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Lightning Recovery is a Tome of Battle maneuver that allows a reroll on an attack d20 if it misses, along with an additional +2 on the second attempt. How can I calculate the value of the damage added per round? Here are some figures we can use:

Rapier Attack: +10/+5
Base Damage: 1d6+2
Extra feat damage: 2d6
Critical: 18/x2
Battle Ardor (warblade ability): +2 to confirm critical threat
Target AC: 20

How much damage per round does the use of this maneuver Lightning Recovery add? I'm guessing it's an array of spread due to the 5e 'advantage'-like nature of the maneuver mechanic? Could that even be averaged?

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    \$\begingroup\$ How much damage per round does the use of this maneuver Lightning Recovery add? => Just to make sure, you do know that once a ready maneuver is used, it is expended and must be recovered (by doing a full-attack action without using any maneuvers, for a Warblade)? This means that you can, at best, only use this maneuver once every two rounds, and on a single attack within each round. \$\endgroup\$ Jun 27 '17 at 17:48
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How much it adds depends on the target’s AC.

For instance, something with 20 AC more than your attack bonus (30 AC in your case), you only hit on a 20, a 5% chance. But if you miss and initiate lightning recovery in response, you get another attack and a +2 bonus—which is another 15% chance to hit. That changes your chance to hit from 5% to 19.25% (not 20% because if you hit in the first place you don’t need to initiate lightning recovery at all, so including the full 15% would be double-counting the initial chance to hit). That represents a 3.85× multiplier on your expected damage for the attack you use it on (but since your expected damage was quite low due to the low chance of hitting, that may not be much in absolute terms).

On the other hand, if you are hitting on a 2 to begin with (AC 11 or less for you), you only have a 5% chance to even try lightning recovery, and your chance to hit with the +2 is exactly the same (since a nat-1 still fails). Your chance to hit changes from 95% to 99.75%, which doesn’t change your expected damage much: only a 1.05× multiplier.

In numerical terms, for your +10 attack bonus and a given target AC, ACtarget, we get a chance to hit with the initial attack, Phit0; a chance to hit with the second attack from lightning recovery, PhitLR; a total chance to hit, Phit; and a multiplier to expected damage of the attack, Dhit/hit0, which is based on the ratio of Phit to Phit0.

ACtarget Phit0 PhitLR Phit Dhit/hit0
≤ 12 95% 95% 99.75% 1.05×
13 90% 95% 99.50% 1.11×
14 85% 95% 99.25% 1.17×
15 80% 90% 98.00% 1.23×
16 75% 85% 96.25% 1.28×
17 70% 80% 94.00% 1.34×
18 65% 75% 91.25% 1.40×
19 60% 70% 88.00% 1.47×
20 55% 65% 84.25% 1.53×
21 50% 60% 80.00% 1.60×
22 45% 55% 75.25% 1.67×
23 40% 50% 70.00% 1.75×
24 35% 45% 64.25% 1.84×
25 30% 40% 58.00% 1.93×
26 25% 35% 51.25% 2.05×
27 20% 30% 44.00% 2.20×
28 15% 25% 36.25% 2.42×
29 10% 20% 28.00% 2.80×
30 5% 15% 19.25% 3.85×
31 5% 10% 14.50% 2.90×
≥ 32 5% 5% 9.75% 1.95×

Even these numbers don’t tell the full story. For one thing, it does not account for the second opportunity to possibly threaten a critical hit. And there is no real good way to quantify the effect of lightning recovery on an entire combat where how often you can or will want to use it may vary wildly based on the circumstances, and then there is action conflict with boosts you might have otherwise used. But more importantly, against things with AC so low you are hitting on a nat-1, it really doesn’t matter what maneuvers you have: these are not significant threats to you. And things that you, a warblade—one of the most accurate classes in the game—can only hit on a natural-20 are probably not things your party should be standing and fighting, but rather things you should be running away from (or figuring out what plot device exposes its weak point or whatever).

All that said, it’s a good maneuver that is better against tougher threats. That’s quite a favorable attribute to have.

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  • \$\begingroup\$ Comments are not for extended discussion; this conversation has been moved to chat. \$\endgroup\$
    – mxyzplk
    Jun 28 '17 at 2:53

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