buckler: worth it? (in General)

Hi!

bucklers are not listed in the top shield section. What do you think about them? Are they are not good shields for enchanters and everybody else?

They have low DX penalties and also low Magic penalties, so for enchanter designed to be meat shields also, they are reasonably good yes

I use one, works ok for me, but you need to compare the gains to the losses to make sure it's useful enough.

ie if the Buckler isn't improved enough, the -2% magic may not be made up for by it.
Careful if your enchanter/meat shield casts spells on your other minions as the spell effects will also be reduced.

The following needs verifying as I've not had chance to make sure its correct:

Boosting your Buckler a lot may be fine but if you have lots of high armor already, the 0.1 weighting might be applied to the added PR from the other armor as well as your normal PR.
This does need checking, I haven't been back long and dont know all the rules yet :)

Anubis, may I ask you what is the level you advice for a buckler?

Sorry to take so long responding, I didn't see your reply.
I would like to give some figures but I haven't kept up with how much benefit I got at each level.

mine is at +15
Taking it off makes me lose many fights I normally win
Its purely by chance that I have the Buckler upgraded to this level as I used it for an experiment ages ago and meant to get rid of it.

I don't know what benefit a Mage/Enchanter will get other than on my own Char with my AC. The use of a ToE may make it more worthwhile or indeed less.
I have many trains of thought on it, here are some of them...

The ToE effect is applied after armor and protection.
This means the % damage reduction the ToE does is applied to a smaller level of damage by the time it works.
Adding 5 more armor points normally gives approximately 1% less damage. The damage passed to the ToE is less and the ToE will then remove less overall damage meaning 5 extra armor gives much less than 1% damage reduction overall. This wouldn't matter (other than the cost of upgrading) if it wasn't for the extra AC also raising your PR.
At some point the extra AC will not give enough benefit to make up for the increase in PR you get. This is difficult to judge when you can still hit a bit higher after adding the AC.

I don't know if I am under or over the optimal level of AC for use with a ToE.

Having more armor is a great way for me to take less damage and avoid getting caned by splashback from my own fireball.
Having the AC high enough is what gives it the edge over the -2% spell strength.
This will in many cases allow me to go an extra round which can make a big difference.
The extra armor effect needs to be high enough to balance against the 2% loss of mainly Ablative Shield and AMF in my case.

With no ToE and a Buckler 6+15, I would get (approximately) an extra 3% damage reduction from DD spells and about 4% less from other attacks on the minion wearing it.
(The following assumes a ToE gives 75% damage reduction on the main minion and 37.5% on my second minion. I don't know the true figures as things have changed since I've been away. It works as a good example though)

With a ToE equipped I get 37.5% damage reduction from it on my 2nd Minion.
This is about 1/3 so the effect of any additional AC is reduced by about 1/3 (assuming no protection, that will make it even less!).
so a 15 AC boost will give net damage reduction of approximately 2% with a ToE versus 3% without a ToE.

I also believe that with a ToE (and for Protection) adding more AC follows the law of diminishing returns but I'm too tired to prove it :)
ie you get a little less AC for each +1 you upgrade.

So to sum up some of the points,
without a ToE you are likely to see a larger benefit from a Buckler (if you haven't already got a shield).
With a ToE, you will get more effect from a Buckler on the second minion not wearing the ToE.
The more AC you add, the more your PR goes up. At some point the extra PR won't be worth the extra damage reduction. This point is reached earlier when using a ToE and is really bad on the ToE wearer..

If any of the above can be proved wrong I am happy to hear why.

minor correction:

3rd to last paragraph reads
ie you get a little less AC for each +1 you upgrade.

it should say
ie you get a little less Damage Reduction for each +1 you upgrade.

Thank you very much for answering thoroughly. I have two bucklers +14, and 4 minions team (3ET) with a ToE. I will try to compute with your message if 0, 1 or 2 bucklers are worth.

thank you again

no problem :)
I look forward to what you find.

Anubis, just a small correction, a ToE does not provide a percentage reduction.

It provides a fixed reduction based on a percentage of it's level. This damage reduction is capped at 75% of the damage received.

As for the aura, the amount of direct reduction given is reduced, but the cap isn't. With a large enough ToE, damage will be reduced on all minions by the 75% cap.

Also, as far as I am aware, damage reduction doesn't suffer from any diminishing returns. 1 AC will always reduce (on average) 0.21% damage, regardless of the amount of AC/Endurance/Protection you already have.

With no ToE and a Buckler 6+15, I would get (approximately) an extra 3% damage reduction from DD spells and about 4% less from other attacks on the minion wearing it.
(The following assumes a ToE gives 75% damage reduction on the main minion and 37.5% on my second minion. I don't know the true figures as things have changed since I've been away. It works as a good example though)
With a ToE equipped I get 37.5% damage reduction from it on my 2nd Minion.
This is about 1/3 so the effect of any additional AC is reduced by about 1/3 (assuming no protection, that will make it even less!).
so a 15 AC boost will give net damage reduction of approximately 2% with a ToE versus 3% without a ToE.

