Julia Heartilly
Posts: 257
Joined: 11/26/2005
Credibility: 241 pts
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| Focus on the underestimated: ToHit |
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I've noticed that many people underestimate ToHit buffs.
People think of ToHit as an extension to Accuracy, they think it has the same effect but is of lesser efficiency, that after having put 3 +ACC SOs into a power they could switch to ToHit to extend that very same effect a little more.
This however is far from true.
ToHit, contrarily to Accuracy which follows schedule A (T: 8.35%; DO: 16.66%; SO: 33.33%) regarding enhancements, is enhanced according to schedule B (T: 5%; DO: 10%; SO: 20%) leading people to believe that it's potential isn't nearly as useful as that of accuracy.
However, not even to mention the fact that ToHit comes with boosting powers and thus affects all attack powers unlike accuracy which is slotted on a per power basis, ToHit is applied in a different manner.
There are situations in which both accuracy and ToHit can contribute to making your chance to hit an enemy higher than ever aswell as situations where ToHit will have no effect at all or even situations where your accuracy - no matter how much it is - will have hardly any effect simply because you lack the ToHit required to make your accuracy work in that particular situation.
Now, this may all sound a bit confusing and possibly worse no more than pure speculation so grab a cup of coffee to stay awake and try to stick with me as I'll explain how ToHit works and how it differs from accuracy.
First the ToHit formula, which looks as follows:
b = base ToHit
t = ToHit buff
i = base Accuracy
a = Accuracy buff
d = Defense
x = minmax[ i * (1 + a) * min[ b + t - d ] ] = final chance to hit
NOTE: I left out a few variables which are irrelevant in this topic (ToHit debuff, Defense buff and Defense debuff I think off the top of my head).
Also notice the 'minmax' and 'min' parts, min refers to a minimum result of 0.05 and max to a maximum result of 0.95; I've noticed that some other articles on this matter make the common mistake of also putting minmax where I just put min which is incorrect.
Another common error is that people think base accuracy is bound to a whole set of powers, primary or secondary, while in fact this is defined on a per power basis.
Sidenote...
You can put this formula in MS Excel to easily do the calculations following below yourself if you don't feel like working it out manually.
For this you would use the following formula:
=MIN((MAX(((1*A3)*(1+(1*A4))*(MAX(((1*A1)+(1*A2)-(1*A5));0,05)));0,05));0,95)
In this formula the fields A1, A2, A3, A4 and A5 represent the attacker's base ToHit, ToHit buff, base Accuracy, Accuracy buff and the target's Defense in % respectively.
In the following example situations I'll be working with some values such as defense boost from powers and enhancement bonusses which I haven't checked but are often approximates or even entirely random.
This topic is enough work to write already as is so don't hang me for being off on values which I merely included for the sake of clarifying all this.
EXAMPLE 1
Let's have a look at our first example...
Imagine you're playing an infamous Stalker going by the name of "The Almighty Penguin".
You have AS which has a base accuracy of 120% and you 3-slotted it for +ACC (likely also 3 +DMG unless you only recently upgraded from "The Penguin" but that's irrelevant here) making for an accuracy bonus of... say... 97.4%.
You're up against a Scrapper who, for reasons unknown, just noticed you and now fired up Elude in addition to his other +DEF toggles and auto powers bringing his defense to against melee up to 117%.
You Placate him and attempt an AS.
The ToHit formula should be filled in as follows:
b = base ToHit = 0.5; PvP has a fixed base ToHit value of 50%.
t = ToHit buff = 0; no ToHit buff was used.
i = base Accuracy = 1.2; 120% base accuracy of AS goes here.
a = Accuracy buff = 0.974; enhancement bonus.
d = Defense = 1.17
x = minmax[ i * (1 + a) * min[ b + t - d ] ] = final chance to hit
That's the values done, now for the real work...
x = minmax[ 1.2 * (1 + 0.974) * min[ 0.5 + 0 - 1.17 ] ] = ...
My maths teacher always taught me +0 is rather useless.
x = minmax[ 1.2 * (1 + 0.974) * min[ 0.5 - 1.17 ] ] = ...
x = minmax[ 1.2 * (1 + 0.974) * min[ 0.5 - 1.17 ] ] = ...
x = minmax[ 1.2 * (1 + 0.974) * min[ -0.67 ] ] = ...
Here's where the minimum value of 0.05 (5%) kicks in.
x = minmax[ 1.2 * (1 + 0.974) * 0.05 ] = ...
x = minmax[ 1.2 * 1.974 * 0.05 ] = ...
x = minmax[ 0.118 ] = ...
