Is "Shield" too powerful?

[KarinsDad]

Well, I can calculate it, I just won't because you're basing it on something entirely different than the reality of the game. Kind of like the gamblers fallacy that something is "due" because the opposite has happened X number of times in the past. My math covers ALL possibilities.

1st, shield only works on 20% of attacks and only if those attacks are in the 73% of AC/Reflex attacks. This is EXACTLY 14.6% chance that each time a wizard is attacked shield can be of use.

2nd the halfling power works on ANY attack but only changes the outcome about 50% of the time. This is roughly a 25% chance that each time the wizard is attacked the reroll power can help. PLUS the halfling attack is 95% likely to remove a crit. AND as an additional bonus (pretty hard to compute the exact math number) it can block attacks that are vs will and fort which are vastly more likely to have an additional effect than attacks vs AC.

Ok, let's use your numbers 14.6% for Shield.

25% for Second Wind.

Let's use the case that the Wizard gets hit.

Since he only gets hit 50% of the time of all attacks (using your math here), his chance of stopping an attack is 29.2% for Shield and 50% for Second Wind (the same numbers I posted earlier).

He has to get attacked first to even use the powers. Getting missed does not do anything for these powers.

So, let's take DM adjudication 2E above where the DM tells the player exactly when Shield works and exactly when it does not.

Let's say that the Wizard gets hit 1 time in an encounter.

If he uses Second Wind, he takes (on average) 50% of the damage of the hit or 50% damage.

If he uses Shield, his odds of getting hit are:

70.8% (100% - 29.2%, Shield did not work because it was a Will attack, a Fort attack, or a AC/Reflex attack roll that Shield would not stop) of the damage.

So, do you agree that with DM adjudication 2E, for a single successful hit in a round, Second Wind (50% of the damage) protects better than Shield (70.8% of the damage)?

That's the exact same ratio as your numbers (25% of not getting hit vs. 14.6% of not getting hit), it just ignores the silliness of talking about all attacks. It's really 50% vs. 29.2% of the first successful attack since the attack has to hit in order for Second Wind or Shield to work at all.


But, what if it is two successful attacks hit (in different rounds) in an entire encounter instead of one (this is where your math stops)?


If he uses Second Wind, he takes 50% of the damage of the first hit and 100% of the damage of the second hit, or 150% damage.

If he uses Shield, his odds of getting hit both times is 70.8% first hit * 70.8% second hit = 50.1264% * 200% of the damage. His odds of only getting hit once is 49.8736% * 100% of the damage.

Or, 50.1264% * 200% + 49.8736% * 100% = 150.1264% of the damage.

For all intents and purposes, TWO successful hits in an encounter averages virtually the same damage with Second Wind and Shield. And, this does not even take into account the bonus Shield has with lasting to the end of the Wizard's next turn (note: I used the example of hits on two separate rounds above).


What about 3 successful attacks in the same encounter?

Second Wind does 250% damage (50% + 100% + 100%).

Shield does 70.8% first hits * 70.8% second hits * 70.8% third hits = 35.4894912% * 300% + 64.5105088% * 200% = 235.4894912% of the damage.


With one successful attack in an encounter, Second Wind works better (as you keep claiming).

With two successful attacks in an encounter, Shield has a very slight edge (since one or more AC/Reflex attack can occur in the same round, lasting until the end of the next turn edges this towards Shield, but only ever so slightly).

With three or more successful attacks in an encounter, Shield wins.


The reason this works is because if Shield does not work (with the 2E adjudication) on an earlier successful attack, the Wizard still has it as an option for a future successful attack in the same encounter until it does work.


This is using YOUR percentages (which also happened to be mine in an earlier post).


Are you starting to understand now how your numbers were limited to ONE and only one attack in an entire encounter? Your numbers were great for that. But, your numbers ignored the fact that if Shield cannot be used, then it is still available for use later in the encounter.

One has to look at the bigger picture.


And to be honest, 2E is starting to sound reasonable to me now that I have run the math for it for multiple successful attacks.

