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Fun with numbers (Exploiters vs Locators)
rylanadionysis
Member Posts: 3,359 Arc User
Just going to play with numbers in this thread.
Using a weapon with 1000 base damage doing 100,000 shots
Assuming the Base(1+x) is correct for the calculation of critical hits
Assuming a ship with five tactical consoles
Assuming all else is equal on the ship besides the consoles.
TEST ONE
22 percent crit
85 severity
78000 non crits of 1000 = 78 million
22000 crits of 1850 = 40.7 million
118.7 million
Add exploiters, 22 percent crit, 125 severity
78000 non crits of 1000 = 78M
22000 crits of 2250 = 49.5M
127.5M
Add locators, 30 critH, 85 critD
70000 non crits of 1000 = 70M
30000 crits of 1850 = 55.5M
125.5M
Exploiters win
TEST 2
14 percent crit
110 severity
86000 @ 1000 = 86M
14000 @ 2100 = 29.4M
115.4M
Exploiters 14 critH, 150 sev
86000 @ 1000 = 86M
14000 @ 2500 = 35M
121M
Locators 22 critH, 110 critD
78000 @ 1000 = 78M
22000 @ 2100 = 46.2M
124.2M
Locators win
TEST 3
33 crit H
140 crit D
67000 @ 1000 = 67M
33000 @ 2400 = 79.2M
146.2M
Exploiters, 33 H, 180 D
67000 @ 1000 = 67M
33000 @ 2800 = 92.4M
159.4M
Locators, 41H, 140 D
59000 @ 1000 = 59M
41000 @ 2400 = 98.4M
157.4M
Exploiters win
Using a weapon with 1000 base damage doing 100,000 shots
Assuming the Base(1+x) is correct for the calculation of critical hits
Assuming a ship with five tactical consoles
Assuming all else is equal on the ship besides the consoles.
TEST ONE
22 percent crit
85 severity
78000 non crits of 1000 = 78 million
22000 crits of 1850 = 40.7 million
118.7 million
Add exploiters, 22 percent crit, 125 severity
78000 non crits of 1000 = 78M
22000 crits of 2250 = 49.5M
127.5M
Add locators, 30 critH, 85 critD
70000 non crits of 1000 = 70M
30000 crits of 1850 = 55.5M
125.5M
Exploiters win
TEST 2
14 percent crit
110 severity
86000 @ 1000 = 86M
14000 @ 2100 = 29.4M
115.4M
Exploiters 14 critH, 150 sev
86000 @ 1000 = 86M
14000 @ 2500 = 35M
121M
Locators 22 critH, 110 critD
78000 @ 1000 = 78M
22000 @ 2100 = 46.2M
124.2M
Locators win
TEST 3
33 crit H
140 crit D
67000 @ 1000 = 67M
33000 @ 2400 = 79.2M
146.2M
Exploiters, 33 H, 180 D
67000 @ 1000 = 67M
33000 @ 2800 = 92.4M
159.4M
Locators, 41H, 140 D
59000 @ 1000 = 59M
41000 @ 2400 = 98.4M
157.4M
Exploiters win
Fleet Admiral Rylana - Fed Tac - U.S.S Wild Card - Tactical Miracle Worker Cruiser
Lifetime Subscriber since 2012 == 17,200 Accolades = RIP PvP and Vice Squad
Chief of Starfleet Intelligence Service == Praise Cheesus
Post edited by Unknown User on
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If you have a critical hit chance of less than 20 before adding them, the locators seem to win out
If you have a critical hit chance of more than 20 before adding them, the exploiters seem to win out
If you have a critical hit chance of exactly 20 before adding them, then both consoles will boost your damage by the exact same amount
No matter what your base severity was before you added them.
No matter which number combination I have tried, this is holding true. Mathematically something I said three months ago seems to now hold water, if you have over 20 critH, the tier 2 consoles will always be better. Please mathematically prove me wrong, if you can. because I am unable to produce a result mathematically thus far that disproves the below theory.
If CritH > 20 then Exploiters
If CritH < 20 then Locators.
If CritH = 20 then either will produce identical results
Now im curious if this only holds true on five tac console ships or if its different for four or even three console ships.
Fleet Admiral Rylana - Fed Tac - U.S.S Wild Card - Tactical Miracle Worker Cruiser
Lifetime Subscriber since 2012 == 17,200 Accolades = RIP PvP and Vice Squad
Chief of Starfleet Intelligence Service == Praise Cheesus
For test one if you add four locators and one exploiter you get 127,612M.
