Combat Score Formula!

[MageHunter]

So I have been experimenting and I made a formula to evaluate any character's combat ability. This formula utilizes their attack bonus, and damage.

100-5(AC-AB-1)/100 * (10-H/ADPR)

AC = Armor Class
AB = Attack bonus
H = Hit Points
ADPR = Average Damage Per Round

The first half (before the multiplication) calculates the probability of landing a hit. This uses the average statistics labeled in the bestiary for a monster with a CR equal to your level. The second bit, is how many hits it would take to kill it, if you score average damage. The higher your combat score, the better you are at combat. Also, you could plug this in using the monster's attack stats, and the PC's defense stats. In this case, ideally you'd want a score higher than the monster, but they have to balance several players, and encounters normally are numerous weaker monsters. Here's an example of a player combat score.

The average monster at CR 5 has 55 hit points and an AC of 18.
Our sample 5th level fighter has a +4 str bonus,+1 weapon training, +1 weapon focus, +5 BAB, and a -2 penalty from the feat power attack (with a +4 damage bonus), and a bastard sword dealing 1d10 damage (On average 5). For this formula, his AB = 9, and his ADPR = 13.
So...
100 - 5(18-9-1)/100 = 3/5. 10 - 55/13 = 5. (Always round up, you can't have fractional turns or rounds.) 3/5 x 5 = 3.
The fighter's combat score is 3. I tested this with two other sample characters being a rogue and wizard, and it seems to work. I don't have anything for multiple attacks, but with time I should be able to come up with something. I am interested to see if you guys can break the system so I could fix it.(I am aware you can get a negative score) Overall, I want the perfect formula.
Thank you.

[Create Mr. Pitt]

I suppose I'll be the first to point out that there's no way for that formula to account for a wizard's contribution to combat.

[MageHunter]

Actually...
Wizards have excellent combat scores! You could just replace AC with saving throws, and modify some stuff to be the DC for the spell. Not to mention direct attack spells deal a lot of damage. They're really only weaker compared to others in that they have limited uses of those spells.

[MageHunter]

On second thought however, if you aren't using Blaster wizards I see your point. Those things can't be mathematically recorded unfortunately. :(

[Trinam]

You can't math a good pit.

[Obbu]

From a purely combat perspective, you'd also need to math out iteratives/natural attacks and DR. It would probably be too difficult to math out class-specific features like opportune parry and riposte.

It also doesn't factor in durability/AC/Saves of the PC into a 'combat' score, so it's really more of an 'offense' score, though a defense score could follow a similar idea?

You could do a general caster version of DC/Spell penetration: but it becomes difficult to factor in blasting vs crowd control vs debuffs.

With that said, I do like the idea on principle :) You could avoid many of these issues of comparison by not including them in the calculation at all.

[avr]

The other part it doesn't represent is buff time. It can take some time for divine or gish types to reach maximum firepower. Sometimes you can buff before a fight, sometimes (espec. if using swift actions, see inquisitor, or for a magus there's spell combat) you do buff up after the combat music starts playing.

[Finlanderboy]

Also debuffs are not taken into account.

I have a monk that can automatically frighten things capable of fear he punches.

What about a tank a person that sacrifices his damage for AC so enemies burn their action economy trying to hurt the tank. How does Ac compare to damage?

[MageHunter]

I guess for some of this you would just modify the AC's and whatnot before crunching the numbers. For example, my sample fighter had power attack, so I just included that in. For that stuff to work just add everything. The time to reach stuff does seem difficult to figure out, and after a bit of work I might be able to incorporate damage reduction. I've been thinking of combining it to make defense an aspect as well, but that just seems too much in one formula. I might be able to draw up some variant formulas for things like spellcasting. Definitely on the to-do list is figuring out multiple attacks. Thank you for all the responses and help.

[PossibleCabbage]

It seems like if you want to model "combat effectiveness" you should at least attempt to include CMB/CMD for characters that want to do that sort of thing. Like a good grappler can move, grapple, and pin an opponent in one round, which more or less takes them out of the fight. It's not the be-all-and-end-all but it's something the rest of the party is going to appreciate.

[TriShadow]

Not to pile on here, but you also do not account for combat builds that specifically depend on having a high crit range, like say a magus with spell strike, weapon finesse and keen rapier critting from 15-20. I think there may be too many variations to have an effective formula to come up with a "rating" system. Love the idea though.

[Duiker]

Combat effectiveness is multi-dimensional. You cannot meaningfully reduce it to the single dimension of a number without losing information. The problem's not with the particular equation, it's with the goal itself.

