The “Squishy Caster” Fallacy
There’s a common belief among players that spellcasters are squishy, and martials are not. “Martials have d10 or d12 dice, while casters have a d6 and d8s, and thus frontline martials need to take hits up front and protect the backline casters.” In The Myth of Party Roles, we briefly discussed some of the reasons why this isn’t the case. In this article, we will explore some of the mathematical underpinnings of why casters can be just as or more sturdy than martials, and explore the power of well-built casters in more depth. We’ll explain the strengths of a defensive dip on casters, and the value of increasing AC as much as possible in general. Finally, we’ll briefly go over the various ways casters can increase their sturdiness.
What Determines “Sturdiness?”
The intent of this article is to explicate upon the concept of “sturdiness,” and how a common notion of “squishy casters” is a fallacy. But to do that, we’ll need to establish some common terms.
For the purposes of this article, “sturdiness” is a specific measure of a character’s defensive capabilities. Increasing sturdiness comes down to being able to minimize effects of enemy abilities with save DCs via saving throws, and the ability to avoid enemy attacks via Armor Class. Of course, both are functionally also tied to the total amount of hit points a character has. We will refer to the overall concept of sturdiness at points in this article as “effective hit points”—the idea of a value that combines all aspects of a character’s defenses (total hit points, Armor Class, saving throw bonuses, resistances).
There are other factors that influence sturdiness, such as the ability to deny enemy turns (via control spells and other features), specific party synergies, tactics, battlefield positioning, etc. However, we will not be focusing on those elements here, as they are outside the scope of this article. Instead, we will be diving deep into the other factors previously mentioned, primarily Armor Class and saving throws.
Armor Class
Having a lot of hit points but poor AC doesn’t necessarily make you more survivable than having a mediocre hit point total but high AC—this is our effective hit points concept in action (sturdiness isn’t just about high hit points, but includes some combination of hit points and Armor Class). In fact, given how total hit points scales poorly relative to enemy damage output, having higher AC is often as or more valuable than higher total hit points.
This becomes obvious if you consider the extremes (1 AC character with 100 hit points vs. 19 AC character with 75 hit points), but it becomes more and more difficult to intuitively ascertain what has more effective hit points when the hit point and AC values edge closer together. Clearly, sturdiness with respect to attack rolls is some combination of AC and total hit points. But how can we assess the value of Armor Class and hit points together? Well, first…
The superlinear value of additional AC
Something that many players don’t intuitively understand is that 1 additional point of AC becomes more valuable at higher AC values than lower ones. This doesn’t seem obvious at first. After all, one more point of AC just means a 5% reduction in hit chance, right?
Instead of just looking at hit rate, we’re going to look at a new metric: attacks (or attack rolls) per hit. This means the amount of attack rolls required to land a hit. Let’s construct a specific hypothetical scenario to help us along.
Here’s the example: Snyder and Victor are two members of a level 6 party that have come face to face with a pair of stone giants. Snyder is playing Redyns, an Artificer 1/Wizard 5 multiclass, meaning Redyns can wield a shield and don half plate with no problems (19 AC). Victor is playing Rotciv, a Samurai Fighter wielding a hand crossbow and donning half plate as well, but in order to Attack, they must keep one hand free (17 AC, see the Sage Advice Compendium for more details). Each stone giant picks a puny adventurer of their own to focus on, and they attack.
Let’s look at the stone giant attacking Redyns. 19 AC against +9 means 55% to hit. If Redyns had a +1 set of half plate armor, that would be 20 AC against a +9 for a 50% to hit—a linear reduction of 5%, as expected. That would be 1÷0.55 for 19 AC, around 1.82 attacks per hit. For 20 AC, that’s 1÷0.5 for 2 attacks per hit (this makes sense: a 50% chance to hit means, on average, you would expect 2 attack rolls before a hit). Now we have a more concrete idea of what a 5 percentage point decrease in to-hit chance (+1 AC) really means: about a 10% increase in survivability ((2.00-1.82)÷1.82).
Alternatively, consider a 12 AC Wizard versus a 13 AC Wizard. A +9 has a 90% chance to hit against AC 12, one additional point of AC means an 85% chance to hit. But 1÷0.9 = 1.11 attacks per hit, compared to 1÷0.85 = 1.18. The difference between 12 to 13 AC does reduce the stone giant’s hit rate by the same 5 percentage points that 19 to 20 AC does, but the relative jump in attacks per hit is much lower, 6% compared to the 10% from 19 to 20 (and consider that every jump in AC prior from 13 to 19 is also increasing your survivability). This becomes even more extreme the higher the AC values become, which is why shield on armored casters is so effective. A 12 AC Wizard casting shield increases their expected attacks per hit for that round by 30%, but a 19 AC Wizard doing so increases their attacks per hit by 83%.
The mathematical underpinning for this is because expected hits per attack, x, decreases linearly with AC, but expected attacks per hit, 1÷x, is an inverse relationship where the shrinking denominator makes each successive increase larger than the last in attacks per hit increase faster and faster. (If you care about technicalities: this is only a first-order approximation, and in reality is complicated a bit by critical hits doing extra damage and an effective AC ceiling against certain monsters who would need a 20 to hit anyway, but none of that changes the qualitative relationship.)
We looked at attacks per hit here first because, hopefully, looking at a simplified version of the formula more clearly demonstrated the type of relationship between sturdiness and successively higher AC. This is one of the reasons why we stress armored casters and access to the shield spell in many of our builds: it might be even better than you think!
Attacks until downed
You might be thinking, “I don’t know, Tabletop Builds. This all still sounds like a lot of jargon to me.” Now let’s introduce a concept that’s hopefully more intuitive in the context of a combat encounter called “attacks until downed.” We’re going to combine the expected number of attacks per hit value from above (based off of AC) with the damage on hit of the attack, and the value of each individual character’s total hit points, thus creating a metric of sturdiness that combines AC and hit points, not just one or the other (that would have to be recalculated for every scenario you find yourself in, so again: this is all just a demonstrative example, not some sort of axiom or theory!)
We’ll start off with hits until downed and work our way forward from there.
Hits until downed is simple:
For example, a character with 100 hit points versus a creature that does 10 damage per hit is downed in 100÷10 = 10 hits.
From hits until downed we can get to attacks until downed by multiplying by attack rolls per hit (now, we factor in the hit rate of attacks).
Just to once more hammer home the relationship of attacks until downed to AC (we’re almost done with the math, we promise):
Hits per attack can be calculated as follows:
In other words, attacks per hit is:
So the final formula for attacks until downed is:
You can see that Armor Class ends up in the denominator: this is why there is an inverse relationship between attacks until downed and AC, and why higher AC values are more valuable per point increase than lower AC values.