But, 2E Shield is better in the long run than Second Wind unless your Wizard averages getting hit by 1 or fewer successful attacks per encounter. I really doubt that happens in most games.

Note: I do not discount the fact that Fort and Will attacks have additional effects. However, Reflex attacks also often have additional effects such as ongoing damage, so Reflex attacks cannot totally be discounted either.

 

[Sunglare]

Screw all this math, the DM shouldn't be keeping tracking of players defence scores anyways. THose are there for the player to run not the DM. THe DM should be calling out what he got on the roll after he applies the modifiers. This is a game, it's okay to call out numbers. If the DM is trying to hide all mechanical aspects of the game then the group might as well be LARPing

It's not that hard (figure a level 2 Wizard with 18 INT)

DM: The bugbear approachs you and swings his maul at you. "Does AC 17 hit you?
Wizard: No, I throw up my shield just in time to cause the maul to ricochet off it.

So potentionally the wizard could have a AC that still isn't even close to the Paladin's for one round. If the wizard goes right after the bugbear then he's screwed. Lasting until the end of the wizards next turn is really only beneficial if the wizard just went right before the attacker that caused him to use it.

As I see it, shield got hit with a big nerf bat and I have no problems with it as is. There is a couple times the wizard in the game I'm running could of really used expedious retreat.

 

[KarinsDad]

As I see it, shield got hit with a big nerf bat and I have no problems with it as is.

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.

One reason is that one can start a Wizard out with a 20 Int because Wizards really do not have any MAD.

I ran a first level Human Int 20 Staff Wizard with Leather Armor and AC 18, AC 20 with cover, AC 24 with cover and Shield spell. He rarely got touched all the way to 7th level (when we stopped that campaign).

 

[Elric]

Ok, let's use your numbers 14.6% for Shield.

25% for Second Wind...

This is a much better calculation. The biggest thing you're missing compared to my numbers above is the fact that Second Chance can be saved for critical hits.

Also, I find that number of attacks is a more accurate metric than the number of successful hits (looking back at my calculation, one thing I'd change is that I'd simply assume 0.73 of attacks target AC/Reflex, rather than adjusting the number of attacks, n, directly- this would slightly weaken Shield). Due to the ability to save Second Chance for critical hits, it gets more powerful as the number of attacks increases, above and beyond the benefit from the chance that you'll get to activate it because you're hit at least once.

 

[AngryPurpleCyclops]

Let's use the case that the Wizard gets hit.

This is problematic in that you're instantly discounting all the combats where shield never has a chance to be used.

Since he only gets hit 50% of the time of all attacks (using your math here)

not my math, just a rough number that I used to demonstrate the other calculations. In most combats I have seen, the monsters usually need to roll about a 8-12 in order to hit the party with the vast majority of attacks. 50% seemed like a decent "estimate" to base the rest of the math on. Feel free to point to a flaw in this assumption but try and back it up with fact if you do.

his chance of stopping an attack is 29.2% for Shield and 50% for Second Wind (the same numbers I posted earlier).

Probably should have stopped right there.

He has to get attacked first to even use the powers. Getting missed does not do anything for these powers.

So, let's take DM adjudication 2E above where the DM tells the player exactly when Shield works and exactly when it does not.

Let's say that the Wizard gets hit 1 time in an encounter.

well that's an awful assumption and pretty much ELIMINATES the need for either power.

If he uses Second Wind, he takes (on average) 50% of the damage of the hit or 50% damage.

If he uses Shield, his odds of getting hit are:

70.8% (100% - 29.2%, Shield did not work because it was a Will attack, a Fort attack, or a AC/Reflex attack roll that Shield would not stop) of the damage.

So, do you agree that with DM adjudication 2E, for a single successful hit in a round, Second Wind (50% of the damage) protects better than Shield (70.8% of the damage)?

It's second chance, not second wind and yes I agree that if pc's were hit only once in an encounter second chance has a better chance of being useful.

That's the exact same ratio as your numbers (25% of not getting hit vs. 14.6% of not getting hit), it just ignores the silliness of talking about all attacks. It's really 50% vs. 29.2% of the first successful attack since the attack has to hit in order for Second Wind or Shield to work at all.

