[Lady Frost]

*completely agrees*

The arm wrestling thing is a very good example too.

[brian333]

Why not let them roll their HD die? That way a wizard (d4), rogue (d6), cleric (d8), fighter (d10), and barbarian (d12), each with 18 str would roll a die based on ow robust and physical his training would be. This would only work on Str or Con checks, though.

[minion]

excellent ideas. honesty, i think this could easily have been made a d10 system and reduced the random element to something within the realm of plausibility (particularly if you still include the crit hit/miss concept somehow).

the CL/HD idea isn't bad either, though i would prefer something that worked in all (or at least most) situations to a hodge-podge of approaches for different ones. perhaps sticking w/the d20 for skill checks and combat (where statistics can often off-set even the near 20 point spread of chance, and luck is often nearly as important as skill), but switching to anywhere from d4 to d10 for ability checks (where the die roll is typically 90% if the outcome and definitely shouldn't be)?

(i think we all know that this isn't going to become an official norm here, but i for one would love to see something like it become commonplace. )

[Munroe]

Jul 26, 2009 17:16:48 GMT -5 brian333 said:

Why not let them roll their HD die? That way a wizard (d4), rogue (d6), cleric (d8), fighter (d10), and barbarian (d12), each with 18 str would roll a die based on ow robust and physical his training would be. This would only work on Str or Con checks, though.

In my experience, wizard characters tend to have very high CON, regardless of their d4 hitdice. I guess all the low-CON wizards have already died.

Of course I don't really see a problem with using d20s. Sometimes the 18 STR character is tired. Maybe he pinched a nerve and wasn't fully in the game.

Really though, I think it should probably be a grapple check and the characters should get a BAB bonus and size modifiers. That 18 STR barbarian has +1 BAB per level until 20. The 8 STR wizard has +1 BAB at every other level (beginning at +1 at level 2 and ending at +10 at level 20). So if they're both level 4 and human, the barbarian would have a +4 STR bonus and a +4 BAB bonus. The Wizard would have a -1 STR penalty and a +2 BAB bonus. That's +8 for the barbarian's roll and +1 for the wizard's roll.

If the wizard is higher level, he has an advantage in the arm wrestling from experience. So the level 4 barbarian wrestles a level 12 wizard, for instance, and they have the same stats. The barbarian still has a +8 mod, but the level 12 wizard has a +5 mod now. (-1 STR and +6 BAB). The wizard has a better chance of winning not because he's any stronger than he was, but because he's trying to conserve his strength and looking for opportunities of leverage and things. If the barbarian were the same level (12) and hadn't put any points into STR in those 8 levels, his grapple modifier would instead be +16 versus the wizard's measly +5.

[minion]

*imagines the wimpy little 8-str elven wizard (that can't lift his favorite arm-chair w/o a Bull's Strength) beating the 20-str half-orc barbarian (who could -throw- that armchair -literally- across town) in an arm-wrestling contest because...* wait... i can't even imagine it, but then i have a pretty crappy imagination.

on a more serious note... yes, everyone has their off days, and occasionally some oddly fortuitous success, but that is not what's being borne out in the statistics as we're using them. the die roll is 75% (or more) of most contests that are resolved using ability checks. back to our current example: using carrying capacity as a fair approximation of raw brute power (which is -most- of an arm-wrestling contest), there is virtually -no- way an 8 str char should beat the 20 str char that could literally pick them up with that one arm and throw them around like a rag-doll (yes that would be grapple, with a -10 penalty for only using one hand, but let's leave it at the hyperbole it was intended as), while taking a bite out of an apple from the other hand. i understand that things are more fun when everyone has -some- chance of success (and failure...) and that this is a fantasy game that's all about imagination, but the bigger the nod to physics and statistical probability, the easier it is to get your head in the game. simplicity (for quick/easy play) is as much a necessary evil as complexity (for realism), and we're all trying to find the right balance, which i applaud.

[brian333]

Jul 27, 2009 15:47:52 GMT -5 minion said:

*imagines the wimpy little 8-str elven wizard (that can't lift his favorite arm-chair w/o a Bull's Strength) beating the 20-str half-orc barbarian (who could -throw- that armchair -literally- across town) in an arm-wrestling contest because...* wait... i can't even imagine it, but then i have a pretty crappy imagination.

The wizard grew tired of the barbarian's boasting, and after listening to him win round after round of armwrestling and growing louder and more obnoxious with every win, the wizard decided to do something about it.

The giant laughed as the thin, almost emaciated wizard stood, his bony arm upright on the table before the barbarian. The barbarian tossed back an ale and said, "I won't hurt you too bad!" and with a wink to the barmaid he propped his massive arm on the table.

The two gripped hands, and when the judge said, "Go!" the barbarian sat calmly waiting for the feeble pressure of the wizard. But the wizard had studied anatomy, and knew the placement of every muscle, vein, tendon, and nerve of the human hand. Calculating the exact point he pressed nerve against bone and was pleased to hear a scream as a jolt of pain wracked the barbarian's now limp arm.

