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

[clearstream]

In another thread I wanted to understand a revision I'm making to Sharpshooter, adding "Once per turn" to the power-attack. An obvious question is "If this is good, why not apply it to Great Weapon Master, too?" The answer lies in our tendency to fix no firm value on ranged. We know that dealing damage at range is better, but we generally don't convert that into a commensurable. Here I want to suggest a firm value for ranged, based on the concepts of up-time and damage mitigation.

First background numbers. At 11th level against an expected AC 17

• GWM+Str+Str (20 Strength) Battlemaster (GWF style) with Greatsword with Precision Attack available, likely needs 8 to hit
• Once per turn SS+Dex+Dex (20 Dex) Battlemaster (Archery style) with Longbow with Precision Attack available, likely needs 7 to hit
• Choosing to use −5/+10 that is 13 and 12 respectively, and some misses can be made into hits with the maneuver
• Both use Precision whenever they miss by 3 or less (aiming to expend 2.5 superiority dice per combat)

We expect our GWM fighter to deal about 43 damage/turn from 5' while our SS archer ("once per turn" revision) deals about 32* damage/turn from up to 600'. My thesis is that range makes up the difference, i.e about one-third of effective damage. *With PHB Sharpshooter and Crossbow Expert (losing one Dex increase), using Hand Crossbow, our SS archer deals instead about 40 damage/turn from up to 120'.

Up-time
Up-time means over an average 5-round combat (and over many such combats) how often can I expect to be able to deal my damage? I'm going to assert that the melee fighter gains about 90% up-time. On average, at least every other combat, one attack is lost to closing, repositioning or whatever. Our ranged fighter is online from the get-go and scarcely needs to reposition. I'm going to assert 99% up time. Counting up-time, GWM deals about 39 damage per turn, while SS continues to deal about 32. Our average combat is lasting 5 turns. Note that combats can vary widely and all I am really asserting here is that ranged enjoys at least 10% more up-time than melee. I'm mindful that sometimes ranged will be in melee and want to disengage.

Damage Mitigation
Damage-mitigation is how much of a foes possible damage we avoid taking. At the relevant levels, foes with +10 to hit have Multiattacks that deal an average of 20 damage/attack, against GWM's plate armor needing 8s: for about 26 a turn while in contact. We've asserted they're in contact only 90% of the time so let's call it a 23 damage/turn. Sometimes a ranged attacker will be hitting them without their being in contact. Other times they'll prevent a counter-attack even occurring.

It is difficult to predict how often our SS fighter is in contact with the foe. Certainly less than GWM fighter who actively seeks out contact. I find a worst case of 50% contact plausible over many combats, for 13 damage/turn. In given combats it could be a lot less, even 0%. Or more, even 100% against other ranged opponents (but then, GWM could be kited and get to make 0 attacks!)

A common ratio for damage-mitigation to damage-dealt is 3/5 i.e. damage mitigated is worth only 60% of damage dealt. On that basis, our archer counts about +6 "damage" gain per turn from mitigation. Leading to a conclusion that SS after putting a value on ranged is worth nearly as much as GWM (38:39) using my revision for the power attack ("Once per turn"), and greatly more than GWM using RAW. Noting too that I ignore the benefits of focus fire, and probably low-ball the up-time and damage mitigation discrepancies.

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I hope the concepts of up-time and damage-mitigation will prove helpful in balancing ranged versus melee attacks, through being able to equate damage with range. As a closing aside, these principle apply equally well to ranged versus ranged, where the greater range will usually enjoy more up-time and damage-mitigation than the lesser range.

Aside from combatant and foe stats, the key values are

Up-time
% of turns in reach/range over turns out of reach/range
Up-time discrepancy = combatant A's% − combatant B's%
Discrepancy can be applied as a simple multiplier to one combatant's damage expectation

Damage Mitigation
Contact assumption = number of turns a foe has a chance to make an attack against our combatant / average turns of combat
Damage / turn calculated as average damage * attacks * chance to hit * contact assumption
Mitigated damage worth = 3/5 against dealt damage
Gain = combatant A's worth − combatant B's worth

The side with the greater range will usually enjoy a beneficial up-time discrepancy and effective damage gain.


[Edited to bring case up to date with discussion in thread.]

 

[clearstream]

Based on the concepts of up-time and damage mitigation, I want to suggest a rule of thumb for evaluating range versus damage. First stressing the crucial premise that (damage + range) > (damage) i.e. range has some positive value.

A spread of +10% to +100% for range would probably capture most individual campaigns. A narrower spread - 20-40% - likely works better for the average campaign.

Based on analysis I would count damage at greater range as worth +30% (e.g. count 10 points of raw damage as 13 points when comparing attacks) for D&D skirmish style combats.


[Edited to broaden the suggested rule of thumb to capture a wider spread of campaigns.]

 

[guachi]

Level 11 fighters would probably have a 20 main stat by level 11. You'll have 3 ASIs and one goes to the feat so you get two for your main stat.

