Power of CS

[hwulf]

With Dwarves no longer having CS, I wanted to calculate what amount of WTs would need added to make up for the Damage per Op reduction CS provided.

Internally, my kd was discussing Dwarf/Tact vs Dwarf/Sage, namely one having CS and the other not.

Can someone let me know if this checks out?:

Assuming: Age 71 Dwarf Sage at half max sci (and +25% BE)
And acknowledging that WTs reduce BOTH thievery success rate AND damage while CS only reduces success rate
Also, assuming everything is multiplicative, not additive.

I've calculated that running 15% WTs W/ CS will net nearly the exact same Damage Received Per Op as running %20 WTs w/o CS.

Math:

CS op Success rate: 75%
op Success rate for WT = %15: 73.6% (1 - 26.4%)
%damage for WT = %15: 60.4% (1 - 39.6%)

--> 0.75*0.736*0.604 = 0.333 = 33.3% Damage per Op (compared to no CS or WTs)

op Success rate for WT = %20: 66.6% (1 - 33.4)
%damage for WT = %20: 49.9% (1 - 50.1%)

--> 0.666*0.499 = 0.332 = 33.2% Damage per Op (compared to no CS or WTs)

Feel free to use the prov sheet and check my math but. . . if it's right. . . then adding %5 WTs, in addition to what you'd run WITH CS, should make up for the loss of CS.

5% is no small potatoes, but with all the other goodies sage comes with? Might be worth it?

Also, this doesn't consider the increased TPA a D/sage will have compared to a D/tact due to BE and Thievery sci increase.

It also doesn't consider that higher failure rates, net damage aside, might result in scaring off some thieves after a couple failed attempts.

[Slayerviper]

did some basic inputs on my old spreadsheet, would need 29% WT (with new BE) to match 15% WT with CS (with old BE) as far as a chance to catch perspective.

[StratOcastle]

In summary, dog pile the rogue.

[_Sevve]

Just MV the CS before the op run.

[Persain]

With Dwarves no longer having CS, .....

Your math is correct as far as i can tell.

As dwarf tact will have 150% BE at max science, dwarf sage gets 156.25% BE. So as far as your "math" goes the sage will have 1.25% extra BE over the tact from CS alone. Tact does give the attack speed buff though which is pretty considerable as far as compared BE to rax go. The one thing your missing though is that thinking of CS as a build space reducer is typically the wrong way to go. We ran dwarf sage this age and still put up 30%-35% WT once "unbreakable" the power of cs gave "Extra" def when already maxing the bonus WT gives. When you need to "get safe" asap thats what cs provides



The biggest "issue" with cs though are 2 fold, CS innately isnt that strong against highly coordinated kds because putting it on someone with low wpa just means the enemy has to spend 4-5 casts of MV to remove it before op-ing, most kds will do this. What you want is CS on someone who has HIGH wpa so its hard/impossible to remove CS. So what u "want" is CS on someone who has the wpa bonus sage gives lol. What it'll boil down to is realistically cs kd wide only slows down things like rune/gc stealing/riots. You may slow down NS aginst an uncoordinated kds, but against that tier of kds simply having well built/trained provs and smart tactics will have more of a meaningfull impact than cs/no cs.

[hwulf]

Just to clarify, I'm talking about average damage per op here, not "chance to catch". Two different things, though the former is certainly a function of the latter.

[Persain]

Just to clarify, I'm talking about average damage per op here, not "chance to catch". Two different things, though the former is certainly a function of the latter.

yea, thats the same thing i caculate and as i said your math on that seemed correct. ;)

[hwulf]

haha oops. . . that was in response to Slayerviper. For some reason I couldn't see your post (confirming my math but also making some excellent points I hadn't considered) before I had posted the clarification.

[Slayerviper]

haha oops. . . that was in response to Slayerviper. For some reason I couldn't see your post (confirming my math but also making some excellent points I hadn't considered) before I had posted the clarification.

fair enough I don't factor CS as a way to look at reducing successful damage (only catch) because its not really measurable. You can math it all you want but sometimes streaks happen... ever try to cure plague with NB?

