Sharpshooter — when does -5/+10 beat the to-hit penalty on ranged attacks?

The math (same as GWM, ranged version)

Damage-per-round without Sharpshooter:

DPR_without = hit_chance(A, B) · E[base_damage]

With Sharpshooter (or against a long-range / heavily-obscured target where you'd be at disadvantage anyway):

DPR_with = hit_chance(A + 5, B) · (E[base_damage] + 10)

Break-even at DPR_with = DPR_without gives the same structural rule as GWM — just shifted by a couple of points because Longbow / Heavy Crossbow base damage is lower than Greataxe / Greatsword.

The break-even table

Numbers below assume a Longbow (1d8+DEX) for the base damage. A Heavy Crossbow (1d10+DEX) shifts the table up by ~1 AC point in Sharpshooter's favour; a Hand Crossbow (1d6+DEX) shifts it down by ~1.

So the rule of thumb is break-even AC ≈ attack-bonus + 7 for a Longbow build. One point lower than the Great Weapon Master rule because the lower base-damage roll means the flat +10 has more relative impact on every successful hit.

The damage rolls themselves

Side-by-side: a +5 DEX Longbow attack (left) vs the Sharpshooter-boosted version (right). Same shape, mean shifted right by 10. Click any percentage to see the exact rational.

Variance stays at (8² − 1)/12 = 63/12 = 21/4 for both, since flat modifiers don't shift spread. The break-even AC is determined entirely by the hit-chance × mean trade.

The per-attempt distribution — including misses and crits

The damage rolls above are conditional on a hit. The real per-attempt distribution folds in the d20 attack roll: a probability mass at 0 (miss), the standard damage on a non-crit hit, and a doubled-dice tail on a natural-20 crit. Same Longbow build (+5 DEX, +9 base attack bonus) vs an AC 15 target. Left is the base attack, right is Sharpshooter (−5 to-hit, +10 damage):

The 0-bar is the miss probability. Without Sharpshooter (left), nat 1 misses and nat 2-5 missed against AC 15 with +9 to-hit: P(miss) = 5/20 = 25%. With Sharpshooter (right), the to-hit drops to +4 so misses extend through nat 10: P(miss) = 10/20 = 50%. The crit-on-20 branch is the same 5% in both panels but contributes more damage on the Sharpshooter side because the doubled dice become 2d8 against a +15 modifier rather than +5.

Mean per attempt:

• Without Sharpshooter: (14/20)·7.5 + (1/20)·12 = 117/20 = 5.85 damage per shot.
• With Sharpshooter: (9/20)·17.5 + (1/20)·22 = 179.5/20 = 8.975 damage per shot.

Sharpshooter wins by about 3.1 mean DPR per shot at AC 15 with +9 to-hit, consistent with the break-even table above (which says Sharpshooter is on at AC 16 or below for this build).

Extra Attack — the per-round picture

Per-shot DPR is what the break-even table is calibrated for. The question players actually ask is "should I turn Sharpshooter on this turn?" At level 5+, a Fighter takes two shots per round via Extra Attack, and the full-round distribution is the convolution of two independent per-attempt distributions:

Mean per round doubles cleanly (11.7 vs 17.95). Variance grows too, and the zero-bar shrinks because the probability of missing both shots is the single-shot miss probability squared. For Sharpshooter that's P(both miss) = (10/20)² = 25%; for the base attack it's (5/20)² = 6.25%. Even with Sharpshooter on, you land at least one hit 75% of rounds at this AC.

Action Surge pushes this further (4 shots in one round). Try /strike/1d8+15 @ AC17 +4 attacks 4 to see a Sharpshooter Action Surge round vs AC 17. The kill probability stack against a tier-3 boss starts looking genuinely scary even without crits.

The Crossbow Expert wrinkle

The most common Sharpshooter pairing is with Crossbow Expert and a Hand Crossbow. CBE gives you a bonus-action attack with a Hand Crossbow when you Attack-action with one. So a CBE+SS Fighter at level 5 (Extra Attack) gets three attacks per round at 1d6+DEX+10 each.

The break-even math is per-attack, not per-round. Because every CBE+SS attack is 1d6+5 base (mean 8.5) instead of 1d8+5 base (mean 9.5), the table shifts down by about 1: break-even AC ≈ attack-bonus + 6 for a CBE+SS build at +9, so AC 15, not 16.

The aggregate effect is famously lopsided: three attacks at 1d6+15 against AC 15 produces enormous DPR, which is why CBE+SS Fighter has been the default 5e ranged optimisation answer for a decade. Stack Elven Accuracy on top (half-elf with frequent advantage from Pack Tactics or Reckless-equivalent) and the third-die effect on each of the three attacks comfortably offsets the −5 penalty even against AC 18+.

The long-range wrinkle

Sharpshooter's other clause has two parts: it ignores half-cover and three-quarters cover, and it ignores the disadvantage from long-range shots. The first two are situational; the third is straight-up free. Whenever the GM puts the target past your normal range, Sharpshooter converts the disadvantage to no penalty.

Disadvantage is much worse than a flat −5. It multiplies the miss probability by itself (see advantage and disadvantage for the curve). Against AC 15 with a +9 attack bonus, disadvantage drops your hit chance from 15/20 to (15/20)² = 56.25%, a roughly 19-point swing. The −5 that Sharpshooter charges you to ignore that disadvantage is a 25-point swing in the other direction. Sharpshooter is worth turning on at long range almost regardless of AC, even against targets where you'd otherwise leave it off.

Try it yourself

↦ /vs/1d8+5/1d8+15 — Longbow damage rolls, base vs Sharpshooter, +5 DEX ↦ /vs/1d8+5 @ AC15 +9 / 1d8+15 @ AC15 +4 — base vs SS per-attempt ↦ /vs/… attacks 2 — base vs SS per round (Extra Attack) ↦ /strike/1d8+15 @ AC15 +4 attacks 2 — Sharpshooter Extra Attack round ↦ /strike/1d8+15 @ AC17 +4 attacks 4 — Sharpshooter Action Surge vs tier-3

Drag the HP slider in the /vs view above. Below the Sharpshooter mean (15.5), the +10 dominates; well above, the −5 to-hit starts mattering more — same threshold-vs-tail logic as variance and kill probability, applied per-shot. The @ AC<n> +<m> forms compare the full per-attempt distribution (including miss); the bare-damage forms compare conditional-on-hit distributions only. attacks 2 sums two independent attempts for the per-round view.

Where this matters in practice

The ranged version of the GWM trade lives in three specific build patterns where the AC math actually gets exercised.

BG3 longbow vs heavy crossbow. Longbow at level 5+ gets two attacks per round; heavy crossbow gets one (loading). Sharpshooter's per-shot break-even applies twice per round on the longbow side, doubling the swing of the AC math. See the BG3 ranged table for typical attack-bonus / damage rows.

Crossbow Expert + Sharpshooter at low levels. CBE adds a bonus-action shot, which is another break-even attempt per round. With +5 to-hit and a +1 weapon, CBE+SS is on against AC ≤ 13 — most low-level encounters. The break-even math tracks the same closed-form as Longbow.

Long range with disadvantage. Past normal range, Sharpshooter ignores the disadvantage too. That's a quiet +3 to +5 effective to-hit on top of the −5 trade, which usually pushes Sharpshooter into "always on" territory at long range — even at AC 18+. The advantage curve shows the disadvantage band Sharpshooter erases.