Also, the bonus action attack for the GWM fighter will grant a minimum damage increase roughly equal to the attacker's crit percentage. Three attacks for a Champion gives a 27.1% chance of getting at least one critical so instead of 3 attacks a round you'll get 3.27 attacks a round for a 9% increase. This does not, of course, account for the times you'll drip a foe to 0 HP nor the ability of the GWM fighter to use something like Riposte to get another attack. Though both the SS and GWM fighters could just as easily spend all their dice on Precision to ensure the -5/+10 attack lands.

All told, if you take the bonus action attack into account, the GWM fighter is probably adding 20% more damage from that attack. I've done some calculations and have them sitting around somewhere that attempt to figure out how often a GWM fighter might expect to get that bonus attack.

 

[The Old Crow]

Another great benefit to ranged that I found in play was the ability to be able to hit the right target. Choice of target for any combatant is anything within reach or range, and ranged combatants just have a lot more to choose from. They have an easier time focus firing because any obstacle that is not total cover will not prevent them from attacking, unlike melee. Ranged can spend their attacks more effectively than melee, but I am not sure how to measure that.

 

[Xetheral]

While you have mentioned that "combats can vary wildly", I think the extent of that variation may doom your analytical approach....

In addition to variation within a campaign, campaigns themselves can vary wildly, particularly in regards to whether they emphasize combat-as-war or combat-as-sport.

In a campaign emphasizing combat-as-sport, encounter distances are usually determined by the DM and (IME) often tend to be relatively short. Here, the extra value of ranged damage is somewhat limited, both by reducing the benefit of extra-long ranges and decreasing the ability of the ranged combatants to avoid melee.

In a campaign emphasizing combat-as-war, encounter distances are limited by the environment, but within that constraint are determined either by the aggressors to favor their strengths (in the case of one group attacking another unawares) or by the interaction of two hostile groups each simultaneously manuevering to maximize their own advantages (in the case of two groups aware of each other). When the PCs are on defense the DM may still be choosing the encounter distance (subject to the perceptive abilities of the PCs), but it's a very different calculus than in the combat-as-sport case, where the decision is akin to picking a venue, rather than the result of roleplaying the agressors.

Further complicating matters is that this isn't a strict dichotomy... many campaigns are a blend of both styles. The ultimate point is that encounter distances can vary wildly both within and among campaigns, and encounter distance is critical to determining the relative value of ranged damage over melee.

If that were the only issue, an analytical approach might still be possible in the combat-as-sport context, where encounter distances tend to be more constrained. Unfortunately there is an additional factor that will create wild differences between campaigns: how does the DM roleplay antagonists in combat? If antagonists tend to individually deal with the most immediate threat to them personally, then melee PCs tend to be "sticky", increasing the value of ranged damage. If instead antagonists tend to optimize their strategy at the group level, then it's more likely that individual antagonists will bypass the melee PCs to attack the ranged PCs, decreasing the value of ranged damage.

Given these differences between campaigns, I don't know that a fixed figure (e.g. 30%) can ever be meaningful for analysis, even in the abstract.

 

[clearstream]

Level 11 fighters would probably have a 20 main stat by level 11. You'll have 3 ASIs and one goes to the feat so you get two for your main stat.

That is true, however the expected AC for a foe at the relevant level is 17, not 15. I used AC 15 to make the comparison in cases where the power-attack is worth using. In assuming an 18 ability score I am counting one ASI into it. Hence I felt that I didn't need to make the assumption that the character's last ASI also went into it.

Do you feel it be helpful if I used the expected AC 17 and counted two ASIs (instead of one) into the GWM fighter's primary ability score? If I do, is it fine with you if I add Crossbow Expert to the Archer? As that will prove stronger for SS than the ability score increase does for GWM.

Also, the bonus action attack for the GWM fighter will grant a minimum damage increase roughly equal to the attacker's crit percentage. Three attacks for a Champion gives a 27.1% chance of getting at least one critical so instead of 3 attacks a round you'll get 3.27 attacks a round for a 9% increase.

I counted the chance of a critical (hence Champion!), the extra damage for the critical, and for GWM the bonus attack in the case of a critical. Looking back at the spreadsheet I see I did not count the chance of critical on the bonus attack, but that's a tiny adjustment to the average damage (less than 1 point).

This does not, of course, account for the times you'll drip a foe to 0 HP nor the ability of the GWM fighter to use something like Riposte to get another attack. Though both the SS and GWM fighters could just as easily spend all their dice on Precision to ensure the -5/+10 attack lands.

The GWM Fighter probably isn't a Battlemaster, because they want to critical. Hence Champion. Do you feel a Battlemaster GWM Fighter will do better than the Champion? Remembering they will have 5 dice so we should assume 2-3 per combat, which if used on Precision gets blown on their first attack.

All told, if you take the bonus action attack into account, the GWM fighter is probably adding 20% more damage from that attack. I've done some calculations and have them sitting around somewhere that attempt to figure out how often a GWM fighter might expect to get that bonus attack.

