Author: Soma
Welcome to More Min Than Max, a new article series by Tabletop Builds where we will be discussing common character building and optimization pitfalls that players fall into. For this first entry in the series, we will be discussing a somewhat common belief that players hold: “Because 5th Edition is built upon the foundation of bounded accuracy, I should prioritize maximizing my primary ability score first!” We will be discussing why this fallacy exists, why it’s misguided, and what to do instead.
Note: if you read our race guide, you may have seen an abbreviated section of this in the Variant Human/Custom Lineage section!
First, A Primer On Bounded Accuracy
Search online for “bounded accuracy” and most, if not all, of the search results you see will likely be about Dungeons & Dragons, specifically 5th Edition. The origin of the term as it relates to D&D can be traced to a now-archived development blog posted in 2012 during the D&D Next playtest by Rodney Hudson, a developer for 5th Edition who was an employee of Wizards of the Coast at the time. He is credited in the Player’s Handbook under Rules Development.
In summary, the primary concept of bounded accuracy is to tighten the range of numerical outcomes of any given roll, typically the d20 roll. In Rodney Thompson’s blog post he describes this as follows:
The basic premise behind the bounded accuracy system is simple: we make no assumptions on the DM’s side of the game that the player’s attack and spell accuracy, or their defenses, increase as a result of gaining levels. Put simply, bounded accuracy reduces the weight of level scaling on bonuses to rolls.Bounded Accuracy, Legends and Lore, Rodney Thompson
A more illustrative example would be comparing other editions of D&D. In 5th Edition, attack rolls for melee weapons are calculated thusly: d20 + proficiency bonus + Strength modifier + other modifiers. In D&D 3.5E, the formula for attacking with a melee weapon is d20 + base attack bonus + Strength modifier + other modifiers.
Proficiency bonus versus base attack bonus is the core of bounded accuracy. In 3.5E, for full martial classes, base attack bonus equals your level, whereas in 5th Edition, proficiency bonus starts at +2 and ends at +6, increasing every 4th character level. A 20th level 3.5E Fighter might have an attack modifier of +25 (base attack bonus of +20 and a Strength modifier of +5), while a 20th level Fighter in 5th Edition has an attack modifier of +11 (+6 proficiency bonus, +5 Strength modifier). In addition, 3.5E had many different sources of stacking bonuses, pushing modifiers quite high, compared to the very narrow range of save DCs, skill check bonuses, or attack roll bonuses that 5th Edition has. This is the core of bounded accuracy.
Where Might We Go Wrong?
When you understand the basics of bounded accuracy, it’s easy to see how people come to the conclusion that increasing your primary ability score is powerful. This was, after all, one of the intended goals of bounded accuracy:
Since target numbers (DCs for checks, AC, and so on) and monster accuracy don’t scale with level, gaining a +1 bonus means you are actually 5% better at succeeding at that task, not simply hitting some basic competence level…This means that characters, as they gain levels, see a tangible increase in their competence, not just in being able to accomplish more amazing things, but also in how often they succeed at tasks they perform regularly.Bounded Accuracy, Legends and Lore, Rodney Thompson
Indeed, increasing your attack roll by +1 is much more significant when you might start with a +5 at level 1 and end your campaign at a +9, compared to starting at a +4 and ending at a +40. The difference in marginal benefit is comparatively huge. The problem, however, is that in 5th Edition we have to choose between an Ability Score Increase (ASI) and a feat. The opportunity cost of choosing the ASI over the feat is much, much larger because certain feats are extremely powerful in 5th Edition, and due to the extremely limited rate at which these feats can be obtained, it becomes absolutely crucial to pick up feats as early as you possibly can.
The Math Behind Getting Feats ASAP
Example 1: Melee Weapon Barbarians
The easiest way to demonstrate how strong feats are is to do some simple math comparing builds. First, we will start with your prototypical melee weapon user, the Barbarian. For melee martial characters, the first two feats you want to take are going to be Polearm Master and Great Weapon Master in some order (the order depends on when you can access your first feat). We will be comparing two Hill Dwarf Barbarians: Sara’s character Aras, and James’s character Semaj. Both will start with the same point buy, 14+2/14/15+1/8/12/8, but Aras will take Great Weapon Master at level 4, and Semaj will use his ASI to increase his Strength by +2. To keep things simple, both will be considered subclass-less Barbarians. We will be assuming a single combat encounter of 4 rounds here.
We will use a 65% base hit rate (not using the -5/+10 of Great Weapon Master) when maximizing our primary ability score for our damage assumptions and adjust the hit rate of our feat builds accordingly (this means that taking a feat a level 4 and 8 will drop our base hit rate by 5% each time we take a feat over increasing our primary ability score). Starting at level 2, both characters will be using Reckless Attack constantly to maximize damage output. Both will be using greatswords (2d6).
