Is "Shield" too powerful?

[Old Gumphrey]

Shield might have gotten hit with the big nerf bat, but Wizards did not.

Now that Int adds to AC for them and they can be a Staff Wizard and they can easily wear Leather armor without screwing up their spells, etc., Wizards can easily have one of the highest AC and Reflexes in the game system. Throw them in the back behind cover and they are really hard to hit.

I've got 2 words for that setup: Bugbear Strangler.

 

[KarinsDad]

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.

Not in the least. It assumes nothing of the sort.

It matters not if there if 5 attacks or 10 attacks. If 4 of them hit, how good is Shield? If 2 of them hit, how good is Shield?

Conversely, if 2 of them hit, how good is Second Chance? How much damage does it stop?

You are really getting hung up on standard probability and forcing the question to relate to number of attacks.

That is one approach, but not necessarily the best one when considering game mechanics which only occur on a to hit.

If we were talking a +1 to AC game mechanic, then it affects every single attack against AC. There, it is important to consider attacks because the mechanic affects attacks.

Second Chance and Shield do not affect the initial attack roll. They come into play AFTER an attack is determine. It's a different type of problem.

Shoe horning it into standard attack equations is not quite valid.

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.

And this illustrates two answers to two different questions.

Just like the other two equations do.


I'll get back to what is important for these two powers (and you stated that it was the important metric yourself). What happens when one gets hit and one of these powers can occur. How does it change the damage?

It matters not what happens if the attack misses. That's outside the domain of the scope of these two powers. Instead of using the Set, you are using a Superset.

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.

And, that's fine. You answered a different question.

But at the same time, I did not claim your math was incorrect for what you wanted to solve, you claimed that my math was incorrect for what I wanted to solve.

Going back to this last example:

Miss and Miss = 0%
Miss and Hit = 30%
Hit and Miss = 30%
Hit and Hit = 51%

For me, what is important is that Shield is effective in that encounter 30% of the time on one hit and 51% of the time on two hits. That's what is really important to a player.

Not that out of two attacks, Shield is effective 27.72% of the time. Although related to the important question, it misses the mark slightly.

 

[Doctor Proctor]

Despite all of this math, I have yet to see an explanation of why Shield and Second Chance should even be similar in power.

 

[Elric]

That is one approach, but not necessarily the best one when considering game mechanics which only occur on a to hit.

Second Chance and Shield do not affect the initial attack roll. They come into play AFTER an attack is determine. It's a different type of problem.

Shoe horning it into standard attack equations is not quite valid.

You asked for one calculation; I showed you one calculation. You asked for a second calculation; I showed you a second calculation.

Now, let me pose a question to you: Assuming that Second Chance is reserved for critical hits until some time late in the encounter, how does this change how you evaluate it, mathematically?

 

[keterys]

Despite all of this math, I have yet to see an explanation of why Shield and Second Chance should even be similar in power.

Very unclear why it matters in the slightest. As I read it, the DMG advises DMs to let the player know when his Shield ability will be useful. That does not appear to be breaking anything. Not sure where the rest of the discussion is really going

Hopefully Arcane Power next month will give the wizard more valid choices for a utility power, since the other choices are pretty lackluster. Fwiw, try putting Ethereal Stride on there as well and see if any (non-Eladrin) Wizards use it instead of Shield.

 

[AngryPurpleCyclops]

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

Because probability is not linear it's quite possible that in 2 separate encounters a wizard faced with 14 ATT in both might be hit 10 times and 4 times. Your methodology doesn't account for the fact that random distribution favors the utility of second chance.

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

actually it boils down to you arguing that shield is over powered and comparing it endlessly to second chance which isn't a level 2 power.

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

This is another over simplification and wrong. You're not accounting for minions, a more threatening attack on the battlefield that might cause you to reserve it, the actual hit values, or the added weight that should be attributed to non AC attacks. That said assuming that shield will block 30% of all 1st hits doesn't offend me, nor tilt the scales in it's favor, I'm wondering how you make the leap to it being overpowered.

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?

There are numerous factors not being accounted for in your math. Your number IS NOT exactly correct and no number could be EXACTLY correct with out a very complex environmental model (even then no one reasonable would attribute exact to the model). The only number that can be exactly correct is that shield will be able to block 20% of all attacks vs AC or reflex. Not hits, attacks. We only know the range with 100% accuracy on ATT's and we do not know it on hits.

