Piercer Feat - When statistically should I re-roll the damage die?

[nickl_2000]

So, I'm lazy and don't want to run the numbers.

I'm running a level 4 Swarmkeeper Ranger using a Longbow. Most often right now I'm hitting with the Longbow, Hunter's Mark, and the Swarm damage (so 1d8+4, 1d6, and 1d6). All of the damage I am doing is piercing damage, making all of it eligible for the re-roll from the Piercer feat I took at level 4.

When does it statistically make sense to re-roll the die? Has anyone run the numbers on this?

[Burley]

I think the average damage difference between 1d8 (4.5) and 1d6 (3.5) is 1. So, its almost negligible, but it's better to reroll the d8. I'd say don't worry about what's statistically advantageous. Just reroll a 1 or 2 when it shows up. If you roll low on all dice, reroll the d8.

[nickl_2000]

That was actually what I was curious about though. If I roll a 2 on the d8 and a 1 on a d6, would it be better to reroll the 2 or the 1?

Without running the numbers, I would go with the 1, since it is lower and it feel better not to have a 1. However, I know there are people who really, really enjoy running the numbers to death that could tell me if it really makes a difference.


Also, if I roll a 3 on a d8 as my lowest, does it make sense to re-roll or just take it and run? Of course this changes at level 5 when I get a second attack, but I'm not worried about that yet.

[Greywander]

In a simple case with only one damage die, you want to reroll anytime you roll in the bottom half. E.g. on a d8, you would reroll anything 4 or lower.

With multiple dice, it gets a little more complex, but I think you generally want to favor rerolling a larger die over a smaller one. You also want to favor rerolling a die that is farther from the average. Balancing these two is the hard part. If, for example, you roll a 4 on a d8 but a 1 on a d6, reroll the d6. If you roll a 2 on both dice, reroll the d8.

That said, the Piercer feat is the weakest of the three. I'd consider just getting a straight DEX bump, picking up Sharpshooter, or grabbing the Archery fighting style, if you don't already have it. Any of those should give you better returns than Piercer. If you want something more unusual, then dip into genielock and take the dao patron, then pick up Crusher. Congratulations, you can now push people around with your longbow shots. (It sounds like you've already taken Piercer, though, so maybe it's too late to change it.)

[Keltest]

That was actually what I was curious about though. If I roll a 2 on the d8 and a 1 on a d6, would it be better to reroll the 2 or the 1?

Without running the numbers, I would go with the 1, since it is lower and it feel better not to have a 1. However, I know there are people who really, really enjoy running the numbers to death that could tell me if it really makes a difference.


Also, if I roll a 3 on a d8 as my lowest, does it make sense to re-roll or just take it and run? Of course this changes at level 5 when I get a second attack, but I'm not worried about that yet.

Admittedly im not one of the people who enjoys crunching numbers like that, but my gut says that when in doubt, reroll the die that has the biggest difference between the current number and the maximum roll. So a 3 on a D12 will be a better reroll than a 2 on a D6.

[Segev]

Can you pick between dice on multiple attacks? I thought you had to decide to use the piercer feat before the attack resolved, which means before you roll the next one.

[Silpharon]

Statistically, the expected value of the replaced roll will be 3.5 for the d6 and 4.5 for the d8. This means if you roll a 3 or below on the d6 or a 4 or below on the d8, you should reroll.

An easy way to choose what's best:
1) Consider any dice with values less than or equal to half the die size
2) Subtract the dice values from their half-size
3) Reroll the die with the biggest difference

[nickl_2000]

In a simple case with only one damage die, you want to reroll anytime you roll in the bottom half. E.g. on a d8, you would reroll anything 4 or lower.

With multiple dice, it gets a little more complex, but I think you generally want to favor rerolling a larger die over a smaller one. You also want to favor rerolling a die that is farther from the average. Balancing these two is the hard part. If, for example, you roll a 4 on a d8 but a 1 on a d6, reroll the d6. If you roll a 2 on both dice, reroll the d8.

