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Vulnerability Exploiter consoles are pointless [Warning: Math]
valill1
Member Posts: 0 Arc User
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After feedback and further deliberation, I have corrected my initial approach to this.
The math is corrected in #5.
I used this to create a tool that displays optimal combinations for your setup, explained in #15
Direct link to the tool: STO Magical Mystery Weapon Crit Advisor
Results suggest that Exploiters are indeed worse than Locators in (almost?) all cases when considering average damage. Effects on burst damage are a matter for further debate.
Below this line is the original post. It is largely incorrect, but I'm leaving it here as context for the replies. The 1:10 optimal ratio is not a thing.
____________________________
Let me explain.
If you don't already know, the optimal combination of crit chance and severity is 1:10, or:
sev = 10 * chance
e.g. 5% chance and 50% severity.
Because of this, many games provide modifiers that increment these stats in the same 1:10 ratio, thus [CrtH] = 2% chance, [CrtD] = 20% sev. These modifiers are of equal benefit, provided you keep your overall stats around the 1:10 optimal.
Some consoles maintain this balance - Tachyokinetic and Assimilated increase both stats at 1:10, however others do not - Zero-Point adds 1.8% chance but no severity, leaving an 18% severity deficit. This is compounded when it comes to reputation passives - New Romulus T2 grants a whopping 3% crit chance, and Dyson T2 now gives us severity, but only 10%. That's another 20% severity deficit skewing us away from optimal. I should add that we start off with a base surplus of 25% sev (base crit is 2.5% chance/50% sev), so adding up all of the above we have a 13% deficit.
This is the reason why [CrtD] weapons are better than [CrtH] - Assuming you have all the above consoles, the [CrtD] fills the 13% sev gap, placing you closer to the optimal 1:10 ratio. You are then +7% sev, so [CrtH] is the most effective second modifier (I'm ignoring [Acc] - see caveats below).
Now we come to the new tac consoles. I was really looking forward to these as an alternate means of plugging the severity hole, removing the need for [CrtD] weapons to achieve the optimal. Being able to modify chance and severity with multiple consoles mean that any combination of weapon modifiers could be supplemented to hit the 1:10 ratio. This would be really good and I'm guessing is what the devs were aiming for.
Then I saw the console stats and unfortunately the Locators and Exploiters were not made equal. The Locators provide 1.6% chance and Exploiters just 8% severity. This is a 1:5 ratio, making the Locators double the effectiveness of the Exploiters. I've done the math and there is no point getting the Exploiters - even if you have [CrtH]x3 and thus are really skewed off optimal, the extra chance is still the best option.
I ask that the devs consider changing these consoles to match the 1:10 ratio, so that the Exploiters are actually worth using.
Here's my spreadsheet: https://docs.google.com/spreadsheet/pub?key=0AmsElebV53jRdFUzTmlsY1FGSzNfMEZEc0FZVV9rSHc
Caveats:
I have disregarded [Acc] for the purposes of this demonstration. I am aware that accuracy overflows into crit, but to remove this situational variable, I have assumed 100% accuracy with no overflow.
Weapon specialization skills also affect crit chance and severity. Since the mechanics of how this works are unknown to me, I cannot account for this.
Obviously, I do not have access to either of the consoles myself yet and am going from the information available here: http://sto.gamepedia.com/Advanced_Tactical_Vulnerability_Consoles
Exploiters and Locators are assumed to be of equal cost and availability. Of course, the Exploiters are available sooner (T2 Spire Research vs T3), but I have assumed an end state where all tiers are unlocked.
I have ignored the new crit-triggered procs. You may want a higher crit chance to trigger these more often, but I've not run the numbers to see if it's worthwhile.
After feedback and further deliberation, I have corrected my initial approach to this.
The math is corrected in #5.
I used this to create a tool that displays optimal combinations for your setup, explained in #15
Direct link to the tool: STO Magical Mystery Weapon Crit Advisor
Results suggest that Exploiters are indeed worse than Locators in (almost?) all cases when considering average damage. Effects on burst damage are a matter for further debate.
Below this line is the original post. It is largely incorrect, but I'm leaving it here as context for the replies. The 1:10 optimal ratio is not a thing.