AC reduction is computed before Endurance/Protection, and each is separate from the other, therefore the level of Endurance/Protection does not affect the damage reduction AC gives. In the above example you get a 3% reduction from the AC, then you get a 75% reduction from the ToE calculated separate from this.

i.e. Without ToE and with the buckler - 100 damage becomes 97 damage
With ToE and without buckler - 100 damage becomes 25 damage
with ToE and buckler - 100 damage becomes 97 damage then 97 damage becomes 24.25.
So without ToE - buckler reduced damage 3% (100-97/100=3%)
With ToE - buckler still reduced damage 3% (25-24.25/25=3%)

I also believe that with a ToE (and for Protection) adding more AC follows the law of diminishing returns but I'm too tired to prove it :)
ie you get a little less AC for each +1 you upgrade.

As Gentleman Loser stated, the damage reduction from AC does not diminish as AC increases. Infact AC gives increasing returns (going from 0AC to 1AC means you take 99.79 damage instead of 100 - a .21% reduction, whereas going from 300AC to 301AC means you take 36.79 instead of 37 damage - a .56% reduction)

Good information though :)

As for whether the buckler is worth it - in my opinion no - if the minion doesn't have a tattoo get a BoM instead, same DX penalties, they are pretty cheap to buy, are cheaper to upgrade in the long run, and give a nice bonus to ST.

If your minion is a mage/enchanter I would personally go no shield as I try to avoid magic penalties (plus mages take a lot of damage from AMF anyway which cannot be reduced by AC).

You should also consider how high your HPs and DD are. Is the AC provided by the buckler (and therfore an increase to your HP) worth losing 2% from your DD level.

Depending on the size of your buckler and HP compared to your DD level, you might get a bigger 'bonus' from using the buckler.

But as always, it's a trade off. Higher HP, lower DD.

Thanks for your interest. The trade-off is not between HP and DD, but, between HP and AMF or EC. Complex issue...

the trade off for a buckler is between the Magic penalty and the Damage you block with it.

a [6] (+14) Buckler has 20 AC and thus blocks 4.2% damage

If I use it, I will forge it. This is the last part of the game I never tried.
With a TOE, a little bit more of HP...

still a complex issue because the role of my E are to cast EC and AMF

My bad, I was just assuming it would be used on a Mage (with the 2% penalty). For enchanters, it's 1.5% penalty, so you have to weigh up the increase to HP from the AC the buckler provides to a 1.5% penalty to thier EO level.

Low HP and Higher EO it might not be worth it, but if your Enchanter has a lot of hit points, it might. :)

Good responses, I stand corrected on the ToE being level dependent up to 75% max blocking, thanks for that

To follow up on the extra damage reduction given by adding the Buckler when using a ToE:
I was pointing out that you cannot add the damage reductions together, ie 75% ToE + 3% Buckler = 78% damage reduction which isnt right.

Sacredpeanut, thanks for your info.
Id like to try and qualify my statements.

Your description shows that a full power ToE wearer will get an extra 0.75% damage reduction by adding the Buckler.
Much less than the 3% full effect it has when you don't have a ToE.

It does have a 3% effect, but the 3% is only applied to the final 25% damage that is left, not the whole damage applied.
Adding more AC will follow a law of diminishing returns in the overall damage reduction.
This is what I use as my final measure of the Bucklers worth :)
(see better explanation below)


I corrected this line immediately after posting:
...ie you get a little less AC for each +1 you upgrade.
with this:
...ie you get a little less Damage Reduction for each +1 you upgrade.
I didn't want the first one to be analyzed as it was a mistype, sorry :)

Is there any chance you can explain this please:
"going from 0AC to 1AC means you take 99.79 damage instead of 100 - a .21% reduction, whereas going from 300AC to 301AC means you take 36.79 instead of 37 damage - a .56% reduction"

I'd like to see how you calculated this please.
The statement covers when there is no ToE and no Protection, adding AC should produce a linear increase in damage reduction in this case.


I'll try to prove the case of diminishing returns...

The higher the ToEs damage reduction, the less effect 1 AC will have on the final damage reduction figure.
So by the same tune, the higher your current damage reduction (including your current AC), the less effect each extra AC will have on the final Damage Reduction.
1 extra AC will give damage reduction 0.21% of the remaining damage.
This follows the law of diminishing returns.

Again I look forward to being proved wrong ;)

No. AC is always calculated first. 1 AC will always (ignoring the additional direct reduction it provides first of all) provide on average 0.21% damage reduction.

Each point of AC add this, no matter how much AC you have.

It has no diminishing return.

