Ability Score, Beyond BtB

[sixdemonbag]

In reality, I actually go in the opposite direction and constrict the role of ability scores since I find that they tend to quickly get out of hand. When I run OD&D, ability scores never come into play anyway so I usually just jettison them for simplicity.

Besides, monsters don't have ability scores which is where most comparisons would be made. However, if I had to expand, I'd use Gary's houserules:

For a score of 15 or over:

STR: +1 to hit and +1 to damage if a Fighter
INT: +1 1st level m-u spell
WIS: +1 1st level cleric spell
DEX: +1 to AC, and +1 to move silently
CON: +1 HP per HD (same as a Fighter class gets, +2 if a Fighter)
CHA: +1 (positive) on reaction checks

HPs: Characters are only unconscious at 0 HPs. For each level a character may have a minus HP total equal to the level, so a 1st level PC is dead at -2, a 2nd level at -3, etc.

That's the gist of things.

Gary

To add to Gary's chart above, I'd probably also give a +1 to saves for WIS and +1 to locate traps, doors, passages, and spike doors, etc. for INT.

[sixdemonbag]

Mar 19, 2019 13:00:17 GMT -6 Piper said:

I agree they can get out of hand. My solution is to limit the bonus to +1 only (except in the case of CHA which I run BtB).

That's a good compromise. I really like the small bonuses of M&M. I would even prefer a small bonus to a straight roll-under ability check.

Hopefully, some others will jump in with their custom ability score tables. I always like to see what other tables are out there that people like to use.

[delta]

For the bonus I use the statistical z-score (i.e., number of standard deviations from the expected value on 3d6), which is +1 in 13-15, and +2 in 16-18. Conveniently this scales smoothly further up (giants or magically enhanced strength, etc.).

Pretty standard effects, similar to OP: Str (melee hit/damage), Int (searching), Wis (mental saves), Dex (AC/missiles), Con (hit points), Cha (reaction rolls). My players and I are liking it. (Possibly the Wis mental save bonus gets forgotten on occasion, as it doesn't come up that often.)

[sixdemonbag]

Mar 19, 2019 21:26:23 GMT -6 delta said:

For the bonus I use the statistical z-score (i.e., number of standard deviations from the expected value on 3d6), which is +1 in 13-15, and +2 in 16-18. Conveniently this scales smoothly further up (giants or magically enhanced strength, etc.).

Any chance that you could go into more detail on this? I'm not familiar with z-scores but I really like the range you list here, especially if there's some underlying math behind it. If it's too complicated or in your blog already just ignore and I'll do some research.

Mar 19, 2019 21:26:23 GMT -6 delta said:

Pretty standard effects, similar to OP: Str (melee hit/damage), Int (searching), Wis (mental saves), Dex (AC/missiles), Con (hit points), Cha (reaction rolls). My players and I are liking it. (Possibly the Wis mental save bonus gets forgotten on occasion, as it doesn't come up that often.)

I very much agree with all the above as a "standard" baseline for non-Greyhawk OD&D. What are your thoughts on having WIS applying to all saves? That's how I usually do it when I've used those types of bonuses in the past. That way it gets used more often and is more useful in general.

[delta]

sixdemonbag, thanks so much for asking! One source would be Wikipedia: Standard Score (a.k.a. z-scores). It's a pretty rudimentary (i.e., Stats 101 Day 5) technique for measuring how far a data point is from the average, which almost always falls in the range of ±3 regardless of the data source (hence, "standard"). When someone recalls the rule of thumb, "For normal data, 68% is within 1 standard deviation of the mean, 95% within 2 standard deviations, and over 99% within 3 standard deviations", the z-scores are those 1-2-3 values.

It's defined by taking a data point x, the population mean (average) μ, the standard deviation σ, and computing z = (x - μ)/σ. Note that for the random variable 3d6, μ = 10.5 and σ ≈ 3.0. (See here, click "Calculate probabilities", and note what they're calling "Spread".) So the upshot is that using this metric, every 3 pips increments the z-value one point. Starting from an average of about 10 we get 10-12: +0, 13-15: +1, 16-18: +2 -- which is just so numerically nifty that I couldn't avoid using it.

On Wisdom modifying all saving throws: I might be coming around to that, granted how rarely my (AD&D-style) "mental attack adjustment" rule gets triggered in play. Although to date I've had a hard time interpreting how Wisdom helps against things like poison, dragon breath, hit by falling stone, etc. I suppose we could at least expand to Moldvay B/X-style, all "magic-based saving throws".

[waysoftheearth]

I love it when we talk statistics

Kinda related, I've been pondering the virtue of qualitative advantage over the classic absolute/quantitative modifiers for a while now.

I've haven't thought this through carefully but (sometimes?) it seems to me that what matters is that being relatively stronger (for example) is advantageous. "High" strength is "high" compared to an average specimen, but not compared to another high strength individual. Put another way; are two high strength individuals really both advantaged against each other in melee?

That prolly doesn't help with the OP much, but hey.


Meanwhile, in terms of the regular adds, I like wisdom for saving throws versus enchantments/will power, and for XP adjustment (reflecting the capacity to learn something useful from experience).

