Is "Shield" too powerful?

[Piratecat]

APC, see you in three days after you've had a chance to reread the rules about personal attacks.

 

[KarinsDad]

In a major encounter the pc's might sometimes field 100+ attacks.

Second level. PCs average ~32 hit points each. 5 PCs = 160 hit points in the party.

A major encounter is against third level or higher foes. But I will cut you a break and make it second level foes. Second level foes average +6.5 to hit in the MM, 6.55 points of damage and 9.7 points of damage on a crit (even with minions). Second level PCs average AC 18, so they get hit on a 12 (11.5, but I am cutting you a break here too). 45% chance to hit. The second level foes in the MM all have attacks vs. AC and this equation does not include their special abilities.

100 attacks * (40% hit chance * 6.55 points per hit + 5% crit chance * 9.7 points per crit) = 310 points of damage

You've just TPKed your party nearly twice over.

Even the two Cleric Healing Words only add another 31 hit points and 5 Second Winds add 40 more. An immediate in round one Shield of Faith for 66. Where exactly do the other 14 hit points for one PC to still be standing with one hit point come from? Maybe a Beacon of Hope.


I lowered the total damage by including wimpy minions in these calculations (it's +6.5, 7.7+ damage and 10.4+ damage on a crit without them), I made it only second level foes, I rounded to fewer hits per encounter, I cast Shield of Faith in round one, I did not include any monster special abilities and the PCs are still TPKed or nearly so.


Or put another way, 100+ attacks = 10 opponents, each of which last an average of 10 rounds. Would 10 second level foes really last 10 rounds on average? How about 20 second level foes averaging 5 rounds each?

You must have fairly large fights.

 

[Piratecat]

If someone has been removed from the thread, it is in bad taste to make a post they can't respond to. It is in exceptionally bad taste to make that post full of snide jabs that are meant to bait another fight. Stop doing that, please.

 

[KarinsDad]

If someone has been removed from the thread, it is in bad taste to make a post they can't respond to. It is in exceptionally bad taste to make that post full of snide jabs that are meant to bait another fight. Stop doing that, please.

Sorry PC.

I actually started my response before you posted (this afternoon in fact). I just got interrupted several times and it took some time to research the MM stats. I wasn't trying to start a fight with him, I just like analyzing stuff.

 

[BASHMAN]

To those GMs that don't tell what AC the attack hit (or at least that it was a close one), or won't even tell what defense is being attacked, please do the gaming world a favor and stop. It does not contribute to the fun or mystery of the game-- it is just frustrating.

For some reason, at cons I get stuck with GMs who like to do stuff like this, and it turns something that was supposed to be fun into an adversarial thing. As if the GM were trying to 'get" the players. It is not worth the frustration on the part of the players. I have learned to just get up from the table and leave in situations like this (because it always gets worse in my experience with this style GM).

 

[KarinsDad]

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?

Finally got back to this question.

As we discussed earlier, Second Chance should be saved until either the first critical, or until about the middle the encounter (rough rule of thumb is that 25% of non-minion foes are down, or 50% of non-minion foes are bloodied), or until the PC is seriously wounded and threatened (e.g. PC is 2/3rds damaged).


Assuming a critical does 150% and there ia a 50% chance of being hit, a re-rolled hit goes to no damage 50% of the time, normal 100% damage 45% of the time and 150% damage 5% of the time. Or, 52.5% of the damage instead of the 100% of a normal hit or 150% of a critical hit.

But, this is an "instead of" situation. For Second Chance, we have to calculate how much damage was saved, not how much damage was taken.

If he uses Second Chance, he will always average 52.5% damage taken. But, how much damage he saves is based on whether it is a critical or a normal hit.

On one hit, Second Chance saves 90% * (100% - 52.5%) + 10% * (150% - 52.5%) = 52.5%. Another way of looking at this is that an average hit does 90% * 100% + 10% * 150% = 105% damage and Second Chance does 52.5% damage, hence, the savings on one hit = 105% average - 52.5% taken = 52.5% saved.

On one hit, Shield saves 1-(1-0.3)^1 = 30%.

For two hits, there is a 10% chance that Second Chance stopped a critical on the first hit (97.5% saved) and a 90% chance that it stops 52.5% damage on the second hit. 10 * 97.5% + 90% * (90% * 47.5% + 10% * 97.5%) = 57% saved.