From levels 1 to 3, their damage outputs will be equivalent (8.2 DPR at level 1, 11.2 DPR at level 2 and 3).
At level 4, Semaj increases his Strength to 18, keeping his assumed to-hit rate at 65%. He does 12.1 DPR, an increase of merely ~1 point, coming from the additional damage from his increased Strength modifier.
At level 4, Aras takes Great Weapon Master, upping her DPR to 14.4, despite her assumed accuracy dropping to 60%. We are factoring in the potential for an additional bonus action attack on a critical hit, but assuming a 0% chance of getting an additional attack from reducing a creature to 0 hit points. The chance of getting to make an additional attack this way is highly dependent on the encounter, so we will not include it in every DPR calculation for this article, but it does tip the scales even further in favor of taking Great Weapon Master first (for example, just one additional attack in a 4 round combat here would boost Aras’s DPR to 17.6).
At level 5, Semaj is doing 24.2 DPR and Aras is doing 28.6 DPR.
At level 8, Semaj increases his Strength again, to 20. He keeps pace with enemy AC, hitting at a base rate of 65%, and increases his base damage by 1, resulting in 25.9 DPR. Notice again how little boosting Strength does: just 0.9 damage per attack both times.
For Aras, the math is somewhat more complicated. She switches weapons now, from a greatsword to a d10 polearm. Still at 16 Strength, her assumed hit rate is now 55%. She attacks twice on round 1 (no bonus action attack due to needing to Rage), and thrice on rounds 2-4. We will assume that at least 2 creatures will approach her, but one will be prior to her turn and one will be after her turn, so 1 Polearm Master reaction opportunity attack without Rage, and one with Rage. This comes out to 31.9 DPR, which is still handily above Semaj despite the heavily reduced base accuracy rate. Of note, now that Aras has a readily available bonus action attack, the additional attack benefit of Great Weapon Master becomes close to negligible, merely boosting an attack with a d4 damage dice to a d10.
What if James does some math and takes Great Weapon Master at level 8 instead of boosting his Strength to 20 (using the same assumptions as above, Great Weapon Master barely edges out Polearm Master)? This puts him at 29.9 DPR, though because he does not have a bonus action attack, even one additional bonus action attack from downing a creature will boost his damage more notably than Aras satisfying those conditions would.
While Semaj can now match Aras under extremely favorable conditions, it doesn’t make up for the four levels of playtime that he was handily outdamaged by Aras, with his only advantage having 1 higher Strength saves and Athletics.
| Level | Aras (GWM, PAM) | Semaj (+2 STR, +2 STR) | Semaj (+2 STR, GWM) | Starting Feat (PAM, GWM, +2 STR) |
|---|---|---|---|---|
| 1 | 8.2 | 8.2 | 8.2 | 14.1 |
| 2 | 11.2 | 11.2 | 11.2 | 18.1 |
| 4 | 14.4 | 12.1 | 12.1 | 23.3 |
| 5 | 28.6 | 24.2 | 24.2 | 35.8 |
| 8 | 31.9 | 25.9 | 29.9 | 37.7 |
Note that we do not consider Aras’ build to be the optimal build for melee martials. That would be choosing a starting feat race (Variant Human, Custom Lineage) with 16 Strength taking Polearm Master at 1, Great Weapon Master at 4, and then boosting Strength at 81. This build does significantly more damage than either of the Dwarves (with slightly less points to spare at point buy for one mental ability score), which should really hammer home how much more important it is to grab powerful feats early, than it is to maximize your primary ability score modifier. For this comparison, we wanted to look at two builds of the same race, one that picks feats and one that chooses ASIs. You cannot compare a build that starts with a feat versus a build that starts with an 18 in an ability score but no feat, so we used Dwarves, who get their first feat/ASI choice at level 4 (like all other races). Comparing a build that gets to start with a feat versus one that doesn’t would be quite unfair.
1 An alternate proposition might be starting with Custom Lineage and Crusher. This build has a different starting point buy. Starting with 18 Strength means 70% to hit at level 1 for 9.5 DPR, 12.5 DPR at level 2, 16.9 DPR at level 4 with 65% hit rate, 33.7 DPR at level 5, and 37.2 DPR at level 8 with a 60% hit rate. As with Semaj, not having an at-will bonus action attack until level 8 does mean additional bonus attacks have more impact than that set of circumstances would on a build that already has Polearm Master. Whether or not having the on-hit forced movement from Crusher and a slightly different point buy is worth the lower damage until level 8 is perhaps debatable, and outside of the scope of this article.