That said, the Piercer feat is the weakest of the three. I'd consider just getting a straight DEX bump, picking up Sharpshooter, or grabbing the Archery fighting style, if you don't already have it. Any of those should give you better returns than Piercer. If you want something more unusual, then dip into genielock and take the dao patron, then pick up Crusher. Congratulations, you can now push people around with your longbow shots. (It sounds like you've already taken Piercer, though, so maybe it's too late to change it.)

It is to late at this point. I wanted a half-feat to take my character from 17 dex to 18 because I like half-feats and I don't have any other odd scores. Resilient Dex does work since I'm a Ranger, I didn't really want skill expert since we are very well covered for skills in the party, I don't really like athlete, and the PC is a Wildhunt Shifter (so no Elven Accuracy).

He does have the archery fighting style and I will be getting sharpshooter with my next ASI.

Multiclassing into Warlock isn't an option due to low charisma either.


However, I really appreciate the analysis on the numbers!




Can you pick between dice on multiple attacks? I thought you had to decide to use the piercer feat before the attack resolved, which means before you roll the next one.

You can't pick between dice on multiple attacks, which is why I said things change at level 5 for the numbers. I'm level 4 right now so it was a problem for later. At level 5, I would likely only re-roll on a 1 on the d6 or a 1-2 on the d8 for the first attack,

[Sorinth]

You want to reroll the one that has the biggest delta between what you rolled and the average for that roll. So a 2 on a d8 and a 1 on a d6 doesn't actually matter to the average, you gain +2.5dmg on both dice. Whereas if you say had a 2 on a d10, and a 1 on a d6, you'd reroll the d10 because it would net on average +3.5 dmg compared to the +2.5 damage from the d6.

[Segev]

Oh! Somehow I missed that that was all one attack.

Yeah, essentially, I would recommend rerolling the one you feel most disappointed by. Your gut instinct for that is probably going to be pretty accurate.

If you do want to stop to think about it, though, yes: whichever die has the largest distance between what it rolled and the average roll for the die is the statistically best choice.

[Psyren]

Can you pick between dice on multiple attacks? I thought you had to decide to use the piercer feat before the attack resolved, which means before you roll the next one.

While technically you should resolve your attacks individually, a lot of people roll all the damage dice at once, because rolling a lot of dice at once is fun. Personally, for a difference of 2-3 points of damage per round on average I'm not going to quibble over which attack a given die roll was part of for Piercer purposes.

[nickl_2000]

While technically you should resolve your attacks individually, a lot of people roll all the damage dice at once, because rolling a lot of dice at once is fun. Personally, for a difference of 2-3 points of damage per round on average I'm not going to quibble over which attack a given die roll was part of for Piercer purposes.

I imagine it will be the same at my table. We tend to roll all at once for speed reasons, so we get through our turns faster and combat runs more quickly. However, when it comes up I will ask the DM what he wants and will follow that.

[Greywander]

It is to late at this point. I wanted a half-feat to take my character from 17 dex to 18 because I like half-feats and I don't have any other odd scores. Resilient Dex does work since I'm a Ranger, I didn't really want skill expert since we are very well covered for skills in the party, I don't really like athlete, and the PC is a Wildhunt Shifter (so no Elven Accuracy).
I wondered if it was something like that. Yeah, you don't really have a lot of options for DEX half feats, particularly if you don't have access to any racial feats. Still, in your shoes I would have probably gone for Skill Expert to get expertise in Stealth or Perception checks (I'd probably take Resilient before Piercer, as well). Also, you could have gone for a WIS or CON half feat, then evened out your stats at the next ASI.

To get the most out of Piercer, you need to maximize both the die size and the number of dice. Rogues probably get the most out of it just due to the sheer number of dice they roll for their Sneak Attacks. They're bound to get a lot of 1s and 2s, so they can almost always get around a small boost every round. The highest damage piercing weapon is the lance with a d12 (secret mounted combat feat?), but if you're only making one attack then you'll only be rerolling about half the time. With two attacks, you'd expect to reroll about three quarter of the time. A lance-wielding fighter (four attacks) could probably get about as much value out of Piercer as a rogue; although they aren't rolling as many dice, they're rolling larger dice. Make it a half-orc Champion and you'll crit for 4d12 damage on an 18 or higher (not sure that's worth it, though).


