D&D General Wizard vs Fighter - the math

[M_Natas]

So, after all the Fighter vs Wizard Discussions, I wanted to see, if it is really true that a Fighter is worse than a wizard.

So I did the math.

(Blue - the wizard is stronger by at least 20%. Red - the wizard is weaker by at least 20%, yellow is between 10-20 discrepancy, green is under 10%).

I compared the average damage output per Round in Combat for the Fighter and the Wizard for several scenarios.

First I looked at the number of battle rounds a party can have. A battle can take up 1 to 7 rounds and a party could encounter 1 (2x deadly) to 12 (easy) battles per adventuring day, if we go by the adventuring day rules. So a party could encounter between 2 long rests 1 round of battle or 84. That's a big range of battle rounds. The DMG advices between 3 and 6 battles.
So, I picked some examples:

• 3 Rounds - the typical 5 Minute adventure day
• 9 rounds - I would say on my tables probably the most common number of battle rounds between two long rests.
• 18 rounds - if you follow the DMG an adventuring party should encounter this many battle rounds on average between long rests
• 36 rounds - 12 easy encounters a 3 rounds (I hope nobody does that) or 6 hard encounters taking 6 rounds.
• 72 rounds - 12 easy encounters taking 6 rounds each - if you hate yourself and your players, do that.

Than I looked at at the number of enemies, because the effectiveness of the Wizard depends strongly on AoE spells.
I checked vs. Single Creature, vs 2 Creatures (average AoE Damage x 1,5) and more than 3 creatures (AoE Damage x2).
Fighter and Wizard get a +1, +2 and +3 magic items at levels 5, 10 and 15.

So these are my expectations.

I build a champion fighter and a plain Wizard without subclass features. The wizard takes always the spell that will do the most damage for a certain spell level, he uses up the highest spells first, if he runs out of spells, he will take cantrips. The Fighter damage is accounted for the use of Action Surge and Critical damage.

So, what does my math say?

When there are only 3 battle rounds per long rest, the Wizard will always be better than the fighter by at least 20% except at low levels vs 1 creature. But only at levels 5 and 6 will the fighter be ever stronger vs 1. Creature. The more enemies you have, the bigger the advantage of the wizard.
With 3 or more enemies creatures the wizard usually does more than double the damage of the fighter.
Over all lvls the Wizard will do

• vs 1. Creature on average 137% of the fighter damage,
• vs 2 Creatures 166%
• and vs 3 or more creatures 195% of the fighter damage.

If you have 9 battle rounds inbetween Long Rests, vs. 1 Creature, the Fighter and a wizard are pretty close in damage output. Vs 2 or more Monsters the Wizard will outperform the Fighter.
Over all lvls. the Wizard will do

• vs 1. Creature 98% of the Fighter damage.
• vs 2 creatures 122% of the Fighters Damage
• Vs. 3 creatures 146% of the fighter damage

If you have 18 Battlerounds, the Fighter will outperform the Wizard vs. 1 and 2 creatures while it is pretty close against 3 or more creatures.
Over all the levels, our wizard does

• vs 1 creature 70% of the fighter damage
• vs 2 creatures 86% of fighter damage
• vs 3+ creatures 102% of Fighter damage.

With 36 rounds the fighter is always better.
Over all levels the wizard will do

• vs. 1 Creature 53% of Fighter damage
• vs. 2 creatures 61%
• vs. 3+ creatures 69%

And with 72 rounds, it is the same.
Wizard/fighter

• 1 creature: 45%
• 2 creatures: 49%
• 3+ creatures 53%.

If we look at the extremes (3 rounds vs 32 or 72 battlerounds) the effectiveness in Combat gets reversed. In 3 rounds vs multiple creatures the Wizard does double the damage of a fighter while in 32 rounds vs 1 creature the fighter does double the damage of the wizard.

What can we learn from this?

First of all, what everybody is always already saying is: the 5 minute workday is utterly broken for spellcasters. If you have less than 9 rounds of combat inbetween rests, even at lvl 1 the wizard will outperform the Fighter and latest at level 5 will have spell slots to spare for non Combat situations, paving the way for Spellcaster domination in all aspects of the game from that level on.