Exploiter has +8% CrtD, Locator has +1.6% CrtH their ratio is 8/1.6 = 5:1. This means that when you're adding these you should be aiming for 5:1 final D/H ratio. In your example:
Starting values:
D 85% H 22% ratio ~3.58:1 >> Add Exploiter
Added: Exploiters 1, Locators 0
D 93% H 22% ratio ~4.23:1 >> Add Exploiter
Added: Exploiters 2, Locators 0
D 93% H 22% ratio ~4.59:1 >> Add Exploiter
Added: Exploiters 3, Locators 0
D 101% H 22% ratio ~4.95:1 >> Add Exploiter (it still brings us closer to 5:1 ratio)
Added: Exploiters 4 Locators 0
D 117% H 22% ratio ~5.32:1 >> Add Locator (now adding locator brings us closer to 5:1 ratio; ~4.96:1 vs ~5.68:1)
Added: Exploiters 4, Locators 1
D 117% H 23.6% ratio ~4.96:1 >> Final damage multiplier from crits = 1 + 0.236x1.17 = 1.27612
>>> 100000 hits x (1000 x 1.27612) dmage = 127.612M damage
Likewise, if you where adding weapon mods they have ratio (D/H) of 10:1 so if adding CrtD mods (+20% D) would serve better.
I shall do further tests now. The all or the other crowds are probably wrong altogether in light of this.
Fleet Admiral Rylana - Fed Tac - U.S.S Wild Card - Tactical Miracle Worker Cruiser
Lifetime Subscriber since 2012 == 17,200 Accolades = RIP PvP and Vice Squad
Chief of Starfleet Intelligence Service == Praise Cheesus
Really well explained, thank you.
In regard to "If CritH < 20 then Locators" do you still keep going with Locators even when you bring CritH up to 20? So regardless you just keep boosting up that CritH right?
1. PvE or PvP
In PvE you want DPS. In PvP you need burst damage. And I prefer CrtH for spike damage since I just need that single crit. And in most cases it doesn't matter if it's 45k damage or 60k. But it matters if that BO or HY crits or not.
2. Weapon Mods
Normal vr weapons will give you 3 mods. Leaving Dmg and Acc aside you can choose between any combination of CrtH and CrtD. Since it's obvious that it's easier to push CrtH by adding locator consoles (1,6 crtH vs. 8 CrtD) and superior operatives (2,0 vs. 5) you should choose [CrtD]x3 for +60 CrtD or at least [CrtD]x2 [CrtH].
https://www.dropbox.com/s/1pqjij3945tir5d/Calculator_English.xlsm
Is an Excel spreadsheet which let's you play around with equipment and weapons to find the best combination for your build.
STO-League.com | Weapon Damage Calculator | DPS Web Tools | STO-Center Forums
now this looks pretty solid.
However it seems that only romulans can actually produce crtH at around 20% without calculating in the tac consoles or weapon mods.
this leaves one conclusion: For romulans crtD mods and exploiter consoles will produce the most sustained dmg in PVE.
and for KDF and FED, which normaly have a hard time even reaching 13% crtH (before mods and tac consoles) the locators are almost exclusively better.
and considering that weapon mods crtD and crtH are at a different ration than on the tac consoles, crtD mod > crtH mod on weapons.
Hmmm... Im thinking about it on the back of my head for a while, but I still can't formalize the problem of crtD vs crtH.
Leaving aside factors like positioning, weapon power, crth based weapons proc etc: crtD is a real value and will always stay real, i.e. given 1 crit shot you will always deal your crtD damage.
CrtH however is just probability of crit event occuring or not.
Assuming 100 shots with 10 damage per shot
With 0% crth 0 crtd = 1000 damage
Base crth: 22% crtd: 80% (180%)
22 * (10 * 1.8) + 78 * 10 = 396 + 780 = 1176
5 Locators crth + 9%: crth 31% crtd 80%
31 * 18 + 69 * 10 = 558 + 690 = 1248
5 exploiters crtd + 40%: crth 22% crtd 120% (220%)
22 * (10 * 2.2) + 78 * 10 = 484 + 780 = 1264
--
n = number of shots
d = damage per shot
crth = 0.22
crtd = 180
n * crth * d * crtd + n * (1 - crth) * d => n * d * ( crth * crtd + (1 - crth) )
assuming n, d are scalar constants the damage function becomes
crth * crtd + (1 - crth) => (crth : x, crtd : y) =>
Our final function of damage over crth and crtd
dmg = x * y + (1-x)
--
Lets take 3d function plotter, as im too lazy to do derivative calculus for 2 variables:
http://www.math.uri.edu/~bkaskosz/flashmo/graph3d/
x * y + (1-x)
Parameters:
x = 0 - 30, y = 0 - 220
Bummer... this is a surprise. There's a little bump from 0 to zmax, which proves the claim that there's in fact sweet spot ratio of crtd and crth. Something which I didn't belive for a while.