[JerseyJoe]

It's news to me that cs reduces damage. Last I check it just caused a chance for the opposing prov to fail an op on you.

[JerseyJoe]

Effect: Automatically catches 25% of the thieves' operations conducted against your province. ->> from wiki guide. Unless it wasn't updated then running the same wts you were running before will reduce the same amount of damage. Actually dwarf be is increased so I would assume a little less. They'll just get through more. Which in a sense is more damage I suppose...

(Obviously I'm not a big math guy so I didn't bother with the equations)

[Persain]

Effect: Automatically catches 25% of the thieves' operations conducted against your province. ->> from wiki guide. Unless it wasn't updated then running the same wts you were running before will reduce the same amount of damage. Actually dwarf be is increased so I would assume a little less. They'll just get through more. Which in a sense is more damage I suppose...

(Obviously I'm not a big math guy so I didn't bother with the equations)

whats hes doing is calculating the expected value for damage per op. so if there's a 25% chance to catch theives that means if someone does 1000 theive ops on me i would expect 250 to fail due to CS. In another sense since only 750 were successful i took 750 ns's worth of damage and the thus 25% less total damage since 25% of the 1000 ops never actully hit my prov.

[JerseyJoe]

Wouldn't that also be affect by things like relative nw and racial bonuses? If so then it'd be harder to calculate since nws are gonna vary throughout even the same war and you'd more than likely be getting ns'ed by more than one race/pers type.

[Persain]

Wouldn't that also be affect by things like relative nw and racial bonuses? If so then it'd be harder to calculate since nws are gonna vary throughout even the same war and you'd more than likely be getting ns'ed by more than one race/pers type.

yes and no-ish. Yes the damage you take per op varies based on who is oping you, i.e. a feary does more damage than a orc nsing if at the same success rate due to racial bonuses, or oping someone 400% your nw does less damage/op than oping someone at equal nw. In contrast WT+CS defense dont vary based on whose oping you, they just cause reduced damage/successful op +auto-fail on whatever ops u'd normally receive.

What the op is looking to determine is if i run wt+cs how much total reduced damage from all sources can i expect. He then needs to determine if the people who would normally deal x damage across oping a bunch of times times being reduced by say 66% going to be "enough" of a defense (some of that is auto-failing some of it is reduced damage on successful ops). Its then up to him to decide w/out math if that much reduced damage makes wt/cs viable as a def against theif ops or if he needs to change something like setup/nw spread/.....

[yootohpeega]

Cool test case. Thanks for doing this.

Just for simplicity and generality, here's comparing 0% WTs with CS and x% WTs with no CS, all else equal (no race, no personality, no MVs, just blank slate), to see what % WT is "equivalent" to CS:

0% WTs with CS = 0.75 enemy op effectiveness

Let x% WTs with no CS = 0.75 enemy op effectiveness. Then:
(1-2*x*(1-x))*(1-3*x*(1-x))=0.75
where the first term is from less op successes and the second term is from less damage per op.
Copy paste into wolfram alpha the above and get x = 0.0566323

So the answer is very close to yours. 5.66% WTs ~ CS.

Also, comparing 15% WTs with CS and (15% + y) WTs with no CS and solving for y:
(1-2*(x+y)*(1-(x+y)))*(1-3*(x+y)*(1-(x+y)))=0.75*(1-2*x*(1-x))*(1-3*x*(1-x)); x=0.15
Plugging the above into wolfram alpha gives y = 5.47%.

Comparing 25% WTs with CS and (25% + y) WTs with no CS and solving for y:
(1-2*(x+y)*(1-(x+y)))*(1-3*(x+y)*(1-(x+y)))=0.75*(1-2*x*(1-x))*(1-3*x*(1-x)); x=0.25
Plugging the above into wolfram alpha gives y = 5.99%.

So basically, assuming all else equal, CS is "equivalent" to +5% to +6% WTs.