When it comes to ability scores in D&D, there are two main tensions at work:
• How do you balance the fun of random scores against the disparity between players who roll well vs. those who roll poorly?
• And, intimately related to this, how much should a good roll or a bad roll impact the character? In other words, how you balance "scores should matter" vs. "scores shouldn't matter that much"?
The first question speaks directly to ability score generation. What's preferred? What's ideal? 3d6 in order ("Ironman")? 4d6k3 ("Gygaxian")? Soulless point-buy systems? Group dice (i.e. roll 18d6 to the table and let all the players use this same roll to build their own set of six 3d6 rolls)? Each has their pros and cons, but a quick run-down of the old-school orthodoxy goes something like this:
• Point-buy (where, for example, everybody has 75 points to distribute among six ability scores) has a few redeeming features: everyone is certain to get an acceptable set of ability scores, all of the players start off more or less on the same footing, and it's impossible to cheat the system. But on the down side, it's boring, it's time-consuming (as the players weigh advantages and disadvantages, add a point here, subtract two there), and it winds up being pointlessly time-consuming since once a player has optimized their scores, those scores are going to look pretty much the same for any other character of that class. You get no variety with point-buy; only enforced equality, and the illusion of choice. It is the least desirable method of score-generation in an old-school game (and in fact, it's not "generation" at all, but apportioning).
• Group dice at least involves some fun. You roll eighteen dice to the table, record the rolls, and then the players have to figure out how to place three rolls into each of the six ability scores to give them the character that they want. The advantages are the same as with with point buy—everyone's scores are more or less even, and the players can customize to their heart's delight and pretty much pick the class they want to play. The disadvantages, though, are also pretty much the same: it's slow, and it produces "samey" optimized characters with no real quirks or surprises, Excellent for a game 2nd edition AD&D. Not so great for a game of OD&D.
• The Gygaxian method (roll 4d6, keep three; six times, and arrange to taste) is the standard in AD&D. It's okay, I guess, but it does tend to make most rolls higher than average, which is highly desirable in the various editions of AD&D where the bonus tables look like they do; in OD&D, not so much. There, it would be a pointless inflation of numbers; it's still swingy enough that you get some players having much better rolls than others; and once again it's not really character "generation" if the player chooses where to put the stats.
• That brings us to good old Ironman method. 3d6 in order, end of story. (Yeah, if you're playing by-the-book OD&D you get those 2:1 and 3:1 stat adjustments for your class prime requisite, but that's after the fact; I'm taking about bare-bones score generation here.) This method remains the gold standard for old-school games, because you can be surprised. You can wind up with a good number in an offbeat stat. You can wind up playing a class you hadn't considered. It's true character generation.
But there are some inherent problems with Ironman stat-generation. It's pretty darned swingy. You can easily wind up with a nigh-unplayable character, if you're playing a version of D&D where the stats have modifiers or matter at all. So there has to be some minimum threshold of acceptability, a means of determining when a character is so poor that an immediate re-roll is warranted.
(I'll take a moment here to digress about die-rolling methods other than straight 3d6. You have 4d6k3, 3d6-reroll-1s, 3d5+3, 5d4−2, 1d10+8, and many and sundry other methods to produce an ability score somewhere on the higher end of the 3–18 range. I've tried them and decided against all of them. Ditto for re-rolling individual low scores. The only truly organic way, in my experience, to guard against unplayable characters with disappointingly low stats is to look at the whole set of scores, decide whether the character is acceptable or not, and if the whole set is too low, "take a mulligan"—scrap the character and re-roll everything from scratch.)
To find that minimum threshold, though, I have to examine the scores themselves and the modifiers that key off of them, and that leads right into our second question: how much should scores matter?
My feeling, after a lot of thought and experience, is this: scores shouldn't matter too much in combat. They should matter a great deal when it comes to character skill and background.
After all, that's the reason why most old-schoolers are so enamored with the simple LBB/Holmes style modifier tables, right? Where (to cite Swords & Wizardry White Box as an example), you have a table where a score of 6 or lower is a –1 penalty, a score of 7 to 14 is no adjustment, and a score of 15 or higher is a +1 bonus, and that's it? A plus or minus one is a big deal, because that's all the scores can do for you, but honestly it's not such a big deal that a bad roll will gimp your character forever? It produces a kind of uniformity (±5% here or there), where the scores don't matter anywhere near as much as how you play the character and what equipment they find—in terms of characters' combat effectiveness.
On the other hand, if you use 1d20 ability checks, there's a big difference between a score of 7 and a score of 14. Then the scores matter a lot. Maybe even too much.
So in order to square this circle (because the ideal should be that the characters are pretty uniform in terms of combat efficacy, but highly varied in terms of their "non-combat" skills), I cooked up this new ability table:
Score … Mod … Check
1 … … … −2 … 2
2–3 … … –2 … 3
4–5 … … −1 … 4
6–7 … … −1 … 5
8–9 … … ±0 … 6
10–11 … . ±0 … 7
12–13 … . ±0 … 8
14–15 … . +1 … 9
16–17 … . +1 … 10
18–19 … . +2 … 11
20 … … .. +2 … 12
Note that the modifiers (at least, within the 3–18 range) are the same as the table that I put up two posts ago. That's just sort of an odd coincidence. You see, what I did here was to imagine that each score keyed to two modifiers—an "ability check" modifier which ranges from −5 to +5 (i.e. half the score, rounding down, minus five; just like the d20 System editions) and a "combat modifier", which is the ability check modifier halved and rounded down yet again. And this works really well—now we're cooking with gas here, people.
