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After checking out about 8 of the most forum-recommended mass combat systems (in no order : War Machine, GURPS, Kingmaker, Heroes Of Battle, Conan, Die Men!, Green Ronin, Cry Havoc), I focused my attention on Kingmaker because it was by far the simplest system, using much of the existing system’s structure, with the fewest army “specs” (numbers), and melee rolls that are very similar to ordinary combat (d20+“to hit” bonus vs. AC, with a damage bonus if successful). It incorporates many tactical options into the attack, AC, and damage modifiers, thus allowing players to implement tactical choices easily.
As a computer programmer with decades of experience, I decided to simulate the Kingmaker mass combat system, to see how well things worked or didn’t.
First off, I am using the system described at http://kingmake.wikidot.com/armies. I discovered it first, and wasn’t aware of the Pathfinder SRD rules until I was done with the analysis. In general, the Pathfinder rules use *larger* bonuses and penalties, so the Pathfinder SRD results will be even MORE extreme than those shown here (mostly the Tactics). And many of the results will be identical.
If people express enough interest, I could re-run the analysis with the Pathfinder SRD values.
Keep in mind in all of the following that “CR” refers to the *army’s* CR, which varies by its size and the kind of creatures in it. So an army that is 3 CR smaller than another could have fewer soldiers, or soldiers with a smaller individual CR, or a little of both. But it could also have higher-CR troops, just very few of them (somewhat counter-intuitive).
In all cases, I pitted two identical armies against each other from CR=1 to CR=20.
Everything was always significantly different for CR=1 to 5, so the following results ignore CR 1-5 battles. These are probably pretty uncommon anyway, requiring small numbers of low-CR creatures.
The average duration of a battle is about 6 rounds at the lowest CRs to about 12 rounds at the highest.
There is always about a 5-10% chance that both armies are defeated (die, routed) on the same round. The lower the CR, the better the chances of a tie.
If the CRs differ by more than 3, the smaller CR army WILL lose. This does not account for all the other modifiers discussed below, which can make a significant difference.
Next I wanted to see how much each individual Tactic, Resource, Special Ability, and Battlefield Condition tipped the odds in favor of one army over the other (still with otherwise evenly matched armies). Each modifier was used thruout the entire battle. The results were surprising.
In general, each army has about a 46% chance of winning (with the remainder going to a tie). So if some modifier increases that army’s chance of winning to 56%, that’s listed as a “10% increase to winning”. Note that when the *increase* gets to be about 50% or more, that’s a guaranteed win!
First off I found that the increases to winning that single bonuses to OM (attack bonus), DV (AC bonus), or DM (damage bonus) are :
Boosting the OM by +N gives a 10*N% increase to winning (example : a +2 to OM increases the chance of winning by 20%)
Boosting the DV by +N gives a 12*N% increase to winning
Boosting the DM by +N gives a 6*N% increase to winning
The above only applies for +1 to +3 bonuses. So +1 does not correspond to +5%.
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TACTICS (note that any Tactic that can only be used once per battle could not be simulated = N/A)
Bolstered Resolve : 5%
Cavalry Experts : 10% vs. un-Mounted opponents
Cavalry Skirmishers : 12% vs. un-Mounted opponents
Dirty Tricks : N/A
Defensive Wall : 6%
Expert Flankers : 2%
Extermination : N/A
False Retreat : N/A
Flawless Retreat : N/A
Guardian : N/A
Hinder : N/A
Hold the Line : 15%
Relentless Brutality : 2%
Siegebreaker : N/A, but essential for taking out siege engines
Sniper Support : 12% vs. un-Ranged opponents
Spellbreaker : see below
Spell defense : see below
Taunt : N/A
Terror Troops : 5%
Triage : guaranteed win (see Healers, below)
Wallsmasher : see below
RECOMMENDATIONS :
1. Either drop or modify the Expert Flankers and Relentless Brutality tactics – they provide no significant advantage. (NOTE : these are implemented differently in the Pathfinder SRD.)