However, I really appreciate the analysis on the numbers!
Glad you found it helpful. I think a simple rule of thumb is to just reroll the lowest roll, and if they're equal, reroll the larger die. So if the d8 is a 2 and the d6 is a 1, reroll the d6. I think in either case the expected increase is +2.5, so they should be roughly equivalent, but at least you're guarantied to not get something lower.

[nickl_2000]

I wondered if it was something like that. Yeah, you don't really have a lot of options for DEX half feats, particularly if you don't have access to any racial feats. Still, in your shoes I would have probably gone for Skill Expert to get expertise in Stealth or Perception checks (I'd probably take Resilient before Piercer, as well). Also, you could have gone for a WIS or CON half feat, then evened out your stats at the next ASI.


I already have expertise in Perception. Tasha's Ranger is very nice to get expertise at level 1, it may have helped to get expertise in stealth as well but that isn't who Wrennet really is.

I don't regret Piercer as a feat, it may be the weakest but having a martial who can lay down some serious damage it very helpful in the party and the selection of that feat gave me +1 to hit, +1 damage, and the other piercer stuff. I've played one session with it and it made a significant difference (twice the re-roll killed someone who wouldn't have died otherwise). So, long run it may not be perfect, but I don't mind right now.


Long term with him I'm still debating what to do, but I planning on the next ASI being Sharpshooter, then +2 dex. Then possibly Fey touched, but that is so long in the future it will change at least 150 times between now and then. Heck, I haven't even decided whether I want go full class ranger, ranger/monk, ranger/druid, or ranger/fighter (yes I know Rogue is awesome, but I'm playing a rogue in my other campaign and Cleric is out since he is a Shifter in Eberron who still has some hard feelings about the Church of the Silver Flame trying to eliminate shifters).


One thing I may see if my DM will allow, since he is getting more into homebrew for this campaign than he original planned is using a feat from Keith Baker's Exploring Eberron.


Superior Shifting:
+1 Stat
2 shifts per short rest instead of 1
Shifting lasts 10 minutes instead of 1


Being a Wildhunt Shifter, 10 minutes of Advantage on all Wis based skills is a pretty big boon and having temp hp last longer than 1 battle could be nice as well.

[Crucius]

I remember from a sorcerer guide on empowered spell that you should reroll the die size / 2 - 1, rounded down (so a d12 you reroll on 1,2,3,4,5), but I can't find the source anymore.

The thinking behind it is that, even though the expected outcome is a 6.5, you are sacrificing a potential 5 to get a 1.

So sad that I can't find that article anymore. There was math and everything.

TheUser has it written in their guide I see, but I'm pretty sure I remembered graphs and stuff from another article.
https://forums.giantitp.com/showthread.php?526062-New-updated-Sorcerer-Guide!

[Bobthewizard]

I remember from a sorcerer guide on empowered spell that you should reroll the die size / 2 - 1, rounded down (so a d12 you reroll on 1,2,3,4,5), but I can't find the source anymore.

The thinking behind it is that, even though the expected outcome is a 6.5, you are sacrificing a potential 5 to get a 1.

So sad that I can't find that article anymore. There was math and everything.

TheUser has it written in their guide I see, but I'm pretty sure I remembered graphs and stuff from another article.
https://forums.giantitp.com/showthread.php?526062-New-updated-Sorcerer-Guide!

That involves expending a resource of sorcery points to choose to to use empowered to reroll so you'd be a little more conservative. If it's resource-free, I'd reroll a 3 on a d6, 4 on a d8, 5 on a d10, unless you think your current damage is enough to KO the target.

Agree with the suggestion above to reroll the die that has the largest delta to its average. If it's mathematically even, then choose your risk level with the larger die giving more risk for potentially more reward.

[Witty Username]

First, always reroll 1.
Second, don't reroll if damage is already lethal if you have that info.
Third, your average damage will go up if your roll is half the max value.
The quick math d8
If 4, this is the value of a reroll
-3, -2, -1, 0, 1, 2, 3, 4.
Avg = .5 gain
If a lower roll, this math is more favorable.
If higher, you will lose damage on average.
Fourth, if only max value is lethal, reroll. This requires info but if the attack can be lethal, it is always favorable to reroll a non-lethal hit, this is because even with 1d12, they will have at most 11 hp remaining, reasonably within a single attack. Risking average damage does not risk failure of the follow up attack and has the possibility of killing the target without a follow up attack.

