Is "Shield" too powerful?

[KarinsDad]

Why is it you're so unable to grasp the concept that by ignoring attacks you increase error in you calculation?

Unable to grasp the concept?

HAHAHAHAHAHA

You're a funny guy.

Missed attacks DO NOT MATTER to Second Chance or Shield because those powers cannot come into play then. Missed attacks are non-events, just like movement or encumbrance or XP or many other game elements are non-events for Second Chance or Shield.

One has to actually get hit to use these powers, so only hits are relevant. The player cannot just randomly decide to use these powers.

Your POV here is like saying that the Turn Undead power matters when fighting Elementals. Sorry, but you are flat out wrong on this and you will not get anyone on this forum to support such a silly POV.

If you could just post ONE serious non-refutable calculation that matters to show a mathematical difference between all attacks vs. all successful attacks to support your POV, it would be great. Course, you haven't so far.

On average, Second Chance helps 50% on one single successful hit (more if one waits to use it on a critical and still uses it during the encounter), it does not help 25% on all hits. Your 25% number is just plain silly and has no point to it in the conversation. It's only important in your mind.

 

[Elric]

Unable to grasp the concept?

HAHAHAHAHAHA

You're a funny guy.

Missed attacks DO NOT MATTER to Second Chance or Shield because those powers cannot come into play then. Missed attacks are non-events, just like movement or encumbrance or XP or many other game elements are non-events for Second Chance or Shield.

One has to actually get hit to use these powers, so only hits are relevant. The player cannot just randomly decide to use these powers.

Your POV here is like saying that the Turn Undead power matters when fighting Elementals. Sorry, but you are flat out wrong on this and you will not get anyone on this forum to support such a silly POV.

If you could just post ONE serious non-refutable calculation that matters to show a mathematical difference between all attacks vs. all successful attacks to support your POV, it would be great. Course, you haven't so far.

On average, Second Chance helps 50% on one single successful hit (more if one waits to use it on a critical and still uses it during the encounter), it does not help 25% on all hits. Your 25% number is just plain silly and has no point to it in the conversation. It's only important in your mind.

I can post a calculation for him. As I mention in my previous post, doing it the way you do slightly increases the chance that Shield works. Suppose that you are hit with an average of 4 successful attacks in an encounter (with each attack hitting you 50% of the time) and that 75% of the attacks that hit you target AC/Reflex. What is the chance that Shield will work on one of them?

The unconditional chance that Shield works on a given attack is 15%. The chance that Shield works on a given attack, conditional on the attack hitting, is 30%.

If we start from n=8 attacks, each with a 50% chance of hitting, we get
Prob (Shield works)= 1- (1-0.15)^8 = 72.75% of the time.

If we start by assuming that there are 4 successful attacks, we get
Prob (Shield works)= 1-(1-0.3)^4= 75.99% of the time.

The latter calculation cannot be used as a proxy for the answer in the former calculation (as you seem to be implying it can be). The answer you think you are getting is wrong.

This occurs because the chance that Shield works is concave in the number of (edit- successful) attacks, and from there it's a consequence of Jensen's inequality.

 

[Trebor62]

While this might not apply to a invisible attacker the PC's who are being attacked can curtainly judge for themselves how easily their attacker is beating down there defenses or not. Afterall there "right there" facing the monster trying to kill them.

And why should only the DM have all the information as to how easliy or not the PC can hit the monsters? To maintain balance and realism within the game frame the information should be equal available to monster and PC. Why should monsters only be privy to all the details of the PC defenses but not the PC's of the monsters? Afterall the PC's are "Heroes" head and shoulders above oridinary people in terms of ability. Why should a lowly dumb goblin for example have a better understanding of the PC's strengths and weaknesses than the heroes do of the Goblins. If I understand your point you would reserve that information for the monsters run by the DM but deny it to the PC's as something they could not know, while it is something the DM controlling the monsters cannot help but know and be influenced by to some degree.

 

[AngryPurpleCyclops]

Unable to grasp the concept?Missed attacks DO NOT MATTER to Second Chance or Shield because those powers cannot come into play then. Missed attacks are non-events, just like movement or encumbrance or XP or many other game elements are non-events for Second Chance or Shield.