2. Drop the Triage tactic. Yes, it could really help an underdog, but in an otherwise even fight, it’s a guaranteed win.
3. My personal opinion is that Cavalry vs. non-Cavalry should have a higher advantage, so make the bonuses for Cavalry Experts and Cavalry Skirmishers +2. Ignore this if you disagree.
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RESOURCES
Fortification Builders : 35%
Healers : 30% used once, 45% used twice
Improved/Magic Weapons (+1, +2) : 10%, 20%
Improved/Magic Armor (+1, +2) : 12%, 24%
Mounts : N/A
Poison (+d6) : 20% on average
Ranged Weapons : N/A
Siege Engines : N/A
Smokesticks : N/A
RECOMMENDATIONS :
1. BP cost for resources should be about 1/2 the increase in winning they provide. In particular :
Healing : 15 BP *per use*, max 2 times per battle
Improved/Magic Weapons : 5, 10 BP
Improved/Magic Armor : 5, 10 BP
Poison : 10 BP
2. Fortification Builders is odd – it provides a huge bonus to winning, but it takes a day to implement, and only works while the workers are there. So for any army that has a day to prepare before battle (and is willing to stay immobile), it provides a huge benefit. Guess that’s balanced…???
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SPECIAL ABILITIES
Breath Weapon : 14% on average
Construct/Plant/Undead : N/A
Energy Drain : guaranteed win
Fast Healing, Regeneration : +8% for 1 HP/round
Fast Healing, Regeneration : +16% for 2 HP/round
Fast Healing, Regeneration : +26% for 3 HP/round
Fear : N/A
Mobility : 24% vs. those without the situational advantage
Paralysis : guaranteed win
Poison : 20% on average
Rock Throwing : 21%
Significant Defense : guaranteed win
Spell Resistance : see below
Spellcasting : 21% for max spell level = 1
Spellcasting : 38% for max spell level = 2
Spellcasting : guaranteed win for max spell level = 3 or greater
RECOMMENDATIONS :
1. Do not use anything that results in an automatic win if the two armies are otherwise equally matched!
2. A suggested “BP cost” (in case the DM is building an NPC army with Special Abilities) is half the increase in winning they provide. Anything that’s an “automatic win” should cost at least 25 BP.
3. The spellcasting rules are broken. See below for more details.
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BATTLEFIELD MODS
Advantageous Terrain : 24%
Ambush : N/A
Home turf : 38%
Fortifications (+8 default) : guaranteed win
RECOMMENDATIONS :
All but one of these provide tremendous advantages. The opposing side should look for Tactics and Strategies which would increase their OM mod to offset the large bonuses to DV that these provide. Or, the CR of the opposing side should be higher to compensate.
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Next, I tried giving one army one Tactic, and the other army the counter-tactic or not. The first number is the %increase in winning the Tactic gives to the first army, and the second number is the result when the opposing army has the given counter-tactic. Note that I used a +2 bonus for the Cavalry Tactics, and the +8 “default” value for fortifications suggested by the rules.
Cavalry Experts (+2) vs. Hold the Line : 20% --> 18% (no real improvement)
Cavalry Skirmishers (+2) vs. Relentless Brutality : 24% --> 11%
Spellcaster(SL=1) vs. Spellbreaker : 21% --> –20% (the side with spellcasters loses *more* often!)
Spellcaster(SL=2) vs. Spellbreaker : 38% --> 0% (evenly matched battle)
Spellcaster(SL=3) vs. Spellbreaker : WIN --> 18%
Spellcaster(SL=4) vs. Spellbreaker : WIN --> 34%
Spellcaster(SL=5) vs. Spellbreaker : WIN --> WIN
Spellcaster(SL=1) vs. Spell Defense : 21% --> –23% (the side with spellcasters loses *more* often!)