Not in the least. It assumes nothing of the sort.

It matters not if there if 5 attacks or 10 attacks. If 4 of them hit, how good is Shield? If 2 of them hit, how good is Shield?

Conversely, if 2 of them hit, how good is Second Chance? How much damage does it stop?

You are really getting hung up on standard probability and forcing the question to relate to number of attacks.

You're really missing the point that because of random distribution sometimes either power will face a higher percentage of hits for x number of attacks and conversely sometimes there will be a lower percentage. This works to shields detriment as the variability dramatically increases the number of encounters where shield will remain unusable.

That is one approach, but not necessarily the best one when considering game mechanics which only occur on a to hit.

If we were talking a +1 to AC game mechanic, then it affects every single attack against AC. There, it is important to consider attacks because the mechanic affects attacks.

and yet you steadfastly ignore the comparison to shield of faith. Please explain how shield is over powered and shield of faith is not?

Second Chance and Shield do not affect the initial attack roll. They come into play AFTER an attack is determine. It's a different type of problem.

Shoe horning it into standard attack equations is not quite valid.

Ignoring the problems with your model is what's not valid. The question is and always has been is shield overpowered. Ignoring attacks and concentrating on hits increases shields power relatively to second chance.

I'll get back to what is important for these two powers (and you stated that it was the important metric yourself). What happens when one gets hit and one of these powers can occur. How does it change the damage?

It matters not what happens if the attack misses. That's outside the domain of the scope of these two powers. Instead of using the Set, you are using a Superset.

Repeating yourself endlessly doesn't make your argument valid it's just a tactic people with no case use to deflect from the real issue. When comparing how effective shield is to second chance you MUST try to account for the varied distribution of hits from encounter to encounter. Especially if you're trying to decide which has the highest average damage reduction. I'm not too interested in highest average damage reduction though it's certainly a factor in determining which is more powerful. What really matters is which power will save your bacon more often. If you block some damage in an encounter that doesn't matter it's somewhat less important.

And, that's fine. You answered a different question.

what question have you answered?

For me, what is important is that Shield is effective in that encounter 30% of the time on one hit and 51% of the time on two hits. That's what is really important to a player.

based upon blocking 40% of all hits 75% of the time? It's baffling to me that you can't see both the 75% and the 40% are flawed. Is it your experience that every time the dm rolls an 11 he hits and every time he rolls a 10 he misses? If your answer is no, then you're agreeing that 50% hits is an approximation which by definition introduces some error to the math. Using 20% of attacks avoids this error. When using the distribution formula's elric has been using the error created by this assumption is magnified exponentially.

Very unclear why it matters in the slightest. As I read it, the DMG advises DMs to let the player know when his Shield ability will be useful. That does not appear to be breaking anything. Not sure where the rest of the discussion is really going

I made this point several times. The thread is asking if shield is over powered and we're 100+ posts in talking about second chance. There's not even a significant basis for comparing them as one is a racial power and the other is a level two utility power. I repeatedly asked KD to compare shields defensive value to Shield of Faith (another level 2 utility that prevents damage so MUCH MORE RELEVANT) but he's really just interested in steam rolling the thread down his tangential path.

 

[Doctor Proctor]

I made this point several times. The thread is asking if shield is over powered and we're 100+ posts in talking about second chance. There's not even a significant basis for comparing them as one is a racial power and the other is a level two utility power. I repeatedly asked KD to compare shields defensive value to Shield of Faith (another level 2 utility that prevents damage so MUCH MORE RELEVANT) but he's really just interested in steam rolling the thread down his tangential path.

Yeah, but there's 3 people in this thread, only one of whom is KD, that are throwing around giant posts talking about all the Second Chance vs Shield math.

Also, if you want another power to compare it to, how about Shielded Sides? It's also a level 2 Utility, but it only grants +2 AC and REF. However, it's an on-demand power that you can use before you get in the ****, and more importantly, it cancels any CA bonuses. For a Fighter this is an AWESOME ability because then I can go and attract 4 or 5 with an AoE burst power, drop Shielded Sides, and then know that I won't be granting +2's to every guy surrounding me.

 

[AngryPurpleCyclops]

Yeah, but there's 3 people in this thread, only one of whom is KD, that are throwing around giant posts talking about all the Second Chance vs Shield math.