[sixdemonbag]

Ah I see, so the z-score is an expression of the standard deviation (sigma). Thanks for the info, as the term was unfamiliar. Interestingly, despite always liking the B/X ability bonus table...

3	-3
4-5	-2
6-8	-1
9-12	None
13-15	+1
16-17	+2
18	+3

...your table actually models reality better statistically:

3-5	-2
6-8	-1
9-12	None
13-15	+1
16-18	+2

I really like it! And yes, of all the saves, poison is the most problematic to link to "WIS" from a logical standpoint. You would almost have to treat a WIS-based save bonus as "luck" or some such, which is kinda meh.

The CHA and Loyalty tables also closely follow your model, although I'd guess it came about intuitively rather than derivatively. How would these principles apply to a 2D6 throw?  I know 1d6 models cumulative standard deviations (in half-steps) extremely closely. I did a post about it here: 

odd74.proboards.com/post/201948/thread

and here:

Sept 13, 2017 3:10:33 GMT -6 sixdemonbag said:

For reference:

Cumulative normal distributions in 0.5 intervals: 16% 31% 50% 69% 84%
Compared to d6: 17% 33% 50% 67% 83%

That's a d**n near perfect match!!!

[chicagowiz]

I could "justify" WIS against poison as someone having the wisdom/common sense of avoiding drinking that mysterious pool of water that you happen to find in a dungeon... things like that. It's a stretch, but I could make a case for it.

[Zenopus]

If one views Wisdom mostly as the "Cleric Prime Requisite", one could justify applying it to all saving throws as a form of divine favor. The wiser one is, the more attuned to a deity, the better the saves. Like luck, but deity based.

Alternately, with respect to Poison, high Wis could reflect choices that make you poison resistant (clean living, healthy eating) and/or instincts that reduce the chance of being poisoned (pulling away from the fangs before they go all the way in, sucking out some of the poison).

[delta]

Mar 20, 2019 9:54:19 GMT -6 sixdemonbag said:

The CHA and Loyalty tables also closely follow your model, although I'd guess it came about intuitively rather than derivatively. How would these principles apple to a 2D6 throw?  I know 1d6 models cumulative standard deviations (in half-steps) extremely closely. I did a post about it here: 

odd74.proboards.com/post/201948/thread

and here:

Sept 13, 2017 3:10:33 GMT -6 sixdemonbag said:

For reference:

Cumulative normal distributions in 0.5 intervals: 16% 31% 50% 69% 84%
Compared to d6: 17% 33% 50% 67% 83%

That's a d**n near perfect match!!!

Holy crap. I didn't know that, and didn't even believe it when I first read that. That's a really sweet observation, thanks for sharing that!

For 2d6, μ = 7.0 and σ = 2.4. I'll take half-standard-deviation steps to use as cutoffs between integer bonuses. z_(−1.5) = 3.4, z_(−0.5) = 5.8, z_0 = 7.0, z_(0.5) = 8.2, z_(1.5) = 10.6. So this model suggests you use 2-3: −2, 4-5: −1, 6-8: +0, 9-10: +1, 11-12: +2. Pretty elegant. (It's one pip off the Vol-1 NPC Reaction table on the high and low ends.)

And I agree with you about the B/X ability modifiers. Have you ever seen Mentzer's Immortal Rules? He has this completely lunatic system for extending the ability scores up to a value of 100 -- the category/tiers expand and contract as you go up with almost no recognizable pattern.

[talysman]

Mar 19, 2019 11:15:04 GMT -6 sixdemonbag said:

In reality, I actually go in the opposite direction and constrict the role of ability scores since I find that they tend to quickly get out of hand.

Same here, only more so. No bonuses other than the Dex/Con/Cha bonuses listed in M&M.

Where I do expand is in using ability scores to judge when to allow or require a 5+ on 1d6 check for various situations. Crossing a perilous chasm on a log might require a check to avoid falling off, which I might rate as a Dex score. If the PC's Dex is => the score, no check is needed. If the PC lies on the log and wraps arms and legs around it to crawl across, I might substitute Str for Dex.

In a few cases, I might have saves for "mundane" dangers. I only use the standard five saves for supernatural situations (+ poison,) but for natural things like system shock, I would use a reaction roll under an ability score, or half the ability score under extreme situations. Roll over the score = failure, roll under = degrees of success, using the reaction table to define the degrees (A Very Bad result that's under Con might mean just barely survived, but incapacitated for several days, while a Very Good result means the character springs back into action almost immediately.)

[waysoftheearth]

Mar 20, 2019 9:54:19 GMT -6 sixdemonbag said:

Ah I see, so the z-score is an expression of the standard deviation (sigma). Thanks for the info, as the term was unfamiliar. Interestingly, despite always liking the B/X ability bonus table...

