D&D 5E Evaluating Range versus Damage (SS vs GWM) - putting a price on range

[Bacon Bits]

If a game is taking place primarily in a dungeon or similar enclosed space (building, set of caverns, the burrowed tunnels of a creature inside the skull of a deceased god floating on the Astral plane, whatever), then I think melee is often more powerful than ranged. However if your game is taking place primarily in the wilderness of similar open space, then I think ranged is often more powerful than melee.

This is the only thing to be aware of.

Ranged is not always going to be available due to cover and concealment. Furthermore, it's not like PCs have to choose between one or the other and can never switch. If you're running melee, you can often still switch to ranged when you really need it. No, you won't be as optimal, but it's not important to always be optimal because circumstances will prevent that often enough.

 

[clearstream]

He was just listing the damage if you didn't have sneak attack.

Oh right. From ranged you can stick with PHB SS/CEx anyway.

 

[guachi]

I miscalculated how useful Precision is.

It's not like I haven't done these calculations before, but I messed up in a previous post. I said that using Precision when you miss by 4 or less means you'll hit 70% of the time with your d10 maneuver die. This is only true if you miss by exactly four. In fact, you'll hit 85% of the time, on average. If you miss by 1, for example, you'll always hit when you use your maneuver die. Since you're using Precision 20% of the time your overall chance to hit increases by 17%.

This changes the chance to hit for a GWM fighter to:
65% (base) - 25% (GWM) + 17% (Precision) = 57%.

Also, if you care to come up with how often you think a GWM fighter gets his bonus action attack from dropping a foe to 0, consider the following. A level 11 Battlemaster will not crit at least once 85.7% of the time. The 85.7% of the time he doesn't crit each of his attacks do 12.13 damage.

Max HP and current HP of a foe varies wildly, but if I had a feature that gave me a bonus attack if I dropped a foe to zero I'd always attack the foe with the lowest HP (adjusted by hit probability). E.g., if I were a 3rd level variant human with GWM facing goblins and an ogre I'd always, always, always attack the goblins and I wouldn't even use the -5/+10 part. One regular hit will drop them. Then I'd take my free attack on the ogre.

That being said, let's assume our 11th level Battlemaster is, with his buddies, facing some CR 5 creatures. They average about 100 HP. So a very rough estimate is our Battlemaster drops a foe 12.13% of the time (because he's doing 12.13 damage per attack on our 100 HP foe). In a round where he doesn't crit he has a 32.16% chance of dropping at least one foe. This 32.16% chance occurs on the 85.7% of rounds without a crit or 27.56% of the time. Add this to the 14.3% chance of getting at least one critical and our Battlemaster gets a bonus attack 41.86% of the time.

This yields average damage for our GWM friend of 46.88. This assumes you also use Precision attack on your bonus action attack.

 

[clearstream]

I'm not certain how, in the in-game fiction, you'd know someone had the Sentinel feat until you used it.

If there is an orthodox tactic that consistently pays off, then those experienced creatures whose lives depend on it will learn how to deal with it. Remember, we're the guy with the flickering green blade dishing out damage: why the heck would a creature ignore us!? Additionally, combats must at least sometimes evolve so that we have no nearby allies. Assuming 100% up-time on Sentinel triggers is implausible. That said, I really wanted to open up this conversation.

But if the DM is going to do such shenanigans like having telepathic enemies that know you have Sentinel, then you have to come up with other things to do to reduce the likelihood you are attacked like cast mirror image or blur.

I think you would accept that premise that Sentinel up-time is < 1. Let's try and understand how much by? You offer dismissive terms like "shenanigans" and "telepathy", but I can give simple, plausible cases -

• Creature appropriate for level 11 faces two or three PCs. A-priori, its choice of which to strike is random. The chance of choosing the character with Sentinel is 50% or 33%.
• Let's say that this time, it chooses a different character, and strikes... and is struck at by the Sentinel user. Why do we think that it won't now change its behaviour? If the creature dies two rounds later, it struck at the Sentinel user in two out of the three turns it had to act.
• Occasionally, for whatever reason, the combat evolves so that our Sentinel user has no nearby allies. Perhaps they're busy with another threat, or prevented from joining right now.

I'm not really interested in using rhetorical characterisations to make a case seem more compelling. I'd like to know why we think a creature can't be attacking the Sentinel user half the time?