Barbarians exist on the battlefield to do concentrated amounts of damage to a single target, since being able to take hits alone is not enough. If you’re lagging behind in this area, you’re not pulling your weight. Catching up at level 8, or not at all, can be a significant hindrance. By Dungeon Master’s Guide guidelines, that’s around 94 average difficulty encounters that you were contributing subpar damage to. The superior damage output you can contribute over the course of that many encounters by taking feats early is much more valuable than the utility of a slightly higher Strength save and bonus to your Athletics skill
Example 2: Ranged Weapon Fighters
A similar example can be delineated with ranged weapon users. First we have Laura’s character, Arual, a High Elf subclass-less Ranger with 16 Dexterity, 16 Constitution. She will grab the Crossbow Expert feat. Next we have Raven’s character, Nevar, a High Elf subclass-less Ranger with 16 Dexterity and 16 Constitution.
As before, we will use a 65% base hit rate (before factoring in the Archery Fighting Style, and not using the -5/+10 from Sharpshooter) when maximizing our primary ability score for our damage assumptions.
From levels 1 to 3, Arual and Nevar will have identical DPR, as there are no differences between their builds (shooting a heavy crossbow, 5.8 DPR at level 1, 6.7 DPR at level 2 due to Archery Fighting Style).
At level 4, Arual takes the Crossbow Expert feat. At 60% base accuracy (70% due to Archery), she does 9.5 DPR, attacking twice with her hand crossbow after having changed weapons.
At level 4, Nevar increases his Dexterity to 18. Maintaining his 65% base accuracy (75% due to Archery), he does 7.4 DPR.
At level 8, Arual picks up the Sharpshooter feat. Her base accuracy drops to 55% (65% with Archery), and now she does 20.3 DPR, attacking thrice with her hand crossbow.
At level 8, Nevar grabs an ASI, boosting his Dexterity to 20, keeping his base hit rate at 65% (75% due to Archery). He does 14.7 DPR, shooting his longbow twice now that we have Extra Attack.
| Level | Arual (CBE, SS) | Nevar (+2 DEX, +2 DEX) | V!Human (CBE, SS) |
|---|---|---|---|
| 1 | 5.8 | 5.8 | 8.8 |
| 2 | 6.7 | 6.7 | 10.1 |
| 4 | 9.5 | 7.4 | 15.2 |
| 5 | 19.0 | 14.8 | 22.8 |
| 8 | 20.3 | 14.7 | 24.2 |
As with Aras and Semaj, we can see how Arual starts out-damaging Nevar when she starts to take feats and he continues to improve his Dexterity. That’s not to mention that Arual benefits from the secondary abilities of Crossbow Expert and Sharpshooter, such as being able to attack in melee without disadvantage and ignoring half and three-quarters cover, benefits that Nevar does not have access to. In exchange, Nevar’s Dexterity saves and ability checks are 1 point higher. As mentioned before, Nevar won’t begin to catch up until he himself takes Crossbow Expert and Sharpshooter, which could happen at levels 12 and 16, levels that campaigns seldom reach.
Disclaimer: As a final note, please do not consider these estimated damage calculations to be extremely accurate benchmarks of actual DPR for builds.2 We do not say this to disparage the idea of DPR calculations themselves, but to point out the reality that they inherently rely on base assumptions, which will vary from table to table or even within campaigns at the same table. The calculations in this article are based on simplified scenarios to demonstrate an argument (the power of feats vs. ASIs), as opposed to an attempt to portray the DPR potential of the presented builds as accurately as possible.
Actual damage calculations would require factoring in the length of an adventuring day and other consumable resources (such as concentration or spells for the Ranger). Actual DPR calculations for guides and more in-depth articles will have taken such considerations into account.
Note though, that even in higher fidelity calculations, the core principle of feats being better than ability score increases stays true for almost all situations you will come across.
2If these damage numbers seem a little low, note that we are forgoing any form of concentration, a huge boost in power for Rangers (entangle, pass without trace, conjure animals). Were these characters Fighters, they would benefit from Precision Strike from Battle Master and the like. Sans Path of the Zealot, Barbarian subclasses don’t add as much damage, comparatively, which is why the base damage seems much higher for Barbarians than ranged fighters. Additionally, 2 triggered opportunity attacks from Polearm Master in 4 rounds might be optimistic or pessimistic assumptions depending on how you play and how your DM runs encounters.
Example 3: Concentration Protection
We’ve seen how grabbing feats early can boost the power of martials by an immense amount. Now we’ll discuss how important a concentration protection feat can be for spellcasters.
5th Edition introduced a revamped version of concentration, making it so that certain powerful and long-lasting spells require the caster to maintain concentration on a cast spell to keep it active. Many powerful spells, especially those with strong lasting effects require concentration, so maintaining it is of the utmost importance in combat.
Let us introduce our two casters, played by Miriam and Pim. Miriam’s character, Mairim, is a Hill Dwarf Druid who will take War Caster at level 4. Pim’s character is a Hill Dwarf Druid named Mip, who will boost his Wisdom at level 4. Both will use a 10/14/14+2/8/15+1/10 point buy.