The combat modifier is the one that applies to whatever you want the scores to modify: to-hit rolls; damage rolls (in some campaigns); saving throws; hit points; and also all those fiddly Charisma stats, like reaction rolls and follower morale; and to languages for Intelligence.
Ability checks, meanwhile, are made on 1d20; and a normal, untrained ability check passes if the roll is less than or equal to 7 ± the full (3e/4e/5e style) ability modifier. (7 is chosen as the base because 7-in-20 is quite close to 2-in-6; my previous campaign used 4-in-12 as the base for the same reason.) Or, put another way, we can keep the "combat modifier" and just call that the modifier/adjustment, and otherwise dispense with the skill/ability modifier—because you find the check value directly with a simple formula (halve the score, round down, add two). That produces the above ability table.
(Additionally, I'm using Secondary Skills in my new campaign, so that everyone starts with at least one "background" skill describing a broad profession that they're good at. This grants a +5 proficiency bonus to ability checks that directly relate to the secondary skill, or a +2 familiarity bonus on tasks that might be tangentially related to it.)
Now, there's one last wrinkle I need to bring into this: I mentioned in my "new campaign" post that I'm going to pare the list of ability scores from six down to four for this campaign, because Constitution and Wisdom are kind of unnecessary. Other stats can "fill in" for what they cover. So my new campaign is using a list of four stats (Strength, Dexterity, Intellect, and Charisma), and here's what they do:
Strength modifies mêlée to-hit rolls and (in limited fashion) hit points
Dexterity modifies missile to-hit rolls and armor class
Intellect modifies languages and saving throws
Charisma does the usual charisma stuff, modifying reaction rolls and follower morale
Let's put it all together. Rolling 3d6 in order four times: I get 8, 11, 6, 7. Yep, those are some crummy rolls. Most of them are below 10. In fact, I think this is a good indicator of when a character isn't much worth playing, not because the scores would have a negative impact on gameplay per se, but simply because of player psychology. We want to see some "good" double-digit numbers on the character sheet—at least half of them, anyway. Now, the average roll of four stats in the 3–18 range would be 10, 10, 11, 11—which sums to 42. Hey, look, the answer to life, the universe, and everything. That's going to be my criterion from now on: if the sum of the four numbers is less than 42, take a mulligan and re-roll. That's very easy for nerdy D&D-playing types to remember. Let's roll again: 7, 15, 11, 14. Better. A playable character, if not by any means a fighter.
Now, quick reminder from the earlier post: my new campaign uses four classes—fighter, expert, tech, mage—each one specialized in one of the ability scores. Just looking at this spread, I'm looking at an expert. Thus:
Str 7 — −1 to melee and Lv1 hp — 5-in-20 chance to pass a Str check
Dex 15 — +1 to missiles and AC — 9-in-20 chance to pass a Dex check
Int 11 — ±0 to saves and languages — 7-in-20 chance to pass an Int check
Cha 14 — +1 to reactions and ML — 9-in-20 chance to pass a Cha check
So my expert will have 5 hp, melee to-hit +1, missile to-hit +3, saves on 7-in-20, and his AC 1 point better than whatever armor he wears.
The only class ability 1st level experts get is a bonus secondary skill. Let's make a traditional thief and pick "burglar" and "confidence man" for his secondary skills. These grant a +5 bonus on ability checks directly related to such activities (the character would have, for example, a 12-in-20 chance to find traps and secret doors, from Intellect; a 14-in-20 chance to disable traps or pick locks, from Dexterity; a 14-in-20 chance to spin a convincing bullshit story, from Charisma) and, at the referee's discretion, a nice little +2 bonus on tasks that are kinda-sorta related to the secondary skill.
Hit Points: I'm honestly not a big fan of the Con-mod to hit points at every level thing. It causes even a +1 bonus or a −1 penalty to essentially shift a character's hit die type up or down into the next strongest or weakest class. But having a modifier to hit points apply only at level one is a bit too weak. Yes, it can be the difference between life or death on very rare occasions, but it's not really going to matter much beyond 3rd level or so.
And that's a good threshold for when to apply the modifier again—at about 4th level (when characters become "Expert Set" level and fighters are called "heroes")—and then again at 8th level (when fighters are called "super-heroes"), and every four levels thereafter. So, for example, my expert class character with his −1 Str penalty would have a hit point table that looks like this:
Lv1: 5 hp
Lv2: 8 hp
Lv3: 11 hp
Lv4: 13 hp
Lv5: 16 hp
Lv6: 19 hp
Lv7: 22 hp
Lv8: 24 hp
Lv9: 27 hp
Lv10: 29 hp
This way, it has something of a meaningful impact—at 10th level, the character is a full 3 hp (one whole level's worth for an expert) behind where a character of average Strength would be. But at no point does that Strength penalty utterly ruin the character, the way −1 to HP at every level would.