Or be a Battle Master/Rogue and take Riposte to make them pay no matter whom they attack. Or, like I said earlier, use a whip so you can Sentinel at 10 feet and stand behind your buddies. Or stand at the end of a 3-person battle line and your whip to Sentinel a foe 10 feet from you that can't reach you (unless he has 10 foot reach as well)

This is the route my character is taking. Superiority dice become a limit here. You can only afford to Riposte on average half the time. Again, I believe about 50% of the time is a robust estimate. If it is not, we need a clearer picture why not. Are we switching to whip? Dropping our damage dice to d4?

That being said, I have no good in-game evidence for how often people get to use Sentinel. But if I had a party member with aSentinel that averaged 12.60 per attack, I'd work hard to get him to use it. It's a resource-less ability.

Well, I'm playing a character using Sentinel in TotYP. The reaction attacks are by no means a gimme.

 

[guachi]

Some extra silliness with GFB I just calculated.

Level 12
Battlemaster 4
Arcane Trickster 8
Shield Master
Sentinel
Variant Human (so you can have two feats and a level 20 main stat)
Green Flame Blade

You only get one attack a round, but if you can knock a foe prone you'll get advantage on the attack. Since you only have one attack you can afford to use Precision every single time you miss. You'll also rarely miss if you can prone a foe. In fact, if you can get advantage on the attack you'll hit 96.0% of the time. Who cares if you only get one attack a round if it's almost Magic Missile-like in its ability to hit?

If you can prone a foe you can sneak attack regardless. But here's how the damage works out including sneak attack and GFB on a prone foe:
Target 1: 35.80
Target 2: 10.48
Sentinel: 17.50

Total: 63.78

This is pretty good damage. You'll succeed on knocking foes prone so often that you would use up your 4 superiority dice after 26 rounds of combat. There probably won't be 26 rounds of combat between short rests. So you can probably use your superiority dice to Riposte.

If they hit you, you Uncanny Dodge. If they miss you, you Riposte. If they attack your friend, you Sentinel.

 

[EternalRain]

It would come into the up-time assumption. And I agree with you about its importance and probably haven't factored it in strongly enough. I've assumed 10% better up-time/target-selection for ranged. It could be a lot more than that.

Part of the reason I chose 10% is I wanted a number that was thoroughly credible, i.e. that it would be hard to argue should be made smaller. With that low-balled number, we still show that ranged damage is worth 1.3x melee damage!

Thank you for the clarification!

 

[clearstream]

I said that using Precision when you miss by 4 or less means you'll hit 70% of the time with your d10 maneuver die. This is only true if you miss by exactly four. In fact, you'll hit 85% of the time, on average. If you miss by 1, for example, you'll always hit when you use your maneuver die. Since you're using Precision 20% of the time your overall chance to hit increases by 17%.

This changes the chance to hit for a GWM fighter to:
65% (base) - 25% (GWM) + 17% (Precision) = 57%.

I'll take another look at it. Precision is looking good. It will boost our Archer too, of course. I will make the additions to both sides.

Also, if you care to come up with how often you think a GWM fighter gets his bonus action attack from dropping a foe to 0, consider the following. A level 11 Battlemaster will not crit at least once 85.7% of the time. The 85.7% of the time he doesn't crit each of his attacks do 12.13 damage.

Max HP and current HP of a foe varies wildly, but if I had a feature that gave me a bonus attack if I dropped a foe to zero I'd always attack the foe with the lowest HP (adjusted by hit probability). E.g., if I were a 3rd level variant human with GWM facing goblins and an ogre I'd always, always, always attack the goblins and I wouldn't even use the -5/+10 part. One regular hit will drop them. Then I'd take my free attack on the ogre.

Sometimes, there is no nearby foe to cleave. Other times, the foe we're hitting doesn't die. Yet other times, we rolled a critical AND killed the foe at the same time. Occasionally, an ally will kill the foe before we can. Sometimes foes will flee. We can't mix up our levels too much here. Our fighter's damage is based on being 11th level. Foes appropriate for that level have to be expected. You suggested 25% of the time, and I used that value in my spreadsheet.

That being said, let's assume our 11th level Battlemaster is, with his buddies, facing some CR 5 creatures. They average about 100 HP. So a very rough estimate is our Battlemaster drops a foe 12.13% of the time (because he's doing 12.13 damage per attack on our 100 HP foe). In a round where he doesn't crit he has a 32.16% chance of dropping at least one foe. This 32.16% chance occurs on the 85.7% of rounds without a crit or 27.56% of the time. Add this to the 14.3% chance of getting at least one critical and our Battlemaster gets a bonus attack 41.86% of the time.

