Tier 1 damage


Pathfinder Online

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Sovereign Court Goblin Squad Member

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I spend all day coding up analyses (particle physics), so why not do it for PFO damage? This is all based on the Goblinworks blog "Murder by Numbers". Following the details in that blog I decided to make a simple python script to simulate damage. Plots are made with ROOT.

For my first study of this I looked at 'tier 1' as that is what everyone will be initially:
-always take the minimum of the 3 attack rolls
-total defense is set to 50, modified by skills

To simulate the effect of differing attack bonuses and defense bonuses, I simply took the difference between them (as that's what will matter). I varied this from -10 to +9 (20 different differences). Positive is the attacker has more of a bonus and negative is the defender has more.

Another key thing based on the blog seems to be the number of keywords on weapons and armor. So I vary those as well in the range 0, 1 and 2 for attacker and defender.

Finally I vary what type of armor the defender is wearing (light/medium/heavy). Cloth is left out for the moment.

Since we only have one example weapon of the longsword (base damage of 40 and damage factor of 1.4), I only used that.

Then for *every one* of the above possible variations (20*3*3*3) I simulate 10,000 attacks and calculate the damage. Computers can do amazing numbers of calculations quite quickly! (To give you an idea: it took less than a minute.) If you want to know how the damage is calculated please read the blog over at https://goblinworks.com/blog !

Note that this is only for tier 1 attack vs. tier 1 defense. I want to study how a geared out player will do against a noobie and vice versa later.

I've made 3 plots. In each of the plots the horizontal axis is the average damage. The vertical axis represents the difference in relevant keywords (# attacker's keywords minus # defender's keywords). Each 'dot' represents the average damage of 10,000 attacks.

The first plot is versus light armor. The second is versus medium armor. The third is versus heavy armor.

Just follow the arrows in the presentation!

https://docs.google.com/file/d/0B912ZssD14EJcm0zNUc1X0o5RXM/edit?usp=sharin g

Results:

1) Armor type is clearly the most relevant factor in play here. Improving your armor type (light/medium/heavy) reduces the damage against you by something on the order of 10 per attack. Note that the blog mentions having ~400 hit points.

2) For light armor adding a defense keyword decreases average damage by ~1-2 per keyword. For medium armor it's more like ~2-3. For heavy it's ~3-4. Again armor type really matters!

3) Adding an attack keyword increases average damage by ~5-6 per keyword.

4) Increasing the attacker's advantage over the defender in terms of skill is a small effect. A change of 20 skill points means ~3-4 extra damage against light armor, ~2-3 extra damage against medium armor and ~1-2 damage against heavy armor.

Conclusion:

Invest in heavy armor!

Caveats:

This is EXTREMELY preliminary and can easily become irrelevant if the mechanics change. If I interpretted the information in the blog incorrectly then these plots are worthless. Also, more variations in input are needed as this is only for noobie vs. noobie with a longsword.

I also want to look at more than just the average damage. How much the damage varies should be interesting as well!

Goblin Squad Member

Interesting.

I hope they make the system a bit more balanced though...

Link to Op's Results

Sovereign Court Goblin Squad Member

Sorry, I always forget hyperlinks!

Goblin Squad Member

I think there is also some variables left out from that conclusion,

Each armour type does act as DR in way.

Murder by Numbers wrote:
Damage Resistance: Each set of armor provides resistance to damage in the same types as weapon damage types. In general, armor provides mostly physical resistance, but can be enchanted to provide energy resistances. Lighter armors can hold stronger energy resistance enchantments (so an arcane caster may be weak against physical damage, but stronger than a heavy armor wearer against energy damage). For physical resistance, clothing provides 0, light armor starts at 9, medium armor starts at 18, and heavy armor starts at 27. These numbers are increased by keywords and buffs

and to add to that, these questions;

does armour effect speed in PFO?
if so some light armoured PCs could do some hit and run tactics on heavy armour types who move slower and can't catch up to them.

does armour cap stat/ability bonuses in defense (Like Dex bonus on armour in PF)?
if it does then this will shift the graphs a bit.

Goblin Squad Member

Azure_Zero wrote:

Interesting.

I hope they make the system a bit more balanced though...

Link to Op's Results

More balanced in what way? Or rather, what do you see being out of balance here?

