How to balance numbers? (warning: may contain math)

[Lalliman]

So, recently i've created my own simplified D&D version, so that i could DM for my friends who'd never played a PnP game before. It was meant as a stepping stone so that i could teach them D&D 3.5 or 5e later, but we had so much of a blast that we decided to keep using it. But now, without the monster manual to guide me, a problem has become apparent. How do i make balanced encounters?

Everything is dictated by the stats strength, dexterity, constitution and intelligence, which are always between 0 and 10 (on a PC at least). No BAB or skills to worry about.
Attack rolls use either strength (melee) or dexterity (ranged or melee), and a hit deals damage equal to your strength, or 1.5x strength with a two-handed weapon.
Defence (our term for AC) is 10 + half dex + armour. Armour obviously comes from equipment; it can go up to 9, or 11 if using a shield. As in D&D, heavier armour limits your dex bonus to defence.
Constitution determines your HP (currently 10 + 4 x con, though that needs tweaking), and intelligence is mostly for non-combat stuff, since caster PCs are currently impossible. (The whole party volunteered to play martials anyways.)
I hope that gives a good idea of the mechanics.

The mechanics aren't perfectly balanced (anyone with advice on that is free to voice it too), but they're elegant and get the job done. My problem as DM is, how do i use the mentioned stats to make a balanced encounter? Creating an enemy of equal power to a PC is easy; PCs get a 25 point buy* (without diminishing returns) and so do those enemies. But what if i want an enemy who's half as powerful as a PC? Halving their health or damage is an easy way to do it, but that's not always appropriate.

So i ask you guys, how big a decrease in a character's defence and/or attack bonus will make them half as powerful? How big an increase will double their power? Has anyone dealt with this before?

*Edit: forgot to mention, movement speed is also a stat they have to spend those points on.

[noob]

The main problem is that a d20 is widely random and so a monster or monster group will win or loose against the players in function of random things and a monster who spent all in strength is going to give problems while a defensive monster would be useless in fact all monsters should either max strength or dex(if they are ranged only)
then there is problems with huge packs of rather weak ranged monsters: they are going to give more trouble than one strong melee monster even if the total of their stats is very low(for example if they are in a good place the players need to all be ranged).

[Chaos_Laicosin]

I could be entirely out to lunch here, but this is what I've come up with.

For 3.5 at least, a party of 4 can take on a challenge of their level with a decent chance of success. For example, 4 ECL 8 character can take on a single CR 8 monster. To reach that same challenge rating using multiple monsters, each monster must be weaker. So 2 CR 6 monsters would make a CR 8 encounter, or 4 CR 4, or 8 CR 2. Noticing the mathematical trend, decreasing a monsters CR by 2 halves its ability to challenge a party.

Then I tried to figure out the ability values for specific challenge ratings. Using the stats on animals for a rough guide (so I could ignore anything magical), increasing a CR by one increases the total physical modifier by 2 - 3. For example, a wolf (CR1) has +1 Str, +2 Dex, +2 Con for a total of +5. A black bear (CR2) has +4, +1, +2 for a total of +7. A lion (CR3) has +5, +3, +2 for a total of +10. All those animals have the same Int, Wis, and Cha.

So, since your system uses the raw ability numbers for attacks instead of modifiers, I'd say if you want to halve a monsters challenge then knock off around 5 of its ability points compared to the party average. If you want to double its challenge, add 5. Or whatever is the proportionally equivalent amount based on your ability numbers.

Of course, that line of reasoning only takes into account physical abilities and not any magical powers or special attacks or anything.

[Lalliman]

@noob I've considered those things too, so i realize i can never just rely on the numbers to get it right. But that doesn't mean some kind of guideline can't be established.

@Chaos Thanks for putting in the effort for that. I too tried to look to 3.5 for examples, but didn't think to try animals to avoid all those special abilities interfering. There's one thing you may have overlooked though: hit dice. A wolf has 2, a bear 3 and a lion 5, so that accounts for a lot of their power difference. Nonetheless, i tested it and knocking off 5 stat points gets me pretty close to the intended CR.

The tests, however, have also made it obvious just how much better strength is than any of the other stats. I knew that already, but this really drove it home. So before anything else, i'm gonna be reworking the system to iron that out.

[SkipSandwich]

Some systems use Str ONLY for melee damage (and occasionally parry defense vs. melee, if that is a thing), with Dex used for attack and defense.

For balancing HP, it helps if you have a scale of how damaging a typical attack at different levels is, then multiply as appropriate. For example, one scale some mmos use is based on 12, with 'weak' attacks from a level appropriate enemy dealing 1/12th of the average pc's hp in damage, and then scaling up to 4/12ths for really powerful attacks. So at the low end you have a margin where it will take roughly 12-24 attacks to incapaticate an pc, and on the high end you get a 3 hit KO or 2 hits if one is a crit, enough to be scary but with enough wriggle room that a single unlucky roll won't instantly take a PC out of the fight.

[Lalliman]

Some systems use Str ONLY for melee damage
That's what i'm doing with the next itteration.

[Lvl 2 Expert]

Creating an enemy of equal power to a PC is easy; PCs get a 25 point buy* (without diminishing returns) and so do those enemies. But what if i want an enemy who's half as powerful as a PC? Halving their health or damage is an easy way to do it, but that's not always appropriate.


So, since your system uses the raw ability numbers for attacks instead of modifiers, I'd say if you want to halve a monsters challenge then knock off around 5 of its ability points compared to the party average. If you want to double its challenge, add 5. Or whatever is the proportionally equivalent amount based on your ability numbers.

I think this is a good suggestion. Presumably, halving an enemy's damage or health does roughly the same for their overall strength as taking out the same amount of points spread out over different stats. If the average PC has about 7 points in the average stat, having an enemy with about 4 points less in their overall build means they are about twice as weak. This also roughly means that if the party just fought 2 NPC's with 22 stat points each and you liked that difficulty you could throw 4 enemies at them with 18 stat points each, or one with 26.

It sounds ridiculous, honestly, such a small point difference making a character twice as strong, but as you said, if you halve just the attack or just the defense of an enemy they will do half as much damage during a fight, so 4 points off should have about that effect.