If you don’t believe any of the math, here’s a graph of the above function assuming 50 hit points, 20 damage per hit, and a monster attack bonus of ranging from +4 to +9 (though any values within a normal range for CR appropriate encounters would result in a similar graph):
Let’s go back to Redyns and Rotciv. A stone giant can make two attacks per turn with their greatclub, an attack with +9 to hit that does 3d8+6 damage. Redyns has 46 hit points and 19 AC. They have a 55% chance of being hit per attack roll, or 1.82 attack rolls per hit. With critical damage taken into account, one hit from the stone giant does an expected 20.7 damage. Plug these numbers into our formula above:
This means we would expect a stone giant takes at least 4 attacks to down Redyns on average.
Now let’s look at Rotciv. Rotciv does have more hit points than Redyns—58 to 46—but a lower AC of 17 compared to Redyns’s 19, because they cannot wield a shield if they want their Attack action to actually do good damage. Plug in the numbers and we see that means they take 20.5 damage per hit, and with 1.54 attack rolls per hit, and thus we would expect the stone giant would need at least…4 attacks to down Rotciv, a very similar number to Redyns!
You can combine this with the number of attacks per turn the enemy creature can make to get to a number of turns you can survive (or rather: not be put unconscious): in this case, with 2 attacks per turn, we would expect both Redyns and Rotciv live through at least 2 turns.
(Our Wizard friend with 12 AC? Expected to be downed in 2.6 attacks, meaning one less turn for that Wizard compared to his better armored colleague!)
Now, Rotciv does have a slightly higher expected number of attacks until downed. But Redyns actually has something up his sleeve—shield. While this is a resource that must be consumed, resources are meant to be used! Committing to casting shield once would be enough to increase the number of attacks needed to down Redyns to more than 5, not to mention the benefits if the Wizard was targeted by additional enemies (we understand that this is a form of resource expenditure for the Wizard compared to the Fighter). The relative benefits of 1-2 additional points of AC, plus shield in your back pocket, in a game system defined by bounded accuracy can often eclipse the marginal differences in hit die size when it comes to this measure of sturdiness.
This is obviously a simplified example, and there are significantly more variables in actual play than what was presented (after four attacks against each, Rotciv will, on average, have more hit points left over than Redyns, it’s possible that certain breakpoints in the variables of the encounter would result in Redyns being downed in less attacks than the Fighter, it’s possible shield could increase the number of turns lived in the Wizard’s favor, etc). But hopefully this small scenario reframed using the attacks until downed metric, explaining how a “squishy” Wizard with a d6 hit die can in many situations be just as durable to attacks as a “tanky” Fighter with d10 hit die (or at least, survive the same number of turns).
A final note is that we do not take into account features like death ward here either, even if it can increase the amount of attacks until someone is downed greatly, but this is another benefit to playing casters to keep in mind.
Fellow Tabletop Builds author Haen the Heretic has their own blog, Form of Dread, where they have a post that explains this phenomenon more in-depth (see the Damage Dealt versus Damage Taken section). While they present a simplified model and the graph in the post does not factor in damage from non-attack sources, similar to us here, it should suffice to demonstrate the point that an edge in AC can be of comparable, or even notably greater value for sturdiness than the higher total hit point pool afforded by martial classes.
But Tabletop Builds, Wizards wear robes and have 10 AC! This doesn’t make sense!
The Misconceptions Regarding Casters
Casters being harder to hit than martials tends to not align with many players’ perception, in part due to common genre conventions. Casters are thin and frail, wear cloth robes, wave wands around casting spells, and go down at a touch, often called the “glass cannons” of a party. Meanwhile, bulky knights in heavy plate armor shrug off multiple blows and stay upright while nimble rogues and martial artists bob and weave to deftly avoid blows.
However, this classic dichotomy of magic users versus weapon users doesn’t hold up in 5E. There are several reasons for this:
Spellcasters can wear armor too
In 5E, casters only face a downside to wearing armor they are not proficient in (this is a contrast to previous editions, where arcane casters were hit with Arcane Spell Failure rolls). Armor and shield proficiency is easily obtained for casters through multiclassing, race choices, or the Moderately Armored feat. Martials do have access to the Defense Fighting Style, which can boost their AC. However, even if they do have the Defense Fighting Style, casters can still pull even, because…
Spellcasters can wield shields, while damage-optimized martials typically can’t
In 5E, martials primarily exist to do damage. Non-caster martials have very limited means of exerting battlefield control, and any methods they do have for it are typically triggered on attack rolls anyway (Battle Master Maneuvers) or are single-target lockdown strategies of variable effectiveness (Grapple + Shove prone, Sentinel opportunity attacks). As such, the most valuable contribution pure martials can typically provide is in the form of pure single-target damage (which is a valuable contribution, don’t get us wrong!). As far as weapon damage goes, obtaining a reliable bonus action attack and a “power attack” (-5 to hit, +10 to damage) are essential, which leaves few viable paths: Crossbow Expert/Sharpshooter with a hand crossbow, and Polearm Master/Great Weapon Master with a heavy reach polearm (a few builds, such as a Monk with Gunner and Sharpshooter, can also be competitive using a longbow or renaissance era firearm).
With few exceptions,* wielding a shield isn’t possible, either because of the weapon itself needing two hands (as is this case with heavy reach polearms), or because a free hand is needed to reload your hand crossbow. Casters, on the other hand, if they have proficiency, can wield a shield and leave their other hand open to access a component pouch or spellcasting focus. Spell foci are cheap, so you can even have more than one on your person and drop staves and the like if you really need to do some free-hand juggling (check out our article on spellcasting components if you need a refresher).
* The handful of exceptions include having a friendly Artificer to infuse your hand crossbow with the Repeating Shot infusion every day, or having extra limbs (currently, additional limbs dexterous enough to wield shields are exclusive to the Thri-kreen in the Travelers of the Multiverse Unearthed Arcana playtest content). As we’ve noted in an article on ASIs versus Feats and our Race and Lineage Guide, being a starting feat race is imperative for damage-dealing martials builds, and thus we don’t consider extra limbs to be a relevant consideration here.