____________________________
Let me explain.
If you don't already know, the optimal combination of crit chance and severity is 1:10, or:
sev = 10 * chance
e.g. 5% chance and 50% severity.
Because of this, many games provide modifiers that increment these stats in the same 1:10 ratio, thus [CrtH] = 2% chance, [CrtD] = 20% sev. These modifiers are of equal benefit, provided you keep your overall stats around the 1:10 optimal.
Some consoles maintain this balance - Tachyokinetic and Assimilated increase both stats at 1:10, however others do not - Zero-Point adds 1.8% chance but no severity, leaving an 18% severity deficit. This is compounded when it comes to reputation passives - New Romulus T2 grants a whopping 3% crit chance, and Dyson T2 now gives us severity, but only 10%. That's another 20% severity deficit skewing us away from optimal. I should add that we start off with a base surplus of 25% sev (base crit is 2.5% chance/50% sev), so adding up all of the above we have a 13% deficit.
This is the reason why [CrtD] weapons are better than [CrtH] - Assuming you have all the above consoles, the [CrtD] fills the 13% sev gap, placing you closer to the optimal 1:10 ratio. You are then +7% sev, so [CrtH] is the most effective second modifier (I'm ignoring [Acc] - see caveats below).
Now we come to the new tac consoles. I was really looking forward to these as an alternate means of plugging the severity hole, removing the need for [CrtD] weapons to achieve the optimal. Being able to modify chance and severity with multiple consoles mean that any combination of weapon modifiers could be supplemented to hit the 1:10 ratio. This would be really good and I'm guessing is what the devs were aiming for.
Then I saw the console stats and unfortunately the Locators and Exploiters were not made equal. The Locators provide 1.6% chance and Exploiters just 8% severity. This is a 1:5 ratio, making the Locators double the effectiveness of the Exploiters. I've done the math and there is no point getting the Exploiters - even if you have [CrtH]x3 and thus are really skewed off optimal, the extra chance is still the best option.
I ask that the devs consider changing these consoles to match the 1:10 ratio, so that the Exploiters are actually worth using.
Here's my spreadsheet: https://docs.google.com/spreadsheet/pub?key=0AmsElebV53jRdFUzTmlsY1FGSzNfMEZEc0FZVV9rSHc
Caveats:
I have disregarded [Acc] for the purposes of this demonstration. I am aware that accuracy overflows into crit, but to remove this situational variable, I have assumed 100% accuracy with no overflow.
Weapon specialization skills also affect crit chance and severity. Since the mechanics of how this works are unknown to me, I cannot account for this.
Obviously, I do not have access to either of the consoles myself yet and am going from the information available here: http://sto.gamepedia.com/Advanced_Tactical_Vulnerability_Consoles
Exploiters and Locators are assumed to be of equal cost and availability. Of course, the Exploiters are available sooner (T2 Spire Research vs T3), but I have assumed an end state where all tiers are unlocked.
I have ignored the new crit-triggered procs. You may want a higher crit chance to trigger these more often, but I've not run the numbers to see if it's worthwhile.
Post edited by valill1 on
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Would really like to how Acc weapons compare though. I don't know how much of an overflow there is into crit, all we know is that it happens, but not by how much. afaik.
While I agree with you that [CrtD] weapons are in most cases better with Vulnerability Locator consoles, the above assertion is incorrect.
Let D denote the damage you would do without crits. Let C denote your critical chance and S denote your critical severity. Then, your average damage would be
(1-C)*D + C*(1+S)*D = (1 + C*S)*D.
If D is taken to be constant, then to maximize your average damage, you should maximize C*S. I don't know why you think the optimal ratio of C:S is 1:10.
*facepalm* (at self) My reasoning is off. The spreadsheet calculations are valid and conclusions are the same (for my particular universal consoles, passives and available tac slots), but...