--
Also worth noting my friend's little experiment: he parked 9km from ISE gate and for an hour setting his weapons on autofire. One hour with locators, and one hour with exploiters. His results were rather surprising: out of somewhat 1,200,000 dmg dealt in both cases the difference was 40k damage: less than 3%, which is well within experimental error.
I went for DMGx3/CritH mod on all my Fleet AP weapons (hence why my critH % is at 17%). Was this a massive mistake then?
To disprove your hypothesis of a crth 20 threshold for locator vs exploiter, compare the following ratios: crth 4 vs crtd 150. And crth 6 vs crtd 150. Compare the additional damage you will get with either a crth 2 mod or a crtd 20 mod.
To extend this, try testing a ratio of crth 5 vs crtd 150. Either mod goes in this instance. Incidentally this kinda proves the exploiter < locator sayings.
what you ignored is, that the ratio is not linear 1:10...at higher crtH, the less amount crtD you need to reach the dmg increase of a single crtH %.
the optimum ratio moves from 1:10 at <10% crtH to 1:5 at around 20% crtH and so on....you can imagine that at 99% crtH the ratio looks more like 10:1 than 1:10.
i'd asume that at 50% crtH the optimum ratio is 1:1
Brilliant stuff!
One question, though. How does the CrtH/CrtD modifiers of the weps themselves factor into all of this? Should I just add/subtract them from the '20'?
Am experimenting with a spreadsheet, and as crth increases the ratio does change. In fact I'm starting to run into weird instances where marginal damage with additional crth is actually negative!
Summarising this into a quick and easy rule will be the hard part, though.
My results are based on an actual critH of 20, modifiers didnt matter as that was what the ship had. (you could assume it had 12 base, 9 points EWS, and 3xCritH weapons i guess?)
It was just an experiment in math based on another thread, if im honest. It just happened to bear interesting fruit that I see is being confirmed by others in the thread.
Changing ratios, whod have thought eh? I suppose it has something to do with the fact we are in an era where we are no long bound to ships that have 15 crit and 80 severity, we just never knew until we did the math later with 30 critH and 140 severity. We had never been here so we assumed the old tools and rules stayed static.
There was a post shortly after my OP that seems to explain "what to do" when you are close to 20, but not over when you start adding them, too.
Fleet Admiral Rylana - Fed Tac - U.S.S Wild Card - Tactical Miracle Worker Cruiser
Lifetime Subscriber since 2012 == 17,200 Accolades = RIP PvP and Vice Squad
Chief of Starfleet Intelligence Service == Praise Cheesus
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You made a mistake. The expected damage is
n * crth * d * (1 + crtd) + n * (1 - crth) * d.
This is incorrect. As counterexamples, consider a build where you have CritH of 30 and CritD of 200.
Then CritH > 20, but you're better off using Locators.
Or, consider having CritH of 19, and CritD of 50. Then CritH < 20, but you should go with Expoliters.
Finally, consider CritH = 20. Then if your CritD is higher than 140 you should go for Locators. If it is lower than 60, you should go for Exploiters. Between these two values, you should actually go for a combination of both. These numbers assume 5 tac consoles.
I will add, that I didn't need some excel spreadsheet, or some online calculator to figure this out. I did these calculations in my head, and so can you. It is very simple:
http://sto-forum.perfectworld.com/showthread.php?p=15345081#post15345081
The ratio does not change one bit. It stays 10 to 1 til you cap 100% crit hit. Example
example using 1000 base damage
51% crit hit 490% crit sev
1000*49%=490
1000*(1+490%)*51%=3009
490+3009=3499
50% crit hit 500% crit sev
1000*50%=500
1000*(1+500%)*50%=3000
500+3000=3500
49% crit hit 510% crit sev
1000*51%=510
1000*(1+510%)*49%=2989
510+2989=3499
Note the most optimal is at 50% and 500% crit severity. And it's always a 10 to 1 ratio. Just need to always remember to add 1+x% sev. So 100% is actually 200% or x2. and 200% is actually x3, etc.
Also while the OP's math is correct with his examples i can't agree with the if critH>20% use x console. By itself the tac consoles are 5 to 1. So you use the best consoles eg the crit Hit ones and then use your weapons mods as they are 10 to 1 to get you at that sweet spot. And that typically means using critDx2 or crtDx3 weapons.