Spellcasters can cast shield
Shield temporarily increases the AC of a caster by 5 for an entire round, an ability that martials are not afforded unless they dip a level (and is entirely unavailable to Barbarians while Raging). Martials pay a higher price for dipping a level in a spellcaster class before level 5 than spellcasters pay for dipping a level in a class that grants armor proficiency. Even if a martial dips caster levels after level 5, they will have limited spell slots (though they can likely commit all of their resources to personal defenses). Martials will generally have a resting AC of 17 (half plate with 14 Dexterity) or 18 in full plate or with the Defense Fighting Style (our definition of resting AC is the AC a character has with no resource expenditure and no cover). A caster in half plate and wielding a shield, on the other hand, has a resting AC of 19, enough on its own to rival or exceed the effective hit point total of most martials, and can raise that to 24 for a full round with a reaction and a 1st level spell slot. Since each additional point of AC increases effective hit points more than the one before (see the section on superlinear AC values above), spellcasters who manage their shield slots well are extremely resilient to enemy attacks.
Spellcasters can afford to take the Dodge action
Due to the fundamental design of optimized martials, these characters typically have to commit their action and bonus action to attacks in order to deliver the full brunt of their damage-dealing potential. In contrast, maintaining concentration on a powerful control spell such as web, a twinned phantasmal force, hypnotic pattern, spirit guardians, polymorph, etc., is usually a casters’ biggest contribution to an encounter. In many cases, supplementing your concentration spell with area of effect damage from a fireball, utilizing the on-hit forced movement from a Repelling Blast-enhanced eldritch blast, or simply throwing in some minor damage from a damage cantrip will be a good use of your action. However, in some cases, the additional resource expenditure of a spell slot won’t be necessary, and the cantrip damage may not be significant, and holding concentration on the spell is much higher priority. In these cases, casters can afford to Dodge. Some spells with longer durations, like the ones mentioned prior, can even allow spellcasters to Dodge on turn 1! Dodging confers advantage on Dexterity saves and disadvantage to enemies that target you with attacks, which adds another layer of sturdiness and protection against attack rolls (some quick numbers to keep in mind: a 50% to hit becomes 25%, 60% becomes 36%, 70% becomes 49%) and abilities that force Dexterity saves, which we will explain in more depth below. Clerics in particular can get a lot of use out of simply casting spirit guardians, using the shove from the Telekinetic feat to “double dip” an enemy target if they fail their save, and Dodging.
The bottom line is: within optimized 5E play, there is an inversion of the standard trope of a frontline of martials protecting a backline of squishy casters: instead, parties may well be served by having Dodging casters in front of the martials who are hanging back and do damage with their crossbow.
So we can see that spellcasters can acquit themselves favorably in one aspect of sturdiness: Armor Class. But what about against saving throw effects?
Saving Throws
The base class design of 5E indicates that starting saving throw proficiencies were meant to be balanced across classes. Saving throw proficiencies can be split into two categories, which we will dub “primary” and “secondary,” with every class getting proficiency in one of each. Primary saves are Dexterity, Constitution, and Wisdom; secondary saves are Strength, Intelligence, and Charisma. Every class gets proficiency in one primary and one secondary saving throw (no class has proficiency in two primary saves or two secondary saves). The core conceit seems to be that primary saves are more common to face, while secondary saves are more rare. Every class getting proficiency in one primary and one secondary save should mean that saving throws across all classes are balanced…right?
Unfortunately, in actual play this isn’t the case, for a variety of reasons.
Saving Throws are not balanced
First is that saving throws are not perfectly balanced. In our view, which is fuelled by extensive playtime both sides of the table, the six saving throws can be summarized as follows:
Primary Saving Throws (More Common)
- Dexterity: saves are almost always purely for damage, which is generally preferable to more dangerous control effects, especially when they can often be mitigated with absorb elements.
- Constitution: split between damage and debilitating effects. Most notably, casters with Constitution save proficiency can, in addition to bolstering their own defenses, help the sturdiness of the entire party by maintaining concentration on their spells.
- Wisdom: the most debilitating saving throw to fail. Most characters will want to obtain Wisdom save proficiency at some point, though typically the earliest most characters that don’t start with it can afford this is late in Tier 2 or Tier 3.
Secondary Saving Throws (Less Common)
- Strength: typically lower-risk to fail; generally results in the prone or restrained conditions being applied with repeated saves to break free.
- Intelligence: very uncommon but can be risky to fail: see intellect devourers or mind flayers.
- Charisma: very uncommon but can be risky to fail, can result in being banished or possessed.
We can see that failing a mental save typically has devastating effects, while failing physical saves is less debilitating. As spellcasters typically prioritize a mental ability score, they already start with a small leg up here. Additionally, the starting saving throw proficiencies of martial classes do them no favors. Monks (and Rangers, though they are a half-caster class) have Dexterity and Strength proficiency, the least desired saving throw proficiencies of each category. Barbarians and Fighters have Constitution and Strength proficiency, which is a slight improvement, but leaves them with no coverage on mental saves. Rogues have Dexterity and Intelligence saving throw proficiency, which at least pairs nicely with Evasion. Paladins, on the other hand, are all set: Wisdom saving throw proficiency and then their Aura of Protection at level 6, which is the best save protection the game has to offer.
Access to saving throw proficiencies
Because saving throws aren’t created equal, that makes obtaining specific saving throw proficiencies more desirable. And builds that have more build flexibility have an easier time building around choosing the saving throw proficiencies they want. We’ve already gone in depth on why martials generally need to commit their first two ASIs to specific feats, while casters don’t—this means that casters can more easily afford to take the Resilient feat early in the game. On top of that, in games that are mostly focused around Tier 1 and 2 play, delaying Extra Attack as a martial means hamstringing yourself for at least one level, which can be a significant portion of your campaign. Almost every class sees a significant power bump at 5th level from either Extra Attack or 3rd level spells, but spellcasters with good 1st and 2nd level spells (like bless, spike growth, and especially web) pay a lower opportunity cost at level 5 for delaying their big bump by a level. Thus, spellcasters can more easily afford a 1 level dip in one class to opt for certain saving throw (and other) proficiencies they want, a choice less available to martials. In all cases, casters have more build flexibility afforded to them to get the save proficiencies they want, while martials do not.
Dodging and absorb elements
There are a couple of other considerations that help spellcasters in this area. As discussed earlier, Dodging is more available to spellcasters than martials. Dodging confers advantage on Dexterity saving throws (and disadvantage on attack rolls, see above). On top of that, absorb elements exists, countering the most devastating type of Dexterity saving throws: those that would typically deal massive amounts of elemental damage. Obtaining access to absorb elements can require some specific build choices, but can typically be bundled together with access to other defensive priorities such as armor proficiency or access to the other 1st level reaction spells (shield and silvery barbs), and so is a presence on the spell list of every optimized caster. Dodging and absorb elements (despite being resource intensive) both serve to mitigate the weakness of no spellcasters (except Bard) starting with Dexterity saving throw proficiency.
