Post/Author/DateTime	Post
#1 FrogReaver Apr 26, 2015 10:17:44	Savage Attacker - "Once per turn when you roll damage for a melee weapon attack, you can reroll the weapon’s damage dice and use either total."   Let's look at a great axe first.  1d12 damage dice   With a single attack you get to roll 1d12 twice and take the highest.   This increases your damage average by (8.49 - 6.5) = 1.99   --------------------------------------------------------------------------------------------------   Increase in damage becomes 2.98 for two attacks that hit.   ***The damage increase for two attacks is theoretical maximum.  This is because it assumes we always will know which attack will grant the lower damage.  This isn't actually possible.  But most of the time we can make a pretty decent prediction of which will be.
#2 AaronOfBarbaria Apr 26, 2015 10:38:15	The mean of 1d12 is 6.5. The mean of the highest 1 of 2d12 is 8.49.   You may want to recheck your math, as that is not a difference of 1.53, or explain the unseen variables you are accounting for.
(Reply to #2) FrogReaver	AaronOfBarbaria wrote:
#4 FrogReaver Apr 26, 2015 11:00:51	So what I need to do (for 2 attacks) to find the theoretical best that can be done roll a d12 twice and take the lower.  Then roll another d12 given that lower value and take the higher of those.  Then add that result with the higher of the first 2 d12's.
#5 FrogReaver Apr 26, 2015 11:18:12	So the theoretical max amount of damage that can be obtained from savage attacker with 2 hits of a great axe is:       roll both attacks damges.  Take the higher.  This die should average to 8.49 as discussed above.   The lower dice will average to 4.51.   A quick check (8.49 + 4.51) = 13 which is the damage you would obtain from 2d12.     So now we apply the savage attack die roll to this lower dice.  This maxes the average of this dice result to 7.49.   To obtain that result I took the chance of either dice being a 1 and multiplying that by the expected average of a distrubition that started with that 1 at it's lowest and went up to 12. I then did the same for 2 and so on.   For example the 2 distribution was 2, 2, 3, 4, 5, 6, 7, 8, 9 ,10, 11, 12  (average 6.583) and the probability that the roll was a 2 was (21 / 144).  We multiple the mean of that distribution with the chance of a 2 and repeat for each number.   Adding all these results together we obtain 7.49 is the mean of doing this.   7.49 + 8.49 = 12.98   Increase in damage becomes 2.98 for two attacks that hit.
#6 FrogReaver Apr 26, 2015 11:23:45	In terms of DPR with a 50% chance to hit this equates to   +1 DPR for a single attack character +1.75 DPR for a two attack character   ***Values are theoretical maximums for two attack characters. ***This is because we will not always be able in game to apply savage attacker to the attacks damage that is lower each round.   ***Actual +DPR of Savage attack with 2 attacks will be slightly lower than is listed.
#7 FrogReaver Apr 26, 2015 11:26:55	With a 70% chance to hit:   +1.4 DPR for a single attack character +.84 + 1.47 = +2.31 DPR for a two attack character
#8 Tempest_Stormwind Apr 26, 2015 18:03:31	...What the.... seriously, this is a lot of numbers but no actual math.   FrogReaver wrote:
(Reply to #8) FrogReaver	Tempest_Stormwind wrote:
(Reply to #8) FrogReaver	Tempest_Stormwind wrote:
(Reply to #8) FrogReaver	Tempest_Stormwind wrote:
(Reply to #8) FrogReaver	Tempest_Stormwind wrote:
(Reply to #8) FrogReaver	Tempest_Stormwind wrote:
#14 FrogReaver Apr 27, 2015 8:43:35	Here is my AnyDice attempt at making my algorithm.   output [highest 1 of 2d12] + [highest of [lowest 1 of 2d12] and 1d12] named "FrogReaver's Algorithm"   http://anydice.com/program/5bdf     ***Note this algorithm only approximates my algorithm.  AnyDice could not totally recreate it because it didn't give me the option of only rolling a d12 twice and using that higher and lower value.  Instead I had to roll 2d12 and take the highest 1 time and then roll 2d12 and take the lowest.  This will not change the mean any, however it may change the distribution slightly (considering there will be some instances where rolling 2d12 and taking the highest is lower than rolling 2d12 and taking the lower which is something my algorithm forbids).  Yet it was the cloeset I could get AnyDice to show for my algorithm and since the mean will be the same in either case I thought it was good to show.
