What to Roll and Which System to Use

A couple of recent posts by other bloggers got me thinking. Specifically, we're talking today about rolling ability scores, and the modifiers that you get from those scores depending on the system you use. 

It's probably no surprise that the first post that got me thinking about this was one by Alexis over at Tao of D&D: 

As a DM, I see AD&D's combat/survival structure relying on characters possessing at least two stats above 14.  There are no benefits for any stat less than 15 with regards to strength, constitution and dexterity, upon which the combat system depends.  And though spell-use can mitigate the need for these somewhat, a good mage or illusionist really needs a +1 dex bonus at minimum (in my experience), while a cleric whose going to wade in and fight needs at least some bonuses in strength or constitution.  A cleric who won't wade in hasn't a good enough spell arsenal, and is therefore useless; which is part of the reason why clerics who tried to style themselves as "healers" and not "holy fighters" ended up crying for more healing potential, as the original list doesn't allow this specialisation effectively.

Thus, adding that extra die to 3d6 increases the chance of rolling above 14 sufficiently to hit that window of "practical" character.  I know that many, many voices refuse to believe there is such a thing; that the game needs to adjust for the character, and not the reverse.  Of course I could run a softer, more gutted game for those players with mediocre stats, but having experienced the lessened potential and drooling dullness of such a game, I'm not sold on the concept.  If the reader wants me to go into that, I will, drop me an email, but for the present I'll assume most people here are aware that having bonuses makes players happy, and I like happy players.

Too, the 3d6 alternative produces too many "culls," my term for the selective slaughter of players whose stats are too obviously likely to get them killed.  The penalties for stats of 7 and less can be tolerated if they appear with rarity ... but when they're scattered among multiple players in a party, sooner or later the randomness of unfudged die rolls takes its toll.  I see no reason to roll up characters en masse for the purpose of creating an inferior stock.  No, I prefer the alternative.  A nice collection of characters whose stats average around 73 or better makes a party more likely to survive, thus producing a sustainable game.

Up front, yes, I'm one of those DMs that Alexis talks about who thinks that high scores aren't absolutely necessary for an effective character. I like it when my players roll well for their characters. I like for them to have competent characters. But I've also played enough average characters in my life to know that while that extra 5% chance to hit or avoid being hit, or the extra hit point or extra point of damage on each attack can matter, it's perfectly feasible to run a character without them. 

And this is slightly off topic, but I find it funny that a commenter on a previous post thought a 5% or 10% XP boost is really meaningless. Granted, we're talking a vastly different scale between a d20 roll to hit and the thousands of XP needed to gain levels, but a percentage is a percentage. 

Anyway, back to the topic of ability scores and how we roll them. Alexis prefers AD&D's ability modifiers which, at least for combat bonuses, don't start giving bonuses until a 15 or 16. But scores of 15 or higher are really rare on a flat 3d6 roll, so he needs to use 4d6-L to give players a decent shot at getting not just one, but two scores with bonuses, and radically reduce the number of scores that get a penalty. 

I have no problem with this. I use 4d6-L in my game these days, after experimenting with a few other options over the past few years. 

But before I go on, I need to introduce the other blogger that spurred this post, Anders H. of the Mythlands blog, who was writing about not just discrete mechanics for different tasks, but discrete bonuses for different ability scores being a feature not a bug of AD&D design: 

AD&D in general however, revels in lack of homogeneity. There's a ton of derived stats from ability scores and they are all different, with different progressions and determining the math behind the curve of progression is not at all transparent. 

I suspect there is none and that Gygax et al used a more powerful tool than mathematical progression - Deciding on modifiers based on gaming impact. And this one of the great virtues of game design that are lost with streamlined mechanics. 

Modern games, I posit, suffer from a tyranny of number harmonies and easy calculation. Everything must be transparent, easy to calculate and preferably limited to a few basic methods the recur throughout the whole gaming engine.

But does the game actually play better when STR gives the same bonus to hit as it does to damage? Or CON an equivalent bonus to hit points? Does it yield the desired results at the actual game table or simply look pleasing in the rulebook and easy to memorise?  Harmonies do not necessarily equal better game play.

I've gone on record before saying that I'm not a fan of the way AD&D does ability score bonuses. They are inconsistent across the different scores, there is way too big of a doughnut of scores with no adjustment up or down, and then there are things like Fighters getting percentile strength bonus on an 18, or only Fighters getting more than +2 hit points for a high Constitution, or the needlessly fiddly % to Know spells Int modifier for Magic-Users or Chance of Spell Failure for Clerics. 

Exactly the things Anders is praising are the things that annoy me about AD&D ability scores. I do agree with him on most of his other points, though. Clerics and Magic-Users don't need identical spellcasting power. Different rates of advancement for different classes is a good thing. Categorical saving throws are cooler and more interesting than just rolling against your ability scores. And any complex calculation that can be boiled down to a simple hard number on a not overly complex character sheet is a good thing. 

And again, let's get back to ability score adjustments and how to roll those abilities. 

Anders makes the case that the diversity of adjustments in AD&D are due to the different roles that those abilities play in the game. Alexis makes the case that a playable character should have at least two scores with a positive adjustment. 