Spellcaster(SL=2) vs. Spell Defense : 38% --> 0% (evenly matched battle)
Spellcaster(SL=3) vs. Spell Defense : WIN --> 26%
Spellcaster(SL=4) vs. Spell Defense : WIN --> 43%
Spellcaster(SL=5) vs. Spell Defense : WIN --> WIN
Fortification (+8) vs. Wallsmasher : WIN --> WIN
Fortifications (+8) vs. Rock Throwing + Wallsmasher : WIN --> 33%
RECOMMENDATIONS :
1. There is no existing Tactic that’s good against Cavalry Experts.
2. The “adding spells to armies” rules are broken - spell levels past 2 are automatic wins if the other side doesn’t use the right tactic, and even with the right tactic, spell levels past 4 are still automatic wins! Even the Spell Resistance Special Ability only delays the inevitable a little longer. I’m experimenting with a simple add-on for spells, but that’s for another thread. :)
3. Wallsmasher is too weak against any significant fortification. Making it +4 works much better.
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STRATEGIES
Defensive : –16% (loses more often compared to Standard)
Cautious : –9%
Standard : 0%
Aggressive : 8%
Reckless : 17%
NOTE : Pathfinder’s damage modifiers are MUCH larger than those used here, so their chance-to-win results will be much bigger (both positive and negative)!
While being Defensive or Cautious might lose you the battle in the long run, they extend the duration of the battle (Defensive doubles it!), giving more time for help to arrive.
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Finally, I tried pitting 1 large army against 2 smaller armies, again without any other modifiers.
The mass combat rules claim that “two CR 9 armies should make for a relatively even battle, but so would a CR 9 army against three CR 6 armies”. And one of Paizo’s creative directors also implied in a forum that the CRs of the armies should combine by the regular CR rules. Following the CR rules for a 2 vs. 1 battle, the battle should be evenly matched if the two armies have a CR that is 2 less than the single army, but I found this was NOT true.
To produce an *evenly matched battle*, the simulation shows that the CRs must be :
CR1 : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
CR2 : - - 1 2 3 4 4 5 6 7 8 9 10 11 12 12 13 14 15 16
Diff : 1 1 2 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4
(sorry, the proportional font destroyed my formatting)
The “sweet spot” for 2 vs. 1 is that the CR of the 2 armies should be 3 less than the single army, across CR=7 to 15 (probably the most typical CRs). So the CR ratings of the armies does not combine as it should.
As a BTW, a single army always wins against two armies whose CRs are 5 or less than the single one’s CR. So a CR=15 army will always beat 2 armies whose CRs are 10 or less. Again, this is without any of the many modifiers, which can make a significant difference.
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None of the bolded conclusions is meant as a criticism of the system, or to imply that it's broken, they are just things that any DM using the system should be aware of.
Please keep in mind that all of these tests assumed equal-CR armies. Things could change radically when one army has a higher CR than the other. For example, a “low-CR” army with Energy Drain or Paralysis would probably be evenly matched against a much larger CR army (but I don’t know how much larger).
Also, I can usually only test the effect of one change at a time, and the number of ways Tactics can combine with Strategies is so large it cannot be accounted for. Not to mention that the number of Resources you can add to an army depends strongly on the situation.
Finally, in any single battle, the roll of the dice is WAY more important than the average bonuses shown here.
Wow, very impressive work. I really appreciate the effort you put in here, I knew that the Reckless Strategy was best but you really have spelled everything out! Thanks!
a big thanks for the effort even if i don't use those rules, you are doing a great service to the community
Some corrections and additions :
Adding Energy Drain to an army increases its chance of winning by 41%.
Adding Paralysis to an army increases its chance of winning by 32%.
Any "automatic win" conditions can be converted into a "CR+" value, where the army WITHOUT the condition must be so many CR higher than the army with the condition to make it a fair fight.
Fortifications : CR+3
Special Defenses : CR+4
Spellcasting, +3 to OM, DV : CR+2
Spellcasting, +4 to OM, DV : CR+3
Spellcasting, +5 to OM, DV : CR+4
So if one army is CR 10 and has Fortifications, an otherwise identical army would need to be CR 13 to have about a 50/50 chance of winning.
Do a rerun with the SRD rules. Please? Pretty please with sugar on top, and sprinkles, glitter, rainbows and everything?
I'm unsure the damage bonuses are meant to be added. It makes no sense since damage is determined by OM-DV; why have a separate, additional modifier?