Goblinworks Executive Founder

Note that the attack is 3d200, not 3d20. You can find the distribution of each tier in the space.

Instead of running a finite number of trials, I took the distribution curve of the attack roll and found the expected damage per attack by running the math; I didn't explicitly model for keywords, but I did throw some numbers out that show that there could exist a weapon that is more effective than the longsword against heavy armor, but less effective than the longsword against light armor.

Check it out.

Is there any specific factors that you would like to be able to adjust not already included, or any output that you would like to see.

Goblin Squad Member

Dario wrote:
Azure_Zero wrote:

Interesting.

I hope they make the system a bit more balanced though...

Link to Op's Results

More balanced in what way? Or rather, what do you see being out of balance here?

Look at my post just above yours.

as I think we only have some of data

Goblinworks Executive Founder

One of the balancing factors is that lighter armor will provide better defense against things that aren't swords than heavy armor does.

Sovereign Court Goblin Squad Member

The resistance to damage is included in my results. It's the reason that there is even a difference between light/medium/heavy armor.

The blog doesn't seem to mention armor anywhere in terms of how the attack roll vs defense is determined. The armor and it's keywords affect only the resistance afaik.

Keywords on weapons only affect their base damage here.

I imagine that there are various benefits to different armor types, eg. magical resistances, but this is only done for physical damage as that's all I had concrete numbers for.

Goblin Squad Member

I think knowing the other factors of each armour type would help in the conclusion.

And knowing if speed is effected, or if stats that are used in defense are capped pending armour, it'll have an effect.

Sovereign Court Goblin Squad Member

Azure_Zero wrote:

I think knowing the other factors of each armour type would help in the conclusion.

And knowing if speed is effected, or if stats that are used in defense are capped pending armour, it'll have an effect.

Definitely! Weapon speed effects would really make armor choice an interesting trade off. Lose dps, but gain survivability. Then there's likely some sweet spot which optimizes your odds of winning, ie. how long it takes you to kill a typical opponent vs. how long it takes them to kill you. The bigger the difference in those times the better.

For now we simply don't have enough information.

Goblin Squad Member

When I said speed, I was referring to movement speed,
but an impact on weapon speed or accuracy by armour type could be another

Sovereign Court Goblin Squad Member

I have our cluster running a job at the moment to expand the results a little. I expect the following is true:

1) Above some threshold in the difference in skills adding more (to the attacker) won't matter as you'll always be hitting anyways. Finding where this is would be helpful as you wouldn't have to waste xp to gain extra skills (at least until defenders catch up in skills). Since buffs affect this difference then this threshold may become important.

2) Conversely if the advantage is to the defender then because the penalty to damage isn't linear then the behavior below some other negative threshold may be important (again modified by relative buffs).

3) Since resistance scales linearly with keywords, there may be some threshold in terms of defensive keywords where anyone without a certain minimum of attack keywords can't even hurt you. Heavy armor with 4-5 defensive keywords may be near that. More powerful keywords (see the blog) only make this matter even more.

The last point really worries me as this could entirely negate GW's stated intentions of making new characters able to contribute as #3 could make it so that new characters are unable to hurt certain high level characters. Heck well geared mid level characters might be able to pull this off.

For example with the longsword (base dmg = 40) vs heavy armor (base of 27 resistance). Heavy armor gets 3 resistance per keyword, 12 per high-Tier keyword. 1 high-Tier keyword on heavy armor and that's 39 resistance. As a reminder, resistance is subtracted from base damage, not final damage. So anything more than that single high-Tier keyword and that 40 damage longsword becomes useless.

Sovereign Court Goblin Squad Member

Azure_Zero wrote:

When I said speed, I was referring to movement speed,

but an impact on weapon speed or accuracy by armour type could be another

Sorry, misinterpreted that. Movement speeds can definitely play tactical roles!

Goblinworks Game Designer

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Heavier armors do, indeed, come with penalties to movement speed, Reflex, spellcasting, and mobility-based skills. This will hopefully balance the fact that they are really good. A heavy armor guy can take much more of a beating than a more lightly armored guy, so you may need to use superior mobility against him in a fight.

We'll be heavily testing this in prototype to make sure it's fun and balanced.