So, we solve for a range of N hits and how much damage is saved on average if the PC uses Second Chance or Shield on the nth hit (in the case of Shield, nth or earlier hit since Shield is used on the first hit it can be used on):

N 2ndCh Shield
1 52.5% 30%
2 57.0% 51%
3 61.1% 65.7%
4 64.7% 76%
5 68.0% 83.2%

10 * 97.5% + 90% * 47.5% = 52.5%
10 * 97.5% + 90% * 52.5% = 57%
10 * 97.5% + 90% * 57% = 61.1%
10 * 97.5% + 90% * 61.1% = 64.7%
10 * 97.5% + 90% * 64.7% = 68%

Shield saves 1-(1-0.3)^N.

We have to look at these numbers in the big picture:

1) This has slightly low numbers for Shield since Shield can stop multiple hits in the same round. Even if this only occurs one encounter in ten for a single extra foe, that increases the percentages for Shield by ~2%. Pro Shield.

2) Second Chance has a chance of not ever being used in an encounter if it is being saved for a later critical, especially in easier encounters. Combat is fluid and it's very possible for a player to think "Oh, it's stilll early, I should save it" and then combat is over in the next round or two due to good player dice rolls or area effects and the PC never gets hit again. Not being used drops the savings to 0%. Pro Shield.

3) A given player might use Second Chance on the third normal hit assuming that combat might be over soon and then get hit with a critical. One cannot just compare N = x between the two, one must realize that the Second Chance choice to use it has risks involved in using it too early. Using it too early on a normal hit drops the percentage down to 52.5% saved automatically, no matter how many hits were not used first. Shield should always be used the first time it can (unless the foe is known to be a wimp maybe). Pro Shield.

4) Second Chance has a better chance to save against specials such as daze because it can affect Fort or Will attacks. Pro Second Chance.


Taking all of this into account over the lifetime of a campaign, it really depends on how many times the PC gets hit per encounter.

 

[Trebor62]

To those GMs that don't tell what AC the attack hit (or at least that it was a close one), or won't even tell what defense is being attacked, please do the gaming world a favor and stop. It does not contribute to the fun or mystery of the game-- it is just frustrating.

For some reason, at cons I get stuck with GMs who like to do stuff like this, and it turns something that was supposed to be fun into an adversarial thing. As if the GM were trying to 'get" the players. It is not worth the frustration on the part of the players. I have learned to just get up from the table and leave in situations like this (because it always gets worse in my experience with this style GM).

I agree. Additional it grants an advantage to the monsters. Being controlled by the DM this knowledge cannot help but influence his handling of the monsters weither it is realized or not. This grants the monsters some degree of advantage that the PC do not have. All of this could be avoided by not withholding the information from the PC's who are face to face with the monsters and would have an excellent idea how effective there attacks and defenses where in the first place.

 

[RigaMortus2]

For the benefit of those who haven't heard the podcasts - he told the players what the attack roll was, and asked if the attack hit their AC (or whatever other defense was being attacked).

Hmmm. That is how I've always played it.

DM: Does a 17 hit your AC?
Player: Nope
or
Player: Yeah it does. But wait, I use the Shield spell, now my AC is a 19, so you miss!

 

[Elric]

So, we solve for a range of N hits and how much damage is saved on average if the PC uses Second Chance or Shield on the nth hit (in the case of Shield, nth or earlier hit since Shield is used on the first hit it can be used on):

N 2ndCh Shield
1 52.5% 30%
2 57.0% 51%
3 61.1% 65.7%
4 64.7% 76%
5 68.0% 83.2%

This calculation seems reasonable. If you consider a distribution of the frequency of successful hits for encounters as something like:

1: 0.15
2: 0.25
3: 0.3
4: 0.2
5: 0.1

Then you can compute an expected value for each of the powers. The above distribution comes out to: Second Chance: 0.602. Shield: 0.605. Of course, this is somewhat too favorable to Second Chance, because, as you indicate, nowhere does the player have to consider that saving Second Chance might mean it never gets used. Since you’ve assumed the number of successful attacks to be fixed, you can’t quantify this tradeoff.

In practice you can do more than save Second Chance for a critical or Fort/Will status effect as your point 4 says—you can save it for a hit from a Brute with higher damage/lower attack bonus, be more likely to use it against a single AC/Reflex status effect, and so on.

Turning to a different issue, Shield of Faith is a hard power to compare to Shield. The reason is that Shield of Faith is a daily, and requires a Standard Action. So at a minimum, making a comparison requires an assumption about the number of encounters per day, and the value of a lost standard action compared to an immediate action (one in the first round of combat, if you want to get the maximum use out of Shield of Faith), plus an assumption about comparing the utility of blocking a lot of hits in one encounter against the whole party vs. blocking fewer hits and only against the Wizard in each encounter.

Here’s one set of (very simple) assumptions you could make:
We’re only concerned with the average number of hits blocked per day. There are 4 encounters per day.
Suppose Shield blocks an average of 0.55 attacks per combat (n=5, 70% of attacks targeting AC/Reflex, 0.2 extra attacks for which Shield will apply each time it’s used gets you this result). So Shield blocks 2.2 hits/day.