Martials have better passive save defenses
All martial classes have some form of innate passive save defenses, which spellcaster classes do not innately have. Monks and Rogues get Evasion, Barbarians have Danger Sense, Fighters get Indomitable, Rogues can use their reaction to use Uncanny Dodge, and Barbarians have resistance to bludgeoning, piercing, and slashing damage while Raging. Rogues and Monks get additional saving throw proficiencies via Slippery Mind and Diamond Soul respectively, both late in Tier 3.
These features are so different and are acquired at such different levels that evaluating them as a whole is difficult. Many of these features come late in the game, especially considering the levels of play that most tables reside in—Monks and Rogues may have access to Evasion for a third of the campaign or less, and may never come close to getting Diamond Soul or Slippery Mind. The reroll from Indomitable is nice, but is a very limited use feature and once again comes at the end of Tier 2. Danger Sense is obtained at a low level, costs no resources, and is one of the best passive save defenses in the game, so no complaints there. Uncanny Dodge costs a reaction, which does hurt for Rogues that are trying to optimize for two Sneak Attacks per round, but comes at a reasonable level for a reasonable cost.
We will not go into individual subclass resources that provide for save defenses for the sake of brevity, but we also would not consider any subclass feature to swing the needle towards one direction or another in our assessment in any way.
All things considered, though many of these features are potent, we consider spellcasters to have a slight edge here as far as defenses against saving throws go. They innately prioritize mental ability scores, which are the most debilitating saves to fail, they have more build flexibility to prioritize the key saving throw proficiencies, they have more leeway to Dodge during combat, and they can typically fall back on absorb elements if necessary. Martials have a larger health pool and more class-based passive save defense features, which are nice, but the most impactful features often come very late in the game and are not enough to sway our judgment in their favor. While spellcasters do have to commit some resources to defenses, even having the resources to commit to defenses makes them more resilient and sturdy in the face of saving throws.
Resistance to bludgeoning, piercing, and slashing damage while Raging is certainly beneficial to effective hit points. However, the reason why we don’t believe that this is a significant boost to the effective hit points of Barbarians is due to the limited number of Rages they have until level 15. For Barbarians to be doing respectable single-target damage, they need to be using Reckless Attack (and the damage from Raging helps as well). Reckless Attack roughly increases the to-hit chance of enemies by 25 to 50%, and if all incoming damage is bludgeoning, piercing, or slashing, using Reckless Attack while Raging is roughly a 25-40% reduction incoming damage (in total, somewhat lower due to it being unlikely that 100% of the incoming damage you face is exclusively bludgeoning/piercing/slashing). Combined with the fact that Barbarians can’t wield shields, the overall reduction in damage ranges from fine to good…if you can Rage.
One of the reasons we don’t rate Barbarians highly here is because we evaluate the game in accordance with our Core Tenets, which assumes a challenging adventuring day featuring 6-8 encounters. Under such constraints, your Rage uptime could be as low as 50%, before considering the risk of dropping Rage early, such as from failing a mental save or simply not attacking or taking damage in a round. Using Reckless Attack without Raging is a 25-50% increase in incoming damage, which roughly evens out, or if you opt not to Reckless Attack to survive, then your outgoing damage is cut by ~33%. All in all, the reduced effectiveness of the Barbarian in non-Raging encounters hampers their performance both in sturdiness and overall effectiveness such that we don’t view it as an improvement to effective hit points. In campaigns where you have very high Rage uptime, however, Barbarians can be much more effective, but we don’t operate under those assumptions.
Summarizing Martial vs Caster Sturdiness
- Martials have a higher total hit point pool, but spellcasters can have equal or greater effective hit points against attacks due to a better resting AC and access to shield.
- Spellcasters can contribute to encounters by concentrating on powerful spells, which opens up the ability to Dodge, which makes casters harder to hit.
- Dodging and access to absorb elements mitigate the lack of Dexterity saving throw proficiency for spellcasters.
- Spellcasters have more build flexibility in obtaining the saving proficiencies that are valuable.
- Martials have better passive save defenses from their base class features.
So we have our three pillars of sturdiness: saves, Armor Class, and hit points, which together can be represented by effective hit points, and we have shown why we believe casters have just as much if not more effective hit points than martials. But how are these things achieved practically, both in build space and in encounters during actual play?
How Can I Build a Sturdy Caster?
We have explained how armored spellcasters can compete with or supersede martials in terms of effective hit points and overall sturdiness with regards to Armor Class and saving throws. Now, let’s focus on how we can actually build such a character.
The Ingredients
To summarize, you should focus on having:
- A high resting AC. Most often, this comes from wearing medium armor and a shield, for a base AC of 19. Some builds, especially Clerics and Paladins, wear heavy armor for a base AC of 20, and some like Forge Domain Clerics or particular races can go even further.
- The reaction spells shield and absorb elements. The prototypical sturdy caster has an AC of 24 during shield, which is significantly higher than the ACs of most martials. Survivability scales superlinearly with AC, so this makes them extremely resilient to attacks. Ideally, the spellcaster has absorb elements as well.
- Concentration protection. This usually takes the form of proficiency in Constitution saving throws, the War Caster feat, or both. Lucky or certain class features can serve as a backup to either. Being able to contribute to combat with persistent effects via concentration opens up our turn up for evasive actions, like Dodging.
Now that we have explained the necessary ingredients for creating a sturdy character, we will now focus on how we can go about obtaining these “ingredients.” Building a sturdy caster is a bit of a puzzle. Every spellcasting class has some defensive elements built in and others that they lack.
Multiclassing
By looking at what pieces each class needs, we can find the best multiclasses to eliminate their weaknesses with minimal investment, resulting in a powerful, well-rounded character. Multiclassing just a few levels is a cost efficient way to gain exactly what you want, but it can be scary to figure out what exactly you should and should not do. To help you along, we will release a guide to multiclassing soon that goes in depth on how to build well-rounded spellcasters. However, we will list some of some the best dips for many of the classes below (consider this a bit of a preview: the actual guide will go into far greater depth).
- Bard: Hexblade Warlock 1-2 and/or Divine Soul Sorcerer 1 with Moderately Armored feat
- Cleric: Divine Soul Sorcerer or Clockwork Soul Sorcerer 1
- Druid: Life or Peace Cleric 1 and/or Divine Soul Sorcerer 1
- Sorcerer: Hexblade Warlock 1-2
- Wizard: Artificer 1 or Peace Cleric 1
Straightclassed Alternatives
If you decide to play a straight-classed build, perhaps so that you can play with wall of force or animate objects before the campaign ends, this doesn’t mean you have to flush defense down the toilet.