You're kind of obtuse. Because you don't actually know the chance that a character will be hit by an attack, (we've been using 50% but that's not the correct number just an estimation) but you do know the exact chance that shield is going to come into play on any attack using attacks is better than hits. Shield always affects 4 numbers out of 20 of any attack vs AC or reflex (unless the creature needs to roll a 16 or above in which case it affects less but I haven't seen a monster that needed to roll a 16 yet so I didn't factor that in.)

One has to actually get hit to use these powers, so only hits are relevant. The player cannot just randomly decide to use these powers.

Well it's pretty clear you're the master of the obvious, but we've digressed far away from the OP. The intent of this thread was to determine if shield was too powerful. We've spent a lot of time comparing it to a racial power with a similar effect. I think it's clear to virtually everyone on the thread second chance out performs shield in utility. This doesn't even factor in how your use of shield totally devastates shields utility. All these numbers are based upon the "full disclosure" method.

And if you want to talk about "funny math" I'm still waiting on you to explain how shield blocks nearly 6 hits out of 20 with your previous example.

Your POV here is like saying that the Turn Undead power matters when fighting Elementals. Sorry, but you are flat out wrong on this and you will not get anyone on this forum to support such a silly POV.

No, this is you applying the straw man logical fallacy to my argument. You're doubling up here and trying to apply the appeal to popularity logical fallacy simultaneously. If you want to "appeal to popularity" take a look at both this thread and the ones on several other rpg forums (gleemax, pen and paper, etc) the vast majority of people feel it's not over powered. On this thread you're one of only two people who have posted it's over powered and the other stopped posting.

If you could just post ONE serious non-refutable calculation that matters to show a mathematical difference between all attacks vs. all successful attacks to support your POV, it would be great. Course, you haven't so far.

actually all my posts have been serious, you just try to circumvent the reality by proposing preposterous counter arguments with horrible math based upon unsupported assumption. You don't seem to have even a rudimentary grasp of intellectual debate, logic, probability or the scientific method. Now you're switching gears and attacking me (ad hominem fallacy) instead of actually rebutting any points being made with anything other than superfluous fluff.

On average, Second Chance helps 50% on one single successful hit (more if one waits to use it on a critical and still uses it during the encounter), it does not help 25% on all hits. Your 25% number is just plain silly and has no point to it in the conversation. It's only important in your mind.

This is you projecting. You did exactly what you accuse me of doing I never implied second chance had a 25% chance of impacting each hit. YOU ACTUALLY MADE CALCULATIONS based upon shield reducing each hit by 29+%. From the get go I have stated that I was calculating the odds on any given hit. You have math on this thread that openly states shield can block more than one hit.

You're just becoming an obnoxious forum troll at this point looking to move your baseless off topic arguments into flames. The thread is supposed to be about shield being over powered. I defy you to show with real math that shield is more powerful than shield of faith (another level 2 utility power).

You rant and ramble endlessly about missed opportunity to use second chance having some meaning but I have stated a half dozen times on here why it doesn't. You can't refute that so you ignore it.

Elric has disputed your math but he is also moving very tangentially into a dissertation on probability of lower expected average damage which really isn't what this is about either.

The real question is how will shield impact the game from a play balance perspective. You've pontificated endlessly with horrible math and baseless assumptions about it's relative power being too great but you haven't shown that to be the case at all.

I tried repeatedly to explain that when you just focus on hits you're introducing more error in the calculation but you refuse to accept that. Elric's last post went to great detail to explain this to you:

I can post a calculation for him. As I mention in my previous post, doing it the way you do slightly increases the chance that Shield works. Suppose that you are hit with an average of 4 successful attacks in an encounter (with each attack hitting you 50% of the time) and that 75% of the attacks that hit you target AC/Reflex. What is the chance that Shield will work on one of them?

The unconditional chance that Shield works on a given attack is 15%. The chance that Shield works on a given attack, conditional on the attack hitting, is 30%.

If we start from n=8 attacks, each with a 50% chance of hitting, we get
Prob (Shield works)= 1- (1-0.15)^8 = 72.75% of the time.

If we start by assuming that there are 4 successful attacks, we get
Prob (Shield works)= 1-(1-0.3)^4= 75.99% of the time.

The latter calculation cannot be used as a proxy for the answer in the former calculation (as you seem to be implying it can be). The answer you think you are getting is wrong.