Mairim and Mip will have the same spell save DC of 13 at levels 1 to 3, and Mip will pull ahead by one at level 4. However, Mairim believes the difference in concentration protection is more than worth it. At level 1, Mairim and Mip both have a +3 Constitution saving throw, so a 70% chance to pass a DC 10 concentration save, which doesn’t seem too bad. But it’s more demonstrative to think about concentration as the average number of attacks you can sustain before dropping concentration. This can be estimated with the formula 1 / (failure chance). From levels 1 to 3, both characters will drop concentration after roughly 3 hits.
At level 4, Mairim takes War Caster. With advantage on concentration saves, Mairim’s individual chance of passing any Concentration save increases from 70% to 91%. The average number of attacks she can take before dropping concentration increases to roughly 11 hits, which is likely more than enough to last her through an entire encounter, or perhaps even multiple if she is concentrating on a spell with a lengthy duration (at this level, it might be more likely that you will die from taking damage 11 times than drop concentration!). On the other hand, Mip’s concentration saves will remain as frail as they were at level 1, all the way up till level 8.
In the early levels, where you might only get to use 1 or 2 meaty concentration spells in a day, that’s devastating. In later levels, when concentration spells become even more powerful, the difference between maintaining and dropping concentration on your highest level slot of the day is crucial. Consider at level 5 when Druids get access to conjure animals. Unlike the 1 minute duration spells where dropping concentration after 3 attacks on average might be enough to get you through an encounter, one of conjure animal’s greatest strengths is its ability to push through multiple encounters per casting, which means many more assaults on your concentration than 1 encounter. This is where concentration protection shines.
Additionally, having a DC that is 1 lower hurts, but it isn’t the end of the world. Some casters, like Druids, might have a gameplan that is not strongly built around save DCs, prioritizing buff spells like pass without trace or summon spells like conjure animals, spells we would recommend for any Druid.
Assuming a 65% spell save failure rate with a 16 in our Spellcasting ability modifier at level 1, an 18 at level 4, and a 20 at level 8, the difference between a DC 14 and a DC 15 on a fireball is 22.3 versus 23.0 average damage per affected target. For spirit guardians, a DC 14 and a DC 15 is 10.7 vs 11.1 DPR per target per turn. On the other hand, if you get attacked twice per round, a 70% chance to maintain concentration means you’ll maintain concentration on average for between 1 to 2 rounds. With War Caster and a 91% chance to maintain concentration, you’ll maintain concentration for 5 or 6 rounds, which is a significant increase in uptime. Having an ability score modifier that is 1 lower does mean 1 fewer preparation slot, which is truthfully much more painful than the DC, but still not as bad as having weak concentration protection.
Our Basic Build Druid followed a similar build path. Mairim would probably be best served following in that build’s footsteps, taking Fey Touched at 4 and Telekinetic at level 8.
Resilient (Constitution) is the other option for concentration protection, but at lower levels War Caster is the superior option in terms of concentration protection. It isn’t until late tier 2 Resilient becomes better than War Caster for this purpose. Needless to say that pairing War Caster and Constitution save proficiency results in the strongest concentration protection you can get through feat choices, and so should always be a strong consideration for spellcaster builds. Another consideration for Resilient (Constitution) is that it doesn’t only help you protect your concentration, but also from the various other Constitution saving throws that your character will probably encounter.
Thus far we’ve elaborated on how to increase your Concentration saves, and the beneficial effects thereof on spells that have effects on failure and on save. “But Tabletop Builds,” you might interject, “what about save or suck spells, which do nothing when enemies save? Don’t you consider spells like hypnotic pattern to be some of the best in the game? Isn’t having a high save DC for those important?” A great point! Let’s look at that example in some more detail.
Hypnotic pattern is a spell whose virtues we extol often (we pick it up on every basic build where it’s possible). Again assuming a 65% spell save failure rate when maximizing our primary ability score, we have two Wizards, one with a DC 14 save (16 Intelligence) but War Caster (91% chance to save on a DC 10 Concentration save), and another with a DC 15 save (18 Intelligence, 70% chance to save on a DC 10 Concentration save). If both cast the spell and can hit 4 enemies with it, the average number of enemies that fail the save is 2.4 enemies for DC 14, versus 2.6 enemies on a DC 15.
But if you’re fighting some intelligent enemies that recognize you as the control caster, and they focus their fire on you, the caster without concentration protection is going to be targeted. If you are damaged twice per round, our Wizard with no concentration protection drops concentration, on average, between 1 and 2 rounds. That’s 2.6 enemies x 1⅔ rounds of concentration, denying an average of 4.3 enemy turns per hypnotic pattern. For our Wizard with concentration protection, 2.4 enemies x 5½ rounds of concentration is an average of 13.3 enemies turns denied. That could very much be enough to totally incapacitate half of the enemy combatants in an encounter.
