Goblin Squad Member
|
Would 5 lvl 1s be enough to take 1 lvl 4 down? (only one lvl 1 surviving though)
I also had fun with it and decided to see what would happen with the level 4 vs the level 1 from the blog. Spoiler: the level 4 can probably take on a small swarm of them.
In a toe to toe fight (standing there just hacking at eachother) with the numbers we've been given and assuming the level 4 is in heavy armor?
Not a chance. They'll bring the level 4 down some, but 5 level 1's toe to toe wouldn't bring the level 4 to half hp. If they're all wearing heavy armor they might hit half hp on the level 4.
Using hit and run tactics of swooping in/kiting the slowed down level 4 and using magic against his likely much weaker magic defenses?
With skilled players ... maybe if they go magic heavy or know how to kite well. But without knowing specific numbers it's hard to say.
My gut instinct is:
5 level 1 fighters? The level 4 wins. He simply out-damages them too much.
A mix including mobile melee and casters*? The melee die and the casters bring the level 4 down. The melee would be purely to distract the level 4 as the casters do the majority of the damage.
* I assume for this guess that caster damage works the same way as melee damage, but against different defenses. As plate is probably weak against magic (as Stephen Cheney has hinted), then it would be something similar to the casters seeing resistance on par with what light armor gives against melee.
|
Goblin Squad Member
|
The analysis is really forming a picture for me here! Thanks again.
I think the level 1-5 or so is steeper difference than a comparable 5 level difference further along the power curve, has been said to be an intention for GW (for various good reasons) So the numbers here seem encouraging in that they are likely in terms of power curve the more/most extreme difference it gets with sole power comparison ignoring variables such as player skill, group tactics etc etc?
|
Goblin Squad Member
|
Gut instinct based on how the min/middle/max of the 3d200 system (mentioned in the blog) works is that you are right that this is the steepest part of the power curve. Taking the minimum (tier 1) gives higher odds to very low damage due to the way that damage is calculated than taking the max or middle roll. So my very preliminary guess is that as you increase tier then relative attack vs defense skill becomes less important. Basically the color contours become more horizontal on the color map (I think). Then base damage vs. resistance becomes the more important factor.
(I've had to tie up the cluster for the weekend with real work so can't run any numbers for the moment.)
Having a good mix of which defenses your group attacks (fort/ref/will) seems like it will be very important. Your target may have one or two really good defenses, but against the third you can probably take them down relatively easily. So various members of your group may switch it up in terms of who's the biggest hitter depending on what you're fighting.
My prediction:
Initially melee will go for heavy armor as they see how incredibly effective it is against other melee. Then they will learn other that people will attack their other defenses and try to balance it up more in order to not have such a glaring weakness. Light armor isn't overly effective against melee, so I'm going to say that medium armor is going to wind up being very popular for melee. From the level 1 vs level 4 example changing from medium to heavy armor when badly outclassed doesn't help much, so you might as well stick with medium and improve your other defenses. That or lug around specialized suits of armor.
|
Goblin Squad Member
|
Great presentation! It's so refreshing to see someone actually state their assumptions up front instead of trying to sell complex equations and gloss over the input.
Key point: "The relationship is surprisingly linear around skill difference = 0" for T1 vs T1. However when you start comparing different Tiers, I would suggest not using weighted distributions but run full brute force: the distribution of "how many newbs" may not be nice and symmetric.
What scripting/programming language are you using? There may be enough competence here that you should consider sharing your code, at least when a combat simulator is released (next year?) and we get a better handle on variables and ranges.
Two comments:
-try using far less (or thinner) equi-curves to make it clearer, on my screen the middle portion looks like solid colour.
-the conclusion "one lvl 4 = 16/13 lvl 1" seems to be is they are lining up and fighting one at a time. 5 attackerscould get (1+2+3+4+5) = 15 attacks when zerging for every (1+1+1+1+1)= 5 when lining politely up (ie: terrain is important!)