More than 0.05 and less than 0.95, so no problem there.
x = 0.118 = 11.8% chance to hit.
As you see the chance to hit this scrapper now is not much but surely can be enough to score a lucky hit.
Unfortunately, you're not that lucky... and you don't... :-)
Next you try it again, but this time you first use Build Up / Focus Chi or whatever it's called in your case.
This power gives a 20% ToHit bonus by default but let's say you have it 3-slotted with +ToHit SOs adding approximately 57% to it's ToHit bonus which results in a total ToHit buff of 31.4%.
The formula will now be worked out as follows:
x = minmax[ 1.2 * (1 + 0.974) * min[ 0.5 + 0.314 - 1.17 ] ] = minmax[ 1.2 * (1 + 0.974) * min[ -0.356 ] ] = minmax[ 1.2 * (1 + 0.974) * 0.05 ] = minmax[ 1.2 * 1.974 * 0.05 ] = 0.118 = 11.8%.
Now that's funny, +31.4% ToHit and no noticable effect...
Let's have a look at the formula and figure out what causes this.
x = minmax[ i * (1 + a) * min[ b + t - d ] ]
Notice how your target's defense is substracted from your overall ToHit (base + buff) before it gets anywhere near accuracy.
The fact that there's a minimum value of 0.05 for the result of that part of the formula means that if your ToHit is not high enough to "survive" the target's defense (e.g. nothing more than 0.05 is left of your ToHit after the target's defense is substracted from it) the rest of the formula won't change a bit.
Conclusion: your ToHit (or more specifically - your ToHit + 5%) must be higher than the target's defense in order to benefit from it.
Since people usually think of ToHit as an extension to accuracy however they will typically try to increase their chance of hitting using ToHit in situations such as these where accuracy alone no longer suffices.
Unfortunately for them ToHit can't help them anymore either unless they achieve an even higher value by using the power 'Aim' for instance.
This power gives a 42.5% ToHit buff by default, the Thorny Assault (Dominator secondary) version excepted which grants an even greater boost of 50% +ToHit.
If you would slot that last one with 3 +ToHit SOs it would boost your ToHit by about 78.5% for a duration of 10 seconds.
Add to this the PvP base ToHit of 50% and with an overall ToHit of 128.5% you would exceed the 122% (117 + 5 (minimum)) required to gain a benefit.
Skipping the calculation for the sake of saving what brain cells are still left alive out there this would result in a 27.2% chance to hit the target.
That is purely theoretical though since we're now talking about a Stalminator (Dominator with AS).
EXAMPLE 2
This time we'll start with the "analyzing the formula" part and then move on to the situation sketch.
As mentioned earlier the first thing that happens is the target's defense being substracted from your overall ToHit.
If you never use a ToHit boost you'll be limited to the 50% (in PvP) base ToHit and thus you need your target's defense to be below (over 5% below) that in order to get a higher value as a result out of this calculation and in turn make your accuracy more effective - since that's multiplied with what's left of your ToHit you want to have some ToHit left for your accuracy to be multipled with a number greater than 0.05 so that the final result in turn can be a higher number.
This also explains why ToHit is useful in the first place, by increasing your ToHit you effectively do two things:
1. You make sure that you can have more ToHit left to "enhance" your accuracy even further against foes with a somewhat lower defense.
2. Foes with a defense that previously negated all your ToHit may now no longer be able to do so resulting in higher accuracy against them too.
Ofcourse the bright lights amongst us that still haven't Alt+F4'd this topic out of their sight in panic will understand that the above two points are exactly the same really but again that's just to make things a bit clearer.
Next up, spots on a newbie; Billy Bonebreaker only recently started playing - in his eternal search for the ultimate in strength and power he picked... *sigh*... an Invul/SS Tanker.
Billy likes to punch people around with the power 'Hand Clap' which has a lousy base accuracy of 80%.
Also he hasn't figured out yet what ToHit is (all the more reason to visit GameAmp after I submit this) and he has yet to be told that it's not the best idea to slot that power with 6 +DMG SOs.
In a PvP zone he encounters a blaster with a defense of... 6.1%!
Easy prey he thinks and attacks.
x = minmax[ 0.8 * min[ 0.5 - 0.061 ] ] = minmax[ 0.8 * 0.439 ] = 0.351 = 35.1%
He misses - no wonder; 80% base accuracy, no accuracy buff and no ToHit buff.
Attacking a target with 6.1% defense against his Hand Clap and still only 35.1% chance to hit.