[MageHunter]

Really great input here. I guess this can only measure one thing, which is the typical bashing in heads fighter. I think it would be interesting to delve further with this formula though. I considered crit hits, but once I got into probability and multiplication, it started to be a bit too much. I do want to see where this goes however. Thank you for all the support! :)

[MageHunter]

The largest trouble for me was finding a system where the higher the score was, the better. I will say, that took me a while.

[Alex Mack]

What does your formula achieve in addition to a simple DPR calculation?

If you have a good answer to that question proceed otherwise exit and calculate DPR versus level specific AC.

If you wanted to calculate a composite indicator of combat efficiency you could additionally generate some sort of defense indicator but I feel like there would be too many moving parts in such an equation.

However as others above have pointed out this will only work for martial characters. Those that do dem spells are gonna be hard to rate.

[My Self]

The most effective wizards play intelligently and operate laterally, altering the problem until it ceases to be a problem. They might create a saveless fog around enemies, suffocate them in a dungeon room with a simple wall of stone, or destroy all the enemies' charging lanes by creating a pit out of nowhere. Smart players are difficult to quantify. Less effective wizards will release their arcane might upon anything that dares stand in their way, attempting to slay or control it in a single save-or-die roll. This is slightly easier to quantify, because you can measure the effects of the spell and the save DC required.

However, you're also missing force multipliers. A bard, wizard, and cleric who group-buff and become melee monsters will be exponentially more frightening than any of the three alone, whereas a paladin, swashbuckler, and fighter do not multiply each others' strength. Also, some classes, such as rogues, inquisitors, and witches, function significantly better as team players, while others, such as the druid, summoner, and warpriest are perfectly fine on their own.

[Ellioti]

the 2nd half of the formula is missing. Defense! You should make the same calculation for the monster attacking YOU and then multiply offense score and defense score or something like that. That's your combat score, because if your AC and hp are low, you will never see round 2.

[Alex Mack]

Ellioti wrote:

the 2nd half of the formula is missing. Defense! You should make the same calculation for the monster attacking YOU and then multiply offense score and defense score or something like that. That's your combat score, because if your AC and hp are low, you will never see round 2.

I'd argue that defense is far more complex than offense. You'd also have to consider things like saves, self healing and so forth...

[Callum]

This reminds me of Don Turnbull's Monstermark system for D&D, which was published in 1977:

https://twitter.com/dailydwarf/status/501289696262381568

[MageHunter]

I've done some thinking and I have an overall plan for the future. I'm going to make a whole bunch of different formulas, and to use them just choose the relevant ones. (For example, fighters won't need the spellcasting score formula, and wizards probably won't need the above combat score.) The idea is you find the average of all the scores and that overall rates the character optimization. Formulas for saving throws and defense would be required fields for everyone most likely. It'll take time, but I look forward to trying it out. Also I figured out DR. In general, if your PC can't overcome it (and you are doing a specific monster) then just subtract the DR from ADPR in the formula. Thank you for all the advice and support.

[MageHunter]

Okay so I simplified the original formula and got this.

[(21-AC+AB)/20] * (10- H/ADPR)

Also for multiple attacks. Granted, the accuracy of scoring four hits isn't likely, but damage is also increased accordingly, which should make this balance out.

[(21-AC+AB)/2-] * [(26-AC+AB)/20] * [(31-AC+AB)/20] * [(36-C+AB)/20] * (10-H/ADPR)

Up next is figuring out defense. I'll try to do it based off armor class and total HP. Self healing will be a bit more of a difficult factor. At the moment, my fix is subtracting that from the monster's ADPR. I want to do these formulas for combat maneuvers as well but the bestiary doesn't list average monster combat maneuver defense or bonus. If there is some reliable way to figure that out (Average ability score, BAB, etc.) that would be appreciated. Saving throws and spells should be pretty easy to figure out. Also, as unlikely as it seems, if there is away to mathematically evaluate "controller" classes than any tips or directions would be helpful. As I said before the final product is adding up all these scores to find the average, and thusly find the character score. All help on anything is appreciated. Look forward to much more mathematical and Pathfinder cross geekiness.
Thank you.

[My Self]

You'll probably want to just put this into a spreadsheet.

[Obbu]

MageHunter wrote:

If there is some reliable way to figure that out (Average ability score, BAB, etc.) that would be appreciated.