[Tanarii]

Gain on a reroll d6 is:
+2.5 on a 1
+1.5 on a 2
+0.5 on a 3

Gain on a reroll d8 is:
+3.5 on a 1
+2.5 on a 2
+1.5 on a 3
+0.5 on a 4

In other words, it's the average minus the current roll. If the d8 is one point higher, they're equal in terms of average gain.

Distribution matters though. If you have a 2 on a d6 and a 3 on a d8, you can only lose one on a d6 but stand to gain 4. On the d8 you can lose 2 but stand to gain 5. So when you have a one point higher difference on the higher die, it depends how much of a gambler you are which one you want to choose.

[LudicSavant]

Any time you reroll, the expected value of the reroll is die size/2+0.5. So for example a d6 is 3.5, a d8 is 4.5, etc.

So if you roll a 1 on a d12, your expected gain is the difference between your roll (1) and the expected value (6.5). 6.5-1=5.5 average damage gain.

The part that gets complicated is when you have multiple attacks, and one asks whether or not they should hold off on rerolling that 2 in hopes of rolling a 1 later in their turn.

[Telok]

Over lunch I berfed a javascript. Basically a very fast & dirty sim. Ran a million trials.

Reroll lowest die if that die is below half, starts with the d8, did not add flat bonuses.

Average no reroll 11.5
Average after reroll 13.236
Average improve per reroll 2.1
Total average improve per roll 1.736
Chance to reroll 82.3%

Haven't looked a piercer. Hope theres a real good rider or its a half feat.

[Segev]

Over lunch I berfed a javascript. Basically a very fast & dirty sim. Ran a million trials.

Reroll lowest die if that die is below half, starts with the d8, did not add flat bonuses.

Average no reroll 11.5
Average after reroll 13.236
Average improve per reroll 2.1
Total average improve per roll 1.736
Chance to reroll 82.3%

Haven't looked a piercer. Hope theres a real good rider or its a half feat.It is a half feat, and it also gives +1 die when you score a critical hit with a piercing weapon.

[Telok]

It is a half feat, and it also gives +1 die when you score a critical hit with a piercing weapon.

I can add the crit thing easy. What would the d8+2d6 go to on a crit? 3d8+2d6?

Never mind, got confused from playing all editions and no crit rules matching since tsr.

1d8+2d6 && crit = 3d8+4d6, reroll lowest, d8s first on a tie.
Avreage before reroll 12.3
Average after rerolls 14
Average improve per reroll 2.135
Average overall improve 1.765
Chance to reroll 83%

With crits but without piercer (no reroll & only 2d8+4d6 crits)
Avg before 12.075

[Witty Username]

The part that gets complicated is when you have multiple attacks, and one asks whether or not they should hold off on rerolling that 2 in hopes of rolling a 1 later in their turn.

I think this is less complicated by logic as opposed to math, since this is more game state dependent.
If, the attack is lethal, don't reroll.
Else If, if the attack is <=Max/2. Reroll.
Else don't reroll.

This is because you can't guarantee a second hit most of the time, or if it will be a favorable attack to reroll the damage of. One in the hand, two in the bush and all that.

Edit: I goofed my symbols, fixed. And as per down low. There is argument for "<", as opposed to "<=".

[LudicSavant]

I think this is less complicated by logic as opposed to math, since this is more game state dependent.
If, the attack is lethal, don't reroll.
Else If, if the attack is >Max/2. Reroll.
Else don't reroll.

This is because you can't guarantee a second hit most of the time, or if it will be a favorable attack to reroll the damage of. One in the hand, two in the bush and all that.

It gets a lot fuzzier when you start talking about things like an Elven Accuracy Gunner Samurai rolling over half a dozen attacks with the kind of crit rates afforded by triple advantage.

