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

[Bill Zebub]

I posted this in the thread about Tasha's, but thought it was interesting enough that some people not reading that thread might want to see it...



So I decided to write a little simulation. I wanted to roll millions of dice (in a computer program) to see how much better 16 strength is than 15 strength. The problem was, I couldn't decide which opponent to use.

Then it hit me: make 'em fight each other.

No, I'm not into PvP, but I figured this would be a good test of just how much better that +1 is.

First, I fought two 1st level sword and board fighters against each other. Chainmail, sword, shield, 14 Con, Defensive fighting style.

I ran 100,000 simulated fights to the death, with the two characters taking turn going first.

The guy with 16 strength ("Hutch" in my code) beat the guy with 15 strength ("Starsky) 60% of the time.

So then I bumped them up to 3rd level, meaning HP went from 12 to 28.

Now Starsky won 67% of the time.

Hmmm.

So, next I wondered how that +1 compares to Action Surge. I gave Starsky, but not Hutch, an Action Surge, thinking that would turn the tide in his favor. Nope. Hutch still won (at 3rd level) 58% of the time.

Just to check my code, I reduced Hutch's strength down to 15, but left Starsky with Action Surge. That finally flipped the board, and Starsky won 57% of the time.

Conclusion: the +1 modifier is significantly better than Action Surge, at least in terms of pure damage output. And that's not even factoring in that it's on all the time, not just for one fight per rest.

Epilogue: maybe Action Surge would shine with two-handed weapons, making that bonus attack worth more? I gave them each greataxes, which also meant they lost their shields, and then finally it was nearly a tie, with Hutch winning just slightly more than 50% of the time.

 

[Maxperson]

I posted this in the thread about Tasha's, but thought it was interesting enough that some people not reading that thread might want to see it...



So I decided to write a little simulation. I wanted to roll millions of dice (in a computer program) to see how much better 16 strength is than 15 strength. The problem was, I couldn't decide which opponent to use.

Then it hit me: make 'em fight each other.

No, I'm not into PvP, but I figured this would be a good test of just how much better that +1 is.

First, I fought two 1st level sword and board fighters against each other. Chainmail, sword, shield, 14 Con, Defensive fighting style.

I ran 100,000 simulated fights to the death, with the two characters taking turn going first.

The guy with 16 strength ("Hutch" in my code) beat the guy with 15 strength ("Starsky) 60% of the time.

So then I bumped them up to 3rd level, meaning HP went from 12 to 28.

Now Starsky won 67% of the time.

Hmmm.

So, next I wondered how that +1 compares to Action Surge. I gave Starsky, but not Hutch, an Action Surge, thinking that would turn the tide in his favor. Nope. Hutch still won (at 3rd level) 58% of the time.

Just to check my code, I reduced Hutch's strength down to 15, but left Starsky with Action Surge. That finally flipped the board, and Starsky won 57% of the time.

Conclusion: the +1 modifier is significantly better than Action Surge, at least in terms of pure damage output. And that's not even factoring in that it's on all the time, not just for one fight per rest.

Epilogue: maybe Action Surge would shine with two-handed weapons, making that bonus attack worth more? I gave them each greataxes, which also meant they lost their shields, and then finally it was nearly a tie, with Hutch winning just slightly more than 50% of the time.

One on one is a nearly pointless white room simulation. D&D combats are going to involve 4-6 PCs on average, possible with NPCs in the group, and often multiple bad guys. One on one doesn't show what +1 strength is worth.................................which isn't a whole heck of a lot.

 

[Greggy C]

You can add party of 5 on dndcombat.com and for the one fighter test full blown simulated battles with or without the +1 strength over multiple encounters.
I doubt it will make much of a difference.

 

[James Gasik]

It does show performance over time. How many attack rolls are you going to make before you get an opportunity to raise an ability score by 1 to achieve parity, if one guy has a 15 and another has a 16? How many misses turn into hits, how many times will that extra point per hit matter?

I think there is a huge impact, but because we look at smaller sample sizes, it's easy to dismiss it. Let's look at a swingier mechanic.

How much faster are combats where the party has Bless active than when they don't have it? How many resources are saved by the party because of the presence of Bless?

I'm going to just pull a number out of a hat. Let's say that we have a four man party. Fighty Mc Fighter attacks with a sword almost every turn, to the point that the turns he doesn't are such a small sample size that we can ignore it for this demonstration. He hits typical foes on a 11.

Sneaky Mc Sneakerson attacks with his shortbow almost every turn, same difference. We'll say he also hits his typical foes on an 11.

Healer Mc Healbot is more complicated, since she has spells and Channel Divinity she can use. Let's say she makes attack rolls 75% of the time, and due to needing a high Wisdom on top of "fighty stats", she hits typical foes on an 12.

Wizzy Mc Magicgal is even more complicated. But let's say she's frugal about her magic and likes to use firebolt a lot. So 75% of the time she's blasting things needing an 11 to hit.

Let's assume an in-game day requires 20 rounds of combat. We'll assume half of those combats, Healer Mc Healbot casts her Bless spell.

So, during those 10 rounds, Fighty hits his opponents on a 8.5 instead of an 11, or, 5 rounds he needs an 8, and 5 rounds he needs a 9. I'm not a math guy, but let's call that a 12.5 % boost in effectiveness when Bless is active (or 6.25% for the day).

Sneaky gets the same benefit. We're up to 25%, or 12.5%.

if the other two roll only 3 out of 4 combats, we get another 9.375%.

Adding up these numbers, we see that the party was, overall, nearly 22% more effective today because of Bless spells cast in half the combats. This doesn't take into account higher level abilities like Action Surge or Extra Attack, or other die rolls one might make due to saving throws or opportunity attacks (or even a granted attack if Fighty is a Battlemaster).