Pathfinder Bestiary with Statistics has a lot of the things you are looking for. It doesn't do the stats from all of the bestiaries (I think Bestiary 1 and 2 only), but its reasonably meaningful for checking averages on things that aren't covered by Monster Creation

[MageHunter]

Thanks Obbu. So far my idea for defense, is an inverted offense formula, that is averaged with saving throws and combat maneuver defense. Anything else I should add or am I good?

[Obbu]

I think DR would be useful to include: as it's seen in some cases as a viable alternative to raising AC.

However I'm a bit stumped as to how you can do it in circumstances where it only applies to certain damage types. Perhaps you could simply do a combat score sans DR, and a combat score with DR?

[Claire Lee-O'Blivyus]

100-5(AC-AB-1)/100 * (10-H/ADPR)

Soooooo, my L12 come and get me barbarian has an attack bonus of 32 and an armor class of 11 and DR 6/-. Assuming no charge, he does 3 attacks at 4d6+31 damage plus AoO (fortuitous weapon + Combat Reflexes + Unexpected Strike) with threat on 17-20. Average monster for CR12 has AC 27 and 160 HP.

100-5(27-32-1)/100*(10-160/45)

[(21-27+32)/20] * [(26-27+32)/20] * [(31-27+32)/20] * (10-160/45)= 23.374

Is this what should be happening?

Also, that makes the come and get me barbarian over 7 times as combat effective as your fighter. Furthermore, the barbarian will crit, has multiple AoO per round (mine has up to 5), and ignores a variety of DRs due to golembane scarab, swarmbane clasp, amulet of elemental whatnot...

'Twould be interesting to compare 10x NPC codex classes at levels 1, 4, 8, 12, 16, 20. It would probably give an exceptional feel for the relative combat power of those classes and the levels at which they peak.

I think the 3/4 BAB classes developed by Paizo really mesh well with Pathfinder Society, as everyone is along a similar power curve. Perhaps they use a similar model?

[MageHunter]

I'm still experimenting. Does your build feel op? Do you like get a lot of one hit kills? I imagine such high numbers could be a result of effective optimization. I'll look into testing the npc's. Primarily it'll be direct damage like fighters due to the current formula.

[Anguish]

The problem is that there are so many tweakable aspects to any character that it's meaningless to break everything down to one comparison number.

For instance, between two punch-in-face fighter types, a formula might tell you that one is better than the other, but when you notice the great big gaping hole where the better one should have a decent Will save, you realize it's not.

Kind of what I'm saying is that damage-per-round isn't king. Rounds-to-incapacitate is. And there are so many different ways to incapacitate in the game that you can't meaningfully quantify them.

Not trying to disparage the effort... good for you if you find this entertaining. Just pointing out that I don't see how you can possibly arrive at anything useful.

[MageHunter]

I actually agree. That's why I'm trying a whole bunch of different formulas and you just find the average. This will actually bring down what feels like op scores like with Claire(Great name). Also I like math and pathfinder. less important but good ideas for names? It seems like combat score formula ain't cutting it. MageHunter formula doesn't have to much of a nice ring to it. Thank you for all the replies, each once is appreciated.

[Abraham spalding]

Also without save throws being a balancing factor this is not going to be complete.

[My Self]

It might not hurt to include a calculation for enemies who can hit above and below their effective CR. For example, swarms and troops always hit if you're in their space, no matter how good your AC is. Some enemies can consistently make their targets shaken or sickened, which is a more complex interaction, but might be worth noting. And DPR is also variable for AOE effects, such as shotguns and fireballs.

[Scott Wilhelm]

MageHunter,

For starters, as a system for melting down several offensive and defensive statistics into a single number to help express how good this combatant is on average seems like a useful idea in principle, but I can think of a lot of characters where your Combat Score is not adequate for giving you a picture of what will happen in combat.

It occurs to me that you could add nuance to your system by generating multiple Combat Scores for your character: say one for close melee, one for Reach, one for Short Range, say 30'-50', and one for long range. Making sure you take such things into account might add nuance to scoring A Barbarian with Thunder and Fang against a Phalanx Solder with a Bashing, Quickdraw, Throwing Klar, a Lucerne Hammer, and a good Bow on her back with a variety of Weapon Blanches and trick arrows.

MageHunter wrote:

I am interested to see if you guys can break the system so I could fix it.

Some kinds of characters do relatively better against multiple opponents than against single opponents, and some the other way around. Some characters are more or less strongly affected by opponents' DR, either because they achieve their Damage Per Round with single, high-damage attacks or with multiple, smaller attacks. Some characters have relatively higher or lower attack bonuses vs. relatively lower or lower or higher damage bonuses, and the relative DPR of these characters changes when fighting creatures with higher or lower Armor Class.