Shield of Faith is useful in one encounter. In the encounter when you use it, the party faces, say, 28 attacks against AC. Shield of Faith blocks 0.1 hits for each attack against AC. So Shield of Faith blocks 2.8 hits a day. Using up a standard action on the first round of combat as opposed to an immediate action when you end up using Shield is worth, say, 0.6 hits (wizards really value actions at the start of combat, but that’s less true of clerics; if a wizard had Shield of Faith I’d definitely pick a higher value here). So Shield of Faith gives a net 2.2 hits a day, the same as Shield.

Which power is better until this metric is going to depend heavily on the number of encounters you assume per day. While more attacks per day means that the number of attacks you should expect in the one encounter you use Shield of Faith goes up somewhat (since you will use it at an opportune moment), Shield’s value improves linearly with the number of encounters per day, which will be a significantly faster rate of increase.

 

[KarinsDad]

This calculation seems reasonable. If you consider a distribution of the frequency of successful hits for encounters as something like:

1: 0.15
2: 0.25
3: 0.3
4: 0.2
5: 0.1

Then you can compute an expected value for each of the powers. The above distribution comes out to: Second Chance: 0.602. Shield: 0.605. Of course, this is somewhat too favorable to Second Chance, because, as you indicate, nowhere does the player have to consider that saving Second Chance might mean it never gets used. Since you’ve assumed the number of successful attacks to be fixed, you can’t quantify this tradeoff.

True. However, 5 is not the upper limit, it was just how far I took it out. Obviously, a PC could get hit more often (if the opponents are minions, if the PC gets healed a lot, if the foes roll wimpy damage, etc.).

But, there is probably some practical upper limit like 8 for most encounters (i.e. if hit 8 times in an encounter, most PCs will fall in most encounters, even with heals).

If one were to extend this out to a limit like 8, Shield starts looking nicer. However, most Wizard players probably wouldn't stick around for 8 hits if they could help it and I suspect anything over 5 is rare, at least for a Wizard.

In practice you can do more than save Second Chance for a critical or Fort/Will status effect as your point 4 says—you can save it for a hit from a Brute with higher damage/lower attack bonus, be more likely to use it against a single AC/Reflex status effect, and so on.

Agreed. That is a Pro Second Chance point.

Turning to a different issue, Shield of Faith is a hard power to compare to Shield. The reason is that Shield of Faith is a daily, and requires a Standard Action. So at a minimum, making a comparison requires an assumption about the number of encounters per day, and the value of a lost standard action compared to an immediate action (one in the first round of combat, if you want to get the maximum use out of Shield of Faith), plus an assumption about comparing the utility of blocking a lot of hits in one encounter against the whole party vs. blocking fewer hits and only against the Wizard in each encounter.

Here’s one set of (very simple) assumptions you could make:
We’re only concerned with the average number of hits blocked per day. There are 4 encounters per day.
Suppose Shield blocks an average of 0.55 attacks per combat (n=5, 70% of attacks targeting AC/Reflex, 0.2 extra attacks for which Shield will apply each time it’s used gets you this result). So Shield blocks 2.2 hits/day.

Shield of Faith is useful in one encounter. In the encounter when you use it, the party faces, say, 28 attacks against AC. Shield of Faith blocks 0.1 hits for each attack against AC. So Shield of Faith blocks 2.8 hits a day. Using up a standard action on the first round of combat as opposed to an immediate action when you end up using Shield is worth, say, 0.6 hits (wizards really value actions at the start of combat, but that’s less true of clerics; if a wizard had Shield of Faith I’d definitely pick a higher value here). So Shield of Faith gives a net 2.2 hits a day, the same as Shield.

Which power is better until this metric is going to depend heavily on the number of encounters you assume per day. While more attacks per day means that the number of attacks you should expect in the one encounter you use Shield of Faith goes up somewhat (since you will use it at an opportune moment), Shield’s value improves linearly with the number of encounters per day, which will be a significantly faster rate of increase.

Also agreed.

I think encounters per day is a group type metric. For example, DMs who want to avoid grind and create fewer tougher encounters might see a shift towards Shield utility over Second Chance (due to the fact that Wizards will probably get successfully hit more often in a tougher encounter). But, that also shifts in favor of Shield of Faith over Shield due to having fewer encounters per day.


Btw, have you seen Druid Barkskin? That is something we should be able to compare to Shield. Shield kicks Barkskin's butt, especially at low level. But the "can be cast on any ally" can throw a real monkey wrench into the real utility of Barkskin which the math just might not show adequately.