With fresh eyes this morning, I see that my initial reasoning was backward. The 1:10 arises because that's the ratio of the CrtH:CrtD modifiers. Taking just weapon modifiers in isolation, let A be the number of [CrtH] modifiers and let B be the number of [CrtD]s, we can expand C*S to:
(A * CrtH) * (B * CrtD)
Since CrtH and CrtD are constant, we are wanting to pick a maximal value of A*B, constrained by A+B=N (total number of modifiers we can have), which is of course where A=B. The resulting C:S ratio is the same as CrtH:CrtD, hence the 1:10 "optimal" which essentially means you should split equally between [CrtD] and [CrtH] modifiers (in isolation).
I then included the tac consoles, which due to the different CrtH:CrtD ratio do not combine nicely into this. Let us take X as our number of Locators and Y as the number of Exploiters, with Loc and Exp as our constants (currently 1.6 and 8 respectively).
In isolation:
(X * Loc) * (Y * Exp)
constrained by X+Y = M (number of tac console slots)
We can see that the same X=Y holds. However, because the combination of weapon modifiers and the consoles is additive, merging the two gives:
(A * CrtH + X * Loc) * (B * CrtD + Y * Exp)
with the constraints:
A + B = N (number of modifiers on weapon)
X + Y = M (number of tac console slots)
Finding an optimal A, B, X and Y for a given N and M is now more complicated. Adding in consoles and base values complicates even further.
It is trivial to exhaustively search the possible combinations for our low possible values of N and M. I might create something to do this tonight. In the meantime if anyone could manipulate the above to produce equations for optimal values of A, B, X and Y in terms of N and M, that'd be much neater - This is beyond what I can recall from math class :P
[CrtD] adds 10 times the % bonus of [CrtH], so the ratio to look for is 1:10 for that decision. In other words, if your severity is less than 10 times your chance, it's better to take a [CrtD], if its more than that, a [CrtH] is better.
With the vulnerability consoles, the ratio is apparently 1:5. If your severity is less than 5 times your chance, the ratio will be under 5 and the exploiter console becomes better than the locator.
The lower ratio does mean the exploiter consoles are unlikely to come into play if used with 3x[CrtD]/[CrtH], simply because starting from the base 1:20 you'll hit the 1:10 first and then you can [CrtD]. But if you're using [Acc] for weapons its not difficult to come up with a build where some of the tac consoles should be exploiters.
I have conceded this in #5 above. The optimal ratio is not a thing when taking all factors into account.
I chose [CrtH]x3 as it is the extreme most likely to make an Exploiter worthwhile - The higher chance magnifies any increase severity. [CrtD]x3 is at the opposite end - chance is low, so more severity is less effective. [Acc]x3 will lay between these two - The effectiveness of the Exploiter will be determined solely by your universal consoles and passives (With my setup, a quick play with my spreadsheet shows that Locators still win with [Acc]x3).
Yes, this is the correct approach. But as you said, you have to include your base crit chance, base crit severity, skills, rep passives, captain traits, boff traits, and universal consoles. For the cases I looked at, I found, as you did, that the best combination is [CrtD] with Vulnerability Locator consoles. But I hesitate to say that it is true in every case. It probably depends on your exact build.
The simplest thing to do is to maximize (1 + C*S)*D via exhaustive search. If you know D is constant, then you can just maximize C*S. You could try something fancier like using a Lagrange multiplier technique to find the optimal real values for A, B, X, and Y, but I really don't think it's worth it. I'm not even sure the function you want to maximize is concave.
The above all assumes that you are trying to maximize expected damage. Some players might have other goals. For example, if you want to maximize the damage that your lucky spikes do, then you would probably choose Vulnerability Exploiter consoles.
In PvE where bad guys don't really heal themselves, I find CrtH to be superior in total damage over time than CrtD.
As I only play PvE, when there's a choice between CrtH and CrtD, I always take the former (CrtH).
You can find/contact me in game as @PatricianVetinari. Playing STO since Feb 2010.
Just curious as to what you think that means. Because it looks very much like you just copied the same thing to both sides of an equals sign. Just saying. Or maybe I'm drinking again. Hard saying.
Anyways, whenever chance and severity fall more than a couple of percentage points from a one to ten ratio increasing the lower value first will always increase average damage more than increasing the higher value will.
Each and every time.
Cheers.