With a light push the wizard slammed the barbarian's knuckles against the table and released the hand. "I think I've had enough arm-wrestling tonight," he said, and returned to his book by the fireplace.

[soulfien]

And this is what the 3rd edition lovers get for throwing out 2nd edition because of all the math

2nd edition had a better system because all the die rolls and numbers were different based on each different scenario. That's why I liked it.

For ability checks, the roll was 1d20 and you had to roll your ability score or LOWER.

Forget ability score modifiers- they didn't exist... so if the 18 strength barbarian rolled against the 8 strength wizard, the wizard would have about 1 or even .7 in 20 chance of winning. The wizard would have to roll a good on his own strength check while rolling between 1 and 8 on a d20 while the barbarian rolled a 19 or 20 on his.

Still realistic? not really, but it was a LOT closer. The system we use now is horribly flawed.

--Edited for a typo

[minion]

(psst, brian... there'd be an epic heal check in there somewhere...)



and Soulf, you're going to have to explain to me how they check against each other... if i remember correctly, the system is designed to check success/failure, w/o any consideration of opposed checks. granted it has been nearly a decade since i played 2nd... (feel free to take it to a PM, so as to save everyone else the details. )

(and yes, i love my ellipses...)

(edited to combine posts and save you all some space.)

[Deleted]

I'd suggest using the 3d6 variant rule to decrease variability.

I use this for attribute and skill checks in all my PnP campaigns & have enjoyed it greatly.

[soulfien]

Jul 28, 2009 3:07:20 GMT -5 minion said:

(psst, brian... there'd be an epic heal check in there somewhere...)



and Soulf, you're going to have to explain to me how they check against each other... if i remember correctly, the system is designed to check success/failure, w/o any consideration of opposed checks. granted it has been nearly a decade since i played 2nd... (feel free to take it to a PM, so as to save everyone else the details. )

(and yes, i love my ellipses...)

(edited to combine posts and save you all some space.)

Well, Minion, the way the roll works is the closer you get to your max without going over, the better you did.

So if you have a strength of 8 then you'd want to roll as close to the 8 as possible without going over it.

But if the warrior with 18 strength rolls higher than the wizard and doesn't go over his 18 then he definately wins.... of course he still succeeds on a 2 if the wizard rolls an 8 because he DID roll his strength so it's still a success and the wizard doesn't beat him.... it would mean the fighter's heart isn't in it and still has his arm in the air.

[minion]

soo... you're comparing degrees of success, after checking for failure, instead of comparing two numbers, and you're calling it easier..? *remembers why he and all his pals immediately and irrevocably switched systems as soon as they experienced the blissful logic of 3.X (notable exception of grapple... but nothing's perfect)*

(note: Soulf knows quite well that the snarky tone is intended for his amusement, not to degrade him.)

[Deleted]

Rolling 1d20 in all cases is certainly easier than the 2.x version, but that's not the problem. As Neo states in the first post, a d20 is too much variance if the non-random component of the check is small.

IE a wrestling match between a wizard with 12 strength and a barbarian with 18 strength would be represented as: d20 + 1 vs d20 + 4. This gives almost no advantage to the 18 strength barbarian because the random component is so high in comparison to their strength modifiers.

The solution is either to reduce the size of the random modifier (1d6) as neo suggested, or to reduce the variance of the random modifier but keep the same range (3d6) as I mentioned.

While rolling 1d6 or 1d8 works for opposed checks, I would suggest using 3d6 instead because it has the same range as 1d20, but with significantly lower variance. Having the same range as 1d20 allows 3d6 to be used for DC based checks as well as opposed checks.

[Munroe]

The new Pathfinder RPG (an updated 3.5e-style system) introduces Combat Maneuver Bonus (CMB) and Combat Maneuver Defense (CMD).

Combat Maneuver check basically equals Grapple from 3.5e (d20+BAB+STR mod+size mod), though there's a feat to substitute DEX for STR. Combat Maneuver Defense is 10+BAB+STR mod+DEX mod+size mod+some AC modifiers. In that system, the wrestler with the higher initiative would make a Combat Maneuver check (d20+CMB) against the CMD of the opponent to see if they can pin the arm, then if the arm was not pinned, their competitor would try to pin with CMB vs. CMD on their initiative.

[Thrym]

I personally think armwrestling should simply be resolved by both sides taking 10, no rolling at all unless both sides have the same modifier. Or maybe roll a d2 and add str mod. Anything more then that is in my opinion uhh... pretty silly.

8 and 12 str is the difference between 'that weakling' and a well trained guy with visible musculature.

[Deleted]

Rolling a much smaller die like d2 is not very exciting though, as you'll know who will win ahead of time. Ideally an opposed check will offer some small chance for the character with the lower skill/attribute to win, but favor the character with the higher skill/attribute significantly.

For DC based checks, it's also not very exciting to know that you will always win/lose. However, it can be very frustrating if a quest comes down to a single attribute check and the outcome is mostly determined by luck.

