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DnD 5e - The Fundamental Math of Character Optimization

Last Updated: March 20th, 2019

Dungeons and Dragons represents success and failure as binary values. There is no "failure with stuff" or "success with complications" written into the game, and failing by 1 or failing by 10 is usually the same result. Increasing your successes and minimizing failures is the primary goal of character optimization, but without understanding of 5e's internal math it's difficult to know what we need to target numerically to make an effective character.

For the purposes of this article, we can make some specific assertions about what makes a character "effective". 5e's math assumes that a character attempting to do something which they are good at should succeed 60% of the time, which gives us a perfect metric for how we should build characters. If you can't hit that 60% mark, your character is less effective than intended, and if you're above the 60% mark you're more effective than the game assumes (which is what we want).

Where does the 60% number come from?

Take a look at this table. You may notice that the right-most column Never changes.

  1. Taken from the Monster Statistics by Challenge Rating table, DMG 274
  2. Assumes an ability increase resulting in the PC's ability modifier increasing from 3 to 4 at 4th level
  3. Assumes an ability increase resulting in the PC's ability modifier increasing from 4 to 5 at 8th level
PC Attack Bonus By Level vs. Monster AC
PC Attack Bonus Monster
Level/CR Abl Prof. Total AC1 Hit %
1 3 2 5 13 60%
2 3 2 5 13 60%
3 3 2 5 13 60%
4 42 2 6 14 60%
5 4 3 7 15 60%
6 4 3 7 15 60%
7 4 3 7 15 60%
8 52 3 8 16 60%
9 5 4 9 16 60%
10 5 4 9 17 60%
11 5 4 9 17 60%
12 5 4 9 17 60%
13 5 5 10 18 60%
14 5 5 10 18 60%
15 5 5 10 18 60%
16 5 5 10 18 60%
17 5 6 11 19 60%
18 5 6 11 19 60%
19 5 6 11 19 60%
20 5 6 11 19 60%

This tells us a great deal. First, it solidifies the 60% target. Second, it highlights the fact that 5e was written to be work without feats; instead, it assumes that your first two ability score increases will go into the ability score which you're using to attack. Third, it assumes that you're getting Ability Score Increases at levels 4 and 8 to raise your primary ability score to 20.

What do I do with this information?

That's really up to you. Any time that you fall below the 60% mark, it should be a trade. Whatever you get needs to be good enough to justify what you lose.

Feats are popular, especially among character optimization enthusiasts, but the above math makes the cost of feats abundantly clear. One feat will make you 5% less effective offensively until you get enough ability score increases to get up to 20. If you can mitigate this with things like spells or magic items, it will reduce the impact. Even Bless, a 1st-level spell, will provide a large enough bonus to offset taking 2 feats with an average roll of 2.5.

Perhaps more importantly, this stresses the importance of starting at 1st level with a 16 in your primary ability score. At 1st level when missing an attack by 1 frequently means an early death, there is little room for error, and you really need to squeeze every bit of effectiveness out of your character just to stay alive. Casters may have things a little better because they can rely on indirect options like support spells and spells which don't require attack rolls or saving throws, but I would think long and hard before walking into a game with a 1st-level fighter that doesn't have 16 Strength or Dexterity.