For now, if you want to model the Reflex penalties, they're currently set to -10 for Medium armor and -20 for Heavy armor.

Some of the numbers we're currently testing for a 4th level generic, example fighter are:

  • 650 HP
  • Reflex 64 (Before armor penalty, includes shield and +50 from T1 armor)
  • Longsword +17 attack and 56 base damage (includes keywords and specialization bonus); 1.4 damage factor on average, 20 Stamina attack

And with armors equivalent to the weapon that's:

  • Light: 12 physical resistance, no Reflex penalty
  • Medium: 24 physical resistance, -10 Reflex
  • Heavy: 36 physical resistance, -20 Reflex

Sovereign Court Goblin Squad Member

Stephen Cheney wrote:

Heavier armors do, indeed, come with penalties to movement speed, Reflex, spellcasting, and mobility-based skills. This will hopefully balance the fact that they are really good. A heavy armor guy can take much more of a beating than a more lightly armored guy, so you may need to use superior mobility against him in a fight.

We'll be heavily testing this in prototype to make sure it's fun and balanced.

For now, if you want to model the Reflex penalties, they're currently set to -10 for Medium armor and -20 for Heavy armor.

Some of the numbers we're currently testing for a 4th level generic, example fighter are:

  • 650 HP
  • Reflex 64 (Before armor penalty, includes shield and +50 from T1 armor)
  • Longsword +17 attack and 56 base damage (includes keywords and specialization bonus); 1.4 damage factor on average, 20 Stamina attack

And with armors equivalent to the weapon that's:

  • Light: 12 physical resistance, no Reflex penalty
  • Medium: 24 physical resistance, -10 Reflex
  • Heavy: 36 physical resistance, -20 Reflex

Gladly!

I need to get some sleep (in Japan so out of sync with North America). Will get back to you with those specific numbers in the next day or so.

Goblin Squad Member

Thanks for the data.

So light armour types can do hit and run tactics on slower, more armoured foes.

Goblinworks Game Designer

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And, yes, fully upgraded heavy armor does get to 63 physical resistance from the highest tier keywords. You will be incapable of damaging that character just wailing on him with a Tier 1 martial weapon unless it has 3 or 4 keywords.

However, that same target has a maximum of 43 energy resistance in any energy type (and only has 16 in energies it's not specifically enchanted against). The low-level PCs that can't affect it physically also have the least opportunity cost for switching to a low-level wand and trying out energy damage.

Also, that's literally the best armor in the game, probably brought out for only special occasions or taking up most of the player's threads.

Goblinworks Executive Founder

Thanks Stephen. I'm going to make several unwarranted assumptions that allow me to model scenarios I don't have numbers for and then iterate on the consequences of those assumptions.

Sovereign Court Goblin Squad Member

Stephen Cheney wrote:

Heavier armors do, indeed, come with penalties to movement speed, Reflex, spellcasting, and mobility-based skills. This will hopefully balance the fact that they are really good. A heavy armor guy can take much more of a beating than a more lightly armored guy, so you may need to use superior mobility against him in a fight.

We'll be heavily testing this in prototype to make sure it's fun and balanced.

For now, if you want to model the Reflex penalties, they're currently set to -10 for Medium armor and -20 for Heavy armor.

Some of the numbers we're currently testing for a 4th level generic, example fighter are:

  • 650 HP
  • Reflex 64 (Before armor penalty, includes shield and +50 from T1 armor)
  • Longsword +17 attack and 56 base damage (includes keywords and specialization bonus); 1.4 damage factor on average, 20 Stamina attack

And with armors equivalent to the weapon that's:

  • Light: 12 physical resistance, no Reflex penalty
  • Medium: 24 physical resistance, -10 Reflex
  • Heavy: 36 physical resistance, -20 Reflex

Too excited to sleep, so coding this up.

What do you mean by 1.4 damage factor on average? Is this not a fixed number? If it's not then we'd need more info to properly model this as taking averages of averages is a big no-no. Also I'm unclear as to the effect of 20 Stamina. With what we have I can give you average damage/swing, but without knowing the Stamina cost/swing it's hard to say what absolute dps will be.

Goblin Squad Member

You will surely have a range of damages of which 1.4 is the average. The 20 stamina is probably the cost to make an attack. A heavier weapon would likely cost more stamina to swing where a lighter weapon would take less.