#15 Tempest_Stormwind Apr 27, 2015 11:48:55	The reason why this algorithm isn't useful is because the game assumes attacks are rolled sequentially. As in, you roll an attack, you roll the resulting damage, you roll another attack, you roll resulting damage. Each of those is a discrete event - and once you've moved on to the second attack, you can't retroactively apply Savage Attacker to the first one. You have to decide whether or not to use it when you make the individual damage rolls (which is contingent upon actually having hit the target - you can't use Savage Attacker if you miss.)   As such, what you should be looking for is an overall policy of "what numbers need to show up on the damage roll before I decide to use Savage Attacker?". This is rather different from your goals: This doesn't care about DPR, since it only looks at the damage roll, and not the accuracy of that attack. An attack that misses is akin to deciding, in advance, that you will not use Savage Attacker this attack - because there's no damage roll for you to decide to roll. This also doesn't care about DPR because it has to consider the enemy's current status and the variance of your damage rolls. If you roll, say, an 8 on the d12 from your first attack against a monster that is not showing visible wounds, is it worth using Savage Attacker now, or should you save it for your next attack (which might miss)? What if the target is clearly on its last legs and you roll a 4? (In this case, I'd say the latter is a Yes - the odds are that you'll get a result higher than 4, which will likely result in the monster dropping. If you didn't reroll, 4 might not be enough to drop him - he might have 5 hit points, for instance. A monster that survives with 1 HP is much worse than a monster that drops this round. In the case of the former, you have to balance not only the odds of rolling higher than 8 (this is a question on variance, not averages), but also the monster's current HP (a factor that is totally ignored by DPR). An example of this kind of merit: Let's say the monster has 7 HP remaining, you have a 60% chance of hitting and you score a hit on your first attack, and you roll a 5 on 1d12+2. Should you use Savage Attacker? If you do reroll, you have already hit, so you can ignore accuracy. The question is how likely you are to get at least 7 on 1d12+2. That's pretty easy to check: it's 66.67% (two-thirds).  (In some more detailed examples, you will split this route into two: what happens if your reroll kills it, and what happens if your reroll is higher than your normal result but not high enough to kill it. But that step is skipped here.). If you don't reroll, the monster will take at least 5 damage and fall to at most 2 hit points. Your second attack has a 60% chance of hitting, but if it hits, it's guaranteed to deal at least 3 damage, which will kill the monster - so if you decide to not reroll, you have a 60% chance of killing the monster.    In this case, absent any other conditions, you are in your best interest to use Savage Attacker now (66% vs 60%). This is especially true if you have movement left and a second target is in range - if you can drop a foe with your first attack, that's a second target you can potentially hit this turn.      Because this ignores a-priori accuracy (you can't decide to use Savage Attacker unless you hit, and once you roll damage, you've already hit, so weighting anything by accuracy is unnecessary) and it must, necessarily, consider monster current HP (this governs whether or not the attack will kill the monster or not, which is your ultimate goal; DPR simply looks to maximize the average, and rolls the impact of higher or lower results into an expected value), DPR is not the appropriate metric to be using here. Chance of killing the monster is.       Also, Savage Attacker very strongly favors dice that follow a uniform distribution (greataxe) compared to dice that follow a Gaussian (greatsword). This is because the greataxe has a higher variance, despite the greatsword having a higher mean. When you roll the greatsword damage twice, each roll is more likely to come out a 7 than any other result. When you roll a greataxe twice, every damage result (including 1 and 12) is equally likely.   This is vitally important when you consider if a monster dies this round or not. It is substantially less important if all you're concerned about are the expected values used to compute DPR.   For instance, look at this Anydice result and click "at least". That's the probability of a monster with a given amount of hit points dying once you strike and use Savage Attacker. Look at, for instance, 10 hit points - a monster with 10(+your Str modifier) hit points who's hit with a savage greatsword will die 30.5% of the time, but if he's hit with a savage greataxe, he'll die 43.75% of the time.   Even though the "DPR" is very similar between the two (8.37 sword vs 8.49 axe, each weighted by accuracy), the higher variance and the specific uniform distribution of the greataxe strongly favors the axe for Savage Attacker when you actually translate it into the simple question "Does this kill the monster?".    This is less related to your specific point, but it should show you why focusing on DPR is not the way to proceed here.   (For a theoretical example that gives a better demonstration of the role of variance here, consider damage rolls of 5d4 vs 1d20 (these are exaggerated values to illustrate the point, not actual weapon dice) with a damage reroll against targets with more than, say, 15 HP (that is, the chance of dealing at least 15 damage on either roll). Note that 5d4 has slightly higher expected damage, and both of them have identical "theoretical max" damage of 20, but 1d20has the higher variance - and 1d20 has a much higher chance of actually killing anything at the higher end of that scale. At 15 damage, it's 38% to 51% - and that's entirely due to the variance of the dice, not the DPR.)