The massive advantage of talking about all attacks is because it erases part of the error created by guessing at the hit number and also partially makes up for the fact that shield might be forced to block a relatively minor attack (in the 73% of AC/Reflex attacks you are counting ALL but 1 of the minions for example, if you assume you won't block a minion attack with shield nor second chance, then the math moves even more heavily towards second chance) while second chance might stop the devastating daily power. Talking about all attacks also takes into account that in many encounters shield simply never gets used. Second chance is probably 25-35% more likely to be used in any given encounter.

But, what if it is two successful attacks hit (in different rounds) in an entire encounter instead of one (this is where your math stops)?

No, my math specifically talks about the math on any given attack. This means the math is the same on the first attack as it is on the second or tenth and only changes once the power is expended.

If he uses Second Wind, he takes 50% of the damage of the first hit and 100% of the damage of the second hit, or 150% damage.

If he uses Shield, his odds of getting hit both times is 70.8% first hit * 70.8% second hit = 50.1264% * 200% of the damage. His odds of only getting hit once is 49.8736% * 100% of the damage.

Still second chance not second wind. This is more horrible math and anecdotal evidence. First if you assume the combat is 10 rounds long and then assume that the characters each get hit twice then the chance that the hits are "back to back" is about 20% so in 80% of the situations your math is flawed.

The chance that shield will affect an attack on the round of "sustained shielding" is exactly 14.6% per attack. This is the only number that matters. If there is no attack there is no added benefit. If the attack already missed, no added benefit, if the attack was against fort, no added benefit, if the attack hits by 5 no added benefit. We're trying to determine how much benefit is accrued by the player using the power.

Or, 50.1264% * 200% + 49.8736% * 100% = 150.1264% of the damage.

it's difficult to even understand how you have come to these conclusions. OK, I just went back and studied your post more carefully. I think what you are trying to say is that shield will eventually get deployed. The 50% chance of second chance blocking the damage is expended first time out. I agree. Point taken and while this does change things to some degree not at all in the manner you ramble about in your pseudo math. Please also note that given the "guess factor" you want to apply, shield is also expended the first time out, so when you calculate the usefulness of shield under your system there is NO added benefit gained for subsequent attacks.

For all intents and purposes, TWO successful hits in an encounter averages virtually the same damage with Second Wind and Shield. And, this does not even take into account the bonus Shield has with lasting to the end of the Wizard's next turn (note: I used the example of hits on two separate rounds above).

No, you're quite mistaken. After the powers were expended all subsequent hits are exactly equivalent. The number of hits increases the chance that shield will be useful but it also increases the utility of second chance.

What about 3 successful attacks in the same encounter?

Second Wind does 250% damage (50% + 100% + 100%).

Shield does 70.8% first hits * 70.8% second hits * 70.8% third hits = 35.4894912% * 300% + 64.5105088% * 200% = 235.4894912% of the damage.

If only either power worked like this you would be correct. By extension your math says that if you're hit 10 times in an encounter shield would block 2.92 of the attacks and second chance would block .5, a step further and we see that in 20 hits shield has blocked 5.84 of them and second chance has still blocked .5. Do you see a problem with this?

With one successful attack in an encounter, Second Wind works better (as you keep claiming).

With two successful attacks in an encounter, Shield has a very slight edge (since one or more AC/Reflex attack can occur in the same round, lasting until the end of the next turn edges this towards Shield, but only ever so slightly).

With three or more successful attacks in an encounter, Shield wins.

only in fairy tale math land. There is a mathematical point at which shields odds of having stopped an attack does pass second chance. It's a pretty complex calculation if you try and factor things like not blocking minion attacks, etc. The real "crossover point" is probably somewhere in the neighborhood of having faced 9-10 attacks each. Shield should block more attacks given that it can't block crits, can't block fort/will attacks, and sometimes will not get used at all. You completely skipped over the math where I compared it to shield of faith. I perceive that your issue here is the "sureness" of shield. Something about it working automatically seems to really offend you because in the grand scheme of things it's simply not going to outperform second chance at damage reduction it's just going to work 100% of the time the 15% of the time it works. Perhaps it's you that's lost sight of the big picture.