On top of that, there are unknowns like flanking bonuses, debuffs, AoE attacks etc.
|
Goblin Squad Member
|
Great presentation! It's so refreshing to see someone actually state their assumptions up front instead of trying to sell complex equations and gloss over the input.
Key point: "The relationship is surprisingly linear around skill difference = 0" for T1 vs T1. However when you start comparing different Tiers, I would suggest not using weighted distributions but run full brute force: the distribution of "how many newbs" may not be nice and symmetric.
What scripting/programming language are you using? There may be enough competence here that you should consider sharing your code, at least when a combat simulator is released (next year?) and we get a better handle on variables and ranges.
Two comments:
-try using far less (or thinner) equi-curves to make it clearer, on my screen the middle portion looks like solid colour.
-the conclusion "one lvl 4 = 16/13 lvl 1" seems to be is they are lining up and fighting one at a time. 5 attackerscould get (1+2+3+4+5) = 15 attacks when zerging for every (1+1+1+1+1)= 5 when lining politely up (ie: terrain is important!)
On top of that, there are unknowns like flanking bonuses, debuffs, AoE attacks etc.
It's in python and I use ROOT for the plots. The coloring is based on using a custom color palette I found online for ROOT - ROOT's default coloring scheme is hideous and extremely difficult to interpret. It's possible to reduce the number of colors or play with color schemes. There is another color scheme, but it winds up being loads of green, so I prefer custom.
Ya, the 13/16 on 1 fight is based on simplistic lining up to fight mechanics. (I don't know the effect of flanking etc.). It was just a crude estimate of relative power to be taken with a few grains of salt.
#!/usr/bin/env python
from random import randint
from math import sqrt
from ROOT import TFile, TNtuple # ROOT specific
ntp = TNtuple('ntp','ntp','skill_advantage_including_penalties:damage_factor:dama ge_above_resistance:average_damage') # ROOT specific
iterations = 10000 # number of MC events
tier = 1 #attacker's tier, fixed to 1 for now
tierdiff = 0 #difference in tiers (attacker minus defender)
diff = 50*(1-tierdiff) # if tierdiff is negative then the difference increases (careful with signs!)
def attackroll(tier,x,y,z): # calculate attack roll
if (tier==1):
return min(x,y,z)
if (tier==2): # not used
middle = x+y+z-max(x,y,z)-min(x,y,z)
return middle
if (tier==3): # not used
return max(x,y,z)
def AMD(a,diff,extradiff): # calculate difference between attack roll and defence ('Attack Minus Defence')
return a-diff+extradiff # extradiff is attacker minus defender
"""
def DMG(base_damage,ndamage_keywords,ndamage_major_keywords): # calculate unscaled damage, not used
dmg = base_damage+5*ndamage_keywords+20*ndamage_major_keywords
return dmg
"""
def penalty(amd): # calculate the penalty due to having a lower attack roll
if (amd > 0):
return 0 # no penalty
else:
return sqrt(-amd)*0.05 # since amd=0 gives no penalty this is okay
def damage(above,damage_factor,penalty): # calculate the actual damage
if (penalty>1):
return 0 # needs a 400 difference in skill. just avoiding negative damage messing up results
return (above)*damage_factor*(1-penalty)
for advantage in range(-75,50): # Stephen Cheney's info centers on +3 (+17 vs. 64 = 50+14) and 49+ is auto-hit
for damage_above in range(1,70):
for damage_factor in [1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9]: # no idea what range these have!
result = 0 # should initialize as an integer (I think)
for j in range (0,iterations):
x = randint(1,200)
y = randint(1,200)
z = randint(1,200) # highly non-optimal!
a = attackroll(tier,x,y,z)
b = AMD(a,diff,advantage)
p = penalty(b)
f = damage(damage_above,damage_factor,p)
if(f<0): # avoid negative damage issues
f=0
result += f # int + float should become int
result = result/iterations # get the average damage, now a float
ntp.Fill(advantage, damage_factor, damage_above, result) # ROOT specific
f = TFile('PFO-explore.fast.root','RECREATE') # ROOT specific
f.WriteTObject(ntp) # ROOT specific
(The page doesn't seem to want to preserve my tab spacing for the code, so hopefully those versed in python will be able to figure out where they should be.)