Tharken : keep in mind that the listed "increase to win" for each Tactic is independent of all other Tactics or Strategies. But looking at its bonuses, and remembering the "weighting" for each different bonus, Expert Flankers has +10% from OM, -24% from DV, and +12% from damage, so everything just about cancels out. Same for Relentless Brutality. But Defensive Wall and Hold the Line as described by the wikidot also provide "DR", which makes them much more effective. BTW, are you the original creator of that wikidot? If so, I've got some questions for you, if you don't mind...
Leisner : I will re-do with the Pathfinder SRD rules, but it may take a few days (like thru the weekend). Keep checking.
Meatrace : it's my understanding that the total damage is the attacker's OM check (including the d20) - the target's DV + the attacker's damage modifier. If you look at the SRD itself, under "Strategy Track", they list modifiers to damage for each option. And the Sniper Support Tactic specifically says it does an extra +2 damage. The OM and DV have modifiers for each Tactic and Strategy, why not damage too?
P.S. to all - I've outlined the details to fixing the spellcasting portion of these rules in
http://paizo.com/threads/rzs2q0wj?A-supersimple-fix-to-having-spellcasters- in#3
Please let me know what you think.
Leisner : I will re-do with the Pathfinder SRD rules, but it may take a few days (like thru the weekend). Keep checking
Thank ye kindly.
Nice!
Seconding the request for a re-run on the PRD version.
Meatrace : it's my understanding that the total damage is the attacker's OM check (including the d20) - the target's DV + the attacker's damage modifier. If you look at the SRD itself, under "Strategy Track", they list modifiers to damage for each option. And the Sniper Support Tactic specifically says it does an extra +2 damage. The OM and DV have modifiers for each Tactic and Strategy, why not damage too?
Except there's no verbiage that defines it as such. You are simply inferring from other sources, not following RAW. It's something I'd like cleared up by the designers frankly.
As for sniper support, the bonus damage is in lieu of attacking in both ranged and melee phases.
Except there's no verbiage that defines it as such. You are simply inferring from other sources, not following RAW. It's something I'd like cleared up by the designers frankly.
As for sniper support, the bonus damage is in lieu of attacking in both ranged and melee phases.
It isn't *my* inference, it's the Wikidot that I merely analyzed. He explicitly has damage modifiers for many of his added Tactics.
And with respect, I think you're misinterpreting the wording of Sniper Support. However, I can see how the wording could lead to that conclusion, it could be worded better.
But I'm not going to debate the issue - it's a free multiverse. :)
P.S. to all - working on the PF analysis right now, should be ready well before Tuesday at the latest (very possibly by Sunday)...
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I believe that more thought has been put into this thread than went into writing those rules in the first place.
Pupsocket - thanks! Considering the potential overlap between people-who-program and people-who-play-FRP's, I'm surprised that more systems aren't "playtested" by computer simulations these days. I've simulated many different published systems over the years, to see how well they work.
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An analysis of the ***PATHFINDER SRD*** mass combat system
Fortunately, only the modifiers for the various Tactics, Special Abilities, and Strategies are different.
Note that smaller %increase in winnings can be converted into a CR+ value as well :
+21% = +1 CR
+42% = +2 CR
So a %increase in winning of about 19-22% could be balanced by making the opposing army 1 CR higher, etc.
For ease of reference, I’m going to list each Tactic, Resource, Special Ability in the Pathfinder SRD even if it did not change compared to my first post. Only items marked with a * changed from the original post.
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TACTICS (note that any Tactic that can only be used once per battle could not be simulated = N/A)
*Cautious Combat : –20% (has a smaller chance of winning)
Cavalry Experts : 20% vs. un-Mounted opponents
*Defensive Wall : 16%
Dirty Fighters : N/A
*Expert Flankers : –2%
False Retreat : N/A
*Full Defense : 2%
*Relentless Brutality : 2%
Siegebreaker : N/A, but essential for taking out siege engines
Sniper Support : 12% vs. un-Ranged opponents
Spellbreaker : see below
Standard : no change
Taunt : N/A
*Withdraw : N/A
RECOMMENDATIONS :
1. Change or remove Expert Flankers, Full Defense, and Relentless Brutality – they give no advantage.
2. The only advantage Cautious Combat has is that it extends the duration of the battle, allowing time for help to arrive.