The reason this works is because if Shield does not work (with the 2E adjudication) on an earlier successful attack, the Wizard still has it as an option for a future successful attack in the same encounter until it does work.

Agreed, shield lingers until it gets an attack that fits its window of opportunity and then is deployed but what if the hit is by a minion? Something relatively weak early in the combat? Frequently shield is not used (I never use it on minions for example)

This is using YOUR percentages (which also happened to be mine in an earlier post).

not quite, I think if you scroll back the original percentages were mine. I guesstimated 75% instead of using your 73% and came up with 15%, I later corrected it to 14.6% to match your numbers so that we would be discussing apples and apples and you wouldn't take us on a tangent disputing the numbers.

Are you starting to understand now how your numbers were limited to ONE and only one attack in an entire encounter? Your numbers were great for that. But, your numbers ignored the fact that if Shield cannot be used, then it is still available for use later in the encounter.

One has to look at the bigger picture.

LMAO, are you seeing that you're still totally incorrect in your math? My numbers were in no way limited to one and only one attack, they just talked about the specific chance of blocking damage on an attack. You're still not accounting for numerous problems with your examples. Here are a list of questions/points you haven't answered/accounted for yet.

First - if we use shield in the manner you suggest, it is indeed totally expended on the first use. This decreases the usefulness to about 1/3 so instead of 14.6% we're looking at 4.9% as compared to second chances 50%. Do you understand this?

Second - you haven't accounted for the weakest attacks being in the 73% that shield is viable for. How much does this devalue shield?

Third - you haven't accounted for the value of 95% chance of blocking a crit. How powerful is this?

Fourth - you haven't accounted for combats where shield can't be used at all because of the variables involved.

And to be honest, 2E is starting to sound reasonable to me now that I have run the math for it for multiple successful attacks.

only because your math is so terrible. Let me know when you're in an epic combat and shield blocks almost 30% of all the damage the pc receives on every single attack.

But, 2E Shield is better in the long run than Second Wind unless your Wizard averages getting hit by 1 or fewer successful attacks per encounter. I really doubt that happens in most games.

Note: I do not discount the fact that Fort and Will attacks have additional effects. However, Reflex attacks also often have additional effects such as ongoing damage, so Reflex attacks cannot totally be discounted either.

I didn't discount reflex attacks, this is another horrible example. Second chance blocks reflex attacks too, so it's already accounted for in both powers. The only thing being discounted is that second chance can block ANY attack and shield is far more likely to only be useful against "simple attacks" and by simple I mean straight damage with no lasting effects.

I honestly can't wait for your reply. I'm wondering if you'll answer the 4 questions, account for the fact other 2nd level utilities are already better than best case shield at reducing damage, or own the error in your math with regard to multiple attacks.

 

[Elric]

Still second chance not second wind. This is more horrible math and anecdotal evidence. First if you assume the combat is 10 rounds long and then assume that the characters each get hit twice then the chance that the hits are "back to back" is about 20% so in 80% of the situations your math is flawed.

No. He is calculating the chance that Shield doesn’t work on each attack, so the chance it doesn’t work on one attack squared is the chance it doesn’t work on both attacks. If it does work, you decrease the damage by one attack’s worth.

If only either power worked like this you would be correct. By extension your math says that if you're hit 10 times in an encounter shield would block 2.92 of the attacks and second chance would block .5, a step further and we see that in 20 hits shield has blocked 5.84 of them and second chance has still blocked .5. Do you see a problem with this?

This is also wrong. He’s doing a similar calculation to that in my post above, but it’s a little less accurate in a way that works in Shield's favor because it’s essentially assuming that of n attacks, exactly half will hit (rather than taking the probability distribution of those attacks into account).

It should all be pretty clear if you look at my post above.

First - if we use shield in the manner you suggest, it is indeed totally expended on the first use. This decreases the usefulness to about 1/3 so instead of 14.6% we're looking at 4.9% as compared to second chances 50%. Do you understand this?