|
Goblin Squad Member
|
Actually with those numbers 5 lvl 1 fighters would win against 1 lvl 4 fighter given that all lvl 1 fighters can attack the lvl 4 fighter at the same time and they are using heavy armor. It takes 10 strikes to down the first lvl 1 fighter, in that time the 5 lvl 1 fighters have made 10 attacks each so 50 attacks. Then before the next falls they have accumulated 90, then 120, then 140. 140 attacks kills the lvl 4 so one to two lvl 1 survives. Your calculations assumes a...
Yes, you're right. Forgot about that. One other issue is that the level 4 has to switch targets, which can sometimes take time in an MMO.
Goblinworks Executive Founder
|
Doesn't Python have a 'median' function that returns the median value directly (Rather than taking the sum and dropping the min and max)?
Or you could go the easy way: for every attackroll from 1-200, calculate the damage done if that value is rolled, multiply by the frequency of that attack roll in that tier, sum, then divide by 8m to get the average. That way your cluster is only doing 200 square roots for each x-value rather than 10,000.
There are ways to optimize it down to about 300-400 square roots for the entire graph; just cover all of the in-domain values of the attack roll+attack bonus-defense bonus-tier bonus once, and then figure the frequency of each outcome based on that.
|
Goblin Squad Member
|
Mostly for developers on relative value of stats.
I left out a lot of plots that lead to the final plot as it's all just technical fitting of curves and the like.
Edit: For the non-mathematical:
skip slide 3 and only look at the last bullet point on slide 4
|
Goblin Squad Member
|
This is for players:
1) I realized cross-tier modelling is unnecessary. To understand how cross tier works, just shift attack skill relative to defense skill. Tier 1 v tier 2: move to the left 50. Tier 1 v tier 3: move to the left 100.
2) Want to know how much attack skill 1 *base* damage is worth? Ie. how to trade off in stats without losing dps?
Caveats:
-fixed damage factor
-fixed weapon speed
-not making huge changes in stats (this is technically a differential change)
On the plots:
vertical axis = FINAL damage (what was previously in color)
horizontal axis = attacker's skill advantage (equal skill means 0)
color = how much attack skill 1 *base* damage is worth
Example:
-equally skilled, but defender in heavy armor. So he gets -20 to reflex. Normally you'd be at 0 on the x-axis, but that shifts you to +20 as it works in the attacker's favor.
-do ~25 damage per swing (this is final damage, not to be confused with base damage)
-look at plots (20 on x-axis, 25 on y-axis). See a color of something in the ballpark of 15. You can therefore trade ~15 attack skill for 1 base damage and keep roughly equal dps (assuming equal damage factor and equal weapon speed). So if you have 2 weapons and you are less skilled with one, but it does slightly more damage you can then decide which one to use (under the above caveats).
These are all the same, but for different image formats.
Edit: the red region (50) really means 50 or more.
|
Goblin Squad Member
|
Different tier armor shifts the x-axis; different tier weapons are more complicated.
Exactly. The probabilities of a given roll change significantly.
Going to be swamped all week so won't be able to do it right away, but the burning question on my mind is how the parameterization of the contours changes with damage factor. If it changes in a predictable way then tier 1 attacker is mostly nailed down. Still need to understand optimization and how crits (against NPCs crits increase dmg instead of giving debuffs) affect dps.
Well, then there's flanking, formations, and other mechanics we haven't been given the rules for.
|
I really feel like PFOL will start to move away from this ridiculous numbers game people have been waging to maximize DPS. The reasoning behind this is because while the game will still be played in real time, the time, and course of player actions play out on a MUCH more stretched out period, or rather, have a slower pace than we have seen swamp the MMO marketplace.
As for PVE, the math on making challenging encounters playable isn't that hard, as long as the team has a handle on what tactics players are likely to wage.