3. Consider adding from the Wikidot : Flawless Retreat, Hold the Line, Terror Troops, Wallsmasher. They each provide bonuses that can come in handy in some situations. Wallsmasher in particular is very helpful against fortifications, especially if you boost its bonus to +4.
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RESOURCES
No changes at all!
Healing Potions : 30% used once, 45% used twice
Improved/Magic Armor (+1, +2) : 12%, 24%
Improved/Magic Weapons (+1, +2) : 10%, 20%
Mounts : N/A
Ranged Weapons : N/A
Siege Engines : N/A
RECOMMENDATIONS :
I can’t comment on how the BP costs for these items should relate to their %win improvement – I haven’t studied Pathfinder’s cost scaling, and these have both initial costs and Consumption costs.
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SPECIAL ABILITIES
Nothing changed in the original list of Special Abilities!
A few of the MANY Special Abilities that PF added are included below, marked with a *
If anyone wants me to try some specific ones, just let me know.
Breath Weapon : 14% on average
Construct/Plant/Undead : N/A
*Damage Reduction : 8% for 1 DR
*Damage Reduction : 16% for 2 DR
*Damage Reduction : 26% for 3 DR
Energy Drain : 41%
Fast Healing, Regeneration : +8% for 1 HP/rnd
Fast Healing, Regeneration : +16% for 2 HP/rnd
Fast Healing, Regeneration : +26% for 3 HP/rnd
Fear : N/A
*Invisibility : 38%
*Mobility : 11% vs. those without the situational advantage
Paralysis : 32%
*Poison (also Bleed, Burn, Ability Damage or Drain) : 20% on average
Rock Throwing : 21%
Significant Defense : automatic win (CR +4)
Spell Resistance : see below
Spellcasting : 21% for max spell level = 1
Spellcasting : 38% for max spell level = 2
Spellcasting : automatic win for max spell level = 3 or greater (3:CR+2; 4:CR+3; 5:CR+4)
RECOMMENDATIONS :
1. Do not use anything that results in an automatic win if the two armies are otherwise equally matched!
3. The spellcasting rules are STILL broken. See below for more details.
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BATTLEFIELD MODS
I did not check all the many added weather conditions (fog, rain, sandstorm, snow, wind) because they affect all armies equally, altho some of the new Special Abilities do negate them.
Advantageous Terrain : 24%
Ambush : N/A
Battlefield Advantage : 38%
*Darkness : 45% vs. enemy who can’t see in darkness (CR +2)
*Dim light : 10% vs. enemy who can’t see in dim light
Fortifications (+8 default) : automatic win (CR +3)
RECOMMENDATIONS :
All but one of these provide tremendous advantages, and Darkness is a virtual win. The opposing side should look for Tactics and Strategies which would increase their OM mod to offset the large bonuses to DV that these provide. Or, the CR of the opposing side should be higher to compensate.
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I wanted to try giving one army one Tactic, and the other army the counter-tactic or not, but the set of Tactics in the PF SRD is so small I couldn’t see combos worth trying.
If anyone wants me to try some specific ones, just let me know.
The results for Spellcaster vs. Spellbreaker are the same as before.
RECOMMENDATIONS :
1. There is no existing Tactic that’s good against Cavalry Experts. It needs to provide just a +2 to DV.
2. The “adding spells to armies” rules are broken - spell levels past 2 are automatic wins if the other side doesn’t use the right tactic, and even with the right tactic, spell levels past 4 are still automatic wins! Even the Spell Resistance Special Ability only delays the inevitable a little longer. See "http://paizo.com/threads/rzs2q0wj?A-supersimple-fix-to-having-spellcasters -in#3" for a tested way to fix this.
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STRATEGIES
Defensive : –28% (loses more often compared to Standard)
Cautious : 0%
Standard : 0%
Aggressive : 42%
Reckless : 49% (automatic win!)
NOTE : Pathfinder’s chance-to-win changes are MUCH larger than those from the Wikidot! Interestingly, Cautious does not increase the chances of losing.
Defensive or Cautious extend the duration of the battle, giving more time for help to arrive.