You have misunderstood the calculation he was doing.

Second - you haven't accounted for the weakest attacks being in the 73% that shield is viable for. How much does this devalue shield?

This wouldn’t be hard to answer, if you simply assumed no one would use Shield on minion attacks and lowered the percentage of attacks that Shield affects accordingly.

Third - you haven't accounted for the value of 95% chance of blocking a crit. How powerful is this?

See my post above, where I do account for this. If you are targeted by 8 attacks with a 50% chance to hit (as in my example above), and crits=1.5 regular hits, optimal use of Second Chance reserving it for crits initially makes it block 13% more damage than a myopic “use Second Chance on the first hit” strategy.

Fourth - you haven't accounted for combats where shield can't be used at all because of the variables involved.

The assumption that some % of attacks will target AC/Reflex is somewhat more favorable to Shield than the idea that in some combats there won’t be many enemies even targeting these defenses (and in others lots of enemies will target these defenses), but this effect is probably minor in the scheme of things. Otherwise, this is pretty much covered. See my post above.

 

[KarinsDad]

This is a much better calculation. The biggest thing you're missing compared to my numbers above is the fact that Second Chance can be saved for critical hits.

I saw your "save Second Chance for a crit" math.

Sound on the surface, but it ignores something fairly basic.

Say your PC gets hit twice in two encounters, each for normal damage (normal damage happens 90% of the time on a 50% chance to hit, critical damage happens 10% of the time on a 50% chance to hit).

The odds of 4 successful attacks hitting with normal damage (as opposed to critical damage on any of them) is 64%, a fairly common and high percentage of the time.

Using the "save Second Chance" strategy, the PC will get hit all 4 times and although he could have used Second Chance twice and only got hit twice, that did not occur. He takes 400% damage. He could have taken 200% damage. Even if the 4th attack would have been a critical, he would have taken 250% damage by using his Second Wind for the critical instead of 200%.

Saving a single extra 50% damage on a critical (approximately), but giving up entire encounter's worth of Second Wind is a mathematically bad strategy.


Spread over the lifetime of the PC, 10% of the times he gets hit, he will negate a critical. Since that will not happen every single encounter, he will lose a lot of Second Winds that he could have used.


And, this too is why APC does not get it. He too thought that saving Second Wind for a critical is important.

It's important for the PC to stay alive.

Sure, if you think your foe is a minion, a player would be smart to not use Second Wind on the off chance that a non-minion might hit him in the same encounter.


And, I read your section on k attacks remaining. I do think that a player could save Second Wind on the first few hits, waiting for that critical if he is fairly sure that he will get hit at least one more time.

But, that too is a guessing game.

The player does not have to use it on the first hit, but should use it somewhere in the first half of the encounter, if only to delay when he goes bloodied (where opponents might have other advantages against him).
But otherwise, it's a mistake to save it for too long over the long haul.

 

[Elric]

I saw your "save Second Chance for a crit" math.

Sound on the surface, but it ignores something fairly basic.
...

I wasn't proposing "save second chance for a critical" the entire encounter. That's a losing strategy compared to only saving it for a critical initially.

And, I read your section on k attacks remaining. I do think that a player could save Second Wind on the first few hits, waiting for that critical if he is fairly sure that he will get hit at least one more time.

But, that too is a guessing game.

The player does not have to use it on the first hit, but should use it somewhere in the first half of the encounter, if only to delay when he goes bloodied (where opponents might have other advantages against him).
But otherwise, it's a mistake to save it for too long over the long haul.

As I mention in my post, assuming that the player knows the number of attacks left against him leads to a more effective solution for how long to save Second Chance for (than if he only knows a distribution of times he'll be attacked again). The player doesn't have to be sure he'll be hit again- it's enough to know he'll be attacked a decent number of times. With n=8, and optimal k=4, the player faces 8 attacks for the encounter, and reserves Second Chance for crits on the first (8-4)=4 attacks. As I indicated above, that change in strategy makes Second Chance 13% more effective under my assumptions.