This yields average damage for our GWM friend of 46.88. This assumes you also use Precision attack on your bonus action attack.

What you are doing here is stating the maximum, not the expected. At most, the fighter might do that. Provided the foes are near enough to move between, and no one else inconveniently kills one, and none flee. The plausible value must be < 41.86%. The value I used was about 60% of it. I could buy 2/3rds, i.e. 28%.

 

[clearstream]

I miscalculated how useful Precision is.

It's not like I haven't done these calculations before, but I messed up in a previous post. I said that using Precision when you miss by 4 or less means you'll hit 70% of the time with your d10 maneuver die. This is only true if you miss by exactly four. In fact, you'll hit 85% of the time, on average. If you miss by 1, for example, you'll always hit when you use your maneuver die. Since you're using Precision 20% of the time your overall chance to hit increases by 17%.

This changes the chance to hit for a GWM fighter to:
65% (base) - 25% (GWM) + 17% (Precision) = 57%.

Also, if you care to come up with how often you think a GWM fighter gets his bonus action attack from dropping a foe to 0, consider the following. A level 11 Battlemaster will not crit at least once 85.7% of the time. The 85.7% of the time he doesn't crit each of his attacks do 12.13 damage.

Max HP and current HP of a foe varies wildly, but if I had a feature that gave me a bonus attack if I dropped a foe to zero I'd always attack the foe with the lowest HP (adjusted by hit probability). E.g., if I were a 3rd level variant human with GWM facing goblins and an ogre I'd always, always, always attack the goblins and I wouldn't even use the -5/+10 part. One regular hit will drop them. Then I'd take my free attack on the ogre.

That being said, let's assume our 11th level Battlemaster is, with his buddies, facing some CR 5 creatures. They average about 100 HP. So a very rough estimate is our Battlemaster drops a foe 12.13% of the time (because he's doing 12.13 damage per attack on our 100 HP foe). In a round where he doesn't crit he has a 32.16% chance of dropping at least one foe. This 32.16% chance occurs on the 85.7% of rounds without a crit or 27.56% of the time. Add this to the 14.3% chance of getting at least one critical and our Battlemaster gets a bonus attack 41.86% of the time.

This yields average damage for our GWM friend of 46.88. This assumes you also use Precision attack on your bonus action attack.

Okay well, it turns out not to matter much. With Precision used as planned (on misses by 4 or less) we get the following

GWM @28% bonus attack = ~45 average/turn
GWM @42% bonus attack = ~47 average/turn

PHB SS/CEx = ~44 average/turn, from 120' (or in melee, and ignoring cover)*

For me it's time to move on to the more interesting case of the Green Flame Blade, as GWM fighter convincingly loses out in the melee versus ranged stakes.


*Revised SS Archer does ~33 per turn under the same conditions, for those interested in using the "Once per turn" tweak.

 

[guachi]

Sometimes, there is no nearby foe to cleave. Other times, the foe we're hitting doesn't die. Yet other times, we rolled a critical AND killed the foe at the same time. Occasionally, an ally will kill the foe before we can. Sometimes foes will flee. We can't mix up our levels too much here. Our fighter's damage is based on being 11th level. Foes appropriate for that level have to be expected. You suggested 25% of the time, and I used that value in my spreadsheet.

Not having a foe in range to attack is not something unique to the GWM bonus action attack. It's not relevant to our calculations compared with any other melee attack we'd be looking at.

All of these of your things are possible, and I take those into account later. My 25% of the time guess was for dropping a foe to 0 on rounds you didn't crit.

What you are doing here is stating the maximum, not the expected. At most, the fighter might do that. Provided the foes are near enough to move between, and no one else inconveniently kills one, and none flee. The plausible value must be < 41.86%. The value I used was about 60% of it. I could buy 2/3rds, i.e. 28%.

This is not the maximum. You could be facing lower CR creatures. You could always choose to attack a creature with the lowest HP in range. It's an average. That foes may be out of range, or dead, or fled has literally no bearing on comparing a bonus action attack to any other attack. Because all the things on a bonus action attack can happen on your regular attack. Why apply factors to a bonus action attack that you aren't applying to other attacks?

When we compare damage, we always assume foes have infinite HP as no one calculates overkill damage from attacks. I've never seen it.