Also, if you want another power to compare it to, how about Shielded Sides? It's also a level 2 Utility, but it only grants +2 AC and REF. However, it's an on-demand power that you can use before you get in the ****, and more importantly, it cancels any CA bonuses. For a Fighter this is an AWESOME ability because then I can go and attract 4 or 5 with an AoE burst power, drop Shielded Sides, and then know that I won't be granting +2's to every guy surrounding me.

I agree, I went down the path of math with KD, I thought we could mathematically demonstrate that shield isn't that powerful. The comparisons to second chance are kind of a boondoggle since even if someone convinces him that shield is roughly equivalent to second chance it's not a level 2 utility. I brought up shield of faith as a counter point, first because it is a level 2 utility and second because it's a damage reducer that works more effectively than shield.

I assume shielded sides is from the martial powers book. Sadly it appears from everything I have seen that martial power and the PHB2 are both going to engage in power creep. It's kind of sad that WotC with all it's money and experience in the industry can't offer us different classes/feats/powers without making the older ones obsolete. I think it's a strategic marketing ploy to make the new books all more "attractive" by putting progressively more powerful spells in each book thus making them more important to power gamers. It's really a shame that this is at the expense of balance. With that in mind I would rather stick to the discussion of powers from the phb when trying to discern if shield is too powerful.

 

[KarinsDad]

I agree, I went down the path of math with KD, I thought we could mathematically demonstrate that shield isn't that powerful. The comparisons to second chance are kind of a boondoggle since even if someone convinces him that shield is roughly equivalent to second chance it's not a level 2 utility. I brought up shield of faith as a counter point, first because it is a level 2 utility and second because it's a damage reducer that works more effectively than shield.

I won't get into a long discussion concerning Shield vs. Shield of Faith.

It will just be 100 more posts.

Shield typically would have slightly more utility if one considers the 2E adjudication above of Shield and one focuses on number of attacks stopped per day. Shield of Faith has more utility in the sense that it protects multiple PCs.

Assuming the Wizard gets hit 3 or more times per encounter and there are 5 encounters per day, Shield is solidly more potent. It will stop 5 encounters * (1-(1-0.3)^3) = 3.285 or roughly 3 hits per day. Shield of Faith, even assuming that it gets cast in round one (which it usually only is if fighting some BBEG like a Dragon) will stop 10% * 5 PCs * 8 attacks against each PC per encounter * 56% AC attacks in the MM = 2.24 hits per day. I'm assuming about 10 rounds per encounter here with some PCs getting attacked 10 or so times and other PCs in the back not getting attacked as often.

At 2 hits per encounter against the Wizard, they are closer. 2.55 vs. 2.24.

Now, one could drop the 56% here assuming that the Cleric only uses it in big vs. AC fights. In that case, Shield of Faith would stop 4 hits per day (assuming every single attack is vs. AC).

In that case, the Wizard would need to be attacked 4.5 times per encounter for Shield to stop 4 hits per day like Shield of Faith.

But, these comparisions are off a bit. The Shield number of hits per day is a little low due to the fact that Shield can stop more than one hit in a single round multiple times per day. And the (latter) Shield of Faith number of hits per day is high because it will not always cast in round one and not all attacks against the PCs will be vs. AC every time. The real number is probably somewhere around 3 hits per day, somewhere between the two extremes.

Shield probably has a slight edge here except on BBEG days against creatures that do nothing but attack AC.

Shield of Faith is good against minion fights, but that's a substandard use of it.

They are probably comparable. Shield has a slight edge if the PC Wizard gets hit 3 or more times per encounter.

But, I won't go another 100 posts with you on this APC.

 

[AngryPurpleCyclops]

I won't get into a long discussion concerning Shield vs. Shield of Faith.

It will just be 100 more posts.

More drivel and only accurate because you're intent on stilting the playing field with EVERY assumption.

Shield typically would have slightly more utility if one considers the 2E adjudication above of Shield and one focuses on number of attacks stopped per day. Shield of Faith has more utility in the sense that it protects multiple PCs.

You're completely devoid of any sense of propriety.

Assuming the Wizard gets hit 3 or more times per encounter and there are 5 encounters per day, Shield is solidly more potent.