Traumatized by this experience Billy decides to enhance Hand Clap with 2 +ACC SOs.
x = minmax[ 0.8 * (1 + 0.666) * min[ 0.5 - 0.061 ] ] = minmax[ 0.8 * (1 + 0.666) * 0.439 ] = minmax[ 0.8 * 1.666 * 0.439 ] = minmax[ 0.8 * 1.666 * 0.439 ] = 0.585 = 58.5%
He notices the substantial increase of 23.4% but it's not enough.
He starts to like actually hitting things and wants more.
This time he uses Rage (no +ToHit enhancements but a default buff of 20%) before attacking.
x = minmax[ 0.8 * (1 + 0.666) * min[ 0.5 + 0.2 - 0.061 ] ] = minmax[ 0.8 * (1 + 0.666) * 0.639 ] = minmax[ 0.8 * 1.666 * 0.639 ] = 0.852 = 85.2%
And look at that... no slotting this time, just Rage (aka Build Up) made for another substantial increase now granting him a overall 85.2% chance to hit his target with that lousy punch of his.
EXAMPLE 3
One last example, no story this time, just a plain and simple indication of what a properly slotted Build Up (or in this case "Focus Chi") - a power that many have but few use for uses besides it's damage buff - can do for you.
Attacker: Stalker with AS, base acc of 120%, 3-slotted, 97.4% bonus and Focus Chi 3-slotted +ToHit, 57% bonus to default of +20% ToHit.
Defender: A whatever with a well decent melee defense of 38%.
Attacker does not use Focus Chi.
Chance to hit = minmax[ 1.2 * (1 + 0.974) * min[ 0.5 - 0.38 ] ] = minmax[ 1.2 * 1.974 * 0.12 ] = 0.284 = 28.4%
Attacker does use Focus Chi.
Chance to hit = minmax[ 1.2 * (1 + 0.974) * min[ 0.5 + 0.314 - 0.38 ] ] = minmax[ 1.2 * 1.974 * 0.434 ] = minmax[ 1.028 ] = 0.95 = 95%
Cap was exceeded, chance reduced to 95%.
Accuracy is nice, ToHit is nice but the combination is the real deal!
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| 08/31/06 16:52 |
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sportgenius
Posts: 988
Joined: 07/26/2005
Credibility: 2355 pts
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| RE: Focus on the underestimated: ToHit |
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i gave u a 10 cause thats a lot to type out, but i got bored reading it. Sry math class doesnt start till 8:10.
btw try submitting this as a guide for 25 cred.
***THIS POST HAS BEEN EDITED***
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| 08/31/06 21:38 |
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Julia Heartilly
Posts: 257
Joined: 11/26/2005
Credibility: 241 pts
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| RE: Focus on the underestimated: ToHit |
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To the best of my knowledge it's 50 cred but it didn't quite cross my mind in the first place, besides I'm not even sure guides are read more at all. :-P
I didn't write it for credit, I did to help people understand that ToHiT is of much greater use than most think.
Edit: Perhaps I should sum up the bottom line numbers of the examples once more in a table at the bottom to make it easier to oversee?
***THIS POST HAS BEEN EDITED***
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| 09/01/06 00:49 |
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Phedre_D
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| RE: Focus on the underestimated: ToHit |
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Great write up! Definately worth a guide. And guides are very much read. And it is much easier to add in a link when somebody asks about tohit buffs in the future.
And although most of your math is a bit lost on me, I usually slot 3x tohit wherever I can. Especially in Invicibility on my inv tanker and Dark Nova/Bright Nova on the Kheldians. I hate missing, and when up against +3's or more that still happens more than I like.
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| 09/01/06 03:17 |
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Warron Peace
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| RE: Focus on the underestimated: ToHit |
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Definitely worth a guide. And yes, a table at the bottom for quick reference would be a good idea, IMO. Also, I read every guide posted. Never know what ppl have to say.
W.P.
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| 09/01/06 18:39 |
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Valentine
Posts: 138
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Credibility: 369 pts
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| RE: Focus on the underestimated: ToHit |
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This guide is def worth submitting as it is the sort of thing MMORPG players crave when switching from the likes of WoW to CoX and such.
But on the chance of playing Devil's Advocate I still suggest players firstly focus more on how their build "feels" to them before they start analysing it to death with this sort of math.
Oh, Hello Mr. Jurassik! Sorry about that arrow, it wasnt aimed at you. I'll just be on my way now... *flees*
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| 09/01/06 22:47 |
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