Of course, as always, you know your table better than we do. If your DM plays enemies in a way such that “backline” casters are almost never targeted, then concentration protection may not be as important. As per our Core Tenets, we are assuming a game that is challenging but fair.
Conclusion
Hopefully, this article has thoroughly disabused you of the notion that maximizing your primary ability score is an imperative that should be done first above all else. For martial damage dealers, we saw how increases to primary ability scores hardly moved the needle in terms of damage, while grabbing the powerhouse feats early contributed greatly to the superior damage output of builds that took feats as soon as possible. With spellcasters, we demonstrated the power of having layers of concentration protection, and how extending the duration of spells, even “save-or-suck” spells, is incredibly valuable. While builds that maximize their primary ability score first and grab feats later may catch up eventually, that’s a lot of playtime and levels where your character was contributing less than they could have. Don’t make that mistake, and make your characters as useful as possible for as many levels as you can! And not only are feats relatively more impactful early in the game, they are generally strong and engaging abilities that make characters more fun to play.
Very insightful post, I struggled with the idea of boosting my primary stat rather than take PAM or GWM when I played a Half Orc Barbarian, and I took GWN at level 4 and +2 STR at 8, when PAM -> GWM would have been a lot better (and more fun to play).
I think, post-Tasha’s, the optimal “standard caster” (ignoring build specific influences) doesn’t actually take a single full ASI, for a lot of the reasons outlined.
This already good article would benefit from the discussion of what AC you should turn GWM “on” and on what AC you should turn it “off”.
I am being allowed the Fighting Style “Tunnel Fighter” as a Paladin. I started with the PAM feat. Should I get a combination of GWM+Sent on lvl 4/8 and an ASI boost or both feats? I have 16 Str.
Sorry no one responded to this until now. We typically recommend maxing Cha on Paladins as soon as you can. In retrospect, Paladin could even use its own section on this article, because Aura of Protection is so strong it throws some of what was presented here out the window. You can see some examples of this Cha early and Cha often approach in both our Basic Paladin and Flagship Paladin builds.
Great article, but I think some examples were a little bit biased.
– For the melee build: Reckless Attack is a huge force multiplier for GWM. Numbers would not be on his favor if we it was a Fighter in the example, even we factor in Precision Strike.
– For the ranged build: Although I totally agree that CBE is a superior use for bonus action, Nevar simply didn’t use his bonus action in the example, which I think it would be fair to assume he was probably using the infamous Hunters Mark — that would decrease a lot the DPR gap between him and Arual. I know it’s DM and campaign dependent, but longbow users can leverage the amazing Bracers of Archery, an uncommon magic item, which once again can equalize the math against CBE users.
CBE + SS + DEX 16 < Longbow + SS + HM + Bracers of Archery + DEX 18
Where does a feat like Lucky play into this? Is having Lucky 3 times a day (when you need it) better than having warcaster all the time?
This is a very important question actually! It largely comes down to how many times you will expect to fail a concentration save in your specific campaign. As you might intuit, Lucky will be superior if this will be relatively infrequent, whereas War Caster will win out in longer, more taxing adventuring days where Lucky would have run out.
I’m confused about the Barbarian build – how does a GWM have the same to hit percentage as someone without when it gives you -5 to hit?
They don’t, we are accounting for the -5 penalty. It’s just that the +10 damage ends up resulting in a higher DPR despite the penalty. We use the same target AC at every point, and Reckless Attack on, for all comparisons. When we say “assumed hit rate” we mean without the Great Weapon Master penalty so it’s easier to compare character with and without— so a character that just increases Strength maintains a 65% to hit rate while a character that has 16 Strength compared to the 20 Strength character has a 55% to hit without GWM— but for the damage calculations we assume GWM and Reckless are on. Does that clarify things?
For example, at level 4, the Str +2 character is making 1 attack at +6, 2d6+6, against AC 14 and does 12.1 damage per round when using Reckless Attack. The character that took Great Weapon Master at 4 can attack at +5/2d6+5, but against 14 AC using Great Weapon Master (+0, 2d6+15) results in 14.4 DPR.
But that way of calculating is unreal, if not wrong.
Calculating the average damage based on the hit percentage does not reflect the real results, because when you roll attack it is not a game where you do damage based on your attack (as it happens in other systems). If you miss, you do 0, so reducing your chances of hitting can result in doing absolutely nothing in a fight.
And that’s not counting the “overdamage” factor. Doing too much damage per hit can mean not taking advantage of that damage, because it’s no use doing 50 damage in one hit, if the enemy has 10 HP. In other words, slightly increasing your DPR like in the examples above is only useful if it’s actually going to kill enemies faster, but that’s rarely the case. Normally you will not leave the enemy at exactly 0 hp, but you will do “over damage”, so having less chances to hit to kill an enemy with the same hits (whatever they are), is not worth it.