Pick an average HP for foes. The range of possible foe HP when you attack will be between 1 and that value. It's (very roughly) linear HP range. From this we calculate the chance of dropping a foe with a hit compared to a random HP value from this range. The simplest way is to calculate average damage divided by whatever HP value you chose. Make a guess on how often you are facing one foe (because it's the only thing relevant to our calculations that's different from SS or crit bonus attack from GWM. You haven't shown any work for foes fleeing or being killed on a your second attack, or whatever for SS. So we can't consider it for GWM dropping a foe to 0)

If you can't plausibly guess it's okay to leave that value at 1 and state you don't know. I don't know. I've never seen any calculations done for it. I've never seen good estimates. It obviously happens. However, we assume a target with infinite HP when we calculate DPR so why not assume infinite foes for our purposes here? Do neither or do both. But if you can come up with a good estimate and justify it then multiply that value by the chance of dropping a foe to 0 assuming infinite foes. Is it 70%? If so, multiply .7*27.56 and add 14.3 = 33.59%. And then calculate the amount of overkill damage and and remove that from all your other calculations. Be consistent.

I don't even know what a good average HP of a foe for a level 11 party is. The UA encounter guidelines suggests one CR 5 foe per party member is just a bit much for a 11th level party. That's one reason I chose it. The other is I calculated average HP for a CR 5 creature a few days ago. I actually think it's a bit less than 100. Swarm the party? Attack with a bunch of CR 3 creatures (average about 60 HP or so, I think). I chose 100 as it's close and it made the math easy.

 

[clearstream]

Not having a foe in range to attack is not something unique to the GWM bonus action attack. It's not relevant to our calculations compared with any other melee attack we'd be looking at.

All of these of your things are possible, and I take those into account later. My 25% of the time guess was for dropping a foe to 0 on rounds you didn't crit.




This is not the maximum. You could be facing lower CR creatures. You could always choose to attack a creature with the lowest HP in range. It's an average. That foes may be out of range, or dead, or fled has literally no bearing on comparing a bonus action attack to any other attack. Because all the things on a bonus action attack can happen on your regular attack. Why apply factors to a bonus action attack that you aren't applying to other attacks?

When we compare damage, we always assume foes have infinite HP as no one calculates overkill damage from attacks. I've never seen it.

Pick an average HP for foes. The range of possible foe HP when you attack will be between 1 and that value. It's (very roughly) linear HP range. From this we calculate the chance of dropping a foe with a hit compared to a random HP value from this range. The simplest way is to calculate average damage divided by whatever HP value you chose. Make a guess on how often you are facing one foe (because it's the only thing relevant to our calculations that's different from SS or crit bonus attack from GWM. You haven't shown any work for foes fleeing or being killed on a your second attack, or whatever for SS. So we can't consider it for GWM dropping a foe to 0)

If you can't plausibly guess it's okay to leave that value at 1 and state you don't know. I don't know. I've never seen any calculations done for it. I've never seen good estimates. It obviously happens. However, we assume a target with infinite HP when we calculate DPR so why not assume infinite foes for our purposes here? Do neither or do both. But if you can come up with a good estimate and justify it then multiply that value by the chance of dropping a foe to 0 assuming infinite foes. Is it 70%? If so, multiply .7*27.56 and add 14.3 = 33.59%. And then calculate the amount of overkill damage and and remove that from all your other calculations. Be consistent.

I don't even know what a good average HP of a foe for a level 11 party is. The UA encounter guidelines suggests one CR 5 foe per party member is just a bit much for a 11th level party. That's one reason I chose it. The other is I calculated average HP for a CR 5 creature a few days ago. I actually think it's a bit less than 100. Swarm the party? Attack with a bunch of CR 3 creatures (average about 60 HP or so, I think). I chose 100 as it's close and it made the math easy.

Okay well, it turns out not to matter much. With Precision used as planned (on misses by 4 or less) we get the following

GWM @28% bonus attack = ~45 average/turn
GWM @42% bonus attack = ~47 average/turn*

PHB SS/CEx = ~44 average/turn, from 120' (or in melee, and ignoring cover)**

For me it's time to move on to the more interesting case of the Green Flame Blade, as GWM fighter convincingly loses out in the melee versus ranged stakes.


*Split the difference and go with 46?
**Revised SS Archer does ~33 per turn under the same conditions, for those interested in using the "Once per turn" tweak.