What I think you're trying to say is that as your AC grows, because of the 75% Cap, Endurance provides less protection. It doesn't. If the cap is reached, it will always reduce 75% of the damage that get's through *after* AC reduction.

Yes, you will hit the cap earlier (or I should say with a smaller level of Endurance) the more AC you have, so the direct reduction isn't subtracting as much damage as without any AC, but there is no diminshing return for this. And overall, more damage is reduced in total.

I hope this helps! :)

You are correct the increase is constant, I finally did the Maths (English spelling ;p)

When calculating only the overall damage reduction, it doesnt matter which order Protection/AC/ToE are applied.
They all affect each other in the same way,
I stated an order for easy reading earlier.

Lets call
AC*0.21 = A%
Protection = P%
ToE damage reduction % = T%

Using the basic figures doesnt immediately give you an easy way to work with the figures to find the final damage reduction.
Instead if we work in % Damage Left its easier to see.

% Damage left from AC = 100% - A%
% Damage left from protection = 100% - P%
% Damage left from ToE = 100% -T%

As % is in 1/100ths, we need to divide each one by 100 to represent their real mathematical values. At the end it is multiplied 100 to get % again.
The damage figures can be multiplied together in ANY order to get the final % Damage (TD%) applied to your minions.

TD = 100* ((100-A)/100* (100-P)/100* (100-T)/100) %

I'll do the calculations assuming the following
A (AC damage reduction) = 15%
P (Protection Damage reduction 6) = 6%
T (Toe Damage reduction) = 75%

TD = 100* (85/100* 94/100* 25/100) %
TD = 100*(0.85*0.94*0.25) %
TD = 19.975 %

Meaning for the above you will receive only 18.975% of the damage sent against you.

Now lets increase our AC to give 1% more damage reduction (for the sake of simplicity) to see how much difference it makes to the % Total Damage received:
TD = 100*(84/100* 94/100* 25/100) %
TD = 100*(0.84*0.94*0.25) %
TD = 19.74 %
giving an increase to the TD of 0.235%

Adding another 1% worth of armor)
TD = 100*(83/100* 94/100* 25/100) %
TD = 100*(0.83*0.94*0.25) %
TD = 19.505 %
giving an increase to the TD of 0.235%

I stand corrected lol
Its nice to see the proof.

excuse the typo
18.975% should be 19.975%

and the final increases should be called decreases ;p

Is there any chance you can explain this please: "going from 0AC to 1AC means you take 99.79 damage instead of 100 - a .21% reduction, whereas going from 300AC to 301AC means you take 36.79 instead of 37 damage - a .56% reduction"

Ok I'll try :)
You are correct that adding AC will decrease the amount of damage taken by a linear amount however the percentage of damage reduction increases.

For example lets take the extreme case where a minion is only a couple of AC away from complete damage reduction (not sure the exact number but lets say 476AC is 100% reduction)

At 474AC you will be taking 0.42% of the damage you would take with no AC. At 475AC you will be taking 0.21% of damage you would take. That extra one AC is providing a 50% damage reduction compared to going from say 0AC to 1AC where you are getting just 0.21% reduction (where you are going from taking 100% of damage to 99.79% of damage).

In the first case you are effectively doubling the minions HP for one AC whereas in the second case you are only "increasing" the effective HP of the minion by a small amount.

So a buckler could for example not provide enough "bonus" HP for UltimaSpock with his current AC to cover the loss from the magic penalty however if in a few months his AC has increased the extra HP might be enough to cover it.

That's a nice way to think about the extra AC :)

I think I have found why there is a benefit when using the Buckler.
The benefit is really little I have to admit wearing a +15 Buckler -
I draw a few more fights (I normally win) without the Buckler.
I did occasionally draw anyway but it happens about twice as often when not wearing the Buckler.
There is a small drop in PR from removing the Buckler but I didn't notice an increase in my rewards. It must be there but tiny.

onto the reason...
My ToE is 58% of its max size so "in many cases" I'm easily overpowered as it isn't close to its maximum.of 75% damage reduction on the second minion.
The extra AC from the Buckler is welcome on the second minion with a ToE of this size.

Assuming the Endurance scale is linear I will get approximately an extra 1.6 times my current Endurance with a full size tattoo.
Then the Buckler would make me lose magic and wouldn't make up for it by being at +15. It would need to be probably 1.6 times higher to get the same effect.
Not forgetting the PR, raising the +15 higher also raises PR
Ultimately it shouldn't be used on a Magic dealing Minion with a full size ToE unless you have something special in mind getting Massive AC.

A smaller ToE like mine or less should see a benefit on the second minion if you use a similar team setup to me.
The rise in PR makes me question how useful it is compared to using a slightly bigger ToE :)

thanks for everyones input and to UltimaSpock for raising the question.

thanks again for all these comments