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 fundamental 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 65% of the time, which gives us a perfect metric for how we should build characters. If you can’t hit that 65% mark, your character is less effective than intended, and if you’re above the 65% mark you’re more effective than the game assumes (which is what we want).
Where does the 65% number come from?
Take a look at this table. You may notice that the right-most column never changes.
| PC Attack Bonus | Monster | ||||
|---|---|---|---|---|---|
| Level/CR | Abl | Prof. | Total | AC1 | Hit % |
| 1 | 3 | 2 | 5 | 13 | 65% |
| 2 | 3 | 2 | 5 | 13 | 65% |
| 3 | 3 | 2 | 5 | 13 | 65% |
| 4 | 42 | 2 | 6 | 14 | 65% |
| 5 | 4 | 3 | 7 | 15 | 65% |
| 6 | 4 | 3 | 7 | 15 | 65% |
| 7 | 4 | 3 | 7 | 15 | 65% |
| 8 | 53 | 3 | 8 | 16 | 65% |
| 9 | 5 | 4 | 9 | 16 | 70%4 |
| 10 | 5 | 4 | 9 | 17 | 65% |
| 11 | 5 | 4 | 9 | 17 | 65% |
| 12 | 5 | 4 | 9 | 17 | 65% |
| 13 | 5 | 5 | 10 | 18 | 65% |
| 14 | 5 | 5 | 10 | 18 | 65% |
| 15 | 5 | 5 | 10 | 18 | 65% |
| 16 | 5 | 5 | 10 | 18 | 65% |
| 17 | 5 | 6 | 11 | 19 | 65% |
| 18 | 5 | 6 | 11 | 19 | 65% |
| 19 | 5 | 6 | 11 | 19 | 65% |
| 20 | 5 | 6 | 11 | 19 | 65% |
- Taken from the Monster Statistics by Challenge Rating table, DMG 274
- Assumes an ability increase resulting in the PC’s ability modifier increasing from 3 to 4 at 4th level
- Assumes an ability increase resulting in the PC’s ability modifier increasing from 4 to 5 at 8th level
- This level is an anomaly. Proficiency Bonuses increase, but expected monster AC does not.
This tells us a great deal. First, it solidifies the 65% 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 65% 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.
Let’s Talk Damage
Perhaps the most important reason to stay on the fundamental math is to maintain your damage output in combat. If you can’t hit, you won’t do damage. As your attack bonus lags, so will your damage per round (DPR).
With the introduction of the DPR Calculator, we’ve started including DPR in many of our example builds. While this certainly isn’t a perfect measure of effectiveness (save or suck spells and support spells affect DPR indirectly through multipliers on our party’s individual DPRs or by outright removing enemies), DPR is still a helpful measure for many characters whose primary offensive contribution is damage output.
But how much DPR do you need? What constitutes “good” dpr?
Finding the answer is surprisingly simple. The same rules that we use to find the fundamental math progression for attack bonuses also give us an hp progression for monsters. If we assume a party of 4 and 3-round encounters like the CR calculation rules do, we can divide the top end of the hp progression by 12 to get our target DPR. If your party’s average DPR is roughly that high, you’re doing okay.
I’ve chosen to include four columns of DPR:
- Low DPR: If you’re above this number but below Target DPR, you’re not doing quite as much damage as the game expects on average. If your character is primarily doing other things (support spells, area control, save or suck spells, etc.) this might be perfectly fine.
- Target DPR: The sweet spot. If you’re at least this high, you’re doing fine. If you absolutely can’t get above this number, ensure that whatever you’re doing in combat boosts your party’s total DPR to compensate.
- High DPR: If you’re above this number, you’re doing two people worth of work. You might be your party’s Striker, and in combat you’re the scariest thing that isn’t a save or suck.
- Dude Stop: If you’re above this number, you’re dealing enough damage to feasibly solo encounters. If you can maintain this damage output for three rounds, you’re expected to kill a level-appropriate monster entirely by yourself. Your DM may need to make significant adjustments to the difficulty of encounters to provide you with an adequate challenge. In effect, you’ve won character optimization. Stamp four stars on your character sheet in blue ink and send me a picture on twitter so I can revel in your success.
