Compare gear with hit chance and expected damage
Compare +1 to attack, +1 damage and advantage against AC 16 using the same assumptions, including critical hits and a practical planner checklist.
Does the largest damage number win?
A damage range leaves out attacks that miss. Compare equipment against the same target before comparing its average contribution per attack. The numbers below are calculations under explicit assumptions, not results of an in-game benchmark.
Keep the comparison controlled
Use a target with Armour Class 16, an attack bonus of +5 and ordinary hit damage of 1d8+5. There is no advantage, disadvantage, resistance, extra damage or special critical-hit effect. Dice are uniform and independent; Karmic Dice are outside this model. Only a natural 20 is critical. A critical hit rolls one extra d8, but does not double the flat +5.
Rolls 11 through 20 hit, so the total hit chance is 50%: 45% ordinary hits and 5% critical hits. Natural 1 and natural 20 must also be handled explicitly. A high attack bonus does not simply turn an ordinary attack into a guaranteed hit.
Calculate an attack including critical hits
The average of 1d8 is 4.5. Ordinary hit damage averages 9.5; critical damage averages 14. Use ordinary-hit probability × ordinary damage + critical probability × critical damage. The baseline is 0.45×9.5 + 0.05×14 = 4.975.
| Change | Total hit chance | Expected damage |
|---|---|---|
| Baseline: +5, 1d8+5 | 50% | 4.98 |
| Only attack bonus +1 | 55% | 5.45 |
| Only flat damage +1 | 50% | 5.48 |
| Attack bonus and flat damage both +1 | 55% | 6.00 |
| Baseline attack with advantage | 75% | 7.56 |
Here, +1 flat damage narrowly beats +1 to attack. That result can change with target AC, baseline damage or the value of an on-hit condition. This is a comparison method, not a universal equipment ranking.
Advantage is not a flat +5
For a baseline hit probability p, advantage gives 1−(1−p)² and disadvantage gives p². A 50% attack becomes 75% or 25%. With advantage, the example's critical chance is 1−0.95²=9.75%, leaving 65.25% ordinary hits. Thus 0.6525×9.5 + 0.0975×14 = 7.56375.
If gaining advantage costs a separate action, account for that action too. Adding another source of advantage does not mean rolling three d20s and keeping the best one.
A practical planner workflow
- Hold character level and target AC constant; record the current equipment result.
- Change one slot and inspect attack bonus, hit chance and damage separately.
- Enable conditional effects only when the party can actually trigger them. Identify who applies the required condition first.
- Compare a second scenario without advantage or with resistance, and consider failed concentration.
- Include range, defence, action cost and acquisition timing in the final choice.
What this calculation cannot tell you
Expected damage is a long-run average, not a prediction for the next attack or a kill probability. Damage beyond a target's remaining health may be wasted. Extra attacks, rerolls, expanded critical ranges and additional damage riders need their own treatment. This example is also not a claim that the planner implements every special interaction.