We know that there will be no such thing as "Auto-Attack" already, so trying to weave cooldowns in between attacks is out the window already. On top of that, I really doubt most PVP conflicts will ever really come down to who can do more damage on average per second consistently. The developers have already stated that player crippling burst damage wont feature in the mechanics, and due to this circumstance it follows that combat will necessarily be much more involved than simply bashing all your "win-button" feats, spamming your Magic Sword, and chugging potions to keep every possible buff possible up for your role.
As far as PF goes, Crowd Control, battlefield manipulation, and even Enchantments are all going to destroy any meaningful calculations you can derive based on 2 Units bashing each other dry until they need to refresh. As I understand it, they intent is to disallow a PC from being locked out of being able to react to an attack, and for this reason critical hits do not apply damage to PCs, and any kind of Stun, Freeze, or Mind Control will probably have diminishing returns, but even so I don't expect any one of these effects to last less than 6-10 seconds, unless you have some slotted ability like freedom on movement, or a magic item to help.
SO, PC's will have enough health to stand up to another player 1) Burst attacking them with all damage, and probably poison type moves, 2) Following up with a Stun or Disable, and 3) The PC should (from what the design goals are) still be on his feet, and able to defend himself in some fashion.
Depending on the combat time frame all this takes place in a minimum of 12 seconds, up to a max of around 20 seconds. I've played a number of MMOs and PVP games, and I think it will be a real challenge for the design team to design a combat scheme where any two tier 1 players can face off, with either PC at a huge advantage, and the other one should be able to at least the defensive capability to withstand, and/or escape the aggressor. Needless to say I think setting up a formula where attack beats defense (So that you can damage people), players will need to have a sufficient amount of health to stay on their feet if "ganking" is to be prevented.
Just my rambling thoughts.
|
Goblin Squad Member
|
I agree that there is more to combat than raw numbers. Though in the words of the 'Wuuf' (the old Flintlocke cartoon):
"What I'm saying is that if you're going to sink hours and hours of your life into this game, you've got to at least take a few minutes to understand the damage formulas."
The better we understand the damage system on its own, the better we can see if there's any critical problems with it. And it's inevitable that anyone who partakes in combat in PFO will have to make choices about their combat stats. Sure, a merchant may not put much into those stats, but he'll eventually have to fight with those limited stats when some bandits don't bother with a SAD ... or know how to limit damage against him so he can run away.
Weighing pure attack/damage stats vs. stuns/escapes etc. is highly non-trivial, so that has to come later when we have some information on those mechanics and a feel for how they actually work in game. Right now all we have is the damage calculations in the blog to play with, so might as well.
One of the things to worry about in particular is scaling. The idea that new characters can meaningfully contribute to the game becomes more difficult to achieve if the damage formulae have unintended scaling effects that no one bothered to study. A newbie who does 0.01% of the dps of a high level character isn't exactly going to feel like they can make a contribution. Better to learn about the issue now in pre-alpha than 2 years into the game when the first characters start closing in on completing an archetype (supposed to be ~2.5 years I think).
At the moment it looks like that 0.01% issue won't crop up when everyone is still in tier 1, though 1 on 1 pvp fights will be damn near impossible for those new PCs to win. In my example of a level 4 vs a level 1 (both with similar equipment for their level), the level 4 kills his opponent ~13 times faster (relative to eachother's hp). It takes a significant amount of crowd control (even more so with diminishing returns) and general player skill to win a fight when you're that badly outmatched in relative damage!
For the record, I'm leaning towards my main being an enchanter wizard. I love illusion in TT, but it's been mentioned that illusions are graphics intensive and might not be developed for a while. So she'll excel at crowd control in whatever form it appears in PFO. She'll pick up illusions when they get into a more polished form.