- Warlock: A very simple warlock using Eldritch Blast, Hex, and Agonizing Blast with an ASI in Charisma at levels 4 and 8. This can be helpful as a baseline character to compare yourself to if the Target DPR numbers feel too abstract.
- Rogue: A rogue using two-weapon fighting with short swords. Assumes that the rogue can deal sneak attack every turn. Like the Warlock column, this is a helpful baseline, but the reliance on Sneak Attack for damage means a smoother DPR progression.
| CR or Level | Max Expected HP | Low DPR | Target DPR | High DPR | Dude Stop | Warlock | TWF Rogue |
|---|---|---|---|---|---|---|---|
| 1 | 85 | 3.5 | 7.1 | 14.2 | 28.3 | 6.3 | 10.47 |
| 2 | 100 | 4.2 | 8.3 | 16.7 | 33.3 | 8.25 | 10.47 |
| 3 | 115 | 4.8 | 9.6 | 19.2 | 38.3 | 8.25 | 14.10 |
| 4 | 130 | 5.4 | 10.8 | 21.7 | 43.3 | 8.9 | 14.75 |
| 5 | 145 | 6.0 | 12.1 | 24.2 | 48.3 | 17.8 | 18.37 |
| 6 | 160 | 6.7 | 13.3 | 26.7 | 53.3 | 17.8 | 18.37 |
| 7 | 175 | 7.3 | 14.6 | 29.2 | 58.3 | 17.8 | 21.99 |
| 8 | 190 | 7.9 | 15.8 | 31.7 | 63.3 | 19.1 | 22.64 |
| 9 | 205 | 8.5 | 17.1 | 34.2 | 68.3 | 19.1 | 26.26 |
| 10 | 220 | 9.2 | 18.3 | 36.7 | 73.3 | 19.1 | 26.26 |
| 11 | 235 | 9.8 | 19.6 | 39.2 | 78.3 | 28.65 | 29.89 |
| 12 | 250 | 10.4 | 20.8 | 41.7 | 83.3 | 28.65 | 29.89 |
| 13 | 265 | 11.0 | 22.1 | 44.2 | 88.3 | 28.65 | 33.51 |
| 14 | 280 | 11.7 | 23.3 | 46.7 | 93.3 | 28.65 | 33.51 |
| 15 | 295 | 12.3 | 24.6 | 49.2 | 98.3 | 28.65 | 37.13 |
| 16 | 310 | 12.9 | 25.8 | 51.7 | 103.3 | 28.65 | 37.13 |
| 17 | 325 | 13.5 | 27.1 | 54.2 | 108.3 | 38.2 | 40.75 |
| 18 | 340 | 14.2 | 28.3 | 56.7 | 113.3 | 38.2 | 40.75 |
| 19 | 355 | 14.8 | 29.6 | 59.2 | 118.3 | 38.2 | 44.38 |
| 20 | 400 | 16.7 | 33.3 | 66.7 | 133.3 | 38.2 | 44.38 |
The Power of Teamwork
While the DPR for attacks is straightforward and easy to calculate with our DPR Calculator, how do we determine the numerical DPR of indirect help? This is less straightforward, but still a simple calculation.
Using Bless as a simple example, calculate the normal DPR of your targets, then assume the average of +2.5 and calculate the new DPR. The difference between these two DPRs is the DPR of that Bless spell. As all parties will be different, the DPR of any given Bless spell can be all over the place.
This same kind of calculation can be done with several kinds of spells that don’t directly do damage, such as Web imposing Restrained, which in turn grants Advantage to attackers or Hold Person imposing Paralysis which both grants Advantage as well as automatic critical hits to attackers within 5 feet. You may find that your “Assist DPR “ is still hitting or exceeding Target DPR in addition to the defensive benefits these crowd control and buffing spells have.
Further Reading
If you have made it this far, you clearly see the value in understanding the game’s math. If that’s you, you might also enjoy our SRD Monsters Stats Analysis.