Overkill is a factor that slightly diminishes the utility of additional damage, yes. This reduction is very slight, however, especially beyond the early levels (and at the early levels, +10 damage often lets you one shot kill smaller enemies, because it’s just a massive number for those levels). Nevertheless, average damage is a useful proxy for your ability to eliminate enemy threat to your party, because damaging things kills them. Note that we’re not, actually, doing 50 damage per hit – we’re doing 16.5, which will overkill stuff, yes, but even pessimistically by less than 10 damage in expectation. Sure, I would rather 50% to hit for 5 damage than 5% to hit for 50 damage (sans accuracy boosts like *bless*), but those aren’t the choices we make here: we’re choosing between 45% for 16.5 and 75% for 6.5. In principle it’s better to be more accurate than more damaging *for the same DPR*, without other external factors, but when you’re dealing more DPR you’re dealing more DPR. Also note that spells like *bless* and other factors like advantage further increase the value of dealing more damage with each hit.
(And to avoid overkill, you can not use the -5/+10 feat against enemies at low health)
Statistical probability is the only meaningful way to calculate and compare the results. When they say 14.4 dpr, that doesnt mean that each hit will do 14.4 damage. It means that some attacks will hit and do 22 average damage, while other attacks will miss and do 0 damage. Since we know the probability of hitting AC 14, we can calculate the average to be 14.4. Put another way, if that character attacked the same target 10 times, we would expect around 144 damage.
Overdamage isnt really a factor. It’s only lost if the target had less hp than the average damage of just a weapon attack, which in the example is 10. If the enemy has less than 10hp remaining then you can just attack normally. But more importantly, killing an enemy activates GWM bonus attack, which lets the character deal even more damage.
Fascinating article, thanks! I do have a question about the logic behind the equation of anticipated hits before dropping concentration. How does it work, exactly? Is this the number of hits before the cumulative chance of success drops below 50%? Or is it some other factor?
Fair warning, this is gonna get into some probability math and involves an infinite series.
The formula we gave in the post is the expected value — that is, the probabilistic average — of the number of times you can roll a DC 10 concentration save before you fail one. So, for example, if you have a 25% chance of failing any given roll, then there’s a 25% chance you fail on the first roll, a 75% x 25% chance you fail on the second roll, a 75% x 75% x 25% chance you fail on the third roll, etc. So, in general, if you have a probability p of failing any given roll, the average number of rolls you make before failing (where we consider failing on the nth roll to be a result of n) is
1*p + 2*(1 – p)^1*p + 3*(1 – p)^2*p + …
The nth term in this series is n*(1-p)^(n-1)*p, and we’re summing for n=1 to infinity, since there’s no hard limit on the number of times you can succeed before failing (although at some point the probabilities get so small that they’re not affecting the result much). This is called a geometric series, and has a nice tidy sum. Specifically, we’re looking at the expected value of a geometric distribution, which winds up being simply 1/p, which you can verify either by using the general formula for geometric series, or by looking up geometric distribution in your favorite reference (such as Wikipedia).
Thanks for that! That makes sense, at least as far as I can understand the math. It’s been a while since I’ve had a math class.
Sharpshooter and GWM have one massive problem that looking only at statistical average DPR hides from sight. Massive drops in accuracy massively increase the chance of effectively having done nothing. A D&D game is after all not an infinte series of idealized die rolls, but a very finite sequence of roughly 4-12 rolls. And sitting at the table, rolling my dice, I’d much rather get the feeling of success more often than the knowledge that statistically, I have made the better choice.
And that’s where you have to look at all of this advice from a personal standpoint as well. Optimization is about helping you succeed do you have more fun. If the “optimal” choice isn’t fun for you and/or your table you don’t have to feel like you have to do it.
You also need to consider the other benefits of increasing ASI, specially dex that is so powerful in 5e.
How can you calculate the benefit of increasing AC, initiative, dex saving throws and stealth in this analysis.
Even gets more complicated if you want to include battle master maneuvers saving throws.
This is very true— Dexterity does have a lot of benefits! Initiative is very important, and so is AC, and Dexterity saving throws are very common. For AC, unless you’re very strapped for cash, even breastplate is equivalent to studded leather unless you pump Dexterity to 20 by level 4, which you’d need a feat to do anyway (Custom Lineage + Dex half-feat), or level 6 if you go pure ASIs. Likewise, it’s hard to put an exact value on what having one higher initiative bonus is, or a one higher save DC, though obviously both are good. There’s a reason we rate Oath of the Watchers as being the best Paladin subclass, for example.
Ultimately, though, we still value the increased damage output of CBE/SS (in the case of ranged combatants) more than bumping Dex. For casters, it’s still more efficient to get better AC with small dips than it is to rely purely on light armor and Dex. One higher AC, initiative, potentially saves for class or subclass specific features, Dex checks, etc are all good things to have, but the reality is feats are so strong— CBE removes the downsides of ranged combat in melee entirely, and Sharpshooter ignoring cover is just so potent— that we would still recommend taking those feats ASAP over maxing Dexterity. I definitely was someone who maxed out ability scores first when I started out in my first few 5E campaigns, and anecdotally I can say that my later characters who started with CBE/SS were notably more effective. Of course, 5E and DnD in general has so much table and player variance that there is no absolute answer.
