Great Weapon Fighting — does the reroll-on-1 actually buy you anything?

The GWF rule (and the engine's r1 notation)

Per RAW: when you roll damage with a two-handed melee weapon you're proficient with, you can reroll any 1 or 2. The 2024 version uses the same trade. Diceplots' parser supports reroll-on-N via the rN suffix: 2d6r1+5 rerolls each die that came up 1 (matches RAW for 1-only rerolls); for the standard "1 or 2" reroll, use r2.

In every case below, "GWF" is shorthand for the more common reroll-on-1-or-2 variant; the math for reroll-on-1-only is almost identical, just smaller.

Greatsword — the headline weapon

Greatsword damage is 2d6+STR. Two dice means GWF's reroll fires roughly twice as often as on a single-die weapon.

Mean shifts:

• E[2d6+5] = 12 — exact.
• E[2d6r1+5] = 12 + 2·(1/6 · 0.5) = 12 + 1/6 ≈ 12.17 for reroll-on-1-only.
• E[2d6r2+5] = 12 + 2·(2/6 · 2) = 12 + 4/3 ≈ 13.33 for reroll-on-1-or-2 (RAW GWF). Per die: P(reroll) = 2/6, and the rerolled die's mean (3.5) replaces the rerolled value's mean ((1+2)/2 = 1.5), so each die gains (2/6)·(3.5 − 1.5) = 2/3 in expectation.

That ~+1.33 per swing (≈11% mean increase) compounds across a campaign — a Greatsword Fighter swinging twice per round at level 5 over a typical adventuring day adds up to a real damage difference.

Greataxe — half the effect

Greataxe damage is 1d12+STR. One die, but a d12 — so the reroll fires less often per attack and the d12 has a wider tail to land in after a reroll.

Mean shifts:

• E[1d12+5] = 11.5 — exact.
• E[1d12r1+5] = 11.5 + 1/12 · 5.5 ≈ 11.96 for reroll-on-1-only. The 5.5 is the mean of the rerolled die.
• E[1d12r2+5] = 11.5 + 2/12 · 5 ≈ 12.33 for reroll-on-1-or-2 (RAW GWF).

So GWF on a Greataxe gives a ~0.83 mean bump at +5 STR vs Greatsword's ~1.33 — about 60% less, in absolute terms, despite the Greataxe's higher raw damage cap. The Greatsword wins because two dice means GWF's reroll fires twice as often per attack (and the smaller die size means each reroll has more relative upside).

The variance angle, the surprising part

GWF cuts low rolls. It doesn't change high rolls. So the distribution gets narrower, not just shifted right, and that has knock-on effects on kill probability that depend on where the target HP sits.

Below the mean (target HP less than your average swing), the higher-variance non-GWF roll wins more often than the narrower GWF roll by a small margin, by the same logic as variance and kill probability. Counter-intuitive but real. Around the mean, GWF is a strict win because it raises the floor without lowering the ceiling. Well above the mean, when you're one-shotting underleveled targets, the variance reduction is irrelevant; both rolls pulp the target.

So GWF is genuinely better mean DPR, but the reduced variance means you'll see slightly fewer "miracle 24-damage crits". Because the reroll cuts the lows, the high tail becomes proportionally less impressive.

The per-attempt picture — including misses and Extra Attack

The damage rolls above are conditional on a hit. The full per-attempt distribution folds in the d20 attack roll: a probability mass at 0 on miss, the standard damage on a non-crit hit, and crit-doubled damage on nat 20. Same +5 STR Greatsword (+9 base attack bonus) vs an AC 15 target, base vs GWF (reroll-on-1):

Per-attempt mean shifts:

• Without GWF: (14/20)·12 + (1/20)·17 = 185/20 = 9.25 damage per swing.
• With GWF (r1): ~9.37 per swing — about +0.12 mean DPR per attempt. Smaller than the +0.17 conditional-on-hit bump because the miss + crit weights dilute the reroll's contribution.

At Extra Attack (level 5+, two swings per round), the gap doubles to about +0.24 mean DPR per round. Across an adventuring day's 30-40 swings that's roughly 5-9 cumulative damage. Noticeable but not transformative.

The Greataxe variant gives a smaller per-swing bump (~+0.08 per attempt) because the 1-die reroll fires only half as often as on a 2-die Greatsword.

The takeaway

GWF is a real buff, not a flavour-tax. But the per-swing magnitude is small (roughly +0.5 to +0.7 mean damage on common weapons), and the variance reduction means it slightly hurts your kill probability in the regime where you're chip-damaging targets above your single-swing mean. In the regime where you're meeting or exceeding your mean, it's a strict improvement.

Against boss HP, when target HP is well past your single-swing max, the variance penalty disappears entirely (see expected strikes to kill: variance contributes a bounded constant, mean wins linearly). GWF's mean bump translates directly into about half a round saved across a 144 HP fight. That's the regime where it's a no-brainer.

Pick GWF over Defense fighting style if you're DPR-focused and your typical target HP sits around or above your swing mean. Defense's flat +1 AC is more universally valuable and doesn't have the variance-reduction tradeoff. That's the number at the back of any optimisation thread.

Try it yourself

↦ /vs/2d6+5/2d6r1+5 — Greatsword damage rolls, base vs GWF ↦ /vs/1d12+5/1d12r1+5 — Greataxe damage rolls, base vs GWF ↦ /vs base vs GWF per-attempt — full distribution including miss ↦ /vs base vs GWF per round — Extra Attack ↦ /strike/2d6r1+5 — full GWF Greatsword distribution

Drag the HP slider — at low HP (5-8), the non-GWF roll's higher variance gives it a slight edge; at HP near the mean (10-12), GWF takes over; well above, both reliably finish.

Where this matters in practice

Reroll-on-low mechanics are surprisingly common across systems, and the rationals here transfer directly:

BG3 Greatsword Fighter at low level. The +1.33 mean bump on Greatsword (2d6+5 → 2d6r2+5) is ~+11% DPR per swing. Over a typical encounter that's the difference between finishing a target this round or next. See the BG3 weapon table for which weapons qualify (any 2H melee — 2d6, 1d12, 2d8 versatile).

Champion 3 / Greatsword stack. GWF and Champion's expanded crit range both add expected damage, but they interact differently with the crit-chance pillar: GWF lifts the floor (helps low rolls), Champion lifts the ceiling (more crits). Both stack additively in expected damage.

Pathfinder / 5.5e fighting-style variants. Some systems offer "reroll any 1" or "reroll once if total ≤ K" as style options. The closed-form for reroll-on-≤K is the same shape; just substitute K. The syntax reference's NdMrK postfix handles the general case.