How to Fix that as a DM: if you only want to have one battle, make the battle longer and vs. one strong enemy. Give the creature more hitpoints to last longer (at least for 6 rounds, better 9). You have to adjust the damage output of the creature, because the damage is usually balanced around 3 rounds of survival, so in 9 rounds it can do way more damage to your party than the CR would tell you.

For 9 rounds, it depends on the number of enemies. If you as the DM always use one appropriate monster to challenge the party, the Fighter and wizard will be equal (98% similar damage output). but the Wizard will from level 5 on have spell slots to spare for other situations. Vs. 2 or more creatures, the Wizard will outdamage the fighter, and he will have spell slots to spare.
So if you want to have few battles and not a lot of combat rounds (not a lot defined as 9) in one day, use single monsters to challenge the party and give the Fighter a chance to shine.

18 battle rounds between long rests seems to be the sweet spot between fighter and wizard.
The fighter will outperform the Wizard vs 1 and 2 creatures and will be equally good vs 3 or more creatures and the Wizard will have to use up to level 12 all his Spellslots to keep up with the fighter. So now the wizard needs to decide, if he spares some ressources and be less effective in Combat or blast everything in Combat and doesn't have utility outside of combat.
18 battle rounds could be 6 fights a 3 rounds or 3 fights a 6 rounds or a big boss fight with 9 rounds and 3 smaller fights a 3 rounds.
But what we see here, is, that the Adventure Day guidlines in the DMG work as intended. 6 encounters a 3 rounds is the balanced sweet spot between long rest ressources (spellslots) and at will powers (fighter).

36 battlerounds and above

This is fighter land. Wizards don't need to apply.
But having a lot of battlerounds - I realistically can only see that working, if the Gritty Realism Rest rules are used. Than you can stretch out the battles over several ingame days.

Conclusions without rules changes

So, if you are DMing a game and feel like, that the martial classes are underwhelming at your table and the casters are overpowered and dominating every aspect of the game, without rules changes to the classes themselves, you can do the following things:

• Increase the number of battlerounds either by having more battles or making battles longer (more hitpoints for the monster) - the sweetspot is 18 Battlerounds per long rest, as low as 9 can be fine, when you ...
• use single creatures to reduce the effectiveness of AoE spells.
• use gritty realism rest rules

Conclusions for rules changes

It seems that the number of battles (and battlerounds) in a day is at the modern gaming table drastically lower than what the makers of D&D expected.
That has several reasons:

• 6 battles a day doesn't fit most modern narratives - dungeon crawling is not the standard mode of play anymore
• players optimising the fun out of the game and being risk adverse by taking every long rest they can (from a mechanical standpoint, long resting after every battle is the optimal strategy).

Mechanically, there are several solutions:

• Alternative Rest rules to stretch out the time between long rests or make long rests less effective (like giving back as much spellslots ad you have Prof. Bonus)
• reducing the number of spell slots available per day (more akin to warlock)
• strengthing the fighter - in order to keep up with the wizard in a 5 Minute workday day environment, the Fighter needs 40% more damage against single targets and he needs to get AoE Damage capabilities that increase his damageoutput against multiple targets by at least 100% to make them as good as Wizards. So increase that even more, so the fighter is best at fighting while the Wizard can keep his utility abilities. Make the stronger abilities daily powers so that if their is suddenly an increase in battle rounds that the fighter will not overwhelm everything (like the wizard does right now with few battlerounds).

 

[James Gasik]

I appreciate that you did all the math, but what about non-damaging effects the Wizard can use to dramatically blunt the ability of enemies to act in the first place? You discuss balance modifications based solely on Wizard damage and not how a spell like Hypnotic Pattern has the potential to leave half the enemies in an encounter staring off into space while the other half scrambles to snap them out of their daze- the Wizard has done zero damage, but in this scenario prevented an entire round of enemy attacks while your party can focus a single target down.

 

[Stormonu]

Yeah, the problem between Wizard-Fighter isn't in DPR, it's in what they can do in the first place. The Wizard's utility spells can circumvent not only combat but also have a dramatic effect or possibly even circumvent having to make rolls in the Social and Exploration pillar. Meanwhile, the fighter has two skills to choose from that gives them about a 10% better chance (i.e., +2 PB) in one of the three pillars.

