Quote from: Arminius;860452Averages don't necessarily tell enough of the story--some games are going to have a fairly high variance in damage per round, which would militate in favor of building a good margin of safety into your "CR".

That said, if a game's combat system doesn't offer much in terms of options, I have to wonder why have CR. If there are interesting options in combat, then you might want CR in order to keep combats balanced enough that the players can exercise those options in a meaningful way.

For a simple game, frankly, the bulk of interest with the combat is exploring and learning what you can handle and what you can't, and deciding what's worth risking. A CR system deprives players of that experience by guaranteeing that they can run into every combat without thinking.

I'm looking for numbers/ranking so I can know if I've created an easy or a tough encounter. By easy, I mean you can reliably expect the characters to win. By tough, I mean you can reliably expect the characters to win. Or something in between--with something in between or tough you can give the players enough hints via description of the opponent, or their sheer numbers, that they need to do something other than a head on attack.

I took BoL's intro adventure and ran the three beginning characters against the guards and a trio of three animals whose name escapes me. The animals are described in the book as apex predators (or words to that effect) and even without Hero Points, the characters tended to wipe the floor with the animals in simulation. But it is described as a really tough battle in the book.

Unless I'm running a "gritty" campaign, I don't really want to accidentally let loose a monster or villain that can one-hit kill my player's characters. (On purpose is another matter.)

What's your standard of 'reliably'?

If you're doing a D&D type thing where you've got, say, 5 figures getting into an average of 4 fights per session for 50 sessions, that's 1000 chances to get killed. If the odds of surviving a fight are 'only' 99:1, that's an average of 10 characters -- two parties' worth of adventurers -- killed.

A figure killed doesn't necessarily mean the party loses the fight, or vice versa. This is just a start on figuring out what you really do mean. It's easier to hit a target when we know what to aim for in the first place!

If you had a single combat factor and switched to a roll-off of 2d6+bonus for each side, lower takes a hit, then the difference in bonuses would yield a ratio that goes up pretty quickly. For the most part that's close to what you'd get with 3d6 'reflexive' (from 11+ each to 12+/10+, then 13+/9+, etc.).

Note that this way, it's just the difference that matters; +10 vs. +3 is the same as +8 vs +1 (about 84 to 1).

Tod13,

Well, your simulation approach is the right one, I guess, for what you're trying to do. I assume there isn't much in terms of positional maneuver, and also that you aren't too troubled by targeting issues.

In military simulation there's something called the Lanchester Equations or Lanchester's Laws, which you might want to look up.

Basically, the more freedom each "unit" has in terms of which enemy it can target, the greater the effect of outnumbering. If combat is restricted to a series of 1:1 battles, with each new "duel" only forming after both units become unengaged, then outnumbering doesn't matter so much. On the other hand if maneuver or ranged firepower can allow the creation of local situations where multiple combatants on one side are only facing a single opponent (even if you ignore the tactical effect of outflanking), then things aren't so simple, and outnumbering also matters more.

So just how simple is your overall combat model? Is there any range, movement, and positioning involved?

Quote from: Phillip;860500What's your standard of 'reliably'?

If you're doing a D&D type thing where you've got, say, 5 figures getting into an average of 4 fights per session for 50 sessions, that's 1000 chances to get killed. If the odds of surviving a fight are 'only' 99:1, that's an average of 10 characters -- two parties' worth of adventurers -- killed.

A figure killed doesn't necessarily mean the party loses the fight, or vice versa. This is just a start on figuring out what you really do mean. It's easier to hit a target when we know what to aim for in the first place!

For my testing, mostly one on one, I figure 70% is "reliably" at this point. Given multiple players, in my case three, I assume (to be tested later) that means that one of the other two people can help the player who falls into that 30% category.

Quote from: Phillip;860505If you had a single combat factor and switched to a roll-off of 2d6+bonus for each side, lower takes a hit, then the difference in bonuses would yield a ratio that goes up pretty quickly. For the most part that's close to what you'd get with 3d6 'reflexive' (from 11+ each to 12+/10+, then 13+/9+, etc.).

Note that this way, it's just the difference that matters; +10 vs. +3 is the same as +8 vs +1 (about 84 to 1).

This is me thinking through this...

It makes sense when you say it, I'd have to simulate it too see what "really" happens. For certain values of "really".

One thing I though of while doing this was: one thing is that I'm looking for outcome results, not to hit/damage results. Which party wins the encounter?

That's just for hitting--that is, you've confounded to hit and defense.
But then you've got damage and armor.
Maybe use the difference for damage and similarly combine damage/armor into the to hit and defense?

That is, a combat turn between two opponents would be:
2d6 + A's bonus versus 2d6 plus B's bonus
Highest score wins.
Difference between scores becomes the damage.
Hmmm. I kind of like this as simple and somewhat elegant.

I kind of want to keep the idea of armor of a certain level being proof against attacks below a certain level, which adds complications in determining outcome.

What does it do to the ranking if you have two rolls per turn? That is, first you have the A's attack versus B's defense, and then B's attack versus A's defense. The attack and defense values are the same for a particular person, but only the attacker can do damage. (This allows you to handle defending against someone you don't want to kill, while your friend gets the sleep spell running.) That should still work.

I say the values are the same, I think what I might do is add add the appropriate stats, skills, or whatever that go into armor, to hit, and defense, and make that the "combat value". It sort of even makes sense, with better armor, you're defending less and can attacker better.

How would this handle "touch" type attacks? That is, whatever happens isn't a damage type roll but an effect? I guess it still works, with the level of difference being meaningless.

