Mechanic: Opposed Combat Rolls

[Hiraevun]

I'm brainstorming on ways to resolve combat. I'd like a fairly simple mechanic that also allows for a wide range between stunning success and utter failure. I also think combat should be quite dangerous. Here's what I've got for starters:

Opposed Combat Rolls

Combat between characters is resolved in a simple manner:

1. Attacker rolls % dice, adds the appropriate offensive skill, and adds a base number for the attack (such as a weapon base or magical attack base). This yields the Attack Total (AT).

2. Defender rolls % dice, adds the appropriate defensive skill, and adds a base number for defense (such as armor or magical shielding). This yields the Defense Total (DT)

3. If the AT is > DT, subtract DT from AT. The result is the damage inflicted.

4. If the DT is > AT, no damage is taken. Furthermore, if the DT is > AT by 100 or more, the defender gains a free counterattack.

Note that a typical beginning character might have between 70 and 100 in any one of his vital statistics (body, mind, or soul), and this is what is taking damage. In an attempt at realism and to create a real sense of risk in the favorite PC pastime of "beating up baddies", I'm interested in creating a combat system with the possibility of massive trauma from a well-placed blow.

[fmitchell]

I like it, in that it makes percentiles consistently "roll high", and the two parties merely compare totals to find the victor. My only reservation is that adding two two-digit numbers does require a little more thought than adding one-digit numbers or numbers in the 1-20 range; the time does add up, especially if players are arithmetically challenged.

One solution is to raise skills in increments of 5, and/or express weapon and armor bases similarly. On the other hand, if the tens places are far apart, a simple comparison might suffice. I guess it depends on whether skills and bases are typically in the twenties or the seventies.

(As a counterexample, RuneQuest and its descendants roll under a skill percentile; a fraction of that skill a "critical" or "special" success, and 95-00 counting as a "fumble". If attacker and defender succeed to the same degree, some variants resolve the tie with the highest die roll, so as not to penalize highly skilled characters. GURPS, using 3d6, is consistently roll low, but to resolve ties you have to subtract your roll from your skill level, with the greatest margin of success being the victor. Subtractions require more thought than addition, which requires more thought than comparing two numbers.)

The probability distribution will be pyramidal (specifically, 2d100 - 101 +/- differences in skills and bases, if I'm not mistaken), which is another advantage of opposed rolls: extreme results are relatively rare.

[Hiraevun]

Thanks for the thoughtful response, fmitchell.

My only reservation is that adding two two-digit numbers does require a little more thought than adding one-digit numbers or numbers in the 1-20 range; the time does add up, especially if players are arithmetically challenged.

One solution is to raise skills in increments of 5, and/or express weapon and armor bases similarly. On the other hand, if the tens places are far apart, a simple comparison might suffice. I guess it depends on whether skills and bases are typically in the twenties or the seventies.

This is a helpful point. I am planning on increments of 5 or 10 for skill/power improvements. I agree that adding numbers like 14, 19, and 53 together would be a pain, and it's not at all desirable to make players want to bring calculators to game night. A typical combat round would look more like:

1. Attacker rolls 48%. Her appropriate offensive skill is 60. Her weapon base is 30. The AT is therefore 138.

2. Defender rolls 75%. His appropriate defensive skill is 55. His armor base is 15. The DT is therefore 145.

3. The DT, 145, is > the AT, 138, so no damage is inflicted.

4. The DT, 145, is not +100 or more than the AT, 138, so no free counterattack is gained.

The probability distribution will be pyramidal (specifically, 2d100 - 101 +/- differences in skills and bases, if I'm not mistaken), which is another advantage of opposed rolls: extreme results are relatively rare.

I'm not quite following your equation. Where does the "-101" part come from? Math is not my strong suit, but I am interested in hearing analyses of the proposed system from people who have insight into the world of probability and statistics.

Thanks for the feedback.

[cliff]

This is a helpful point. I am planning on increments of 5 or 10 for skill/power improvements. I agree that adding numbers like 14, 19, and 53 together would be a pain, and it's not at all desirable to make players want to bring calculators to game night. A typical combat round would look more like:

Out of curiosity, except for the obvious desire to not be mistaken for a game based on the "d20 ruleset", if your increments are going to be 5, then why not keep the increments at 1 and use a d20? You simplify your math while maintaining the same probabilities.