This occurs because the chance that Shield works is concave in the number of (edit- successful) attacks, and from there it's a consequence of Jensen's inequality.

He's obviously been in college much more recently than I have but I worked at Intel for 6 years and statistical analysis and probability were part of my every day job. I couldn't have pointed you to Jensen but I repeatedly tried to make you understand that your position was faulty. I think it goes beyond this, in that looking at the entire 20 number range also eliminates half the error created by assuming 50% hits.

These calculation still don't take into account that minions probably account for 10% of all the attacks so we should be starting from 70% and not 75% and we're still discounting the fact that second chance is much more likely to block a power with a debilitating ongoing effect.

 

[Lord Ernie]

I just don't understand why you're all so bothered by this. What's the point in even taking shield if you have no idea what defense was being attacked, or how hard the hit was. Heck, why not have the DM keep track of HP too? Should the PC's really know how close they are to death? Isn't that metagaming? </sarcasm>

I know you're joking here, but I seriously had a DM once in 3.5 who did this. He kept track of our HP, and the only way my druid could determine how wounded anyone was was to make a Heal Check DC 15 (trivial, but he had it cost me a move action), and then he'd give me a general idea ("just scratched", "on the brink of death", etc.). Anything else than that he felt was far too much metagaming.

I'm going to start playing in a 4th Campaign of his in a couple of weeks (and yes, I'm playing a Wizard)... I'm rather curious to see how it turns out. Much like I didn't usually pick save-or-die/suck spells in 3.5 with a certain DM who didn't like his bad guys to go down like that, I probably won't opt for Shield if this DM continues in his trademark style. Call me metagamey, but there's such a thing a shooting yourself in the foot.

PS: Mathematics aside, the design of the Shield Power and the overall tone in the DMG clearly seems to indicate, IMO, that the results of the attack roll and the defense under attack is known when you choose whether or not to activate it. I don't like playing "gotcha" with my players, so when I DM I announce that sort of thing all the time, myself. To each their own, of course.

 

[KarinsDad]

I can post a calculation for him. As I mention in my previous post, doing it the way you do slightly increases the chance that Shield works. Suppose that you are hit with an average of 4 successful attacks in an encounter (with each attack hitting you 50% of the time) and that 75% of the attacks that hit you target AC/Reflex. What is the chance that Shield will work on one of them?

The unconditional chance that Shield works on a given attack is 15%. The chance that Shield works on a given attack, conditional on the attack hitting, is 30%.

If we start from n=8 attacks, each with a 50% chance of hitting, we get
Prob (Shield works)= 1- (1-0.15)^8 = 72.75% of the time.

If we start by assuming that there are 4 successful attacks, we get
Prob (Shield works)= 1-(1-0.3)^4= 75.99% of the time.

The latter calculation cannot be used as a proxy for the answer in the former calculation (as you seem to be implying it can be). The answer you think you are getting is wrong.

I had a lengthy response, but ENWorld went down and lost it when I hit submit last night.

So, I will give you the Reader's Digest Condensed version.

First, I am not solving the former equation. Some other people here might want to solve for that, but I am not. I am solving for how well Shield and Second Chance protect.


Having said that, let's take a slightly different look at it. Let's have a 50% chance on average that the Wizard will get attacked on any given round for 16 rounds, a 50% chance that the attack will hit, and a 75% chance that any given attack is versus AC or Reflex.

The unconditional percentage = 7.5%

n=16 rounds,
Prob (Shield works)= 1-(1-0.075)^16 = 71.2745% of the time.

Didn't you state that the chance was 72.75%? Obviously, the number of rounds are important if there is a 50% chance to even attack the Wizard. How could you have been mistaken?


The reason your first equation is incorrect is the same reason that the third equation here is incorrect. And yes, I absolutely understand that your first equation is the default equation anyone would consider writing when doing this type of problem using normal probability (and why APC is absolutely convinced I am wrong on this, we are comfortable with what is familiar).

The number of rounds do not matter. The misses do not matter. The only thing that matters is the hits when calculating this. Rounds (or attacks) which do not involve a hit do not do damage and are not a consideration when figuring out the math. They are non-events. We are only concerned with how well Shield protects. Our set is not a superset of everything, it is a set of when damage occurs.