Let's take my rom toon for example. Stats are as follows.
ship/attack/acc=25%
ship/attack/crit hit=22.7%
ship/attack/crt sev=113.2%
energy weapon spec 99 points
additional crit hit 2%
additional crit sev=25%
opponents def=-15%
To hit=128.57%
acc overflow
additional crit hit=28.57*.125=3.57%
additional crit sev=28.57*.5=14.28%
Total crit hit=28.28%
Total crit sev=152.48%
Using rom plasma beams with critDx2 for an extra crit sev=40%
Using 5x 1.6% crit hit consoles
36.28% crit hit 192.48% crit sev
1000*63.72%=637
1000*(1+192.48%)*36.28%=1061
637+1061=1698
Using 5x 8% crit sev consoles
28.28% crit hit 232.48% crit sev
1000*71.72%=717
1000*(1+232.48%)*28.28%=940
717+940=1657
As you can see the crit hit consoles won in this situation by 2.47%. So the answer is never quite that easy.
good spot
I did however accounted for crtd value being 100% + x. However, a correction of
dmg = x * (1 + y) + (1-x)
will not change the shape of the function.
yes i was wrong in my statement that the optimum ratio is not linear, i'm sorry for that. It was also not what i meant.
what i was trying to say was, that once you get over a certain point of crtH, your crtD falls off, because accumulating crtH is much easier.
This results in a deveation from the 1:10 ratio for optimal dmg.
so the question remains, or rather the statement i made to solve this question: How much more crtH do i need to compensate for the discrapency between crtH and crtD if i'm unable to increase crtD.
the further up i go with crtH, without the ability to increase crtD, the more crtH i need, to get the same results as if i was able to get my crtD up within a 1:10 ratio.
That's what i meant with "the ratio is not linear"...the best crtH/crtD ratio remains 1:10...BUT in the case of STO, where there is a cap to crtD stacking due to itemshortage, the question of how much crtH i'd need remains.
to get to amount of dmg X, you need y% crtH and z% crtD...the optimum way is y=1 and z=10...so much is clear.
but since z can't be raised indefinately due to the itemisation and shortage of crtD items, consoles, skills,...
To achieve X, how large does y need to be, when z is constant (or in our case can't be increased)
would this be linear? wouldn't it mean that every bit of crtD i get to fill up the gap between the crtH and crtD imbalance (1:10 ratio) be many times more valuable than crtH initialy was?
your calculations demonstrated, that as long as you remain inside the 1:10 ratio and add and substract crtH or crtD accordingly, the dmg output does not change.
i poorly formulated my statement on which you responded, proberbly because the subject confuses me myself a lot. i hope this new post is somewhat clearer.
So how do you account for this...
BTW, just a little experiment
=====TEST FIFTEEN (yes i really did 11 more i didnt publish trying to prove myself wrong) =========
Romulan with 27 CritH 90 severity (reputations, SROs, universal consoles, etc, its very easy to get here with a romulan, this is actually one of mine)
1 + (.27*.9) = 1.243
Same romulan with critDx3 mods on his weapons
1 + (.27*1.5) = 1.405
Same romulan add 5x locator
1 + (.35 * 1.5) = 1.525
Same romulan with 5x exploiter instead
1 + (.27*1.9) = 1.513
Same romulan with 4xE 1xL (lets see if we can beat 1.525)
1+ (.286*1.82) = 1.5205
Same romulan with 3xE 2xL (This surpasses 5x locators)
1 + (.302*1.74) = 1.52548
Same romulan with 2xE 3xL (Optimum)
1 + (.318*1.66) = 1.52788
Same romulan with 1xE 4xL (going down again)
1 + (.334*1.58) = 1.52772
This romulan with 27 critH and 90 severity who then adds critDx3 weapons needs to use 2 exploiters and 3 locators to achieve optimal DPS. Even with critDx3 weapons, exploiters are still good (especially when mixed with locators to achieve the closest 5:1 ratio D/H). Locators alone actually hurt the DPS of the build.
Fleet Admiral Rylana - Fed Tac - U.S.S Wild Card - Tactical Miracle Worker Cruiser
Lifetime Subscriber since 2012 == 17,200 Accolades = RIP PvP and Vice Squad
Chief of Starfleet Intelligence Service == Praise Cheesus
This is why I'm against telling people about the 1:10 rule. It creates misunderstandings. Forget about whether the ratio is linear or not; in fact, forget about the ratio altogether. There isn't really an optimal ratio to achieve. If you want a rule to follow, then use this one:
If you are changing crit chance and crit severity only while keeping all other factors the same, then to maximize expected damage, maximize the product of your total crit chance and total crit severity.