3	-3
4-5	-2
6-8	-1
9-12	None
13-15	+1
16-17	+2
18	+3

...your table actually models reality better statistically:

3-5	-2
6-8	-1
9-12	None
13-15	+1
16-18	+2

Mar 20, 2019 21:08:08 GMT -6 delta said:

For 2d6, μ = 7.0 and σ = 2.4. I'll take half-standard-deviation steps to use as cutoffs between integer bonuses. z_(−1.5) = 3.4, z_(−0.5) = 5.8, z_0 = 7.0, z_(0.5) = 8.2, z_(1.5) = 10.6. So this model suggests you use 2-3: −2, 4-5: −1, 6-8: +0, 9-10: +1, 11-12: +2. Pretty elegant. (It's one pip off the Vol-1 NPC Reaction table on the high and low ends.)

I love the concept of differentiating the "arbitrary" numeric ability scores relative to their position in the population distribution.

The part I'm struggling with is: why do we choose to assign an adjustment of, say, "+1" and is it meaningful? Why not +2 or +3?
Moreover, we know that +1 is of greater significance on a d6 than it is on a d20, so presumably one should require a higher ability score to get that +1 adjustment on a d6 (I posted something about this way back, but I can't find it now).

So to put it another way: What adjustment to a throw of 1d6, 2d6, 3d6 or 1d20 would increase the mean result by one standard deviation?

[sixdemonbag]

Mar 29, 2019 23:19:27 GMT -6 waysoftheearth said:

I love the concept of differentiating the "arbitrary" numeric ability scores relative to their position in the population distribution.

The part I'm struggling with is: why do we choose to assign an adjustment of, say, "+1" and is it meaningful? Why not +2 or +3?
Moreover, we know that +1 is of greater significance on a d6 than it is on a d20, so presumably one should require a higher ability score to get that +1 adjustment on a d6 (I posted something about this way back, but I can't find it now).

So to put it another way: What adjustment to a throw of 1d6, 2d6, 3d6 or 1d20 would increase the mean result by one standard deviation?

First of all, your question kinda broke my brain, lol, but I think I understand your struggle. Even if we model the die ranges into std. devs. that still leaves the bonuses themselves as somewhat arbitrary. I think we can agree that fractional bonuses are gross, so we can eliminate even thinking about those (gotta draw the line somewhere and for me it's whole pip numbers.)

Now, amazingly, for the common d6, your question is easy to answer. Turns out, that each +1 is almost exactly 1/2 std. dev. (cumulative, i.e. 2 or higher, 3 or higher, etc.) So for the d6, +2 is almost exactly a cumulative increase of one std. dev. This might explain why the d6 just "feels right" as it does a good job modeling nature in a very simple, intuitive way. Also, on a d6, if you want to stay within the range of the die itself, for gaming purposes, you are basically limited to a +4 bonus which is almost exactly 2 std. devs. Once you get to +5 or more, you reach or exceed the range of the die and thus make the randomizer almost meaningless. The d20 equivalent of this would be +19 or higher. This makes +18 on a d20 the effective maximum of gaming usefulness. A digression to be sure...

For the d20, +7 comes very close to an increase of one std. dev. (again, cumulative). But it's not as elegant as the d6 since sometimes it's closer to 6 and other times 8. +7 would do in a pinch though. Come to think of it, the advantage/disadvantage mechanic of 5E is almost exactly a 1/2 std. dev. increase while a similar mechanic for the d6 would be also be a 1/2 std. dev. increase. Not sure what that means beyond coincidence though and another brain break. I'm starting to feel like a numerologist!

I'd have to research how this would work on the nonlinear 2d6 and 3d6. It's late here so maybe my thinking is totally wrong here or I completely misread your question.

[smubee]

Not sure if I got this from another version of D&D or something, but I've always used the ability scores as the "real estate" that a player has if they have to make a check or something.

For example : Trying to jump through the door as it seals shut? Say the character has a DEX of 14. If they roll a d20 and get 1-14, they succeed. If they get any higher, they fail.

[delta]

Mar 29, 2019 23:19:27 GMT -6 waysoftheearth said:

The part I'm struggling with is: why do we choose to assign an adjustment of, say, "+1" and is it meaningful? Why not +2 or +3?
Moreover, we know that +1 is of greater significance on a d6 than it is on a d20, so presumably one should require a higher ability score to get that +1 adjustment on a d6 (I posted something about this way back, but I can't find it now).

So to put it another way: What adjustment to a throw of 1d6, 2d6, 3d6 or 1d20 would increase the mean result by one standard deviation?

A fair question. For me, I just use the same bonus on either d6 or d20 rolls. I rationalize that by saying d6-type rolls are "unskilled" and dominated by natural ability; while d20-type rolls are "skilled" and dominated by training, knowledge, and experience (usually involving addition of the character's level or something close).

If one did want probabilistically high-fidelity conversions, then I would take d6 modifiers and multiply by 3 for equated value on d20.

[retrorob]

As for the abilities I use two house-rules.

1) there is a possibility to increase an ability after getting a level. There is 10% chance for this. If the player rolls 10, then rolls again for a random characteristic (1-STR, 2-INT and so on) and adds 1 to it. This house rule is based on EPT.

2) as I don't like simple ability checks, I developed a rule based on a percentage chance for withstand. For example a character withs STR 13+ has 100% chance for pick some boulder up, the one with STR 10 has 70% etc.