And like anyone else has mentioned, if you're going for a build that optimizes crit chance then of course blah blah blah.
Cheers again.
Oh and damage isn't always constant. Just saying. I'm not even sure what you folks are considering damage as being. But if it helps, after accuracy your damage mods are the most important.
Triple cheers!;)
Can someone please explain to me why a 1:10 Crit/Severity ratio is "Optimal"?
You can find/contact me in game as @PatricianVetinari. Playing STO since Feb 2010.
Well, seems it is, when i do all the hard numbers 1:10 seems to be most damage dealing ratio. It is a really small difference but still...
And having 1.6 crit chance versus 8% crit damage is worth having up to the point.
I will do the numbers and try to calculate at what point is 8% severity is better than 1.6 chance .
I think it could be when you have current ratio 1/5 or less
I'm not sure why you are confused. The two sides of the equality are different expressions of the same quantity. Surely, that is the standard usage of the equals sign.
Where mathematically does this 1:10 ratio come from? It doesn't just depend on whether crit chance or crit severity is lower; it also depends on the magnitude of the additional increase to crit chance or crit severity. If crit chance were 20% and crit severity were 50%, then a 10% bonus to crit severity would be better than a 2% bonus to crit chance.
Perhaps, "constant" was a poor choice of terminology. I didn't mean that in the middle of the battle, your damage stays constant. I meant consider the damage D you would do without crits, but all other factors taken into account. Then, evaluate what would happen as you change your crit chance and crit severity while keeping D the same. For example, if you were just choosing between a [CrtH] and a [CrtD] modifier on your weapon, then you could consider D to be constant. However, if you were evaluating whether to move skill points between "Starship Energy Weapons" and "Starship Energy Weapon Specialization", then you couldn't consider D to be constant, because you are changing other factors besides crit chance and crit severity.
STO Magical Mystery Weapon Crit Advisor
My code is a little better than my calculus. Given your active consoles/rep passives/set bonuses as well as the number of weapon modifiers you wish to dedicate to crit (reduce this if you want to reserve modifiers for, say, [Acc]), and the number of tactical console slots available, it lists all possible weapon modifier and tac console combinations, ordered by their average effect on damage over time.
As mentioned, there are a bunch of things, like skills, that aren't accounted for.
Let me know if there are any global (not weapon/damage type-specific) crit modifiers I've missed.
Maybe it's to control the ability of players to one hit KO as often as possible? Crit severity can be stacked pretty high already. I mean this just looking at all the possible avenues of buff, I'm not running the math. It's probably not as high as it seems, but it sure does look like a lot at first glance. I'm almost certain there's more critD enhancing avenues in game than CritH currently, maybe it counteracts that?
Maybe it was just an intentional nerf to force competetive players to grind all the way to tier 3? The spire does seem to be somewhat of a barren holding when compared to the others. Maybe the mine just spoiled me though..
If so, then this is exactly like the Mk X and Mk XI rep rewards that now don't exist in Dyson rep. Items that are outclassed by the next tier and not worth wasting dil/marks/credits on. I would hope that this was not the devs' intent.
I suspect that this is the misconception at the core of this. The severity numbers *look* overwhelming because they are numerically larger, but the math indicates that they do not contribute as much to average damage as the Locators in any situation.
I hope that I've shown well enough that Exploiters are not as effective as Locators. As a side-effect, this shifts the most desirable weapon mod further in favor of as much [CrtD] as you can get. What would help now is an indication of whether this was the devs' intent.
If I have missed any global severity bonuses, please let me know.
The way I calculate it, if you have 2,000 base dmg per normal hit then in 1,000 hits:
20% CrtH / 50% CrtD = 2,600,000 Dmg
20% CrtH / 60% CrtD = 2,640,000 Dmg
22% CrtH / 50% CrtD = 2,660,000 Dmg
Right?
If so, then it seems 2% CrtH bonus is better than 10% CrtD bonus.
I admit my math could be wrong, but I can't ever find a ratio where having more CrtD is better than more CrtH over time. In other words, while severity may have merit if you're looking for burst, if you want to increase your overall damage then chance is better.