You are unlikely to have an absolute dps except as an item's potential: to achieve damage it must be used by a character, and characters will vary in skill/effectiveness. Or so I would surmise.

Sovereign Court Goblin Squad Member

I mean absolute dps as a function of skill difference and keywords.

As I read the blog the damage factor scales the final damage. It's a multiplicative factor and thus not really something you average. What you get in the end is averaged, not the multiplicative factor itself.

Goblin Squad Member

Then the fact that the developer said 'average' implies something, wouldn't you say?

Sovereign Court Goblin Squad Member

Being wrote:
Then the fact that the developer said 'average' implies something, wouldn't you say?

Definitely. That's why I asked for clarification. Right now I've been treating it as a constant (a fixed number).

Goblinworks Game Designer

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A basic attack with a longsword that just does damage and uses the longsword's standard speed and stamina cost has a 1.4 factor. Different attack feats have different damage factors based on whether they're faster or slower than normal, cost more or less Stamina, and have different secondary effects and restrictions.

But we're not ready to reveal those yet :) .

Sovereign Court Goblin Squad Member

Stephen Cheney wrote:

A basic attack with a longsword that just does damage and uses the longsword's standard speed and stamina cost has a 1.4 factor. Different attack feats have different damage factors based on whether they're faster or slower than normal, cost more or less Stamina, and have different secondary effects and restrictions.

But we're not ready to reveal those yet :) .

Fair enough. :)

I'm doing something slightly different than requested: a full scan of parameter space. Vary the following:

- weapon damage (base damage + benefits of keywords)
- damage multiplier
- total resistance (base resistance + benefits of keywords)
- difference in skills between attacker and defender (this can include any penalties imposed by different armor types

Calculate damage! (tier 1 vs. tier 1 only)

(Just don't tell anyone that the cluster is running a non-physics job ;) )

RPG Superstar 2012 Top 16

Thank you Nightdrifter and DeciusBrutus. It's great that you're bringing your specialised skills into the discussion - I love having more in depth insight around the way that combat will turn out.

Stephen Cheney wrote:
Some of the numbers we're currently testing for a 4th level generic, example fighter are: [...]

I'm also interested that thinking about characters in terms of class levels still makes sense, at least as a shorthand within the dev team.

Goblin Squad Member

Nightdrifter wrote:


(Just don't tell anyone that the cluster is running a non-physics job ;) )

A non-physics job that may take up several seconds of cpu time...

I'll admit my first thought was "why would he do a brute force calculation on such a simple problem?" (ie all independent calculations), but then my second thought was "right, he has a cluster".

and it's vastly more useful than some stuff i spent supercomputer cpu time on as a student ;-)

that aside, the discussion thread for the blog has some quick math on tier 1 vs 2 vs 3 and use of average, variance etc. Since T1 and T3 are highly asymmetric, the avg(T2-T1) is quite different from avg(T2)-avg(T1). Sweeping parameter space could like you seem to do could give very useful input for GW balancing the maths without needing to juggle asymmetric distributions in their minds.
(just remember to get some sleep, or bugs will eventually start to breed in your code).

Goblinworks Executive Founder

ASSUMPTION: There might exist weapons with lower base damage but higher damage factors than the longsword (and vice versa).

Conclusion: There could be weapons which could be more effective than the longsword against opponents with low physical resistance but less effective than the longsword against opponents with high physical resistance.

Further assumption: All weapons gain the same +5/+20 to base damage from having applicable common/masterwork keywords
Further conclusion: Keywords will provide a larger percentage increase to weapons with lower base damage, and a lower percentage increase to weapons with higher base damage.

Unless more information is revealed, I'm going to consider attack abilities which modify the die roll/attacker skill, modify the base damage (before keywords) by multiplication, modify the damage factor by addition, and/or bypass a percentage of Damage Resistance. On the radar is non-physical damage types.

Goblinworks Executive Founder

@Nightdrifter:

Rather than running more than 200 rolls, try figuring the damage for each of the 200 possible outcomes of the attack roll and take the weighted average, using the likelihood of that outcome as the weighing factor? (The discussion thread of the blog post has the likelihoods of each roll for each tier of weapon).