Please note that I do take the bonus attack into account. Against foes that don't die instantly or aren't conveniently clustered, I estimate the expected damage from GWM bonus attacks is (critical%*hit%*damage + critical%*damage (from dice only)). Against AC 15 that's (0.1*0.45*20.5) + (.01*6.5). So the possible bonus attack yields about 1.5 more damage per turn. Do you estimate it to be greater?

 

[Nevvur]

As with any such thesis, table variation means YMMV. As you said, ranged will usually enjoy greater damage, about +30%. My experiences as a DM and player generally agree with your conclusions, but I think there's a lot of swing on that 30%.

 

[clearstream]

Further complicating matters is that this isn't a strict dichotomy... many campaigns are a blend of both styles. The ultimate point is that encounter distances can vary wildly both within and among campaigns, and encounter distance is critical to determining the relative value of ranged damage over melee.

If that were the only issue, an analytical approach might still be possible in the combat-as-sport context, where encounter distances tend to be more constrained. Unfortunately there is an additional factor that will create wild differences between campaigns: how does the DM roleplay antagonists in combat? If antagonists tend to individually deal with the most immediate threat to them personally, then melee PCs tend to be "sticky", increasing the value of ranged damage. If instead antagonists tend to optimize their strategy at the group level, then it's more likely that individual antagonists will bypass the melee PCs to attack the ranged PCs, decreasing the value of ranged damage.

Given these differences between campaigns, I don't know that a fixed figure (e.g. 30%) can ever be meaningful for analysis, even in the abstract.

The argument is a broad one that works well across campaign types, through being abstract. The steps are simple and I believe quite hard to argue against, as follows

1) I state that damage has value and that damage+range has greater value? Essentially I say that (10 damage) < (10 damage + range).
2) I suggest some concepts for equating a damage value with a range value
3) I suggest that once equated, the application of range counts for about a third more damage in common cases, that the rules support

To fixate on 30% is to miss the point. Once we accept that premise that damage + range is worth some amount more than damage, we have a logical construct that applies to whatever kind of game we play, with one tuning value that we can derive in whatever way makes most sense to us. Crucially, we can say that something is up if a ranged attack does equal raw damage to a melee attack.

 

[clearstream]

As with any such thesis, table variation means YMMV. As you said, ranged will usually enjoy greater damage, about +30%. My experiences as a DM and player generally agree with your conclusions, but I think there's a lot of swing on that 30%.

The crucial point is the premise that damage < damage+range.

 

[clearstream]

Level 11 fighters would probably have a 20 main stat by level 11. You'll have 3 ASIs and one goes to the feat so you get two for your main stat.

Also, the bonus action attack for the GWM fighter will grant a minimum damage increase roughly equal to the attacker's crit percentage. Three attacks for a Champion gives a 27.1% chance of getting at least one critical so instead of 3 attacks a round you'll get 3.27 attacks a round for a 9% increase. This does not, of course, account for the times you'll drip a foe to 0 HP nor the ability of the GWM fighter to use something like Riposte to get another attack. Though both the SS and GWM fighters could just as easily spend all their dice on Precision to ensure the -5/+10 attack lands.

All told, if you take the bonus action attack into account, the GWM fighter is probably adding 20% more damage from that attack. I've done some calculations and have them sitting around somewhere that attempt to figure out how often a GWM fighter might expect to get that bonus attack.

With the spreadsheet set up this was fast to check

A = Fighter 11th Champion, Defense style, Strength 20 (two ASIs), Greataxe, GWM.
B = Fighter 11th Battlemaster, Archery style, Dexterity 18 (one ASI), Hand Crossbow, SS, CEx.

Expected damage per PHB RAW against AC 17 foe, who doesn't die to one hit or isn't conveniently clustered with other foes*.
A = about 29 counting critical hits and bonus attacks
B = about 32 counting critical hits and bonus attacks, at 120' range

Expected damage per with SS power-attack "Once per turn" against AC 17 foe, who doesn't die to one hit or isn't conveniently clustered with other foes.
A = about 29 counting critical hits and bonus attacks
B = about 24 counting critical hits and bonus attacks, at 120' range

Attacks are equal if 29-r=24 (where r is range)
Let's assume the value or r is unknown, but positive (range has some value)

Is it credible that range is worth < 5% (required for r to be < 1)?
Is it credible that range is worth ~21% (required for A=B)?
Is it credible that range is worth >21% (required for A<B)?

I think these sorts of questions strongly suggest that once per turn is correct for Sharpshooter, and more generally I feel like it is super-hard to argue that range has a value of <5%.

If DMs used a value of 10% to 50% for r, they would probably capture their individual campaigns. A narrower spread - 20-30% - probably works for the average campaign.



*The objection that GWM might face numerous foes tightly clustered I believe is easily countered by the objection that SS+CEx might encounter foes they can easily kite.