These are valid concerns, especially for DEX, which is a skill that does actually have relevant game statistics attached to hit, so lets go through them. I’ll have a look at monks, rangers, fighters, and rogues, as those are the classes that most reasonably take DEX ASIs:
1) Benefits to increasing AC:
rangers and fighters can use medium armor, which caps at 15+2 while studded leather caps at 12+5, so they don’t actually lose AC. Melee monks don’t have competing feats so they *will* be taking DEX, rogues do have competing feats but their impact is very minor and the optimal straight class build maxes DEX first via elven accuracy, so they tend to take DEX anyway and feats are a genuine tradeoff. It should also be noted that melee monk and any rogue’s inability to make great use out of feats is a big reason why they just… aren’t that great, which we have many build on this site to show why and how that is.
2) Initiative:
This one is quite easy to approximate; while not an exact science, you can say a +1 bonus to initiative gives you 1/20th of a turn more to do at the start of a fight, an a round 1 turn is worth about twice as much as a round 3 or 4 turn (because killing enemies earlier denies more actions). So +1 initiative is worth somewhere short of a 5% damage increase, which we can easily account for when comparing things.
3) Stealth:
This one, quite counterintuitively, isn’t actually that big. A huge problem for Stealth users in 5e is that the scouting role is served just as well by a ritual: Find Familiar, so you likely shouldn’t be doing that with a PC that can get caught and murdered. Which leaves getting surprise, but surprise is based off of the lowest stealth roll result in the party, so that’s unlikely to be you. Suppose you have 3 allies with a stealth modifier of +2 and you are debating between keeping your +5 or making it a +6. We can throw that situation in a program like AnyDice and see what it takes to surprise a monster with passive perception 12 (which is about average for a monster). You can view the program i created here: https://anydice.com/program/296b8
With +5, your party has a 11.65% chance to gain surprise, with you having +6 instead your party has a 12.48% chance to gain surprise, so your chance to gain surprise increased by 0.83% points, so once every 120 encounters that you attempt to surprise you will gain surprise that you otherwise wouldnt have (just 1/0.83% to get the expected number).
We can damage approximate this value by assuming your party deals as much damage as you and you all together get 4 free turns while normally only taking 3 turns in combat each. We can also maximize the effect of the increased skill by trying to get surprise every single encounter (which tbf, you should anyway). So this is 0.83% x 4 extra turns divided by the 3 turns we normally would take, or a 1.1% increase in turns taken, which we can again just short of double in value for being round 1 actions. So our total damage average advantage from Stealth is 2% (which, writing this, is actually a staggering increase to me considering we are talking about a 1/120 chance for this to occur).
As a sidenote, if your party utilizes Pass Without Trace, they gain surprise 100% of the time in this scenario, and your stealth modifier doesn’t matter at all – this is why ranger is extremely powerful, and we have some guides coming out on that in the upcoming weeks.
4) Dexterity Saving Throws:
Really easy to quantify, let’s look at the most common DEX save of all: Fireball! 1/20 times we will succeed instead of fail due to our increased modifier and manage to avoid half the spell’s damage. Fireball deals 28 damage on average (3.5 x 8). So our defensive benefit is quite easily (1/20)x0.5×14=0.35 hp per fireball thrown at us.
5) Catch-all category, battlemaster maneuvers
These are indeed awkward to quantify, but decidedly not impossible. I’ll go for a simplified argument here: Something like Sharpshooter increases our hit damage from d6+3 to d6+13, this obviously increases the value of Precision attack by more than double (since it makes more than double the damage hit), it also increases the value of trip attack, since gaining advantage (from the crossbow expert +sharpshooter combo against prone targets) on -5+10 attacks adds more damage than gaining advantage on “normal” attacks. Now you have to compare that to the benefit of tripping the target 1/20 times more often – I think it should be intuitively obvious that a trip 1/20 times does not *double* the value.
We can’t well generalize this and actually do need to look at every character individually to figure out their opportunity cost, but what we present in the article applies to almost all situations
Totalling up the benefits: We’re looking at +1 AC for rogues and melee monks, 5% damage from initiative, and 2% damage from surprise, and 0.35 hp saved per fireball. We also get +1 to hit and damage
Rogues and melee monks will actually look at fast DEX increases a lot of the time, so for these your argument is entirely valid – though as mentioned earlier, and shown with builds on the site, playing these types of characters is, as the title puts it “more min than max” anyway.