But, I am willing to admit that I make mistakes late at night. If you can explain why your first equation must be correct, but my third equation is incorrect, I am willing to listen.

Think carefully about it. While you are at it, make sure that the 20% (or 40%) can be multiplied by the 75% inside the equation. Just because it works for n=1 does not necessarily mean that it is correct.


For 4 hits and 4 misses in an encounter, the equation is:

1-((1-0.30)^4 * (1-0)^4))

which reduces to your second equation.

For 4 hits and 10 misses in an encounter, the equation is:

1-((1-0.30)^4 * (1-0)^10))

which also reduces to your second equation.

Shield protects exactly the same in these two encounters, even though the number of attacks are different. Food for thought. I also used "only when hit" when calculating Second Chance. So, since you claim that I upped the odds slightly for Shield, I also must have done that for Second Chance.


You started your word problem here with "Suppose that you are hit with an average of 4 successful attacks in an encounter". That is not the word problem your first equation solves.

Your first equation solves the word problem: "Suppose that you are attacked with 8 attacks in an encounter".

The problem sets are slightly different.

 

[Elric]

I had a lengthy response, but ENWorld went down and lost it when I hit submit last night.

So, I will give you the Reader's Digest Condensed version.

First, I am not solving the former equation. Some other people here might want to solve for that, but I am not. I am solving for how well Shield and Second Chance protect.

Having said that, let's take a slightly different look at it. Let's have a 50% chance on average that the Wizard will get attacked on any given round for 16 rounds, a 50% chance that the attack will hit, and a 75% chance that any given attack is versus AC or Reflex.

The unconditional percentage = 7.5%

n=16 rounds,
Prob (Shield works)= 1-(1-0.075)^16 = 71.2745% of the time.

Didn't you state that the chance was 72.75%? Obviously, the number of rounds are important if there is a 50% chance to even attack the Wizard. How could you have been mistaken?

Indeed, I’ve been quite up front from the beginning that I’m setting the number of attacks constant as a simplification. As I have mentioned repeatedly, thinking about an optimal use of Second Chance (in terms of average damage blocked) requires a simplifying assumption. One could, I suppose, think of the number of rounds as known constant and the chance a character would be attacked per round as another known constant, and solve from there for optimal strategies for Second Chance use as a function of the number of rounds, but I haven’t done that.

Changing from 8 rounds at 1 attack/round to 16 rounds at a 50% of an attack per round changes the probability distribution over the number of successful hits (as you can see, in the former case it’s not possible to get successfully hit 9 times, but this is possibly in the latter case), even though the average number stays the same. Changing to 32 rounds at a 25% chance of an attack per round would change the odds as well, though the average number of attacks would be the same in each case.

As I said in a previous post, which addressed this issue quite directly:

Indeed, the number of successful attacks is the metric that directly matters. What I am doing is generating a probability distribution of the number of successful attacks through a hit probability and a set number of attacks. Now, you’ve both taken issue with my assuming a set number of attacks, which could in theory be changed as well at the cost of much more complication.

By looking at successful hits directly without any probability distribution on it, you have made a more restrictive assumption than what I am assuming—essentially, you have not only assumed the number of attacks, but you have also assumed that the results of those attacks will be the average number of successful hits.

If I assumed a set number of successful hits, I couldn’t evaluate the tradeoff of not using Second Chance now on a regular hit, which lessens the chance that you’ll get to use it at all, but raises the chance you’ll get to use it on a critical. The way you do it also increases the chance Shield gets used at all.

The reason your first equation is incorrect is the same reason that the third equation here is incorrect. And yes, I absolutely understand that your first equation is the default equation anyone would consider writing when doing this type of problem using normal probability (and why APC is absolutely convinced I am wrong on this, we are comfortable with what is familiar).

The number of rounds do not matter. The misses do not matter. The only thing that matters is the hits when calculating this. Rounds (or attacks) which do not involve a hit do not do damage and are not a consideration when figuring out the math. They are non-events. We are only concerned with how well Shield protects. Our set is not a superset of everything, it is a set of when damage occurs.

But, I am willing to admit that I make mistakes late at night. If you can explain why your first equation must be correct, but my third equation is incorrect, I am willing to listen.