See? Useful data! You need a larger sample size to see the difference between 15 and 16 Strength, but remember, Strength applies to two die rolls, not one, attack and damage. The benefit may seem small, but in aggregate, it's definitely present.

 

[Lyxen]

I think it's still an interesting computation, but the main point is that, unless you spend all your time fighting, the la of great numbers will not have time to assert itself significantly compared to all the other factors in the game, situations, gear (for example, the greater the AC of your typical fighters, the greater the effect of the +1, but monsters have significantly lower AC on average), type of monsters, luck, etc.

And I'm not surprised about action surge, especially at level 3. It's value is highly situational for critical situations, not for averaging like this.

 

[Bill Zebub]

It does show performance over time. How many attack rolls are you going to make before you get an opportunity to raise an ability score by 1 to achieve parity, if one guy has a 15 and another has a 16? How many misses turn into hits, how many times will that extra point per hit matter?

I think there is a huge impact, but because we look at smaller sample sizes, it's easy to dismiss it. Let's look at a swingier mechanic.

How much faster are combats where the party has Bless active than when they don't have it? How many resources are saved by the party because of the presence of Bless?

I'm going to just pull a number out of a hat. Let's say that we have a four man party. Fighty Mc Fighter attacks with a sword almost every turn, to the point that the turns he doesn't are such a small sample size that we can ignore it for this demonstration. He hits typical foes on a 11.

Sneaky Mc Sneakerson attacks with his shortbow almost every turn, same difference. We'll say he also hits his typical foes on an 11.

Healer Mc Healbot is more complicated, since she has spells and Channel Divinity she can use. Let's say she makes attack rolls 75% of the time, and due to needing a high Wisdom on top of "fighty stats", she hits typical foes on an 12.

Wizzy Mc Magicgal is even more complicated. But let's say she's frugal about her magic and likes to use firebolt a lot. So 75% of the time she's blasting things needing an 11 to hit.

Let's assume an in-game day requires 20 rounds of combat. We'll assume half of those combats, Healer Mc Healbot casts her Bless spell.

So, during those 10 rounds, Fighty hits his opponents on a 8.5 instead of an 11, or, 5 rounds he needs an 8, and 5 rounds he needs a 9. I'm not a math guy, but let's call that a 12.5 % boost in effectiveness when Bless is active (or 6.25% for the day).

Sneaky gets the same benefit. We're up to 25%, or 12.5%.

if the other two roll only 3 out of 4 combats, we get another 9.375%.

Adding up these numbers, we see that the party was, overall, nearly 22% more effective today because of Bless spells cast in half the combats. This doesn't take into account higher level abilities like Action Surge or Extra Attack, or other die rolls one might make due to saving throws or opportunity attacks (or even a granted attack if Fighty is a Battlemaster).

See? Useful data! You need a larger sample size to see the difference between 15 and 16 Strength, but remember, Strength applies to two die rolls, not one, attack and damage. The benefit may seem small, but in aggregate, it's definitely present.

FWIW, you inspired me to add bless to my sim. Starsky, with bless, won over Hutch (with greater Strength) 50.8% of the time. So an always-on bless seems to be very slightly better than...but really about equal to...+1 Strength mod. Or a +1 sword.

Update: I realized I did that with greataxe. With sword and board, bless and +1 were almost perfectly equal.

 

[James Gasik]

Well you don't even have to spend all your time fighting. How many combat rounds do you see before you hit a benchmark like 4th level where you can "catch up"? People taut the "6-8 encounters per diem" a lot, so how many combat rounds does 7 combats require?

I am not willing to look at the DMG to figure out how many combats it takes to go up 3 levels, but i'm going to assume it's quite a lot. Let's call it, I don't know, 35. In 35, 3 round combats, you will make 100 attack rolls as a Fighter easily. 100 rolls you were 5% better at, and theoretically 100 points of damage (though when/where that makes a difference is almost impossible to gauge). It's not meaningless, but I'm not a statistician. Maybe one will wander along and tell us what kind of bell curve we're looking at.

 

[James Gasik]

FWIW, you inspired me to add bless to my sim. Starsky, with bless, won over Hutch (with greater Strength) 50.8% of the time. So an always-on bless seems to be very slightly better than +1 Strength.

Oh absolutely, Bless is absolutely broken with bounded accuracy, but it tends to get ignored because of small sample sizes. That's why I chose it, it's easier to look at it's effect over a single day of combats than the value of a +1 to hit. When you get to the point that every combat can have Bless going, bounded accuracy is a joke, but you rarely hear complaints about it, because it's just one more tool in the player's arsenal.

 

[Bill Zebub]

The fallacy of these "sample size isn't large enough to make a difference" arguments is that a small sample size only means it's a lot more swingy...not that that the effect isn't there. Yes, the small sample size means you are more likely to see no effect from the +1, but you are equally likely to see an even greater than expected result.

For example, if 10 tables each have two fighters, one with 15 Strength and one with 16 Strength, and each table fights a million rounds of combat, they are all going to see roughly the statistically predicted difference.

If each table only fights 10 rounds of combat, though, one or two tables will report no difference, one or two tables will report a huge difference, and the rest will report something in the middle.

And, really, the more fundamental mistake here is that "small sample size" is only an issue if you are using the sample to generate your hypothesis. If I said, "At last night's game we had two fighters, and the one with 16 Strength was WAY better than the one with 15 Strength" then it would be justified to say that the sample size was too small.

 

[James Gasik]

Ideally I think you need a monster with a lot of hit points, but a terrible chance to hit (I know they're out there, I just can't think of one off the top of my head). Put Starsky and Hutch in solo combat with the monster, calculating how many misses become hits, and at what point the +1 damage per hit matters (assuming the monster can't put them down before they win).