For Fighters and Rangers though. I’ll be using a base assumption of 65% to hit a target’s AC if the character starts the game with 16 DEX and increases it to 18 at 4 and 20 at 8 while gaining no other accuracy boosts, which is a decent enough approximation of reality and 5% here or there won’t really matter. Note that both these classes get another +10% from archery:
What are we getting for this opportunity cost? The top 2 feats for DEX characters are Crossbow Expert and Sharpshooter.
1) Crossbow Expert (CBE), looking at pre level 4 and starting with a +3 or getting +4 from race:
we can shoot a heavy crossbow once with +4, or a hand crossbow twice with +3, so the damage advantage of a hand crossbow is:
(2×0.75x(3.5+3)+0.05×3.5)-(0.8x(5.5+4)+0.05×5.5)=2.05; divided by the damage of the heavy crossbow, we get the relative damage increase of 2.05/(0.8x(5.5+4)+0.05×5.5)=26%
Note that this damage increase already accounts for the alternative build having more damage on a hit and to-hit. We also need to subtract the 7% damage that we expect DEX first to get from initiative and skills, so the increase is only 19%. our AC stays the same because of medium armor.
So in this scenario we are looking at 19% damage from the feat, or 0.35 hp per fireball saved from DEX, everything else stays the same – I find this an easy choice. Note that this 19% damage advantage will be reduced once you get extra attack (but it will still be well in the positives), but we will see later, in point 3, why that doesn’t matter.
2) Sharpshooter (SS)
Let’s have a look at the same scenario as above but with this other feat. Using the -5 of SS will reduce hit chance by 25%, but SS can use the same heavy crossbow
(0.5x(5.5+3+10)+0.05×5.5)-(0.8x(5.5+4)+0.05×5.5)=1.65 damage advantage for SS over the DEX increase, relative increase of just short of 21%, make that 14% after accounting for initiative and surprise from DEX. I’m still taking 14% more damage over 0.35 reduced fireball damage.
3) SS AND CBE
Now this is the part where all this compounds and becomes something bigger than the part of its components. This stage of the game is level 5 for characters that got a feat from their race (start CBE, pick SS at 4), or level 8 for races without feats (pick SS at 4 and CBE at 8). Our comparison character will be rocking 20 DEX and a longbow (had to swap off the heavy crossbow due to the loading property not working well with Extra Attack). Also, technically the damage increases from DEX are sublinear, but we can just add them for easy of argument here, which overestimates them to 14%. Surely having +3 DEX instead of +5 must be detrimental?
Well, let’s look at the math, note that CBE SS is getting way reduced hit chance from its DEX disadvantage and -5+10, 35% of the time it just does not hit while the other does! It’s 45% chance to hit versus 80%:
(3×0.45x(3.5+3+10)+3×0.05×3.5)-(2×0.8x(4.5+5)+2×0.05×4.5)=7.15 damage advantage, or a relative increase of just over 45%, subtract the 14% from initiative and surprise and the CBE SS person with 35% less to hit is beating the ASI-first build by 30% in damage, and all the DEX maxer has to show for it is 0.7 HP damage reduction on fireball.
Also note that the value of CBE SS builds goes up WAY stronger than the DEX max build when you gain advantage for any reason, get hit by the Bless spell, or gain a magic weapon – because all these are either static accuracy increases, or in the case of advantage, the benefit of advantage is greatest when hit chance is around 50%. Getting a 10% point increase to your 80% accuracy is gonna increase your damage by 10/80=12.5%, getting the same 10% increase on your 45% is gonna increase your damage by 10/45=22%. So once we account for teamplay, the feat build has even more going for it.
Overall, you ARE correct that there are tradeoffs; but they do not add up to the 45% damage advantage the feat build has, which I hope I could convincingly show.
Thanks for reading and I hope you have a nice day!
Wonderful guide!
I’m curious about the bonded accuracy claim, and love the premise. Much respect on this article, and love what this site is all about.
Math is not my forte so I’m struggling a bit, can you clarify, if testing Rodney (Hudson? Thompson?)’s premise: “Since target numbers (DCs for checks, AC, and so on) and monster accuracy don’t scale with level, gaining a +1 bonus means you are actually 5% better at succeeding …”
Bonded Accuracy as a game design choice seems also a lot to do with average monsters AC, over time.
Does the DPR math work out the same if you increase the Base Hit Rate of Semaj to 75%, While keeping Aras’s at 65%? Is it worth thinking about in this regard? That is how I may have irroneously perceived the topic.
de facto monster AC *does* increase over time, which is why the article calculates the Strength ASIs as keeping pace, rather than going from 65% to 75%
However, the scenario you outline favors Feats EVEN MORE: both characters will effectively gain 10% points accuracy (going from 65->75 and 55->65 respectively), so they just add 10% of their base damage on a hit to their total DPR for each attack they make. The character with the GWM Feat has nearly double the base damage, so they gain nearly twice as much as the STR maxing character from this change in perspective