What if you use the bonus or "combat value" as a dice pool instead?
Hmmm (These numbers may be wrong. Anydice is down and I'm not as familiar with Troll.)

2d6 average 7
3d6 average 10.4
4d6 average 14
5d6 average 17

I'll have to run some simulations and see what the results are.

Quote from: Arminius;860506So just how simple is your overall combat model? Is there any range, movement, and positioning involved?

As simple as makes sense for the situation?

Movement and positioning is mostly abstract. You can use cover or concealment. There are bonuses/minuses for ranges and for surprise or unaware. I'm not going to try to track facing directions but if someone invisible/stealth-cloaked hits you from behind, they get a good plus.

I haven't gotten far into the details, as I wanted to get the basics down first. Basics being the basic dice mechanics and ranking system.

For Lanchester's Laws a la outnumbering, I'll look into that, but I'd probably handle that more with either GMing/roleplaying the tactics.

Not saying you should incorporate Lanchester's Laws into your mechanics, but that the theoretical underpinning and general considerations of the Laws can enlighten your analysis.

Although, if you wanted to abstract to high degree, you certainly could add general modifiers for situational advantages--such as terrain, speed/agility, or "tactical coordination" allowing one side to concentrate their attacks and minimize exposure to the enemy. Personally, I think that would be more difficult to do right than just using a map, but it would be an interesting angle.

Quote from: Tod13;860514One thing I though of while doing this was: one thing is that I'm looking for outcome results, not to hit/damage results. Which party wins the encounter?

You can multiply an advantage by requiring more wins of rounds to win the contest. For instance, if I have a 1/3 chance of winning one then I have only 1/27 of winning 3 in a row.

With just that one toss to consider, the odds are trivially clear. Complications mount as you add things such as "first to win 3", "first to add up so many points from a die tossed each won round", etc.

One thing's pretty clear, though: if your spread of decisiveness (e.g., "damage points" dealt relative to what's sustainable) is big, then you've got a big spread in how many rounds there will be.

More rounds gives more chances for swings of luck to cancel out, so you get a bulge of frequencies around your average outcome and the extremes become more rare.

using difference between scores in a roll-off for damage jacks up advantage in a big way. Adding more dice adds only very slowly to the usual spread, the sums adding more tiny tail probabilities.

Even with 4d6 per side you're typically looking at just 4 points or so with no advantage. It makes even a single pip a very big deal.

This gets very weird for various reasons in Tunnels & Trolls, but in a way that means a straight melee is usually close enough to deterministic. Missiles and magic and stunts done with saving rolls shake things up.

Zenobia uses difference in 2d6 roll-off, with armor deducting from damage. You can save your points scored IF you keep winning rounds, and then deliver especially nasty "critical hits". That's groovy for a gladiator who has things well in hand, and maybe a worthwhile gamble for someone who is just looking anyway at close enough to certain death.

Phillip, combining the numbers does make the combat value for 1:1, 1:2, 1:3 a useful comparator, but there is a narrow band of chance.

2d6 + bonus versus 2d6 + bonus
HP = bonus * 6

One on One
If the bonus values are equal, this is 50/50 with an edge to the first to go.
At 1 point difference, the lower bonus has a 5% chance of winning.
At 2 points difference, the lower bonus has less than 1% chance of winning.
At 3 points or greater difference, the lower bonus never wins.

One versus Two
If the single is lower, the pair always wins.
If the bonuses are equal, the one has a 1-2% chance of winning.
If the single is 1 point greater than the pair, the single has a ~50% chance of winning.
If the single is 2 points greater than the pair, the single has a ~95% chance of winning.
If the single is 3 points or greater than the pair, the single always wins.

One versus Three
If the single is equal or lower, the triple always wins.
If the single is 1 point greater than the triple, the single has a ~15% chance of winning.
If the single is 2 points greater than the triple, the single always wins.

(bonus)d6 versus (bonus)d6
HP = bonus * 6

One on One
If the bonus values are equal, this is 50/50 with an edge to the first to go.
At 1 point difference, the lower bonus has ~1% chance of winning.
At 2 point or greater difference, the lower bonus never wins.

One versus Two
If the single is lower, the pair always wins.
If the bonuses are equal, the one has a 1-2% chance of winning.
If the single is 1 point greater than the pair, the single has a ~75-90% chance of winning.
If the single is 2 points or greater than the pair, the single always wins.

One versus Three
If the single is equal or lower, the triple always wins.
If the single is 1 point greater than the triple, the single has a ~25-30% chance of winning.
If the single is 2 points greater than the triple, the single wins 99% of the time.
If the single is 3 points or greater than the triple, the single always wins.

"Edge to the first to go" is not part of what I was talking about. I was talking simultaneous, as in Fighting Fantasy: either you tie (no hit), or one of you scores a hit.

Your two-on-one, etc., are I presume upping that swing in decisiveness: a single round can mean getting whacked so many times as much. A heavy loss in a round tends to mean fewer further rounds, a synergy compounding effects of any further oddities in the same favor.

Quote from: Phillip;860653"Edge to the first to go" is not part of what I was talking about. I was talking simultaneous, as in Fighting Fantasy: either you tie (no hit), or one of you scores a hit.

Yea--I mentioned I changed that in my long meandering initial response, to allow for defense only. So, the one person will have three "attacks"? Let me run those numbers too.

You could give him three chances to hit, or you could say he gets just one and can at best fend off the two other attackers. (This could be a matter of expertise.)

Again, three rolls on the outnumbered guy's part will yield less swing than a single toss against the opponents' three, and less still than the three likewise getting just one throw for all.