Relative combat power idea

[Chris Goodwin]

I've got an idea for determining the relative combat power of characters. Before I post it, though, I was wondering if there was anyone out there with more programming ability than me who would be willing to turn it into a GUI-based (or, heck, text-based!) application, because it's pretty calculation intensive.

 

In general, the idea is that it takes two characters and applies a couple of formulae to determine the relative combat power. A GM could also use the campaign's average CV, SPD, DC, and so forth to see where a character falls in relation.

 

Any takers?

[Guest Keneton]

Look at the free stuff

 

Not to toot my own horn, but have you read DH#3? I wrote The effectiveness rating. There is a spreadsheet that does the math in the free stuff section. Please check it out and see if you like it. It does consider all relevant power stats.

 

If you have any questions or need info, please ask. Good luck on your project as well.

[Chris Goodwin]

Mine is quite a bit different. Essentially, it takes two characters, treats one as the attacker and one as the defender, then sees approximately how much STUN per phase and per turn the attacker will do to the defender. There's suggestions that the GM do up a matrix for each hero vs. each villain or each hero vs. the campaign average values.

 

What the heck, I may as well post it.

 

Determining Combat Utility in the Hero System

 

This formula determines one character's combat effectiveness when acting as an attacker against another character. The GM can work it out for each PC vs. each NPC, at least major ones, before the game starts. Alternately, he can pick representative character "types" (for example, normal, low powered agent, high powered agent, low powered super, high powered super) or just use average values for SPD, CV, DC, DEF, and the like.

 

You'll need to know both the attacker's and the defender's OCV, DCV, SPD, attack dice/DC, resistant and total PD, and resistant and total ED. Optionally, include each character's REC and CON as well.

 

First, determine the attacker's percentage chance to hit based on 11 + the attacker's OCV - the target's DCV (see chart). Make sure to take skill levels, range (see below) and 1 Hex Accurate into account. Read the percentage chance as a decimal (thus 62.5% becomes 0.625).

 

Determine the attacker's average STUN damage by multiplying the number of dice in the normal attack by 3.5, or by multiplying the number of dice in the killing attack by 3.5 to find the BODY, and multiplying that by 2.66 for a standard STUN multiple, or 2.87 if you are using hit locations, or 3 if you are using that house rule (for each +1 to STUN multiple, add .75). Optionally, if you want to take the so-called "stun lotto" into effect, use a multiple of 3, +1 for each +1 to STUN multiple.

 

Subtract the target's defenses from the attacker's average STUN damage, to determine the average STUN damage the attacker does to the target. Make sure to take Armor Piercing, NND, or other Damage Class-affecting Advantages into account. Make sure to take any of the target's Vulnerabilities or Susceptibilities into account as well.

 

Multiply this by the attacker's percentage chance to hit to determine the average STUN done per phase. You can work this out for BODY as well if you wish.

 

Multiply the average STUN per phase by the attacker's SPD. This is the average STUN done per turn.

 

Optionally, subtract the target's REC from his STUN taken per turn to find out his net STUN loss per typical combat turn. The GM can work this out for as many of an the attacker's attacks as he wants to take the trouble for.

 

If a character has multiple attack Powers, the GM may, if he wishes, work the numbers out for each of the character's attacks.

 

Additional assumptions:

 

Assume for simplicity that all ranged attacks are at 10" (-4 OCV). You can vary this if you tend to run combats in larger (wide open fields) or smaller (inside buildings) areas.

 

For attacks with no range, assume the attacker is in range of the target 50% of the time, +/- 10% per point of SPD differential, +/- 10% for every 2x combat movement, or 0% if the target has special movement modes the attacker does not. If you don't want to mess with it that in-depth, assume 50% and 0%.

 

1-Hex Accurate attacks: Assume the target has a DCV of 3.

 

If a target is CON Stunned by an attack, assume the next attack hits the target at DCV 0. Or, just don't mess with it if you feel it's too complex.

 

There are some things this can't and won't take into account: multiple attackers against one target, knockback, Flash, certain kinds of exotic attacks or highly limited defenses.