I don't think we've ever had 5 encounters in a day. This is only accurate if a large percentage of your encounters are easy. 5 is certainly not average. Many days might have 1-2 encounters. On an easy encounter not only is your figure for number of hits too high, you're still using "average" hits per encounter as a fixed number which artificially favors shield yet again. On an easy encounter shield doesn't matter and you wouldn't use shield of faith either.

It will stop 5 encounters * (1-(1-0.3)^3) = 3.285 or roughly 3 hits per day. Shield of Faith, even assuming that it gets cast in round one (which it usually only is if fighting some BBEG like a Dragon) will stop 10% * 5 PCs * 8 attacks against each PC per encounter * 56% AC attacks in the MM = 2.24 hits per day. I'm assuming about 10 rounds per encounter here with some PCs getting attacked 10 or so times and other PCs in the back not getting attacked as often.

Lets count the errors shall we. First, you MUST use attacks and not hits or else you favor shield. Easy encounters don't even matter so blocking an attack in a combat where you got hit 1-3 times likely has almost zero impact on pc survival. You assume that shield of faith will be employed in an encounter lasting 10 rounds and once again take the 3 hits number. You also imply that the bad guys only get 40 attacks in 10 rounds. This is idioticly low or else you've simply never played the game. Do you employ your dailies in easy encounters?

At 2 hits per encounter against the Wizard, they are closer. 2.55 vs. 2.24.

even given your ridiculously stilted assumptions EVERY one of which favors shield some of them massively, this is the best you came up with to support the words "solidly more potent"? You have no interest in the truth or finding a mathematically correct answer to a problem.

Now, one could drop the 56% here assuming that the Cleric only uses it in big vs. AC fights. In that case, Shield of Faith would stop 4 hits per day (assuming every single attack is vs. AC).

In that case, the Wizard would need to be attacked 4.5 times per encounter for Shield to stop 4 hits per day like Shield of Faith.

Of course the party is going to be attacked at least 10-12 times each in an encounter where you're deploying this daily.

But, these comparisions are off a bit. The Shield number of hits per day is a little low due to the fact that Shield can stop more than one hit in a single round multiple times per day.

I'm beginning to think you have a learning disorder. The shield number is obscenely high because you based it on 5 encounters per day EVERY day. I used google to find threads on this topic on 4 different forums. The vast consensus of players put the high end of encounters per day at 4 unless you're facing lots of easy encounters. This means that your assumption of 5 encounters per game day not only is 200% above average, it totally ignores that the number isn't constant and only in the major battles does it even matter which spell out performs. As I stated above easy encounters simply don't matter for the real utility of this spell, because no one gets killed by easy encounters and we're supposed to be figuring out if shield is over powered. Overpowered really is only relevant in how shield or shield of faith changes the outcomes of encounters.

And the (latter) Shield of Faith number of hits per day is high because it will not always cast in round one and not all attacks against the PCs will be vs. AC every time. The real number is probably somewhere around 3 hits per day, somewhere between the two extremes.

In a major encounter the pc's might sometimes field 100+ attacks. 60-70 is a pretty good number to use. If you assume that the cleric reserves this spell for when most of the creatures are AC hitters we can knock this down by 10-25% at most not 44% as you would like. Even if you use only 50 attacks vs AC the number blocked is 5 attacks per day. If there were only two encounters on that day, shield can block at most 2 attacks (slightly more if you want to factor in the next round bonus which is about a 5-10% chance per use) This means that even if you take what I would consider the low end of shield of faith utility it's possible it outperformed shield by 250%. I've certainly been in combats where shield of faith blocked 8-10 or possibly more attacks.

Shield probably has a slight edge here except on BBEG days against creatures that do nothing but attack AC.

only in the deluded fantasy land of your mind.

Shield of Faith is good against minion fights, but that's a substandard use of it.

as it is a substandard use of shield.

They are probably comparable. Shield has a slight edge if the PC Wizard gets hit 3 or more times per encounter.

Only if we accept your assumptions as realistic and they're simply not. your math is bad and your understanding of distributed probability is nonexistent. You simply can't assume 5 encounters every day and x number of hits every encounter.

But, I won't go another 100 posts with you on this APC.

blah blah blah, it's your ridiculous assertions and almost obsessive off topic tangents that drove this bus to the crazy place it wound up. I have to resign myself that you don't really care what the right answer is to a question you're totally interested in "winning" even if you have to lie, cheat and steal to make that happen.