Edit- if you believe that it's important to use a defensive power in the first half of an encounter in general, and we apply this requirement equally strictly to both Shield and Second Chance (instead of just raising it as an objection to saving Second Chance), this will favor Second Chance, because even with the "save it for a critical initially" Second Chance strategy, the rate of increase in expected damage blocked as a function of the number of attacks is higher for Shield. So anything that effectively shortens the time you have to use the defensive powers favors Second Chance.

 

[Doctor Proctor]

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>

The fact is that racial powers and other abilities are not comparable. Bold =/= other abilities that grant saving throw bonuses, and Nimble Reaction =/= Defensive Mobility (especially since they actually stack). I play a Dragonborn, for example, and I get an encounter Breathweapon attack. It's not as powerful as many of the Wizard Encounter powers, so where's the outcry over that?

There's no outcry because I'm a Fighter and that's the only way I'm going to be getting a Close Blast 5 attack. There's no rule that I'm aware of that specifies any sort of balance between class and racial powers, so why are we arguing about it. They're different, deal with it.

As for Shield itself though, I think this is a bit ridiculous that we're even discussing this. There is no official ruling, and if some DM wants to play "gotcha" with his players, let him (even though the creators said that they were trying to get rid of "gotcha" powers...). Of course, I would also expect that you will see a DRAMATIC drop in the usage of shield in those games...

As for my group, our DM tells us what he rolled. So he says stuff like "Does a 23 hit your AC", and I say "yep". I don't see a problem with this as it makes the game flow a lot faster and gets rid of those "gotcha" powers. I also wouldn't be bothered if I hit one of the monsters and said "Does a 23 hit your AC" and the DM said "Well it would, but I used an interrupt power to boost my AC against that attack, so you miss".

Under the rule that some of the posters are using where a Wizard wouldn't know if Shield would work or not, would the DM follow the same rule in the case of interrupt powers? Does he give all the monster AC's to the PC's to track so that they don't have to tell him what their hit roll was in order to make him guess at the effeciveness of the power? Somehow I doubt that...which to me, makes it sound like we just have some very controlling DM's who want to have all the information and give none to the players, thus setting up a huge power imbalance between the PC's and monsters. If that's the game you want to play, then go ahead.

Edit: One last thing... One of the false assumptions that's being made here is that the Halfling will be using Second Chance (seriously...it's not WIND) as frequently as the Wizard. This is false. Part of the reason that racial powers aren't balanced against class powers is that a race can take any class.

So, if you have a Halfling Fighter (not as crazy as it sounds considering the Halfling Bounder PP in Martial Power) or a Halfling Rogue, they would get hit a lot more than the Wizard. In the case of the Fighter, he might be getting attacked 20 or more times per encounter...I know my Fighter sometimes does. In these cases, crits can actually happen quite frequently. You can very easily set up some conditions such as "don't use Second Chance unless there's a crit or I'm below 25% HP" to determine when you should use it, which really increases it's effectiveness a LOT.

Another thing is that you can combine Second Chance with other powers, which is something you can't do with Shield. Imagine, for example, a Halfing Wizard. He uses Shield to block one attack, but the second is a crit. Well, he can use Second Chance on that crit and take no damage during that round! Or he could be a Fighter using Shielded Sides when he's hurt and surrounded, and then save Second Chance for any attack that makes it past Shielded Sides. Doing so further increases it's utility because the enemy as less than a 50% chance to hit because of the AC bonus from Shielded Sides...so it's got a much better chance of negating the attack. Shield can't really do that though because it's a typed power bonus and won't stack with other abilities like Shielded Sides (in the case of multiclass Wizard/Fighter that was trading a higher level Utility to get Shielded Sides, or vice versa).

 

[Mort_Q]

As for Shield itself though, I think this is a bit ridiculous that we're even discussing this. There is no official ruling, and if some DM wants to play "gotcha" with his players, let him (even though the creators said that they were trying to get rid of "gotcha" powers...). Of course, I would also expect that you will see a DRAMATIC drop in the usage of shield in those games...

I retrained Shield, as it had proved almost useless... I think it saved from a hit once over three levels.