[fmitchell]

The probability distribution will be pyramidal (specifically, 2d100 - 101 +/- differences in skills and bases, if I'm not mistaken), which is another advantage of opposed rolls: extreme results are relatively rare.

I'm not quite following your equation. Where does the "-101" part come from? Math is not my strong suit, but I am interested in hearing analyses of the proposed system from people who have insight into the world of probability and statistics.

Essentially your system is 1d100 - 1d100. I can't cite a proof -- this is more of an empirical observation -- but that's equivalent to 1d100 - (101 - 1d100), or 2d100 - 101. (101 is the highest roll plus the lowest roll; 101 - 1 = 100 and 101 - 100 = 1. The probability is symmetrical -- flat, actually -- so this works.) 2dX rolls form a pyramid rather than a true bell curve, but it's close enough.

There are various probability calculators on the web, to understand probability distributions:

http://www.anwu.org/games/dice_calc.html (text only)

http://ojaste.ca/dice.html (color-coded vertical graph of most and least probable outcomes)

http://topps.diku.dk/torbenm/troll.msp (uses a mini-language to explore nearly any dice mechanic)

[Hiraevun]

Out of curiosity, except for the obvious desire to not be mistaken for a game based on the "d20 ruleset", if your increments are going to be 5, then why not keep the increments at 1 and use a d20? You simplify your math while maintaining the same probabilities.

The increments of 5/10 would be for PC core abilities, skills, and powers. The die rolls would be percentile, which gives a wider range and different probability of results than d20. FMitchell's link to http://ojaste.ca/dice.html helps illustrate this.

I do see your point, though, cliff: why not simplify? Instead of having a base of 15 for core abilities, I could divide that by 5 and start with a base of 3. From there, abilities could be increased by intervals of 1 rather than 5, and d20 could be rolled rather than d100.

I suppose I just prefer a wider range of possibilities. If players and GMs are inclined to have non-base 5 increases, that option is there. A wider range of numbers also may increase the drama and risk. This is debatable, because as you've pointed out, you can simplify the wide range of numbers to a smaller range and have almost the same system. I think my gut feeling is that with a wider range of numbers, there's a wider range of possibilities. It's certainly something worth taking a critical look at, though, and I appreciate the question.

Does anyone else have an opinion on a % range as compared to a 1-20 range?
--- Merged from Double Post ---

...which gives a wider range and different probability of results than d20. FMitchell's link to http://ojaste.ca/dice.html helps illustrate this.

Actually, it is the same pyramidical distribution, isn't it?

Hmmmm. Touché. You make a really good point.

[cliff]

The increments of 5/10 would be for PC core abilities, skills, and powers. The die rolls would be percentile, which gives a wider range and different probability of results than d20. FMitchell's link to http://ojaste.ca/dice.html helps illustrate this.

Actually, it doesn't really have a significantly different probability. If your skill range is in increments of 5, just to simplify, then the range of identical effect on your d100 would also be a range of 5... which comes out to a 5% chance, or the equivalent of a single number on a d20 - and a single skill point. It has a very minor difference in contested rolls, but only inasmuch as the players can occasionally have an additional 4% chance to be able to do better than the other guy - but only when they are close enough together that the smaller increment make a difference... this will not be that common an occurrence.

Please note - I'm not arguing against d100 as a flavor choice... but if you are going to go with d100, perhaps you shouldn't have your skill increments be 5 but instead make them 1. It will help to contribute to the flavor more, and will make the probability more different.

[Hiraevun]

I've begun a revision of the character creation process and the opposed combat rolls mechanic using the d20 base. I may compare it to the % mechanics, or I may just flesh out the mechanics using the d20 base.

Cliff, I appreciate you pointing the probability similarity and the d20 simplification to me. This thread began with a brainstorm and implicit in the OP was a request for feedback. This thread is doing exactly what I'd like it to: hammering out the kinks in my proposed system.

[cliff]

As I said, though, the feel at the table could be very different, in playtesting it definitely seems like you should try both to see which is more fun.