At base, something like a Wizard or Sorcerer with mage armor, shield, and a high Dexterity and Constitution isn’t actually much less durable than a martial. When one of these characters has shield up, their AC is likely 20 or 21, which is still better than a martial wielding a two-handed weapon or a crossbow—the standard that we expect from damage-optimized martials. These casters also have smaller hit dice, but compared to the d10 of a Fighter, a d6 hit die only results in about a 25% reduction in maximum hit points—and remember that in terms of “effective hit points,” the increased AC will do enough to offset this. Relying on shield makes these casters less survivable if they have to take attacks for many rounds, but the vast majority of the time, casters thought of as “squishy” really aren’t all that squishy in the first place!
Still, we can do better, mostly through feats. Any spellcaster should consider Resilient (Constitution) or War Caster to protect their concentration, which is their biggest contribution in combat. Bards and Warlocks should also still take Moderately Armored to gain an AC comparable to those of martials. But what about Sorcerers and Wizards? These classes can pick a race that provides an armor proficiency, the most powerful of which is Hobgoblin and take Moderately Armored at level 4. This route is not as robust as a multiclassed one, as it results in weaker concentration saving throws, but it still thoroughly trounces any notion of squishiness.
Conclusion
This was a long article and a bit of a dry and technical one, so hopefully you all made it here. Our goal here was to show how just looking at the larger hit die of martial classes, combined with some pre-existing notions of how the game is or should be played, can lead to misleading perceptions of how sturdy or survivable casters actually can be compared to martials. Hopefully this leads you to re-examine how blended “party roles” can be in 5E, and build more survivable characters of your own!
Great article and the fact that things are contrary or nearly inverted to classic fantasy tropes is rather bothersome to me.
I use your articles and analysis to fuel my homebrewing efforts. My ability to do that has kind of gone down hill somewhat because I start from the perspective of Level Up:Advanced 5e now.
Some of my ideas on how to address the issues you brought up though might not make casters happy. Like having dodging interfere with concentration saves (you can do internal or external attention not both). And having ranged spell casting require enough focus that they trigger opportunity attacks. Prone casters or ones hit while casting grant advantage on saves by the targets of their spells. Making keeping range a doubly important thing.
And also empowering martial types (starting with level up where all martials get maneuvers) including homebrewing ones for instance I have martial analog to Silvery Barbs (called Disruptive Ploy).
I know you do your analysis based on raw but I would like to see you starting from a raw perhaps which is a more adjustable and slightly more balanced version of 5e.
These seem like some really interesting changes that definitely could have positive impacts. They would certainly help enforce the ranged spellcaster playstyle, although that is what most casters, despite their better defenses, want to do anyway.
Level Up has some fantastic changes, the martial maneuver system is definitely well deserved, and the exploration additions seem very interesting, but there are some others that probably aren’t for the best. Feat nerfs, fireball nerfs, free conjure animals, a second level sleet storm, no buffs to haste and unchanged web and hypnotic pattern, to name a few. The removal of half casting from rangers (my second favorite class thanks to its unique semi spellcaster playstyle) is also a really large change that probably wasn’t needed – the class is more than playable as it is.
It doesn’t seem to introduce anything that really changes the armor dipped casters at higher optimization levels, but I haven’t finished reviewing it yet, so there certainly still could be potential.
You could also just disallow multiclassing for optimization purposes at your table, that’s usually the easiest solution to these sorts of builds that can torpedo game balance if your whole table (including the DM!) aren’t on board.
Yeah, I’ve increasingly become of the opinion that multiclassing should just be banned, or at least never allowable by default barring DM permission.
The fundamental problem of multiclassing in D&D 5e is that you either will likely be less fun to play, especially due to reduced power, or allows for broken combinations.
I’m especially looking at Warlocks here, as they have certain abilities that are way more useful for multiclass characters than single class, and in particular it has all it’s subclass features come online at 1st level, making it a huge source of dips into that class.
Also, the fact that Coffeelock exists as a build really goes to show how ridiculous multiclassing can get.
This is not enough to make the issues with the game solved, but this definitely will alleviate a lot of problems, and nuke all of the Flagship Builds.
I generally dislike OneD&D for a lot of reasons, and won’t play it, but I do respect WotC trying to reduce the power of multiclassing by making all subclasses start at level 3.
Barbarians can wield shields, though
The issue is not that martials aren’t capable of wielding a shield, merely that their efficiency significantly decreases when they do, unlike spellcasters who only need one free hand for peak output.
Very interesting analysis and probably spot on, though I shudder at the thought of actually playing or running this sort of “highly optimized” play. 😛
I do take one issue with an early example, though: “(1 AC character with 100 hit points vs. 19 AC character with 75 hit points)” – how in the heck is 18 points of AC worth a mere 25 hp? Clearly if you’re comparing extremes it should be 1 AC vs 1 HP. Or just 1 AC vs 20 AC at the same hit points… Ugh!
Sorry yeah it’s really minor but it rubbed me the wrong way.
My (fairly simple I thought) homebrew solution to the martial class dip for armour proficiencys is to say that armour proficiency from multiclassing only comes online at L3 of the mutliclass dip.
For me, this makes it still available/a reward for anyone willing to commit to the dip a bit, but also makes it an actual decision rather than a given for optimising purposes (due to the delay in the on-class spell level progression).
From a realism/RP POV too, a single level dip potentially giving up to 3 different about type proficiencies also ses insane considering the ASI/feat cost (and availability) of the armour proficiency feats.
Could I get a quick sanity check for some homebrew related to this?
First, remove Shield, Absorb Elements, and Silvery Barbs from all spell lists; they no longer exist as spells.
Second, give all Barbarians, Fighters, Monks, and Rogues (maybe Rangers and possibly Artificers too) the ability to effectively cast any of these spells as a reaction proficiency bonus times per long rest at 1st level. Only, slightly tweaking them to be non-magical abilities. Instead call them Desperate Parry (Shield), Distracting Maneuver (Silvery Barbs (I kinda want to call it Pocket Sand!, but it could also include things like shining a glint from your blade in your opponent’s eyes or anything else that seems appropriately distracting)), and Stiff Upper Lip (Absorb Elements; hopefully I’ll come up with a better name)), all falling under the umbrella of an ability called Skillful Defences.
The aim here is to improve balance and build diversity by diverting some of the most key defensive abilities in the game away from the full casters and toward those classes with more of a reputation for sturdiness. It’ll still probably be optimal to dip the martials to gain access to these, but at least it costs more of a strain on spell slot progression this way, and as homebrew goes it’s fairly simple.
