Here are some thoughts, but I'm interested if anyone disagrees or can find an issue with the line of thinking:

As a preliminary note, an n-sided die with an even number of sides averages (n+1)/2. So d6 averages 3.5, d12 averages 6.5, and so on.

Step 1: ignoring crits

Expected attack damage is E(damage | hit)P(hit). E.g., a 1d4 + 4 attack averages 6.5 on a hit, so the expected DPR is 6.5*(hit chance). Abbreviate this as dh -- d for expected damage, h for hit probability (0 to 1). Ignore crits for now. (I'll include them later.)

Increasing accuracy by 1 increases hit probability by 1/20, or 0.05. This changes dh into d(h+0.05) = dh + 0.05d, increasing DPR by d/20. Increasing expected damage by 1 (e.g. increasing a die size) changes dh into (d+1)h = dh + h, increasing DPR by h.

Therefore, if h > d/20, then given the choice, it would be better to increase damage by 1. If d/20 > h, it would be better to increase accuracy.

Example: a level 1 rogue with 18 dexterity does 1d4 + 4 on several at-will powers. With advantage, a base rogue does an additional 2d6 damage (or 7 on average). Thus, the expected at-will damage with CA is 1d4 + 11, or 13.5. Backstabber increases this expected damage to 15.5, while Nimble Blade increases the hit rate by 5%.

Thus: (d+2)h = dh + 2h, and d(h+0.05) = dh + d/20 = dh + 13.5/20 = dh + 0.675.

So as a possible answer to my own question, if crits are ignored, Backstabber beats Nimble blade as long as 0.675 > 2h. I certainly expect most rogues (or even any non-optimal PC) to have a hit rate better than 0.675/2 = 33.75%.

Step 2: including crits

A standard critical strike at level 1, taking maximal damage, would be 1d4 + dex mod + 2d6 = 4 + 4 + 12 = 20. With Backstabber, that increases to 24.

A standard swing crits 5% of the time, and the rest of the hits do standard damage. I.e. damage is no longer dh, but 0.05*(crit damage) + (h-0.05)d.

With Nimble Blade and no Backstabber, this becomes 0.05*20 + ((h + 0.05) - 0.05)*13.5 = 1 + 13.5*h. With Backstabber and no Nimble Blade, this becomes 0.05*24 + (h - 0.05)*15.5 = 1.2 + 15.5h - 0.775 = 0.45 + 15.5h.

If 0.45 + 15.5h > 1 + 13.5h, then Backstabber beats Nimble Blade on average, including crits. This is equivalent to saying 2h > 0.55. I certainly hope a rogue with advantage, or any PC in 4e, hits more often than 0.55/2 = 27.5% of the time.

The reason the cutoff is lower than before is that accuracy does nothing to improve critical strike damage, but increasing damage dice does.

Conclusion

This should answer some basic questions and set a template for Sly Flourish vs. Piercing Strike type questions, although it's hard to include debuffing in the mix. Draji Palatial gives an automatic -2 attack debuff regardless of whether it hits, but it's hard to compute the relative merit of the party having +2 defenses against single opponent vs. the expected damage tradeoff of, say, a more accurate Piercing Strike.

Thoughts? Corrections? Disagreements?

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