Consider using the Wikidot’s more moderate modifiers for Strategies (altho Cautious extends the duration without lowering the chance-to-win, which is kind of nice).
ZenFox
Great work! "In God we trust; all others bring data."
I'm playing Kingmaker now but haven't arrived to the mass combat stage so don't know the rules. However, I've read quite a bit of military history. A couple of comments:
- It is that it's a myth that cavalry is so powerful. Cavalry does tremendously well versus skirmishers but not versus well-trained infantry, because horses naturally avoid charging into walls of shields or swords.
- How would your analysis change if the size (CR) of armies were capped/limited to a commander's ability (maybe leadership score)? Meaning, what if an "army" composed of 9-40 brigades (I don't know what CR would be brigade) met another army of 6-30 brigades? How does the math change?
cheers
Jubal - in this system, an "army" is a unit of identical creatures. The CR of the army is based on the CR of an individual creature, modified by the # of creatures. There's no names for units by size (platoon, brigade, etc.).
So you build your army with N creatures who each have a challenge rating of CR, do a lookup on a table, and figure out the CR for that army. The army's CR is the "base" from which everything else is derived.
I *think* that makes your question moot, but if you disagree please re-phrase it and/or explain it in more detail, and I'll see what I can do. In particular, what does "9-40 brigades" mean? Are you saying there's a (possibly random) range in the number of brigades? That just won't work with this system...
P.S. - great quote!
OK. Let me rephrase. Historically, there appears to be an upper limit on how many troops can fight completely aligned. Even if you had 10,000 infantry, it would probably be split into phalanxes, cohorts, or battalions of about 300 to 1,300. My question comes from the adding CR conclusions that you made. So my question is: how does the math change if you model a roman legion of 6000 heavy infantry as one unit of 6,000 or 6 cohorts of 1,000 (actually they weren't exactly split this way, but close enough).
Further, how does the math change if an asymmetrical army faces a symmetrical army? Say 20,000 infantry versus 10,000 infantry, 5,000 archers, and 5,000 cavalry (or less cavalry to let the rider and horse equal to 5000 riders/infantry). Is this a CR adding situation, too. How advantageous is it to be symmetrical?
cheers
Well, the rules only go up to 2000 creatures per army anyway, altho I suppose you could follow the obvious pattern and create larger armies. Remember, this system was made to be *abstract* and *simple*! :) Are you aware that there's no map placement or movement involved?
Actually, now that I think about it, I suppose there's no reason why you couldn't just multiply all the #troops in the table by 10, altho I haven't thought that thru at all...
The rules do assume that each army is made up of all the same kind of *creature* (or pairs of creatures, if mounted). So in your example you'd *have to* make the cavalry a separate army (BTW, I think 1000 mounts and 1000 riders counts as a 1000-creature army, for purposes of determining CR).
Regarding the other types (archers, spellcasters), those are all factored into the OM/DV/DM bonuses for that army. And in the case of the cavalry, you can use a Tactic that boosts their bonuses.
Based on the results from the 2-armies-on-1 simulation, with all other things being equal, multiple small armies are a match for armies much bigger than them. If all the armies are made up of the same CR 6 creatures, then two CR 10 armies (500 troops each) are a match for a single CR 13 army (roughly 1500 troops total). So 500+500 is a match for 1500.
That's why the CR-combining rules do not apply here, because according to them, two CR 10 "things" should be a match for one CR 12 "thing", which here would mean 500+500 is a match for 1000. I think the system designers were hoping the CR-combining rules would apply, but unfortunately they don't.
If this doesn't answer your questions, please let me know.
This definitely adds to my suspicions of the strategy track. It's borked!
I don't suppose you could run a simulation of various strategies without the +Damage modifier (just +/- OM and +/- DV), see what shakes out. Maybe various strategies against one another, rather than against the Standard track. It would be interesting to see if, say, Reckless wins against ALL other strategies, including Defensive, automatically.
That's why the CR-combining rules do not apply here, because according to them, two CR 10 "things" should be a match for one CR 12 "thing", which here would mean 500+500 is a match for 1000. I think the system designers were hoping the CR-combining rules would apply, but unfortunately they don't.