Several players, including myself, have explained the mathematics behind that rule in other threads. The latest thread, by cerealplayer, is here:
http://sto-forum.perfectworld.com/showthread.php?t=1034191
if x/(y/5)<1 use locator
if x/(y/5)=1 optimal
if x/(y/5)>1 use exploiter
However if you're just looking at your stats listed under ship/attack that wouldn't be enough data. You'd have to list your weapon mods. You'd have to figure out energy weapon spec which is a 12.5 to 1 ratio. And calculate acc overflow which is a 4 to 1 ratio. So the answer is never that simple.
And i have to mostly agree with the last poster. Still though it is best to use a calculator specific to this game for the most optimal results. There will be quite a few cases where exploiter consoles will be the better choice. Although you should try to avoid this with other choices.
What's with that low 80% severity? With an absolute base of 50%? (The real base in game is higher than that, btw) How often do you hear people having such low severity? News for you, weapon specialization skills add bigger portion severity than chance, and acc overflow adds 1% severity per point. You'll far overshoot that based on skills alone in a ship with no consoles using white non-ap non-dhc weapons that has no modifiers.
What's with that 20% chance? Good luck getting that high chance if you're not a Romulan with a whole bunch of superior operatives. Sure, you hear some non-romulans reaching it these days by filling their boat with every universal console under the sun, but that's after a full set of Locators...
Oh, and the 1:10 rule of thumb doesn't come from CrtH modifier being 2% and CrtD being 20%. It comes from the typical tac newbie asking questions in the academy: He would have crit chance in the high single digits or low teens, and severity already well above 100 based on specialization skill, acc, dhc, ap, and a mix of odd modifiers. It assumes he has no resources, but the right skill set for tac. While making no sense mathematically, this rule of thumb shows wisdom and intention to help by the person who came up with it, and not egoism and intention to deceive, like OP of this thread.:rolleyes:
It's on a per weapon modifier basis. If you think the 1:10 comes from CrtD having an extra zero, that's 1:100 for you.:D
And it doesn't make a 1:5 rule for loc/exp. Exploiters having half the bonus that it's supposed to have merely makes it a bad console. The chumps who end up using [crtH] plus exploiters instead of [crtD] plus locators deserve the nerf they get.
Here:
http://comatoes.github.io/sto-crit-calc/
This is a solid calculator, and illustrates the issue nicely. Look through the options on left hand side. It applies whether you're in the masses or the extreme minority who has a full set of superior operatives. Unlike this thread, the calculator does not deceive, whoever you may be.;)
/thread
Actually that calculator does deceive. It has no option for being a Romulan which adds crit hit and crit severity at a 1 to 5 ratio. It's also using the wrong formula for acc overflow.
If your char is an Romulan Operative, did it not occur to you to add an "Opertive" trait? It's on the left hand corner. And the character trait is not 1:5 ratio, btw, nor any boff traits.:rolleyes:
And there's no "formula" for acc overflow to call "wrong" or "right" for. It assumes stf conditions, and your acc skill is maxed out. If it's not, that's your problem. Acc over flow is subject to too many conditions, it won't be pinned down exactly by a calculator, or any person in this thread or elsewhere. ("Accruate" character adds a pecentage based on certain criteria, but not others. Overflow is broken for faw atm. And how targets fly, when you hit them, are completely fluid. The calculator does the best job that can be expected of anyone on acc)
Of course conditions will effect acc overflow. But there is a right and a wrong and the calculations are wrong for acc overflow. If you want to point people to that calculator you should maybe point out the inaccuracy of acc overflow by telling them, to ensure they don't use that portion of it. But as acc overflow calculations are incorrect the weapons with acc are listed higher then they should be. So even choosing not to enter your accuracy will still show incorrect results for weapons with acc. And that you can't ignore. So you'd be better off using something else or point out to not use acc overflow and devalue or ignore the weapons with acc? Geez this just gets more complicated. Better off if the calculator was redone.
And you're correct the operative trait is not 1:5 it's 1:2.5. ty for the 2 corrections.
And what's this "wrong" value you're referring to? Values used are the official ones given by Cryptic. Many have tried doing trial runs, but weapon hits in game vary too widely, deviation from each trial run way too large, not to mention visible and hidden conditions to skew the results. They couldn't get a statistically significant result from any realistic number of trial runs, and the source code just isn't available for us to just check. So what Cryptic says, goes. If you're seeing these and coming up with conspiracy theories, take it up with them.;)
Besides, it's not as if any of the deceptive posts by OP took acc into account at all. If anything, it's less accurate than the calculator, to say nothing of the starting values.:rolleyes: