D&D 5E What is +1 Strength worth?

[Bill Zebub]

Was 2nd wind and/or subclass features factored in?

No. Anything that would prolong the fight equally on both sides, as we have seen, would only strengthen the relative value of the +1, so that's all that would happen with 2nd wind.

Any subclass features would likewise either increase the value of the +1 if they were defensive (prolonging the fight) or decrease the value of the +1 if they were offensive (made the fight go faster).

But if you wanted to compare the value of the +1 to a subclass feature, I could give Starsky that feature (similar to what I did with bless and action surge.). Was there one in particular you were interested in? If it's simple to code I can try it. (If it's complex to code I might not get around to it.)

 

[FrogReaver]

No. Anything that would prolong the fight equally on both sides, as we have seen, would only strengthen the relative value of the +1, so that's all that would happen with 2nd wind.

Any subclass features would likewise either increase the value of the +1 if they were defensive (prolonging the fight) or decrease the value of the +1 if they were offensive (made the fight go faster).

But if you wanted to compare the value of the +1 to a subclass feature, I could give Starsky that feature (similar to what I did with bless and action surge.). Was there one in particular you were interested in? If it's simple to code I can try it. (If it's complex to code I might not get around to it.)

That’s not quite true. 2nd wind isn’t a flat hp bonus. It’s variable. And variability tends to help the ‘weaker’ character win more often in comparison to the stronger character. My expectation would be that it would lessen the gap, not increase it.

If you want to do a test try +1 con. +1 initiative won’t matter as much as the fight lasts so long.

 

[Bill Zebub]

Was 2nd wind and/or subclass features factored in?

Was an alternate racial bonus given and it’s impact measured?

I expect +1 initiative or +1 con could easily swing the results to the other fighters favor.

Multiple encounters per day could as well - where the randomness of hitdice recovery can easily overcome the difference in attacks.

One thing I don’t buy is that the action surge fighter is generally worse. That finding was a result of pushing AC high instead of taking the dueling fighting style IMO. In general an extra action is like having an extra round of combat. The impact there is going to be much greater than +1 str unless the battle goes on for a large number of rounds.

In this case it would as high ac and low damage setups push this fight to last well over 10 rounds.

Take this encounter to level 5 or 6 and I think you’ll find action surge makes a huge difference.

So first I switched fighting style from Defensive to Dueling. At level 3 Hutch's win rate dropped, as would be expected, from 83% to 63%.

Next, leaving it like that, I gave Starsky +1 to initiative (which required refactoring the code to actually roll initiative, rather than alternate who goes first) and the result surprised me: no discernible change. Huh? I started keeping track of who won initiative, and sure enough Starsky is winning around 52-53% of the time, but the overall outcome is the same.

 

[FrogReaver]

So first I switched fighting style from Defensive to Dueling. At level 3 Hutch's win rate dropped, as would be expected, from 83% to 63%.

Next, leaving it like that, I gave Starsky +1 to initiative (which required refactoring the code to actually roll initiative, rather than alternate who goes first) and the result surprised me: no discernible change. Huh? I started keeping track of who won initiative, and sure enough Starsky is winning around 52-53% of the time, but the overall outcome is the same.

The fight goes on so long that initiative doesn’t matter ‘much’. Shorter fights initiative matters a lot more.

 

[Bill Zebub]

That’s not quite true. 2nd wind isn’t a flat hp bonus. It’s variable. And variability tends to help the ‘weaker’ character win more often in comparison to the stronger character. My expectation would be that it would lessen the gap, not increase it.

But it's variable for both characters. The net result is that they each have a larger pool of HP, which prolongs the fight, which advantages the higher Strength. If you don't understand/believe that logic I can run it.

If you want to do a test try +1 con. +1 initiative won’t matter as much as the fight lasts so long.

At level 1 (shorter fights) +1 initiative reduced Hutch's win rate from 60% to 59%. So, yeah, it starts to show a difference.

If Starsky has +1 Con instead of +1 Dex it drops to 55.5%. At level 3 it's 57% instead of 63%. (In both cases with dueling rather than defensive fighting style.). So +1 Con does a lot more for Starsky than +1 Dex does.

 

[Bill Zebub]

The fight goes on so long that initiative doesn’t matter ‘much’. Shorter fights initiative matters a lot more.

Yes, mathematically 1% is infinitely more than 0%. So that would count as "a lot more."

(I jest. There must have been a difference at level 3; I was just rounding to 0.1% so didn't see it).

 

[FrogReaver]

But it's variable for both characters. The net result is that they each have a larger pool of HP, which prolongs the fight, which advantages the higher Strength. If you don't understand/believe that logic I can run it.

It being variable for both characters is precisely the point. Let's walk through a hypothetical example.

Hutch rolls a 1 for 2nd wind. Starsky rolls a 10. Husky restores 4 hp. Starsky restores 13.

Starsky normally loses 60% of the time. That means this +9 hp difference matters enough to flip the outcome some portion of that 60% of the time.

Reverse the situation with Hutch Rolling the 10 and Starsky the 1.

Hutch only loses 40% of the time. That means this +9 hp difference matters some portion of that 40% of the time.

Hopefully you can see where this is going. X*60% > Y*40%

At least for X > 2/3*Y (and X is extremely unlikely to be less than that).

Thus variable healing will lessen the gap (but never overcome it entirely).

At level 1 (shorter fights) +1 initiative reduced Hutch's win rate from 60% to 59%. So, yeah, it starts to show a difference.

If Starsky has +1 Con instead of +1 Dex it drops to 55.5%. At level 3 it's 57% instead of 63%. (In both cases with dueling rather than defensive fighting style.). So +1 Con does a lot more for Starsky than +1 Dex does.