To further increase the cost to casters of dipping for these abilities, at the expense of making the martials marginally weaker, I’ll also propose that martials can choose one of these Skillful Defences at each of 1st, 2nd, and 3rd level.
I think the suggestion above about class dipping is way more reasonable. The article focus on high optimized builds, on the top of the notch and most of the times, players that want to break the game (IMO).
The everage caster player on my tables never thinks about doing those things and getting crazy with AC, the last time I saw it was with War Caster and Sturdy, to protect CON saves. Removing shield and absorb elements from those players would make me just kill then too easily with any ability.
Silvery Barbs is a broken spell and everyone on my table agrees that is not healthy to the game, caster gains way to much power with it.
Commiting to a build with high AC, with 3 levels on artificer like suggested above messes up all your spell levels and can really be detrymental to casters.
One of the things that I like to enforce strongly is that you need to have 1 hand free to make somatic components, and you need to have another one to material, but if you already have the other hand occupied with the arcane forcus and other with shield, you can’t cast somatic components. (This is with the assumption that you do not have War Caster feat, that I think needs a rebalance too).
And the way you coming, you should remove Sanctuary, one of the stupidiest spells IMO, and on one of the best spells lists that is Cleric.
And I love the ideia of giving more maneuvers for martials, this is something that I was discuting with my players about, to implement on Barbarians, Fighters and Monks, the others one don’t need it because they already have spells to have fun. More maneuvers is always a good way to give martials more options and is something that 5e should work for martials.
A very well thought out article. However, I don’t find the argument “casters have absorb elements” to be wholly convincing. Firstly, Martian’s can get access to the spell in the same way that casters can access AC, either by playing a half caster such as a ranger, or through feats/multiclassing. Second, absorb elements has holes. With the addition of a growing number of monsters that deal massive amounts of non-absorbable damage types to less common saves (gem dragons, for example), the extra 25% hp can mean the difference between life and death. A caster’s shield spell, armor, and spells are unlikely to keep them standing in such an encounter, and these types of challenging encounters are common in optimized gameplay.
martials continuing to grow as martials will not gain access to more spell slots to use Absorb Elements or Shield with. Casters only need one dip to always have better armor
I can’t wait to play the lute (or almost any other musical instrument) with my bard while I wear a shield. This looks very confortable and really brings up the fantasy of the class (almost as much as full armor mage with a metal shield.)
The fact that you can do this RAW only shows how bad RAW can be. And no, playing 1 hand instruments doesn’t fix this problem since at this would make every bard just play a harmonica.
I mean, Bards can also tap dance, sing, or recite poetry, none of which require hands at all, and all of which are at least more interesting than yet another lute player.
But more than that, I’ll direct you to the https://tabletopbuilds.com/flavor-is-free/ article. Also be sure to remember and avoid the Stormwind Fallacy while you’re at it. And if you want to see the Flavour is Free principle taken to its logical extreme and made the central feature of a system, have a look at HERO System/Champions RPG.
I mean, we’re in agreement, RAW can be really terrible. But you have more freedom to operate within it than you might think.
Counter argument: Sturdiness is meaningless to survive. AC won’t stop a narutal 20. In my experience if a PC dies by dmg in a fight it’s normally because of a critical hit. Not because it took too many 24 dmg hits, but because it took a 60 hit that couldn’t prepare for. IMO “optimal sturdiness” just means to be very effective protecting yourself from something that it’s not going to kill you anyway. Having a suboptimal AC in exchange of having more HP is more likely to save your life than having the optimal sturdiness.
An interesting and fair point.
Counter-counter-argument: while AC and saves aren’t the be all and end all of sturdiness, they do at least help keep your HP from getting chipped away enough for crits to be particularly threatening. And they also often have access to effects like Aid and Twilight Sanctuary that boosts their HP higher than martials can reasonably achieve on their own (even the fact that casters tend to be more SAD gives them more build freedom to invest in a higher Con modifier).
But even more than that, many of the tools casters have to improve their effective AC also serve to drastically reduce the likelihood of suffering a crit. For example, engaging from range with a relatively autonomous Concentration spell and taking cover can make them basically untargetable. And the combination of Dodge and Silvery Barbs can reduce the chance of an attack critting to 1/8000. Silvery Barbs can even be cast to save an ally whose Shield has proven insufficient, in which case the higher the proportion of the party who are casters the more resistant to crits they all are.
But critically, none of these additional tools interfere with casters pumping their AC and saves, meaning they basically get the best of both statistical sturdiness and protection from crits. Which is nice, because AC and saves scale statistical effective HP exponentially, to a whole host of benefits.
I think my problem is that the sturdiness theory works wonderfully in the best case scenario. You have spells, good possitioning, etc… And in this scenario, sturdiness won’t be that great anyway, and it will be an overkill in safety because you are already in a good spot. Do you really need 24 AC and advantage when you can have 22AC and advantage?
However the worst case scenario will eventually happen: you will be out of THP, low on spells, you won’t see your enemies comming, you will be at 70% of your HP, the enemies will have nasty abilities to attack with advantage or paralyced… name one, the campaings are long and these things will happen more than once. And then, if a bad scenario combines with a 20 roll, in my experience, more HP will be more likely to save your life. In my experience, the more likely you are to die to dmg, the less important AC becomes and the more importat HP becomes.
I will name the 17AC and 100HP PC Jhon, and the 19AC and 75HP PC Mike. And I will put them in different scenarios that come from my personal experience.
A) Enemy attacks, it’s a16, Jhon doesn’t get hit nor does Mike. Both play safe and they survive the encounter.
B) Enemy attacks, Jhon gets hit by 20 and Mike doesn’t get hit. Both PC start playing safe and they survive the encounter.
C) Enemy attacks and gets a crit, Jhon gets hits by 80, starts playing safe and he survives. Mike is KO and might even die and the whole encounter turns into a nightmare.
D) Enemy attacks and gets a crit, Jhon gets hit by 80 but since he had lower AC and was at 60 he goes down and so does Mike because he had 75 HP at full HP. The whole encounter turns into a nightmare.
E) Enemy attacks and chips Jhon HP because of his lower AC, Mike is fine. However since the HP of Jhon was slowly taken away the fight didn’t turn into a nightmare because Jhon was still useful for some turns, even if it was just tanking some hits.
F) Enemy attacks, gets a 20, but the crit is low, 60 dmg. However Jhon because of his lower AC had less health and gets KO. Mike survives at 15 HP. Jhon’s party fight turns into a nightmare.
Optimal sturdiness is not absolute and suboptimal sturdiness might just be as effective. And in some scenarios (than in my experience happen more ofter) it might even be better.