You can find/contact me in game as @PatricianVetinari. Playing STO since Feb 2010.
Fact of the matters is clear, going from a 26.6 consoles to 31.8 consoles time however many tac consoles you have will result in an increase in damage. The CritH vs CritD debate will rage on, there are other factors we aren't discussing here. Factors like Hitting, the rate of fire, decreasing defense, do you hit shields or hull etc. That math has not going to be settled definitively. CritH and CritD are important and you want both that much is certain. So determine where you want to spend your FC and how it will work with your fleets provision budget and call it a night.
My PvE/PvP hybrid skill tree
It shouldn't be hard to add skills. Take a look at the chart below, if you haven't already.
http://home.comcast.net/~amicus/Skill%20Point%20Effects.htm
Also, I think the base crit chance is 2.5% and the base crit severity is 50% without any skills or gear. I might have misremembered though, so you should double-check that.
I don't follow your calculation. I would calculate the average damage like this:
(1 + 0.2*0.5) * 2000 * 1000 = 2200000
(1 + 0.2*0.6) * 2000 * 1000 = 2240000
(1 + 0.22*0.5) * 2000 * 1000 = 2220000
I would like to know where people got this idea that the optimal ratio of crit chance to crit severity is 1 to 10. It's not supported by the math. The optimal crit chance is 100%. You should aim for the highest crit severity you can get. It's only when you need to make a trade-off between crit chance and crit severity that there is a constraint. And this constraint is dependent on your specific build.
To see that this idea of an optimal ratio makes no sense, consider the following scenario. Suppose you have a crit chance of 5% and and crit severity of 50%. Now, someone offers you a bonus of 2% crit chance with no downsides. Are you going to refuse just so that you can maintain your 1:10 ratio? Obviously, not. You will take 7% crit chance and 50% crit severity over 5% crit chance and 50% crit severity.
Good point. I've been avoiding weapon-specifics so far, but it should be included. There's also the built-in 20% severity for antiproton weapons.
Nice find, thanks! It's a nice easy calculation so I will definitely add these.
Everyone please listen to frtoaster. I was wrong in my original post. It's not as simple as having an optimum ratio to aim for. I've tried editing the OP to explain this but it seems there's no re-closing this can of worms :P
Everybody is forgetting the hits without crits.
[Base DMG * (1 - Critical Chance/100)] + [Base DMG * Critical Chance/100 * (1 + Critical Severity/100)] = Average DMG
One more thing:
1/10 doesnt have to be optimal ratio.
10% crtH / 100% crtD is the same as 20% crtH / 50% crtD and it is same as 5% crtH / 200% crtD
Let's assume some basics (since we really only care about choosing between Locators/Exploiters, or a mix of the two):
Base DPV: 1000
Base CritH: 2.5%
Base CritD: 50.0%
No other CritX Modifiers
Calculations:
[Chance of Crit] = [Base CritH]+([# Locators]*0.016)
[Crit DPV] = ([Base CritD]+([# Exploiters]*0.08))*[Base DPV]+[Base DPV]
Per 100 Volleys =
(100*[Chance of Crit]*[Crit DPV])+(100*(1-[Change of Crit])*[Base DPV])
Therefore:
Per 100 Volleys:
Locators x 0, Exploiters x 5: 102250 Total Dmg
Locators x 1, Exploiters x 4: 103362 Total Dmg
Locators x 2, Exploiters x 3: 104218 Total Dmg
Locators x 3, Exploiters x 2: 104818 Total Dmg
Locators x 4, Exploiters x 1: 105162 Total Dmg
Locators x 5, Exploiters x 0: 105250 Total Dmg
Have I made a mistake in the math? Please let me know.
No, I didn't forget that. You said the same thing I did, but in different notation.
That's what I've been trying to explain from the beginning.
Yes, that is correct. Of course, in your actual build, you probably have one or more of the following: skills, rep passives, captain traits, boff traits, weapon modifiers, and universal consoles.
Sorry, i guess i wasnt looking the whole formula.
I wonder, at what point of critD and severiity the weapon damage modifiers becomes more useful than 2% chance or 20% severity modifiers. It has to be at some point with very high crtD and crtH