Exploring a first principle approach to D&D Combat Optimization
a different perspective on thinking about D&D combat
This week a short break from the Moth, the mysterie story centered around Audrey, a woman captured in a web of tentaculous intrigue. Today, I’m sharing another theorycrafting piece. From Moth to Math as it were.
So this week something different. Besides occasionally playing solo RPGs and writing strange stories about them, I am mostly a DM and player in tabletop RPGs. Currently, I'm playing 5e in a Westmarches campaign and in a Genesys urban fantasy campaign, and DM a 5e campaign set in the Savage Frontier.
As regular readers may know, I enjoy theory crafting about RPGs. Recently, I've read some wonderful articles on how combat actually works in D&D.
Combat is a peculiar thing in D&D. On the one hand, the majority of the rules revolve around combat and its derivatives (monster stat blocks, magical items, etc.). On the other hand, actually playing or DMing combat is often a bit dull: a combat quickly turns into two groups of hit point bags facing each other, dealing blows until one of the bags is empty.
Since the mid-90s, alongside being an RPG enthusiast, I've also been a Magic: The Gathering player. One of the things I enjoy about MTG is reading theory craft pieces (like "Who is the Beatdown I/II" by Mike Flores and Zvi Mowshowitz and Rob Hahn’s "Schools of Magic") and applying them to my gameplay and deck building. For D&D combat, I hardly know such pieces. Dragna carta’s ‘A Unified Theory of 5e Combat Design’ here on his substack one of the few examples.
Now, I wanted to write one for D&D. I believe that when everyone at the table understands combat better, it becomes more enjoyable. So, I started searching for existing content. I found excellent YouTube channels like PackTactics and TreantMonk, and sites like TableTopBuilds. However, these sites and channels mainly focus on character optimization, not on optimizing combat itself.
But fortunately, Reddit to the rescue. The great post "Action Economy - A Reddit Guide" by u/naturalcard in the subreddit 3d6 was the starting point, in which the author explores strategies such as increasing party action efficiency, reducing the number of actions by the enemies, and diminishing the action efficiency of enemies in D&D.
In the following week and a half, I tried to write a short, concise piece for both DM and player on how to optimize combat which goes beyond the conventional focus on defeating enemies, as opposed to optimize character building.
I devoured all content I could find and put it into a math formula. During this, I encountered my ability to think mathematically (dropped it in high school because I got a 3/10), so I was very kindly assisted by a few friends to articulate this content clearly.
If you know of any other content on this topic, I’d love to know about it.
Without further ado
Exploring a first principle approach to D&D Combat Optimization
This is a terse article that combines the sources that I could find on the internet and puts them in a single formula. This article aims to provide a model for effective choices in combat, it is about optimizing player character and/or monster actions. It is not about character optimization.
First of all, combat is only one of the pillars of play in D&D, and a battle not fought is a battle won: always consider alternate approaches to combat when appropriate. Also, fought battle is won by reaching its objectives, not by killing enemies. Apart from the choices in the game, an organized character sheet and a well-managed combat zone contribute significantly to clarity and ease of access. D&D combat is managing a lot of information. Organizing this information as clear as possible really helps.
The thesis of this article is that combat optimization, which is defined as making optimal choices as a party, can be abstracted as:
Σx = CQ⋅Qx⋅CA⋅Ax⋅(Tx⋅(1+F(Qy,Ay)))
Where Σ is combat strength and x is whose combat strength,CQ =……. etc it is, and y is the other side of combat.C is the weight of Q, A and T.Then party Combat Advantage (Θ) is : Θparty = Σparty-Σenemy
Action Quantity (Q) is the product of the number of rounds, combatants, and actions per combatant. Each round, a combatant has one action, one bonus action, one reaction, the ability to interact with an object, and the option to move at full speed.
Action Quality (A) is defined by a combatant’s effectiveness in choosing impactful and timely actions, managing resources, and contributing to the combat objectives. A is the ability of the party to use its Q to minimalise the opponents Q and A.
Tactical Versatility (T) is the party's skill in optimizing non-Q and non-A combat variables, including group optimization, effective communication, rule understanding, battlefield awareness, and a growth mindset. T's significance grows with encounter difficulty, marked by high enemy Q and A attributes.
Q: Increasing Action Quantity: Qnew = Qold + Additional Actions.
Add additional actions through surprise, summoning, healing downed allies, removing status conditions, etc. Utilize actions, bonus actions, reactions, movement and interactions to their fullest potential. Buff before combat and persuade NPCs to align with your cause.
Q: Reducing enemy Action Quantity: Effective Enemy Actions = Total Enemy Action Quantity - Reduced Actions.
Reduce enemy actions through area control effects (eg. web, entangle, hypnotic pattern), doorway dodging, and focusing fire. Target high-efficiency enemies: those concentrating on a spell, adding to battlefield control, having high DPR etc. and enemies you excel against: damage vulnerabilities, etc.
A: Increasing Action Quality: Quality actionx ∝−−ΔQy−ΔAy
An action is effective proportional to the negative change in action quantity and quality of the enemy. High-quality actions involve optimal ability use, significant damage per round (DPR), effective environmental control, and collaboration with group tactics. Surpass the expected 65% chance to hit through buffs and seeking advantage. Use optimal general actions like grappling casters, shoving enemies off cliffs, dropping prone against ranged attacks, maximizing cover, leveraging choke points, and maintaining superior range. Spread out to minimize area-of-effect attacks and optimize initiative order. Use spells, magic items, and consumables early in combat to reduce effective enemy actions. Prioritize offense and preventing damage over healing for optimal action use. Prefer ranged combat over melee engagements. Maintain DPR above the maximum expected HP per level/12, as per DMG p.274. Maximize initiative with Dexterity bonuses, feats, or spells like Bless.
A: Reducing Enemy Action Efficiency: Effective Efficiency = Total Efficiency - Reduced Efficiency.
Reduce enemy efficiency by applying debuffs and control such as blindness/deafness, silence, illusions, counterspell, caltrops, etc. Enhance your defense through dodging, high AC, and imposing status conditions. Control enemy movement by forcing (eg. thorn whip) and thwarting it—prevent escape and impede movement through bottlenecks. Note that limited space reduces the effectiveness of speed.
T: Tactical Adaptability: f(Encounter Complexity, Battle Conditions)
Tactical Adaptability is the player skill to adjust strategies and actions based on evolving battlefield conditions. It includes environmental and combat goal awareness, flexible decision-making, and effective teamwork. Adapt to changing needs, objectives, and terrain dynamics. T scales dynamically with encounter complexity.
Group Coordination: Tgroup = T individual + Group Coordination Bonus
Enhance teamwork through coordinated efforts and communication. Synchronize actions using initiative order, coordinate movement, and create opportunities for focused attacks. Utilize situational strategies, like dragging enemies through spike growth, and establish dominance zones before combat.
Effective Communication: Coordinate tactics and use party features synergistically. Preemptively assess challenges and adjust spell selection and equipment accordingly, considering utility spells that can be cast as rituals without using spell slots.
Growth Mindset: Embrace challenges as opportunities for growth. Reflect on past events, analyze decisions, and formulate new strategies. Reconsider spell choices and seek specialized items for advantages. Actively gather information on adversaries' strengths and weaknesses.
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There it is: all the combat optimalization wrapped into one not too complex model. I hope it helps at your table and if there are any mistakes or oversights I’d love to hear about them. Happy gaming.