 

For Sweep and Autofire attacks, if you want to go into that much detail, assume that for every two points the attacker's OCV is greater than or equal to 11, the attack hits once. If the attacker has PSLs or Combat Skill Levels that specifically affect OCV vs. Autofire or Sweep penalties, factor them in.

Chart:

3d6	Percent
Roll	Chance

3	0.4629%	
4	1.8518%	
5	4.6296%	
6	9.2592%	
7	16.2037%
8	25.9259%
9	37.5000%
10	50.0000%
11	62.5000%
12	74.0740%
13	83.7962%
14	90.7407%
15	95.3703%
16	98.1481%
17	99.5370%
18	100.0000%

[Warp9]

Originally posted by archer

First, determine the attacker's percentage chance to hit based on 11 + the attacker's OCV - the target's DCV (see chart). Make sure to take skill levels, range (see below) and 1 Hex Accurate into account. Read the percentage chance as a decimal (thus 62.5% becomes 0.625).

 

Determine the attacker's average STUN damage by multiplying the number of dice in the normal attack by 3.5, or by multiplying the number of dice in the killing attack by 3.5 to find the BODY, and multiplying that by 2.66 for a standard STUN multiple, or 2.87 if you are using hit locations, or 3 if you are using that house rule (for each +1 to STUN multiple, add .75). Optionally, if you want to take the so-called "stun lotto" into effect, use a multiple of 3, +1 for each +1 to STUN multiple.

 

Subtract the target's defenses from the attacker's average STUN damage, to determine the average STUN damage the attacker does to the target. Make sure to take Armor Piercing, NND, or other Damage Class-affecting Advantages into account. Make sure to take any of the target's Vulnerabilities or Susceptibilities into account as well.

 

Multiply this by the attacker's percentage chance to hit to determine the average STUN done per phase. You can work this out for BODY as well if you wish.

 

Multiply the average STUN per phase by the attacker's SPD. This is the average STUN done per turn.

 

Optionally, subtract the target's REC from his STUN taken per turn to find out his net STUN loss per typical combat turn. The GM can work this out for as many of an the attacker's attacks as he wants to take the trouble for.

 

 

That's nice, and I could probably set up a GUI interface to it. But I think I see a problem with the way that you calculate average damage (or maybe I'm just not understanding the way you do things). It may be kind of "nit-picky" but here goes. . . .

 

I'll give a hypothetical case:

 

Imagine that I'm shooting a 2d6 EB (Energy Based) at a target with 7 ED. I have a 90.7 percent chance to hit, and my speed is 12. (godlike speed--pansy attack)

 

My average damage is 7 points. And after taking off the target's defenses, the average damage is 0. And after all calculations (by your system) comes out to 0 per turn (12 SPD * 0 Stun = 0 damage).

 

But that is not how it works. If you play out the situation (2d6 vs 7 Def), you'll find that the attacker does damage almost half the time. And with a 12 speed and 90% accuracy, that damage could really add up over time. (That would be especially true of BODY damage--BODY damage has a way of sticking with a target)

 

The problem that the average net damage per shot is not really 0. That is because the low rolls don't really cancel out the high rolls. Given a 7 ED, any attack that does less than 7 on the dice, might as well be a 7 because you can't have a negative amount of STUN.

 

To put it a different way imagine that the attacker (on 3 different shots) rolls a 4, 7, and 10. The mathematical average for those 3 rolls is 7 (4 + 7 + 10 = 21) (21/3 = 7) . But the Net damage (after 7 ED) for those 3 rolls is 3 points (or 1 point of Net Damage per roll).

 

I hope that explains what I'm trying to say--if not please let me know. . . .

[Chris Goodwin]

Sure, I see what you're saying, and it does point out a possible flaw in the system. It's not perfect, true. But you've also chosen a situation highly unlikely to come up in actual play. If you assume numbers more consistent with published ranges, I think you'll get better results.