 

[M_Natas]

I appreciate that you did all the math, but what about non-damaging effects the Wizard can use to dramatically blunt the ability of enemies to act in the first place? You discuss balance modifications based solely on Wizard damage and not how a spell like Hypnotic Pattern has the potential to leave half the enemies in an encounter staring off into space while the other half scrambles to snap them out of their daze- the Wizard has done zero damage, but in this scenario prevented an entire round of enemy attacks while your party can focus a single target down.

It is hard to believe, but the Damage Output of the Monsters is a separate thing. That a player character will go down is the big exception in 5e, so for game balance reasons we can focus solely on the damage output of the Player Characters.
And if the Wizard uses hypnotic pattern instead of fireball ... that's a good thing. The Wizard didn't do roughly 56 points of damage, so the fight gets longer, which adds a round or two to combat, so the fighter gets more damage output in comparison to the wizard.
Every time a spellcaster uses a spell that doesn't do damage, it allows the martials to shine more and tilts the balance more in favor of the martials.

But we can also look at it from a ressource standpoint:
So, what happens with hypnotic pattern? It negates enemy attacks. So what did the Wizard actually achieved?
He traded a 3d Level Spellslot to prevent a reduction in the HP pool of the party.
So the wizard traded his limited ressource, his spellslot for a preservation of the limited HP of the martials/the whole party. Which is great. Which helps game balance.

 

[M_Natas]

Yeah, the problem between Wizard-Fighter isn't in DPR, it's in what they can do in the first place. The Wizard's utility spells can circumvent not only combat but also have a dramatic effect or possibly even circumvent having to make rolls in the Social and Exploration pillar. Meanwhile, the fighter has two skills to choose from that gives them about a 10% better chance (i.e., +2 PB) in one of the three pillars.

But that is only a problem, when the wizard has spellslots to spare (so when the party has less battlerounds than spellslots).
When you have 18 or more battlerounds per long rest, the Wizard now has to choose between utility and combat efficiency. It is now a hard choice.
Of course if we have he 5 minute adventuring day, the Wizard can overpower alle three pillars of play.

 

[Vaalingrade]

Damage still isn't the point.

 

[Krachek]

3 rounds of fight per rest, PCs are overpaid!

 

[Asisreo]

Yeah, the problem between Wizard-Fighter isn't in DPR, it's in what they can do in the first place. The Wizard's utility spells can circumvent not only combat but also have a dramatic effect or possibly even circumvent having to make rolls in the Social and Exploration pillar. Meanwhile, the fighter has two skills to choose from that gives them about a 10% better chance (i.e., +2 PB) in one of the three pillars.

Its important to remind people that fighters already do great damage comparatively, though. There's a lot of times where people will argue that "Wizards do more damage than fighters" and outside of a few key areas of obvious oversight from the developers, that's just not true.

Its always important to check our work when it comes to these things, too, because we might see base assumptions change and those could change the results greatly as well.

 

[payn]

What is a battleground?

 

[Oofta]

Some people will never believe there isn't an issue no matter how much math, how much proof you have. I haven't ever seen an issue either DMing or playing; different roles in the game do not make one class "better" than the other. I've seen the same thing in video games like Solasta where you can play modules that shows you (up to level 13 anyway) who wins the DPR contest, 99% of the time it's the fighter.

In addition to not having a 5MWD I would recommend setting up situations where enemies come from multiple directions, showing up in waves. Always showing up in fireball formation is one of the issues. Play monsters intelligently. Have the lurkers lurk and force the PCs to rely on readied actions because if a readied spell never goes off it is wasted. Focus fire on the wizard and take them out quickly. Don't get overly concerned if every once in a while the wizard gets to go nova, let them have fun. Pay attention to the negatives of a spell; a fireball sets unattended items on fire, a person that was charmed remembers they were charmed.

I could go on, but this will just devolve back into the same old back and forth. There is nothing that will "prove" anything to some people nor, it seems, will they listen to suggestions or advice from people who so not have the problem