I'd like to see the delta-DPS for +1 attacker skill, as a function of the difference between attacker skill and defender skill. Right now my gut and initial checks indicate that the best returns of +1 attack or +1 defense are roughly when attacker skill is ~10 above defense skill for T1 weapons and armor.

Sovereign Court Goblin Squad Member

DeciusBrutus wrote:

@Nightdrifter:

Rather than running more than 200 rolls, try figuring the damage for each of the 200 possible outcomes of the attack roll and take the weighted average, using the likelihood of that outcome as the weighing factor? (The discussion thread of the blog post has the likelihoods of each roll for each tier of weapon).

I'd like to see the delta-DPS for +1 attacker skill, as a function of the difference between attacker skill and defender skill. Right now my gut and initial checks indicate that the best returns of +1 attack or +1 defense are roughly when attacker skill is ~10 above defense skill for T1 weapons and armor.

I didn't realize someone had made such a likelihood already. Thanks! That should work for future attempts. Since the cluster is chugging away and I need to run to do other things, it's easier just to let it rather than re-coding this analysis. However, one benefit is that I should be able to produce a very high statistics version of that likelihood now that I'm saving that information into my ntuple.

For future analyses (eg tier vs tier), your suggestion sounds like the best option in terms of computing time. :)

Goblinworks Executive Founder

I'm also seeing that a masterwork longsword vs. masterwork heavy armor is significantly better (~70% more damage) than a longsword with no keywords vs heavy armor with no keywords. That drops to about 32% more damage if you give both weapons and armors 6 common keywords.

The percentage effect is significantly lower on light armor, although the absolute magnitude of is higher. In all cases, adding an equal number of equal-tier keywords to both the attacker's weapon and defender's armor favors the defender, because the only result is effectively a base damage increase.

Abilities which alter the defenders damage resistance by a percentage change this, provided that they increase it by enough.

Goblin Squad Member

DeciusBrutus wrote:
In all cases, adding an equal number of equal-tier keywords to both the attacker's weapon and defender's armor favors the defender...

Is that what you intended to say?

My understanding was that it would favor the attacker.

Goblinworks Executive Founder

Nihimon wrote:
DeciusBrutus wrote:
In all cases, adding an equal number of equal-tier keywords to both the attacker's weapon and defender's armor favors the defender...

Is that what you intended to say?

My understanding was that it would favor the attacker.

Derp. Yes.

Sovereign Court Goblin Squad Member

Very quick look at new results (scroll down)

Google is making the plot look choppier than it should (adding the white lines that aren't actually there in the plot).

damage factor = 1.0 (more values to come in the next day or so, including specific analysis of the numbers Stephen Cheney brought up)

Anyways, what's being plotted:

color = final damage. look on right hand side for scale.
x axis (horizontal) = net skill advantage over defender (exlcuding 50 from tier)
y axis = net damage above resistance (before multiplicative factors)

So to give some examples:

If attacker has +17 attack and defender has 64 total defense (14 from skill/keyword +50 from tier), then x axis would be 17-14 = 3. A skill advantage of 49 or higher is always a full hit as you'd need to get a 1 or higher on the die rolls to match the defender's defense.

If the attacker has a net 56 damage (base damage + keywords) and the defender has a net resistance of 36 (armor + keywords), then y-axis would be 56-36=20.

And yes, attack keywords are worth more than defense keywords in terms of their effect on final average damage.

Edit: clarifying variables

Goblin Squad Member

Link

And we need access.

Sovereign Court Goblin Squad Member

Sorry, should be working now.

Sovereign Court Goblin Squad Member

Zoomed In (scale changes on zooming)

Goblin Squad Member

Wow, it looks good.

Though I did find it confusing at first,
until I looked at the Y axis Title as I thought the Y was Defense value, not [/i]Damage above Defense[/i]

Goblinworks Executive Founder

Nightdrifter wrote:
Zoomed In (scale changes on zooming)

Nice. Can you do the first and second derivitives with respect to the skill advantage of the attacker?

Sovereign Court Goblin Squad Member

DeciusBrutus wrote:
Nightdrifter wrote:
Zoomed In (scale changes on zooming)
Nice. Can you do the first and second derivitives with respect to the skill advantage of the attacker?

Yes, have a bunch to do today, but delta-dps (and delta-delta-dps) are on the to-do list.