I feel like predicting the AC of the monsters you will be fighting is problematic, and that makes it especially difficult to rate something like a Crit Build. How much better is a Falcata really from a Long Sword? Is it better to do triple damage on a Crit, or is it better to spend your Exotic Weapon Proficiancy Slot to learn Bastard Sword and just get the +1 Damage on every hit, which also doubles if you do Crit? To know that, you need to know your chances of Confirming, and to know that, you need to know in advance what creatures you will be fighting, and then it's not an adventure anymore, is it?

Consider PossibleCabbage's character, who does not inflict much in the way of damage at all, but rather Grapples, Pins, and Ties Up opponents. How do you score that?

How does your system deal with other kinds of debuffs? Take, for example, a Ninja/Wizard who can Vanish then cast Ray Spells. Ray Spells are Ranged Touch Attacks, and while Vanished, the target gets no Dex Mod. This character would be scoring hits far more often than his relatively low attack bonus would suggest. There is also the Alchemist Archer who uses Marker Dye Arrows to deliver his Bombs, also Ranged Touch Attacks.

There are other ways of gaining defensive effectiveness than Armor Class. What if your character has Keen Scent, Blind Fighting, and carries an Eversmoking Bottle? This character enjoys a 50% Miss Chance a lot of the time, and depending on the makeup of the party, is a great boon or great bane to his or her fellows.

There is also DR, Fast Healing, and regular Healing. How does your score handle a Protector Tumor Familiar who has half the HP of the host, absorbs half the damage suffered by the host via a Shield Other effect, and the Familiar enjoys Fast Healing 5.

So I just offered a lot of characters your system might not accurately measure, but I don't think that means I broke your system. A lot of effects I described require some very specific cases and elaborate character building techniques (if I do say so myself :P), so it might be just fine if your system just misses some of those sometimes.

MageHunter wrote:

Overall, I want the perfect formula.

I'm not sure that's possible or even desirable. Maybe your hammer is terrible for replacing light bulbs, but that doesn't mean that re-designing your hammer is the answer. It's dangerous to just let the machines do our thinking for us. That's how we got that sub-prime-mortgage financial crisis, because so many banks were approving Liar's Loans because their computer models predicted it would be profitable to do so.

But keep tweaking your combat score system, make it better. Make it more responsive. But don't make it too good: once you can predict the outcome of every combat your character is going to have in his career at the time of his creation, there won't be any point in playing him anymore, will there?

[MageHunter]

Okay so I tested things out and I think I broke the formula. I'll have to add an absolute value thing to negate negative numbers, and overall I'll have to look at things because some of the numbers don't seem to make sense. If any of you want to double check my math feel free to go ahead. Here's what I had testing this out on fighters in the NPC codex.

1rst Level:
Human Fighter (I applied Power attack. On the rest I just did what the stats showed)
Score: 1.2

4th Level:
Halfling Fighter (On all of these I did the primary weapon. For this guy that was ranged. I might do something where I find the averages of all the weapons.)
Score: 0 (Problem here. The 10- H/ADPR ended up in 0. Multiplied to anything that caused 0. )

8th Level:
Gnome Fighter
Score: 1.5

12th Level:
Dwarven Fighter
Score: 3.2

16th Level:
Dwarven Fighter
Score: 5.3

20th Level:
Human Fighter (This guy kind've scares me...)
Score: 39.4

Clearly there was a bit of a jump there. Having the average of multiple scores should make things overall a bit more stable, but some of the numbers seemed a little fishy. My next step is trying to fix this. Thank you for all the replies. If it weren't for the one that recommended looking at NPC's I would've thought this was flawless. Feel free to test this out on your own characters to see if you can break it some more. I am going to get as far as I can on a good system. For me at least, categorization and numbers are pretty fun. Scott, I can't do all the concepts you did at once (which was kind've your point) but I have been considering incorporating senses as that is important. I could be able to pull off concealment. Again thank you for all the replies, and I hope for the best in the future.

[Mr Oger]

I would split the formula into two parts. First is somewhat similar to dpr, but also there includes hit chance (somewhat tohit/15+(2/3)*level), the second is defences - saves (something like ((10+T)/(16+(lvl/2)))*((10+R)/(16+(lvl/2)))*((10+W)/(16+(lvl/2))) - if you have all strong but one that means that you gonna be clucked up) and ac+cmd like formula i did - you can have untouchable ac, but if they can trip you and then just sunnder your armor you are clucked up again)