My destiny's twin is likely going to be an anti-paladin type character (at least thematically - he may end up as a fighter/cleric hybrid instead). If formations turn out well I'd like him to be a formation leader, ie. a war leader of the evil armies that the good guys in this game will face off against. LE is known for brutal efficiency. For him understanding these damage curves (and how to counter them) will allow me to make him harder to kill and better represent that efficiency. I enjoy being the backbone in pvp - the guy who can mix it up in close and take a real beating while keeping his allies alive. His dps may suck, but he'll be hard to kill.
|
Goblinworks Executive Founder
|
Oh, I'm considering the effects of things that work outside of sword-hitting. I'm still assuming that a group that can reduce the HP of the other group to zero first wins (counting an 'opponent retreats' result as a win, even with abilities that modify every aspect of that.
For what it's worth, I don't think that Fighter abilities should simply do more damage, but should limit the ability of the target to do what they want. Reducing enemy stamina directly is just the simplest way I can conceive of to do that.
|
Goblin Squad Member
|
...Depending on the combat time frame all this takes place in a minimum of 12 seconds, up to a max of around 20 seconds....
Unless you are only looking at significantly overmatched melee and the denial of one-shotting I'd up that duration estimate quite a bit since your stamina pulses are each six seconds.
|
Goblin Squad Member
|
I wanted a visual representation of the power curve for PFO, so I took some numbers from some rough estimates in the older blogs.
Like everything here, it's really preliminary:
Info from the blogs:
Level - Time
3 ----> 1 day
8 ----> 1 month
16 ---> 1 year
20 ---> 2.5 years
So for the first few weeks you should see rather dramatic increase in levels and then it starts really slowing down (not particularly surprising). Looking at it, if we assume the Early Enrollment is 9 months as originally intended then PCs will be about level 14-15 in their archetype by the end of EE. Or they could be about level 12 in 2 archetypes by the end of EE.
|
Goblin Squad Member
|
Likely that is the case, with some archetypes having more skills in common (ranger/barbarian) than others (wizard/fighter). However, the blogs do mention levels, which is where I got the above numbers from. Whether the use of the word "level" is a misnomer or not is something the devs will have to clarify.
I suspect that the mention of how long it takes to get to certain "levels" is just a rough estimate of how long it takes to get up certain skill training which would roughly correspond to what we think of as a level. Regardless of misnomers or not, we can still get a good feel for how long it takes to get to a certain point in your training of skills related to a given archetype.
The one thing I'd like to see clarified is hp. Is your hp total tied to "levels" in a class? Is it an archetype specific skill? Is it a general skill that everyone trains such that everyone will max out to the same hp regardless of what archetype they're playing? Is it a hybrid, ie. some from generic skills and some from archetype specific skills?
|
Goblin Squad Member
|
I suspect that there will be some HP that comes as a passive bonus from general skills everyone will be able to train, and some that comes from archetypal skills being slotted. That way everyone gets some HP as they advance, but more durability focused characters will be able to reach a higher total without having to worry about players stacking HP from barbarian, fighter, and ranger to accrue an unbalancing amount.
|
Goblin Squad Member
|
The one thing I'd like to see clarified is hp. Is your hp total tied to "levels" in a class? Is it an archetype specific skill?
There's definitely room for clarification there.
Hit Points: All characters have HP, and enter the dying state when these reach 0. A starting player character has around 400 HP as a minimum, and a fully buffed veteran is unlikely to have more than 2000 HP. In general, HP will roughly triple during a career.
... a starting character probably has 500-600 hit points, meaning while a max level Barbarian (the hit point leaders) will have around 1800 (a max level fighter 1600, rogue/cleric 1400, mage/sorcerer 1200 though this varies as it is an open system and people can buy more if they want) it's not a vast increase.
In the tabletop Pathfinder RPG, you earn the benefits of a level all at once as you hit an experience point threshold. In Pathfinder Online, we've turned the system on its head: instead of using experience points as a prerequisite for improving in a skill, improving skills are part of the prerequisite for gaining new abilities. Your character must earn all the things needed to qualify for a new "level," and then you're rewarded with a special bonus.