Like, if you roll a 5 on on your first attack's d12, under your algorithm that would be a "reroll." And yet the probability of you getting lower d12 roll later on in the turn could be very high indeed!

[kazaryu]

So, I'm lazy and don't want to run the numbers.

I'm running a level 4 Swarmkeeper Ranger using a Longbow. Most often right now I'm hitting with the Longbow, Hunter's Mark, and the Swarm damage (so 1d8+4, 1d6, and 1d6). All of the damage I am doing is piercing damage, making all of it eligible for the re-roll from the Piercer feat I took at level 4.

When does it statistically make sense to re-roll the die? Has anyone run the numbers on this?

so...statistically speaking when you roll any die, you treat that die as having rolled its average value. meaning that, on average, every time you reroll a d6, that reroll is worth a 3.5 (this is also how you can relatively easily calculate the impact of the rerolls granted by the great weapon fighting style, just calculate the average, but replace both 1 and 2 with the die's average value). meaning that (on average) its not worth re-rolling a roll that is greater than average (the reroll's will average out to be less than your initial roll).

this also means that its always worth to reroll anything that is below average.

its almost as simple when you consider 2 damage dice. reroll the one that gives you the better increase. for example: rerolling a 2 on a d8 gives you a new roll of 4.5 (a +2.5 increase) but you get the same +2.5 increase rerolling a 1 on a d6. whereas reroling a 2 on a d6 vs rerolling a 4 on a d8. you want to reroll the 2, since it will give you a +1.5 on average, instead of a .5)

no math required for those situations.

however, for the discussion on 'should i save my reroll for a subsequent attack that might hit harder.'. that is where the math can get complicated. But we can still use the same general principles to establish a baseline. so to start we're going to assume a 100% accuracy (because if its not worth it when the hit is guaranteed...then its not worth it at all...and ignoring accuracy makes the math much easier). so lets say you roll a 3 on a d6. you can reroll now for a guaranteed +.5 to damage. if you wait, you have a 3/6 chance of wasting the reroll (because you roll a 4-6 on subsequent damage) and a 1/6 chance of getting no improvement (from rolling another 3). you have a 1/6 chance of getting a +1 improvement over what you currently have (1.5 vs .5) and a 1/6 chance of getting a +2 compared to what you currently have. by multiplying the odds of a result, by the gain/loss of that result we can come to a combined average adjustment.
1*(1/6)+2*(1/6)+ -.5(1/2) = +.25

so, if you're guaranteed to hit your follow up attack, then its worth it to not reroll a 3 on a d6 . in fact, you'd need a hit chance of <66% for it to be worth immediately rerolling a 3 on a d6. and the math works similarly for rolling a 4 on a d8, but its more lenient on accuracy (50% instead of 66%).

[Witty Username]

It gets a lot fuzzier when you start talking about things like an Elven Accuracy Gunner Samurai rolling over half a dozen attacks with the kind of crit rates afforded by triple advantage.

Like, if you roll a 5 on on your first attack's d12, under your algorithm that would be a "reroll." And yet the probability of you getting lower d12 roll later on in the turn could be very high indeed!

33%. Well, 33% × accuracy%. Do a whazit, 1 -(1- 33%×accuracy%)×(attacks-1) I think that is the right calculation. It has been awhile for me in terms of probability/statistics. Two attacks I think you are safe rerolling a super majority of the time at least, I haven't thought long on the math for 3+ attacks though.

In the spirit of it, assuming 100% accuracy, that would be like 57% to roll a 1-4 In the next 2 attacks. So that could be worth noting in high accuracy builds. 39.9% if you have 70% accuracy (I see 60% accuracy used as a baseline alot, so 70% as its baseline plus archery style).

That is about as much math as I want to do from my phone. But the numbers don't seem good for wade it out, most of the time.

I would say at the very least
if (roll =1 and damage < lethal)
Reroll;

Edit: I have been beaten to it by someone willing to do more math. I think I agree with the above but am still reading it.

Edit 2:
Alright,
It looks like the closer estimate
Is max/2 -1 is the reroll point.
So:
5 on d12
4 on d10
3 on d8
2 on d6

But max/2 is fair for single attack estimates or low accuracy situations.