In both cases, suspense can be maintained by using a random component with larger range but with reduced variance. This makes it possible for a weaker character to win an opposed check (or a low str char to succeed at a dc based check) but far more unlikely than rolling d20s.

This might be best explained by looking a the chances to roll "extreme" values using d20 vs 3d6.

• The chance to roll a 1 with a d20 is 5% or one in twenty. This is the same chance as rolling a 10!
  
• The chance to roll 3 with 3d6 is only 0.5% or one in 216
  
• The chance to roll 10 with 3d6 is over 12%, which means you are 24 times more likely to roll a 10 than a 3!
  

The upshot of changing to 3d6 is that you are far far more likely to roll mid-range values like 7-13 than values toward the extreme of the range. This reduction in variance means that "extreme" outcomes are fairly rare & favors the party with the higher stats. However, since there is still a chance to roll quite high or quite low, suspense is maintained.

[828stingstingneo]

For a glimpse of what the gaming world would be like with d20 checks for everything, see the movie Gamers. It's hilarious, spoofing other funny gaming situations as well.

[Thrym]

Jul 29, 2009 8:19:17 GMT -5 @rjanney said:

Rolling a much smaller die like d2 is not very exciting though, as you'll know who will win ahead of time. Ideally an opposed check will offer some small chance for the character with the lower skill/attribute to win, but favor the character with the higher skill/attribute significantly.

For DC based checks, it's also not very exciting to know that you will always win/lose. However, it can be very frustrating if a quest comes down to a single attribute check and the outcome is mostly determined by luck.

In both cases, suspense can be maintained by using a random component with larger range but with reduced variance. This makes it possible for a weaker character to win an opposed check (or a low str char to succeed at a dc based check) but far more unlikely than rolling d20s.

This might be best explained by looking a the chances to roll "extreme" values using d20 vs 3d6.

• The chance to roll a 1 with a d20 is 5% or one in twenty. This is the same chance as rolling a 10!
  
• The chance to roll 3 with 3d6 is only 0.5% or one in 216
  
• The chance to roll 10 with 3d6 is over 12%, which means you are 24 times more likely to roll a 10 than a 3!
  

The upshot of changing to 3d6 is that you are far far more likely to roll mid-range values like 7-13 than values toward the extreme of the range. This reduction in variance means that "extreme" outcomes are fairly rare & favors the party with the higher stats. However, since there is still a chance to roll quite high or quite low, suspense is maintained.

Well and good, but if one character can barely lift his weapon and the other can juggle refrigerators, I don't see why there needs to be any how ever small chance for the first one to win. It's as if me or you were trying to stop a speeding car by tackling it head on.

Aside from that, I completely agree that 3d6 would be preferable for skill checks in general. Opposed ability checks though should not be rolled at all past a certain difference in the characters ability.

[Deleted]

I agree that it doesn't seem very realistic for someone with normal or a penalty to an attribute to beat someone with outstanding scores in an opposed competition. You could always have a minimum score to be allowed to compete at arm wrestling/etc?

I could definitely understand just using the score in some situations without any randomness, but you could also require multiple checks in a row to win to even further reduce the chance of the underdog winning

[fred]

I do think this 3d6 idea for checks of this sort is interesting. Of course, you'd have to decide under what circumstances you wanted to use that system instead of the d20.

Brian's example of the wizard beating the barbarian is a good one: though I think that didn't sound like a lucky roll on his strength check, it sounded like him convincing the barbarian's player to let him substitute an int check to try to outwit him instead.

[Pookey]

GURPS: FRC!!!!

[Micteu]

Actually, I thought of this problem when I was making my Simplified D&D rules for when I DM pen and paper sessions.

However, I think crit hitting and crit missing is pretty fun. I like the idea of having a more realistic probability in the bell curve with three dice rather than the inverted V probability of two dice, or a straight line of one, but I would say automatic success and failure should land on at least 17 and 4 in addition to 18 and 3.

[Quadhund/Greenhouse]

Personally, I don't necessarily think it is a flaw with the dice rules so much as the definition of strength. For instance, carrying, lifting, and dragging capacity are all based off str, yet each one of those actions uses an extremely different set of muscles.

I refer you to the activities performed in the world's strongest man competition:
en.wikipedia.org/wiki/World%27s_Strongest_Man
and then to here for what those kinds of weights mean in DnD terms:
www.d20srd.org/srd/carryingCapacity.htm#liftingandDragging

Easily any man that performs in that competition is close to if not over 18 str. So maybe your 18 str barb doesn't have biceps the size of tree trunks, but perhaps he has pectoral muscles to fill DD cups.

But yes, I do think it odd that 18 str (4 mod) and 8 str (-1 mod) only gives you a 25% chance win bonus. Also, as far as I know, there are no DnD specific rules to arm wrestling, so str check is a completely player developed idea for determining the winner. I do applaud that this thread seeks to offer suggestions to players who might want alternatives.