Any other requests?

Sovereign Court Goblin Squad Member

Ninja-ing an update between meetings with damage factor 1.5 and slightly different plot style (to better see equal damage curves).

Damage Factor 1.5, Damage Factor 1.5 (zoomed)

Goblin Squad Member

This thread is so awesome...

Goblin Squad Member

I'm following it...and standing stark still..stunned by the nerd-rific mathematical awesomeness that it contains. I am but a worm...compared to your super-cool geek-ness...and I really mean this in all honesty. You guys rock.

The original Big K...hehehee

Goblinworks Executive Founder

The results (if not how to get them) can be explained to just about anyone literate enough to use a calculator.

To use the rainbow graph, first estimate the difference between the attacker's attack skill and the defender's defense skill. Find that point on the horizonal line. Then estimate the difference between the attacker's base damage and the defender's damage resistance on the vertical line.

At that intersection, the color indicates your average damage per attack; find where that color appears on the key to the right to get your answer.

Part of the conclusions I draw from that is that if the attacker is just barely penetrating armor, an extra point of damage is worth a very large attack skill drop. Noting that a keyword is worth 5 extra points of damage there, I can estimate that I might prefer adding the 'sharp' keyword to a longsword (+5 to damage) over 'accurate' (+25 attacker skill) so long as the total damage remains below about 70 and skills are in the same league.

What interests me the most is figuring how how to model the effects and benefits of non-weapon attacks; the arcane spell flare strikes me as one of the tabletop elements that transfers very easily and has interesting effects.

Sovereign Court Goblin Squad Member

randomwalker wrote:
Nightdrifter wrote:


(Just don't tell anyone that the cluster is running a non-physics job ;) )

A non-physics job that may take up several seconds of cpu time...

I'll admit my first thought was "why would he do a brute force calculation on such a simple problem?" (ie all independent calculations), but then my second thought was "right, he has a cluster".

and it's vastly more useful than some stuff i spent supercomputer cpu time on as a student ;-)

that aside, the discussion thread for the blog has some quick math on tier 1 vs 2 vs 3 and use of average, variance etc. Since T1 and T3 are highly asymmetric, the avg(T2-T1) is quite different from avg(T2)-avg(T1). Sweeping parameter space could like you seem to do could give very useful input for GW balancing the maths without needing to juggle asymmetric distributions in their minds.
(just remember to get some sleep, or bugs will eventually start to breed in your code).

Completely missed this post.

I agree that the asymmetry is critically important. I'm doing T1 v T1 in depth for now because that seems like the short term priority. I fully intend to chug out T2 and T3 and cross tier results.

Variance of the damage interests me as well. Average is easier to do and therefore the first pass analysis.

The cluster is seriously under-used, so brute force calculations are no big deal. A little over 80 million damage calculations (including the dice rolls and all, which is what goes into the color plots) takes about 20 minutes. Then another 2-3 for a script to generate the plots. Admittedly my script for making the plots does something that is computationally highly non-optimal, but I couldn't think of a simpler way.

Making these results is largely to help GW, so I've switched my short term focus to looking at damage factor = 1.4 (as that's the example in the blog and in Stephen Cheney's example level 4 fighter).

Update on that soon!

Goblin Squad Member

GJ! The color plots are a really clear way of producing a "big picture" of the implications of the numbers.

Sovereign Court Goblin Squad Member

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@ Stephen Cheney:

This is an analysis of your specific level 4 fighter with damage factor fixed at 1.4. Slides 13-15 are relevant to your reflex penalties for wearing armor.

I apparently used the term curves and contours interchangeably. I mean the same by both.

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.

Edit: uploaded new version.

Goblin Squad Member

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I've added this thread to the Popular Player Threads section of the Guild Recruitment & Helpful Links list.

I consider myself a bit of a math geek ("I do vector calculus just for fun") but I feel completely out of my league after a cursory look at your latest analysis. I want to make sure this gets properly archived, and I have a feeling I'll be spending quite a bit of my free time today trying to make sense of it.

Thank you very much for sharing your work with us.

Goblinworks Founder

Nightdrifter wrote:


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.

Would 5 lvl 1s be enough to take 1 lvl 4 down? (only one lvl 1 surviving though)

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