If this doesn't answer your questions, please let me know.
It does. Actually, I think that your example of two 500 units evenly fighting a 1500 unit is reasonable. One 500 can hold the front while the other 500 can threaten a flank.
thanks
ERRATA!!!!!!!!!!!!
I just discovered that I had typed the bonuses to the Strategies into the program incorrectly. I'm in the process of kicking myself because that 0% on Pathfinder's Cautious should have alerted me. Anyway, here are the corrected Strategies' change in chances of winning, compared to Standard.
First, for Pathfinder :
Defensive : –45% (always loses)
Cautious : –26%
Standard : 0%
Aggressive : 15%
Reckless : 26%
And then the Wikidot (these didn't change that much, except for Reckless) :
Defensive : –18%
Cautious : –7%
Standard : 0%
Aggressive : 5%
Reckless : 9%
Meatrace -
If you remove the damages from the Strategies, they all go to pretty much "no change" in the chances of winning, because a +N in "to hit" essentially cancels a -N in AC, and vise-versa. (Other things like the number of ties and the duration of the battles may change, but I'm generally not tracking them.)
But comparing Strategy vs. Strategy is a great idea! Here's the results, first for Pathfinder :
Defensive vs. Defensive : 2%
Defensive vs. Cautious : –43% (LOSE)
Defensive vs. Standard : –45% (LOSE)
Defensive vs. Aggressive : –45% (LOSE)
Defensive vs. Reckless : –45% (LOSE)
Cautious vs. Defensive : 50% (WIN)
Cautious vs. Cautious : 2%
Cautious vs. Standard : –26%
Cautious vs. Aggressive : –35%
Cautious vs. Reckless : –39%
Standard vs. Defensive : 52% (WIN)
Standard vs. Cautious : 29%
Standard vs. Standard : 0%
Standard vs. Aggressive : –19%
Standard vs. Reckless : –30%
Aggressive vs. Defensive : 52% (WIN)
Aggressive vs. Cautious : 38%
Aggressive vs. Standard : 15%
Aggressive vs. Aggressive : –2%
Aggressive vs. Reckless : –6%, more ties
Reckless vs. Defensive : 53% (WIN)
Reckless vs. Cautious : 42% (WIN)
Reckless vs. Standard : 26%
Reckless vs. Aggressive : 7%, more ties
Reckless vs. Reckless : 0%, many more ties
Note that when both sides use the same Strategy, the change in winning is virtually zero (sanity check). Any two Strategies more than 2 steps apart usually results in a win for the more aggressive strategy. But remember, even tho Defensive always loses, it buys you time.
And then for the Wikidot (lower damages) :
Defensive vs. Defensive : 3%
Defensive vs. Cautious : –11%
Defensive vs. Standard : –18%
Defensive vs. Aggressive : –22%
Defensive vs. Reckless : –26%
Cautious vs. Defensive : 17%
Cautious vs. Cautious : 2%
Cautious vs. Standard : –7%
Cautious vs. Aggressive : –14%
Cautious vs. Reckless : –20%
Standard vs. Defensive : 23%
Standard vs. Cautious : 9%
Standard vs. Standard : 0%
Standard vs. Aggressive : –8%
Standard vs. Reckless : –15%
Aggressive vs. Defensive : 25%
Aggressive vs. Cautious : 15%
Aggressive vs. Standard : 5%
Aggressive vs. Aggressive : –3%
Aggressive vs. Reckless : –12%, more ties
Reckless vs. Defensive : 28%
Reckless vs. Cautious : 18%
Reckless vs. Standard : 9%
Reckless vs. Aggressive : 0%, more ties
Reckless vs. Reckless : 0%, many more ties
As expected, the Wikidot's lower damage modifiers result in far less extreme consequences.
You might want to look at Ultimate Campaign newer Mass Combat rules as well. They might be a bit different.
Thanks for the heads-up. Having looked at http://paizo.com/pathfinderRPG/prd/ultimateCampaign/kingdomsAndWar/massComb at.html, they appear identical. Don't know how those rules compare to the ones in the original book, tho.