 

Overall, given that combination of damage, defense, SPD and chance to hit, you've got about a 62% chance in any given phase of doing no damage at all (missing your to-hit roll and rolling less than 7 on 2d6), about a 2.5% chance of doing 5 STUN, and about a 38% chance of doing any STUN at all. Overall, you'll average about .88 STUN per phase or about 10.6 STUN over the course of a turn (taking your misses and your STUN bounces into account). That all took me about 10 minutes to work out by hand, and it would take probably longer than that for me to work out a general rule. (OTOH, if you're volunteering... )

[Warp9]

Originally posted by archer

Sure, I see what you're saying, and it does point out a possible flaw in the system. It's not perfect, true. But you've also chosen a situation highly unlikely to come up in actual play. If you assume numbers more consistent with published ranges, I think you'll get better results.

You're right, the issue I brought up won't have a major effect most of the time.

 

Originally posted by archer

Overall, given that combination of damage, defense, SPD and chance to hit, you've got about a 62% chance in any given phase of doing no damage at all (missing your to-hit roll and rolling less than 7 on 2d6), about a 2.5% chance of doing 5 STUN, and about a 38% chance of doing any STUN at all. Overall, you'll average about .88 STUN per phase or about 10.6 STUN over the course of a turn (taking your misses and your STUN bounces into account). That all took me about 10 minutes to work out by hand, and it would take probably longer than that for me to work out a general rule. (OTOH, if you're volunteering... )

 

I was too lazy to work out a general rule. I just designed a program to spin through all possible combos for a given number of dice. I'd find the total net damage over the spread (given a specific defense), and find the average net damage for a single shot by dividing the total damage by the total shots. Basically I made my computer do the same thing that you probably did by hand.

 

The only problem with that approach is that, even with a computer, too many dice will take a long while to work through.

[Gary]

Originally posted by archer

Sure, I see what you're saying, and it does point out a possible flaw in the system. It's not perfect, true. But you've also chosen a situation highly unlikely to come up in actual play. If you assume numbers more consistent with published ranges, I think you'll get better results.

 

Overall, given that combination of damage, defense, SPD and chance to hit, you've got about a 62% chance in any given phase of doing no damage at all (missing your to-hit roll and rolling less than 7 on 2d6), about a 2.5% chance of doing 5 STUN, and about a 38% chance of doing any STUN at all. Overall, you'll average about .88 STUN per phase or about 10.6 STUN over the course of a turn (taking your misses and your STUN bounces into account). That all took me about 10 minutes to work out by hand, and it would take probably longer than that for me to work out a general rule. (OTOH, if you're volunteering... )

 

I have a spreadsheet that calculates all the net damages after defenses for normal and killing attacks. This spreadsheet handles up to 24D6.

[Tom McCarthy]

If I was going to go to the trouble to write it up as a program, I'd probably run each hit about 100 times and then average the damage after defences over the 100 hits and use that to judge the effectiveness of the attack.

[Fireg0lem]

The error has a greater degree of effect on your calculations for Killing Attacks. For instance: 2d6 HKA vs. 21 PD. On average, according to your formula, 0 Stun. However, because only three dice are involved, there is a wide range of variance, and many targets could easily be KOd in one hit.

[Warp9]

Originally posted by Gary

I have a spreadsheet that calculates all the net damages after defenses for normal and killing attacks. This spreadsheet handles up to 24D6.

 

Does it use a formula, or does it run through all the possibilities to figure net damage?

[Warp9]

Originally posted by Tom McCarthy

If I was going to go to the trouble to write it up as a program, I'd probably run each hit about 100 times and then average the damage after defences over the 100 hits and use that to judge the effectiveness of the attack.

 

Yeah, that should probably work pretty well.

[Gary]

Originally posted by Warp9

Does it use a formula, or does it run through all the possibilities to figure net damage?

 

All net possibilities. I can't think of an elegant way of doing it as a formula. The spreadsheet also calculates percentage chances of con stunning opponents with normal and killing attacks as well. That's simply a variation of the net stun process.

[Talon]

If you were doing it as a program, the best way would be to calculate each possible die result and take a weighted average of the results. That way you get the same value every time you run the program, which is important if you're using to generate a metric.