I would not be at all surprised if your maximum Hit Points were a function of the number of "levels" you've gained in a particular "class".
|
Goblinworks Game Designer
|
| 4 people marked this as a favorite. |
I suspect that there will be some HP that comes as a passive bonus from general skills everyone will be able to train, and some that comes from archetypal skills being slotted. That way everyone gets some HP as they advance, but more durability focused characters will be able to reach a higher total without having to worry about players stacking HP from barbarian, fighter, and ranger to accrue an unbalancing amount.
This is correct.
We're still working out exactly how extra HP will be apportioned across various passive feats. Ultimately, if you're a long-term veteran who's maxed out, say, Sorcerer and Barbarian, and bought all the persistent HP upgrades possible, you'll still have way more HP when you slot as a Barbarian than as a Sorcerer.
|
Goblin Squad Member
|
I suspect that there will be some HP that comes as a passive bonus from general skills everyone will be able to train, and some that comes from archetypal skills being slotted. That way everyone gets some HP as they advance, but more durability focused characters will be able to reach a higher total without having to worry about players stacking HP from barbarian, fighter, and ranger to accrue an unbalancing amount.This is correct.
We're still working out exactly how extra HP will be apportioned across various passive feats. Ultimately, if you're a long-term veteran who's maxed out, say, Sorcerer and Barbarian, and bought all the persistent HP upgrades possible, you'll still have way more HP when you slot as a Barbarian than as a Sorcerer.
I always get all warm and fuzzy when I find out my intuition is in line with the analysis you guys do. Makes me feel like I'm actally getting a grasp of the system. Thanks for the confirmation, Stephen. =P
|
Goblin Squad Member
|
Update on analysis: I have damage plots for all tiers and a wide range of damage factors pretty much ready and some PVE crit estimates in the works. However, for the moment here's a look at something non-damage related: debuff duration.
Before reading the slides please review the May 15 goblinworks blog on timed debuffs ("timed effects" in the blog).
On the last slide I include a simple rule of thumb for how long to expect your debuff to last on average.
|
Goblin Squad Member
|
Simulations. The actual job took maybe 30s on the cluster, of which 10 seconds is running a setup script.
I've streamlined the code to make 10,000 rolls of 3d200, sort them and then use that like a lookup table. So in a sense it's creating a probability distribution first for the rolls and then using that. Making that distribution this way is very fast (a few seconds tops). It's the later calculations that take time as they have to be done for each of the rolls and for each configuration you want (eg. tier, damage factor, net skill advantage, etc. as appropriate).
|
Goblin Squad Member
|
This is hoping the developers might be willing to provide a little snippet of information:
I've been playing with how much damage increases in PVE content due to crits. However, I need to make certain assumptions in order to model this.
My assumptions:
1) The increased damage (PVE only) is a certain percentage of the final damage (not to be confused with the base damage of the weapon). So if this is a 50% increase and the final damage done is 40 then the crit does and extra 20 damage, ie a total of 60=40+20. In my modelling I can vary this amount, but a ballpark figure would be helpful to know.
2) The roll for whether there is a crit or not only occurs if there is a full hit (as stated in the blog Murder by Numbers).
3) The way the roll is made either:
a) Is the same across all tiers (ie. isn't like the min/middle/max of 3d200 like the attack roll is). So how I've been modelling this is as a single roll. Add attacker's crit rating and if the total is greater than or equal to the defender's crit resistance then a crit occurs. If it's less then no crit.
b) Mirrors the attack roll. Do as in 3a but add the min/middle/max of a 3d200 roll to attacker's crit rating and compare to defender's crit resistance to determine if there's a crit.