Sure. But for casters, it’s generally not an either-or (again, an extra caster providing Aid and Twilight Sanctuary gets the whole party’s HP higher than a martial’s), and they can drastically reduce the frequency of those nightmare scenarios. Like, we haven’t even discussed how summoned minions attract a lot of attacks, or how higher damage and better battlefield control reduces the number of attacks enemies ever get to make.
But most of all, casters simply have more resources to throw at their problems. By the time the party of optimized casters is so low on spell slots that the nightmare situation becomes probable enough to worry about, the party with a couple higher HP martials has probably found the martials begging for a rest for like 3 encounters (or the martials have been a net drain on spell slots due to the extra healing they’ve needed due to their lower AC, likely unaware of the opportunity cost they’ve been imposing on their allies).
Sure, sometimes a higher hit die is the difference between life and TPK, but trading that higher hit die for many more resources and vastly stronger tactics drastically, drastically reduces the odds of those situations ever happening in the first place, and usually gives more options for recovery when they do happen (eg having familiars able to feed downed allies healing potions rather than a still-standing martial having to spend actions saving their allies). And that’s the essence of optimal play.
The superlinear value of additional AC:
I understand the math, but I don’t understand it’s implications. Expected hits, reading the construction, means if the enemy has a 50% chance to hit me. I expected to get hit in 2 hits. But that’s not the probability of getting hit in 2 hits. Cause lets say I had an AC <10 I'm not going to get hit more than once. The probability of getting hit at least one time when attacked twice is 75%. The probability of getting hit twice is 25%.
Isn't probability more useful when thinking about taking damage based on AC calculation instead of expected hits? I think I'm not understanding the importance of this section because of the utility of this expected hit calculation; I'm trying to conflate it with probability. And if they aren't substitutable how is this expected hit helping my assessment with having a higher AC and taking shield?
Thank you fo your time, I'm genuinely trying to understand. It's frustrating feeling like I'm missing something.
The article talks about Effective HP, and that really is the best lens of analysis. It’s not talking about your probability of getting hit for any given attack or round, it’s talking about your ability to survive a whole encounter or adventuring day, the concept of treating your whole health bar as a resource to be managed and spent as needed. There’s a reason the equations use terms like “attacks until downed”, because that’s exactly what’s being measured.
Like, standard probabilistic analysis on whether you’ll be hit this round is still really useful and is the fundamental building block this analysis relies on. But that’s not *really* what you care about, is it? Especially not when planning out your build before your character even sees actual play. All of that probabilistic analysis is in service of greater questions like “how sure am I that I won’t go down in a given encounter, forcing my allies to waste their actions getting me back up and possibly causing a domino effect leading to a TPK?” and “how many party spell slots can be saved for powerful encounter-winning spells and rest casting rather than wasting them on simply keeping me alive due to my HP dropping too low for comfort?” and “how much higher will the party’s dpr be as a proportion of the enemy’s dpr if I’m this much less likely to lose concentration?”.
Knowing whether or not a given attack will hit only matters insofar as it affects party actions and resources, the effects of which will exponentially accumulate over time.
I see your point more. And when I read it in context, I think it makes more sense (the logic, the algebra, the graph). My hangup is this premise: “(this makes sense: a 50% chance to hit means, on average, you would expect 2 attack rolls before a hit).” And I think I’m proof of your statement it’s not intuitive. Cause to me, I don’t think about the construction in 2 attack roles I got hit. Like for example, I tried to make it more intuitive by saying okay, if Redyns got hit 100 times, that means the golem made 182 attack attempts and if Rotciv got hit 100 times that the golem made 200 attack attempts, and that ratio is better at higher AC given 1/x is exponetial when you graph it. But, why would I ignore probability in this set up? Cause it’s possible if I got hit 100 times, the golem in either case made less than 182 or 200 attacks, respectively. And I think ignoring probability does make this example of survivability more elucidating. So I was curious if even if you considered it would the concept still hold true. But, yeah coming back to it that’s not intuitive to me the construction that if the golem in this scenario made 2 attack attempts I got hit (once). I hope I’m not being difficult I just don’t want this to remain “unintuitive.” And let me clarify a little more, what I used to calculate was that if my fighter attacked 4 times, and each hit was 25% chance to hit that meant there was a 100% chance I would hit once, and that’s not true, so that’s what that premise is reminding me of. Please help me understand. Thanks for your quick response as well.
Right, your problem is one of directionality. It’s not “if Redyns gets hit 100 times the golem has made (at least) 182 attacks”, but rather “if the golem makes 182 attacks, Redyns would expect 100 of them to hit on average”.
And that’s just an algebraic rearrangement of “at what number of golem attacks would Redyns find his expected number of times to be hit on average to equal 100? 182.”, which happens to be equivalent to “in the space of all situations where Redyns has been hit 100 times, what is the average number of attacks the golem has made? 182.”
At no point is probability being ignored.
But my thing is why isn’t it 75% for 2 hits; or 50% for 1 hit? Like if probability was 25% to hit based on AC calculations and we did 1/0.25 that would be 4 attacks to hit. But I thought 0.25 x4 = a hit isn’t the correct construction because probabilities aren’t additive. So aren’t we just “assuming” a hit?
Not at all. If I attack twice, there are 4 possible outcomes. Both miss, the first hits and the second misses, the first misses and the second hits, and both hit. At a 50% chance to hit, all of these outcomes are equally likely, so 75% of the time there’s at least one hit.
But the average number of hits is exactly 1. Exactly 50% of the two attacks. What we do is the same as the basic process for calculating the mean average: sum all the terms and then divide by the number of terms. Only instead we add up all the possible hits under the probability distribution (0+1+1+2=4) and divide by the number of possible outcomes (4÷4=1).
This works for any number of attacks. If I attack four times, then there are 16 possible outcomes (one where 0 hit, four where 1 hits, six where 2 hit, four where 3 hit, and one where all 4 hit). At a 50% chance to hit all are equally likely, and so we divide the 32 total hits by the 16 possible outcomes to get exactly 2 hits on average, exactly 50% of the four attacks.
To make the math more general what we can do is multiply each outcome in the distribution by its chance of happening. So if we revisit my two attacks at a 50% chance to hit, outcome 1 where both attacks miss has a 0.5×0.5 chance of happening. Outcomes 2 and 3 where one hits and one misses each have a 0.5×0.5 chance of happening, and outcome 4 where both hit has a 0.5×0.5 chance of happening. Again, all outcomes are equally likely, which makes it very boring and easy to simplify. If we sum the probabilities of each outcome (0.25+0.25+0.25+0.25) then we get 1, which is to say 100% of the total probability distribution.