This made me curious to compare the probabilities of rolling 4d6-L for AD&D adjustment bonuses vs. 3d6 flat for BX/BECMI adjustments. The website AnyDice.com gave me the percentage chances to roll X or higher with each rolling method (yeah, I can do the math myself, but this was faster). And this website has an ability score calculator that can show you the probabilities of getting certain scores or higher on sets of six ability scores, which is handy. 

So to recap: 

In order to get a +1 bonus to any score in Classic D&D, you need a 13 or more in that ability. That's a bonus to hit in either ranged or missile combat, a bonus to damage in melee combat, a bonus to AC, or bonus hit points per level.

In order to get a +1 bonus to any combat relevant score in Advanced D&D, you need a 15 or 16 depending on the score and the variable being adjusted. 

To get a -1 (improvement) to AC, or to get +1 hit point per level, you need a 15 to Dex or Con, respectively.

To get a +1 to damage in melee combat or to hit in ranged combat, you need a 16 in Str or Dex, respectively. 

To get a +1 to hit in melee combat, you need a Str 17. 

According to the die rollers, if you roll flat 3d6, to get a score of X or higher on any particular score, your chances are: 

13+ 25.93% [+1 to any variable in Classic, no adjustment to any variable in Advanced]

15+ 9.26% [+1 to any variable in Classic, +1 to HP or -1 AC in Advanced]

16+ 4.63% [+2 to any variable in Classic, +1 melee damage, +2 HP, +1 ranged attack, -2 AC in Advanced]

17+ 1.85% [+2 to any variable in Classic, +1 melee attack, +1 melee damage, +2(3) HP, +2 ranged attack, -3 AC in Advanced]

18 0.46% [+3 to any variable in Classic, +1 melee attack, +2 melee damage, +2(4) HP, +3 ranged attack, -4 AC in Advanced]

So about one in four rolls will get you a bonus rolling 3d6, on average you can expect one or two scores to be above average. 

If we roll 4d6 and drop the lowest, to get a score of X or higher on any particular score, your chances are: 

13+ 48.77% [+1 to any variable in Classic, no adjustment to any variable in Advanced]

15+ 23.15% [+1 to any variable in Classic, +1 to HP or -1 AC in Advanced]

16+ 13.04% [+2 to any variable in Classic, +1 melee damage, +2 HP, +1 ranged attack, -2 AC in Advanced]

17+ 5.79%  [+2 to any variable in Classic, +1 melee attack, +1 melee damage, +2(3) HP, +2 ranged attack, -3 AC in Advanced]

18 1.62% [+3 to any variable in Classic, +1 melee attack, +2 melee damage, +2(4) HP, +3 ranged attack, -4 AC in Advanced]

The 13+ on 3d6 and 15+ on 4d6-L are highlighted because they have more or less equivalent values. You've got about a one in four chance of getting at least that number on any ability score roll in either system. And while AD&D does grant a few bonuses better than 3 IF you're a Fighter and put that 18 in Con instead of Str or any character with 18 Dex, or you're a Fighter type and put that 18 in Str and roll well on the percentile dice, the Classic system is really more generous. 

If it's imperative to have multiple ability scores with bonuses for characters, you're better off going with the Classic D&D style ability score adjustments, even if that takes away from the bespoke nature of what each score represents, or specialized bonuses for certain classes and not others as in AD&D. 

One more thing. Looking at rolling an entire set of ability scores, according to the Ability Score calculator website linked above, rolling 4d6-L six times gives you a 9.34% chance to roll an 18, so about one in 11 characters should have one. If you need at least two scores of 15 or more, you have a 42.16% chance. To get at least one score of 15+ you have a 79.4% chance. So most AD&D characters rolled this way will be minimally viable, with only one in five not meeting Alexis's minimum threshold, but only 2 in 5 meeting his preferred threshold of two scores qualifying for a bonus. 

And remember, that's looking at the score of 15, which in AD&D only affects hit points and AC, not chances to hit or damage inflicted. 

Rolling 3d6, but needing only a 13+ on a single score, we get an 83.48% chance to get at least one of the six rolls to give a bonus, just slightly better than the chance to get a 15+ on 4d6-L. To get two scores with a bonus, we have a 48.79% chance, that's roughly half of all characters generated. It's not a big difference, but the difference does, I think, matter. One in two suitable characters compared to two out of five. Oh, getting at least one 18 has a 2.75% chance, or one in thirty-six characters. 

Obviously, 4d6-L provides much higher chances of rolling the numbers above the threshold for a bonus, but if you're only concerned with getting at least one or two scores above the threshold, you've got roughly even odds either way, but with a slight edge to rolling 3d6 against the lower threshold of 13. 

The biggest advantage to Classic characters, though, is the regular array of bonuses. Because you need at least a 16 or 17 for certain variables in Advanced, you really NEED to roll 4d6-L (or one of those crazy bucket-o'-dice methods from Unearthed Arcana). And for me, rolling 4d6-L but with Classic bonuses to rolls, most characters are going to turn out fine. 

As an example: Last Sunday, Jeff, who plays in my online West Marches and Star Wars games and is visiting Busan for the month, joined my face-to-face game. His highest score, rolling 4d6-L six times, was a 13. He made a Fighter, and did just fine in the session... although it was one without a lot of combat. But he didn't complain, and he put his usual effort into characterization and had a good time.