Any chance of pointing out whether 3a or 3b is correct?
|
Goblin Squad Member
|
We have to have a system that is fun for both PvP and PvE. While the Pathfinder RPG can do both, some of its systems (such as critical hits multiplying damage) are not ideal for PvP combat. A critical damage multiplier system can make PvP incredibly one-sided, which is not fun for the person who gets killed in one hit without being to do anything about it. Similarly, it's fine to miss a lot due to bad dice luck at a table with friends who can laugh about it, but that's not fun at all against another player who's giving you a fair fight. We've done a lot of things to make the results of combat less "swingy" both for and against you.
and
If the result of the roll plus the attack bonus equaled or exceeded the target's defense, the attack does full damage and has a chance to be a critical hit. This is a separate randomized calculation that compares the attack's crit rating to the target's crit resistance. A critical hit doesn't do more damage, but instead applies an injury that debilitates the target for some time. NPCs (who wouldn't care about long-term drawbacks) immediately expend injuries for additional damage.
|
Goblin Squad Member
|
A critical hit doesn't do more damage, but instead applies an injury that debilitates the target for some time. NPCs (who wouldn't care about long-term drawbacks) immediately expend injuries for additional damage.
I remembered thinking the system was the same for PvP and PvE, and wasn't seeing the relevant part of the quote at first, so I bolded it here.
|
Goblin Squad Member
|
Preview copy of all tier damage and increase in pve damage due to crits is now available. This only includes the case where a single roll is made for the crit (as opposed to something like an additional 3d200 roll as I suggested as a possibility above). There are more things I want to add to the presentation so please let me know if anything is unclear/poorly worded.
|
Goblin Squad Member
|
Updated version of the above slides, including clarification of the vertical axis on crit plots.
Features:
1) damage for all 3 tiers
2) increase in damage from PVE crits for all 3 tiers for both the cases:
a) a single 1dn roll determining if it's a crit
b) a new 3d200 roll (taking min/middle/max) determining if it's a crit
3) a brief look at the trade-off between damage factor and weapon damage and when each is a better stat
More to come when I have time.
Note that the plots may be a bit blurry if you just view them in google docs as opposed to downloading the file (~1.5 MB).
|
Goblin Squad Member
|
For now the best way to view is to download and zoom in. The resolution should be good enough for zooming. If you're refering to the dark blue patches: there's not much difference there and ROOT (drawing program) is already showing the maximum number of contours.
I'll upload some other color scales when I get a chance. Let me know which is easiest for you to view.
The other option is to show the contours explicitly. It leaves some areas uncolored though.
---------------------------------
Oh, haven't put it in the presentation yet, but done basic plots for upgrading the tier of your weapon (assuming equal weapon speed and equal skill with both weapons). Qualitative results:
-the more outclassed your attack skill is (compared to defense skill of attacker) the more valuable that upgrade is.
-the higher the resistance your target has, the more valuable any extra damage is
Example: for t1 vs t1 if you're outclassed by 50 skill points, your base damage is 40, target's resistance is 10 and the new t2 weapon has 70 base damage, then your dps goes up by something like 150% upgrading.
|
Goblin Squad Member
|
@Drakhan Valane:
Which of these older plots do you find easier to read:
(Please download them for a comparison as whatever google docs is using for a viewer has terrible resolution.)
a) Contours
|
Goblin Squad Member
|
| 1 person marked this as a favorite. |
Update to the previous slides with some new features (eg. variability of damage): Damage output in PFO. Slides are much better resolution if you download them!
Embarrassingly, a large part of the delay in an update was in forgetting what I had named the slides ...
Future work on this will be in terms of combat simulation (eg. 'toy monte carlos') to get a feel for how fights will go. Admittedly some things will be difficult to deal with, but very preliminary results look very promising in terms of being able to analyse them. The following plots are from a 'toy' case where two players hack at eachother with the same attack over and over with the same speed as eachother and no regards for stamina. So no crits, stamina, debuffs or combos are included. This could be thought of as a '1st order approximation' to fights.
The plots look quite similar to the error function (which in retrospect isn't too surprising). To be clear, I'm measuring the players' health in terms of the maximum damage their opponent could do with a single hit. Why? All stats are relative!
It also appears that it may be possible to come up with rough conversion factors between different stats. Eg. how much resistance can you trade off for attack bonus in a given situtation?
Tier 1 relative health vs skill: if your opponent needs 20 full hits to kill you then you can see than adding 10-15 bonus to either attack or defense will compensate for needing an extra full hit to kill them. This may or may not hold true when combos, stamina and the like are included and already varies depending on your opponent.
|
Goblin Squad Member
|
It was mentioned that energy resistance will be lower for an armor wearer but what I can't recall is if there will be touch attacks, because those tend to ignore armor completely.