Yep. +1 Con might do even more if there was an additional encounter first such that starskys higher healing hit dice might start to matter.

 

[Bill Zebub]

It being variable for both characters is precisely the point. Let's walk through a hypothetical example.

Hutch rolls a 1 for 2nd wind. Starsky rolls a 10. Husky restores 4 hp. Starsky restores 13.

Starsky normally loses 60% of the time. That means this +9 hp difference matters enough to flip the outcome some portion of that 60% of the time.

Reverse the situation with Hutch Rolling the 10 and Starsky the 1.

Hutch only loses 40% of the time. That means this +9 hp difference matters some portion of that 40% of the time.

Hopefully you can see where this is going. X*60% > Y*40%

At least for X > 2/3*Y (and X is extremely unlikely to be less than that).

Thus variable healing will lessen the gap (but never overcome it entirely).

I can’t test the code right now, but while in some cases the healing will let Starsky win, over a hundred thousand fights it will average out, with the result of prolonging the fight.

But when I get a chance I’ll add the logic. What do you want the trigger condition to be? E.g. HP less than what my opponent can do in one hit”

 

[Bill Zebub]

Yep. +1 Con might do even more if there was an additional encounter first such that starskys higher healing hit dice might start to matter.

Yeah in general I think Con is a strong choice, and it comes down to what kind of fighter you want.

But I did this in the context of the ASI debate, and if you want to play a specific race, Con may not be a choice.

 

[FrogReaver]

I can’t test the code right now, but while in some cases the healing will let Starsky win, over a hundred thousand fights it will average out, with the result of prolonging the fight.

It won't average out because the times it can turn a loss to a win is not constant between the characters. But by all means test it.

But when I get a chance I’ll add the logic. What do you want the trigger condition to be? E.g. HP less than what my opponent can do in one hit”

Let's go with, if i'm (injured more than can be healed by a max roll of 2nd wind) or (injured less than can be healed with a max roll of 2nd wind and opponent has a >X% chance of killing me next turn. We might want to play around with what X% should be. My initial reaction is 85%).

 

[FrogReaver]

Yeah in general I think Con is a strong choice, and it comes down to what kind of fighter you want.

But I did this in the context of the ASI debate, and if you want to play a specific race, Con may not be a choice.

Boosting Con would seem to be part of that debate. Some races boost con afterall.

But even the ones that don't they genearlly offer something else. Many things are much less specific to combat so alot harder to compare. Like what is the value of +1 wisdom? Or the value of magic resistance (looking at gnomes), or the value of darkvision, etc.

 

[Bill Zebub]

Ok, I added 2nd Wind. 3rd level, dueling style, no Con difference. Triggers if hp is low enough that you could die in one hit, which means no part of it is ever wasted.

Without 2nd Wind: Hutch wins 63%.
With 2nd Wind: Hutch wins 65%.

E.g., 2nd wind benefits both equally, prolonging the fight, and thus smoothing out the variability, giving more advantage to the higher strength.

P.S. FWIW, I gave 2nd Wind only to Starsky, and he went from losing 37% to winning 54%. So where +1 Str always gives a bit more damage, and sometimes gives an extra hit, 2nd Wind always gives bonus HP larger than an average hit.

Unsurprising, but interesting to quantify.

 

[FrogReaver]

Ok, I added 2nd Wind. 3rd level, dueling style, no Con difference. Triggers if hp is low enough that you could die in one hit, which means no part of it is ever wasted.

Without 2nd Wind: Hutch wins 63%.
With 2nd Wind: Hutch wins 65%.

E.g., 2nd wind benefits both equally, prolonging the fight, and thus smoothing out the variability, giving more advantage to the higher strength.

Is that die in 1 hit even if crit?

 

[Bill Zebub]

Is that die in 1 hit even if crit?

Oh, I left crits out. They don't change much.

 

[James Gasik]

Actually I would think adding 1's and crits would make things worse to model. A crit gives you another die of damage, a 1 negates damage entirely. These two things are not equivalent.

EDIT: I mean, it's unlikely that you could hit on a 1 anyways, but I've seen it come up once or twice.

 

[FrogReaver]

Oh, I left crits out. They don't change much.

Crits shorten the encounter
Crits lessen the relative difference of dpr values
Crits are highly variable and variability benefits the ‘weaker combatant’

There’s a high chance at least 1 crit happens in each encounter since these encounters take so long.

Probably not enough to matter, but would 1-2% matter? Would crits be enough to impact the percentage that much?

 

[Bill Zebub]

Actually I would think adding 1's and crits would make things worse to model. A crit gives you another die of damage, a 1 negates damage entirely. These two things are not equivalent.

Crits will slightly shorten the fighting, slightly decreasing the value of Str.

Failure on a 1 would negate that, but it’s not an official rule.

 

[Bill Zebub]

variability benefits the ‘weaker combatant’

Well, not really. There’s a sense in which high variability can save your bacon through sheer luck, but it can also swing against you. And it all averages out, especially over 100,000 fights.

 

[CleverNickName]

This is an interesting approach to the analysis, and illustrates how well the attributes and modifiers work together during combat.

But as others have mentioned, Strength isn't just melee attack rolls. Strength affects the kinds of armor you can wear, and the amount of gear you can carry. I wonder what those percentages would be if Starsky had Str 14 (and thus could only wear chainmail at best) and Hutch had Str 15 (allowing him to wear full plate), for example...because now, that +1 to Strength doesn't affect the Strength modifier, but instead it amounts to a +2 to AC.

I'd wager that +1 has a far greater impact than "just five percent."

 

[GMforPowergamers]

what about a Dex based fighter with a rapier and light armor against a str based fighter with a longsword?
the dex increases WAY more than str and still with a finesse weapon adds to attack and damage.