If the chance to hit isn’t 50% then the outcomes aren’t all equally likely, and so you have to take a weighted average. So if I attack twice with a 55% chance to hit, then we take outcome 1 where both miss and say it has a 0.45×0.45 chance of happening. Outcomes 2 and 3 where one hits and one misses both have a 0.45×0.55 chance of happening. And outcome 4 where both hit has a 0.55×0.55 chance of happening. If you add up all of these probabilities {(0.45×0.45)+(0.45×0.55)
+(0.55×0.45)+(0.55×0.55)} you get exactly 1, meaning we did our math right and 100% of possible outcomes are accounted for.
Now, what I was doing above with the equal probability examples was a simplification of what actually happens with D&D. I calculated as if we were rolling 1d2s to find all the outcomes, but in fact we’re dealing with d20s. But in the 50% case there are 10 rolls that hit and 10 that miss so we can simplify and it works out the same. In this 55% chance to hit case there are 11 rolls that hit and 9 that miss. So in outcome 1 where both miss is 9×9=81 out of 400 possible rolls. Outcome 2 where the first hits and the second misses is 9×11=99 out of 400 possible rolls, and the same is true of outcome 3. And outcome 4 is 11×11=121 out of 400 possible rolls. This means out of 400 outcomes there were 198 with one hit and 121 with two hits, or 440 hits in the possibility space. 440 divided by the 400 outcomes equals 1.1 expected hits, where 1.1 is 55% of 2 attacks. Note that this is different from the chances of getting at least one hit, which is 319/400 or 79.75%.
Obviously this same method also works with advantage, disadvantage, Elven Accuracy, Bless, Bane, Blur, Emboldening Bond, cover, and any other circumstance in D&D. Just enumerate all possible combinations of rolls and count how many are hits.
But what you’ll find is that if all attacks have the same chance of hitting, the expected number of hits is simply the chance to hit times the number of attacks. Or more generally you can say that the expected number of hits is the average of the chances of each attack hitting times the number of attacks. I’m not a mathematician and can’t prove that rigorously, but if you run through a few examples you’ll see that it’s correct. But when you do prove that to be the case then you can do even more general things like calculate probabilities involving irrational numbers using straight algebra, not that you’ll ever encounter irrational numbers when computing dice probabilities.
I realize now with the help of my friends that I am being completely dumb all we were saying was that 50% or 55% is equal to in the case of 55% 11/20 And if you divide the numerator and denominator by 11 you will get one over 1.82 or that saying one expected hit for every 1.82 options are rolls or attacks and so I was understanding all the pieces of it together when it was being explained, but it was just connecting the dots in the sequence in my head and it didn’t make sense until I just wrote it out manually on paper. So I just want to appreciate and thank you for the time it took to expound on this, and your patience with me and understanding simple math lol. I thought we were making multiple attack roles at a given percent and coming up with a different expected head rate, which didn’t make sense to me and so I was effectively applying advantage and disadvantage to everything when I didn’t need to be
I could plainly see from the way you were phrasing things that you have some good instincts for statistics, and were making a sincere effort, but were stuck trying to solve a closely related but critically different problem, and just needed the right nudge to get it.
But also, I’m Autistic and so have a lot of experience just… not getting stuff that I get the sense should be basic because nobody thought to explain the one little key piece of context I needed, so I’m not about to leave someone hanging if I can help it.
Anyway, I’m glad you were able to figure things out. And I hope I was able to explain things well enough that you’ll be able to avoid what I’m sure was a very frustrating situation in the future.
Hi Apollo, thanks for your comment! It looks like you and Tor have already had some illuminating discussion about this but I thought I’d offer a reply as one of the “math people” at TTB (I wrote the “Quantitative Primer” articles and contributed to the math in the relevant section of this article).
You’ve got some great insights here, and in particular here:
> But my thing is why isn’t it 75% for 2 hits; or 50% for 1 hit? Like if probability was 25% to hit based on AC calculations and we did 1/0.25 that would be 4 attacks to hit. But I thought 0.25 x4 = a hit isn’t the correct construction because probabilities aren’t additive.
you’re absolutely right that it’s not obvious that we can do this, because in general you can’t take reciprocals with probabilities and assume the obvious thing happens. It just so happens that in the particular case of the _mean_, it holds that E[attacks per hit] = 1 / E[hits per attack], (where E[…] is the notation for the expected (average) value of a quantity that has a probability distribution associated with it). And even that requires that the probability of getting hit stays constant and that the attack rolls are independent (in the sense that getting hit doesn’t change the chance of getting hit on any subsequent attack). If you want more background on the math behind this, you can look up the Bernoulli and Geometric distributions, which describe whether or not a given attack hits and how long it takes to get hit, respectively.
Once we have that fact about the expected values, then it follows that E[attacks until getting hit n times] = n * E[attacks per hit], because the number of attacks until we get hit n times is the number of attacks until the first hit, plus the number of attacks between the first and second hit, plus the number of attacks between the second and third hit, etc., and each of these is a random variable whose mean is E[attacks per hit].
Now, what we _really_ care about isn’t how long we last until we get hit n times, but actually how many attacks we can withstand before we lose all of our HP (say, all of them). If damage were a constant (as opposed to another roll with a random result), the expected value here would just be E[attacks per n hits] for n equal to the number of hits we can survive. And since this is modeled as n*E[attacks per hit], it scales proportionately with both our HP pool (which scales n linearly) and our E[attacks per hit] which scales with our AC (given enemy accuracy), but superlinearly.
There are some things that could add nuance here, like the fact that when damage is a roll rather than a constant, it’s no longer exactly a matter of just setting n, and technically we’d need to do a more detailed probabilistic analysis, but this just refines the specific numbers and doesn’t change the basic insight about the value of AC. One could also argue that we shouldn’t be looking at expected values of “time ’til death”, but instead should look at the probability that we take less than our HP in damage over a given period of time. But that’s significantly more complicated and at some point you have to make some reasonable approximations and roll with them.
One genuine caveat I’d give to this analysis is that if we want to avoid having _anyone_ die, then we do want to pay particular attention to the squishiest member of the party (likely our melee martial), and even if the caster with _shield_ would buy more survival time from the shiny new +3 breastplate we just found than they would, there’s an argument for giving it to the squishy Barbarian instead, because we’re probably going to survive without it, and they might not.
“If you multiclass a spellcaster specifically around defence it’s better than a fighter that has made no attempt at defence at all”
Your statistics are meaningless if the data you feed in is biased as all hell.