Basic Tactics
Heavy Armor Wearer: hit with (ranged) touch attacks.
Dex Monkey: find a way to paralyze/hold them so they lose their Dex and Dodge bonuses.
|
Goblin Squad Member
|
It was mentioned that energy resistance will be lower for an armor wearer but what I can't recall is if there will be touch attacks, because those tend to ignore armor completely.
Ya, Stephen Cheney gave an example of the top end heavy armor earlier in this thread which was weak against energy damage. The post also is highly suggestive of multiple types of energy damage.
I've been implicitly assuming that armor runs in a spectrum.
Against physical damage:
heavy > medium > light > cloth
Against certain energy damage:
cloth > light > medium > heavy
... but that's just my assumption. Whether or not there is any different ranking remains to be seen. Eg. maybe clerics sometimes do holy damage which medium armor is the best against?
All of my plots should apply to not only physical damage, but energy damage as well if the mechanics for energy damage work the same as the mechanics for physical damage (something I consider highly likely as not doing so would add a lot of programming complications). Your resistance will be different, but the calculations are all done in the same way. So rather than analyzing the damage of just physical weapons, this should all be valid for any type of weapon.
|
Goblin Squad Member
|
| 1 person marked this as a favorite. |
I also want to emphasize a key point in all of this:
All stats are relative to your opponent's stats.
Consider tabletop PF for example. You could analyze the average damage per round for a character with a +5 attack vs AC 15, another one with +6 vs AC 16, another with +7 vs AC 17 etc, but that's redundant. Each needs 10 or higher to hit, so all that really matters is the difference between AC and attack bonus, not what the actual attack bonus and AC are. So if you want to understand average damage output in PF you just need to 'scan' over all the possibilities:
-need 2 on the die roll to hit (1 is always a miss)
-need 3 on the die roll to hit
...
-need 20 on the die roll to hit (20 is always a hit)
So if you ignore crits that's only 19 scenarios to understand instead of the hundreds of possible attack bonus/AC combinations. (This applies to single attack rolls only, with multiple attack rolls just meaning you're using combinations of the 19 above scenarios.)
Another PF example:
Two PCs fight eachother.
One does 4.5 damage per round (on average) and has 80 hp.
The other does 8 damage per round (on average) and has 45 hp.
Each takes 10 rounds to kill the other (80/8=10, 45/4.5=10), so even hp can be considered a relative stat.
|
Goblin Squad Member
|
| 1 person marked this as a favorite. |
The same point holds true in PFO, with only slightly more complexity.
Review of damage output:
b = base damage of weapon
r = opponent's relevant resistance*
f = damage factor
p = penalty**
*he'll have many different resistances, but we only care about the one that applies to the damage done by the weapon in question. So if it's physical damage we only care about physical resistance and use physical resistance for r. If it's fire damage we only care about fire resistance and use fire resistance for r. Presumably there could be situations where an attack deals multiple types of damage (eg. fiery longsword), but that can be dealt with by doing the calculations separately and combining the final results.
**penalty is dependent upon the rolls and the tier of the attacker. The rolls work similar to the PF example above where attacker skill and defender skill are relative to eachother. If you want details, please read the murder by numbers blog. You could think of it as using a d200 instead of a d20 and the weapon tier just means that your d200 is weighted in a certain way so that each die roll has different odds of happening. The 3 different tiers then use different weightings for their d200.
Average damage is then calculated as:
(1-p)f(b-r)
Note that if I add 10 to b and add 10 to r that b-r remains unchanged. (In physics this is an example of a 'gauge symmetry' for the curious).
So in everything that I've done I only care about b-r, not b or r separately. Ie. I only care about the difference, not what each number actually is. I also do the same for attack skill and (relevant) defense skill which affect the rolls.
(For those already familiar with the damage system, none of the above is new - I just think that these are points worth emphasizing.)