It’s not that my first equation must be in a deep and abiding sense correct. It’s that it involves fewer simplifying assumptions. We could do this calculation at any level of simplification desired. For example, assuming a distribution of the number of rounds and a distribution of the number of attacks on a given round (round 1, round 2, etc.) would generate its own probability distribution for the number of successful attacks, would be less simplified still. I wouldn't want to try doing it, but it's theoretically possible.

Think carefully about it. While you are at it, make sure that the 20% (or 40%) can be multiplied by the 75% inside the equation. Just because it works for n=1 does not necessarily mean that it is correct.

This requires the assumption that each attack has a set and independent percentage chance to target Reflex/AC in every encounter. As I indicated above in a response to APC, this is only an approximation to a varied set of encounters each with their own separate independent chance of an attack targeting AC/Reflex, which averages out over those encounters to 75% (and again, the approximation works slightly to Shield’s favor).

For 4 hits and 4 misses in an encounter, the equation is:

1-((1-0.30)^4 * (1-0)^4))

which reduces to your second equation.

For 4 hits and 10 misses in an encounter, the equation is:

1-((1-0.30)^4 * (1-0)^10))

which also reduces to your second equation.

Shield protects exactly the same in these two encounters, even though the number of attacks are different. Food for thought. I also used "only when hit" when calculating Second Chance. So, since you claim that I upped the odds slightly for Shield, I also must have done that for Second Chance.

Indeed, you will change the odds for Shield and Second Chance slightly (and in their favor) with your assumptions. However, the effect is going to be much larger for Shield if you are considering a “use it at the first opportunity” strategy for Second Chance. The reason, as I’ve indicated before, is being able to use Shield is much more dependent on being attacked by a decent number of attacks than Second Chance is.

 

[KarinsDad]

Indeed, I’ve been quite up front from the beginning that I’m setting the number of attacks constant as a simplification.

Precisely. But, it is not the only simplification that can be done.

It’s not that my first equation must be in a deep and abiding sense correct. It’s that it involves fewer simplifying assumptions.

Err, not really. It has the same number of assumptions as using "when one is hit".

Indeed, you will change the odds for Shield and Second Chance slightly (and in their favor) with your assumptions. However, the effect is going to be much larger for Shield if you are considering a “use it at the first opportunity” strategy for Second Chance. The reason, as I’ve indicated before, is being able to use Shield is much more dependent on being attacked by a decent number of attacks than Second Chance is.

The percentage change for Shield was approximately 3% for 4 hits.

I'd like to see the two different equations for Second Chance (without saving it for a crit) that illustrate that the change is a lot less than 3% for 4 hits.


Btw, this discussion boils down to one thing: how much does Shield protect?

Using your equations for the first time Shield is used:

1-(1-0.15)^2 = 27.72%
1-(1-0.3)^1 = 30%

If the Wizard gets hit in an encounter, how good is Shield going to protect him?

The answer really is not 27.72%. It's 30%. 3 out of every 10 first hits in an encounter will be stopped.

The limitations that you placed on your problem set force your answer to this question to be slightly low. Mine is not high, it's precisely accurate. Yours is low and understandably so.

Or, are you really claiming that Shield will stop the attack 27.72% of the time?

 

[Joker]

It's like Shield is the new Mind Blank.

 

[Elric]

Err, not really. It has the same number of assumptions as using "when one is hit".

As I have indicated many times before, assuming a set number of successful hits is a stronger form of assuming a set number of attacks. It is essentially assuming (in this case with 50% hit probability) a set number of attacks, exactly half of which will be hits and half of which will be misses.

The percentage change for Shield was approximately 3% for 4 hits.

I'd like to see the two different equations for Second Chance (without saving it for a crit) that illustrate that the change is a lot less than 3% for 4 hits.

Using your method, 4 hits= 100% chance you get to use Second Chance. Using my method, 8 attacks at a 50% chance to hit= 1- (1-0.5)^8= 99.6% chance that Second Chance can be used. Done.

Using your equations for the first time Shield is used:

1-(1-0.15)^2 = 27.72%
1-(1-0.3)^1 = 30%

If the Wizard gets hit in an encounter, how good is Shield going to protect him?

If you notice, this was never the question I was answering. As my very first post on the subject indicated, I'm working with average damage prevented in an encounter.

We're only considering "attacks" something that targets Reflex and AC here, and expected damage prevented (==number of attacks blocked here) is the metric for effectiveness.