D&D 5E Drawbacks to Increasing Monster AC Across the Board?

[ezo]

The encounter building rules in the 2024 DMG work just fine in with 2014 characters and monsters. In fact, IMO (and others) they work better than to 2014 guidelines whether you are using 2014 or 2024 material or a mix of both.

 

[dave2008]

FYI.

Here is the 2014 XP budget for 6 lvl 15 PCs: 38,400 (between CR 21 & 22)

Here is the 2024 XP budget for 6 lvl 15 PCs: 46,800 (between CR 22 & 23)

So for 2024, the encounter should be slightly more challenging than in 2014, not less as you seemed to suggest. Just thought you might want to know as it seems like you are not familiar with the 2024 revisions.

One thing to note is the 2014 monsters, at these CRs, are definitely weaker than the 2024 version. So keep that in mind as well. All other things being equal, you would need a CR 24-26 2014 monster to accommodate the 2024 encounter budget, or basically PC level +10 as noted earlier. You can actually reduce this to about PC Level +7 with the 2024 rules.

 

[ezo]

FYI.

Here is the 2014 XP budget for 6 lvl 15 PCs: 38,400 (between CR 21 & 22)

Here is the 2024 XP budget for 6 lvl 15 PCs: 46,800 (between CR 22 & 23)

So for 2024, the encounter should be slightly more challenging than in 2014, not less as you seemed to suggest. Just thought you might want to know as it seems like you are not familiar with the 2024 revisions.

One thing to note is the 2014 monsters, at these CRs, are definitely weaker than the 2024 version. So keep that in mind as well. All other things being equal, you would need a CR 24-26 2014 monster to accommodate the 2024 encounter budget, or basically PC level +10 as noted earlier. You can actually reduce this to about PC Level +7 with the 2024 rules.

@dave2008 just so you know I really don't care about anything in 2024 D&D. I don't say that to be rude, but just so you don't continue to waste your time. If you feel it is relevant for others, then no worries, but as you were responding to me, I just wanted that clarified.

 

[tetrasodium]

I was not referencing any specific post in my chart. The 65% hit rate was thrown around frequently as the common base point, and so I used that. The damage was just a joe shmoe fighter

In that case it raises questions like what you are trying to model and the details of any non-posterior sourced logic that went into the math involved in deciding upon numbers for the "% chance".

Even beyond that you have entries like the first row that seem to either involve a bad rounddown or serve no function other than salting the rest with distracting negative looking results.

 

[Stalker0]

In that case it raises questions like what you are trying to model and the details of any non-posterior sourced logic that went into the math involved in deciding upon numbers for the "% chance".

Even beyond that you have entries like the first row that seem to either involve a bad rounddown or serve no function other than salting the rest with distracting negative looking results.

I am....so confused.

65% is a commonly quoted number in monster math discussions, and its been used heavily in discussions on this thread. That's why I used it, no more no less. If you think the 65% on a hit is not accurate, that the normal to hit rate is a big deviation from that....fair enough, what to hit value do you think is more suitable for the average?

And the first row....is just the % chance that the two attacks would miss and deal 0 damage, rounded to 2 percentage places. Again, no more, no less. It is absolutely a circumstance that will happen if you attack a creature with two attacks, yes sometimes you completely miss. How is that a distraction?

 

[NotAYakk]

Since there is a lot of discussion about what the hit rate translates to in game I thought this quick chart would be helpful. If you assume a 65% hitrate, two attacks (aka most fighter types). And then we assume a damage of 12.5 (1d8 + 5 str +2 for something like dueling mastery + 1 magic bonus). And then here is the average damage that character will do, the % of the time they do it, both for regular, advantage, and disadvantage. So you can guage for yourself how wide a variance in damage the character will do.

View attachment 405363

Aside: If you want a full model, find an engine capable of handling polynomials.

A 1d8+5+2+1 hit is represented by 1/8 * (x+x^2+...+x^8) for the d8, times x^8 for the flat bonus damage, or x^8/8 * (x-x^9)/(1-x).

Each term of this polynomial looks like (probability)x^(damage done). Take its derivative and evaluate at 1 and you get the average damage of a hit. Its second derivative can be used to calculate variance.

You can model crits and misses and multiple swings with more math.

Let d( n )= x/n (1-x^n)/(1-x)
Then d(8) = x/8 (1-x^8)/(1-x)
(This is just shorthand for (x+...+x^n)/n without the ...s)

0.6 * d(8) * x^8 + 0.05 * d(8)^2 * x^8 is the polynomial describing the damage distribution of "5% crit chance, 65% hit chance (including crits). Two swings is just that squared:

(0.6 * d(8) * x^8 + 0.05 * d(8)^2 * x^8 + 0.35 x^0)^2
tossing it an an algebra engine it produces:
x^8 * 0.6 * (x+x^2+x^3+x^4+x^5+x^6+x^7+x^8)/8 + x^8 * 0.05 * ((x+x^2+x^3+x^4+x^5+x^6+x^7+x^8)/8)^2+0.35)^2
=
6.10352×10^-7 x^48 + 2.44141×10^-6 x^47 + 6.10352×10^-6 x^46 + 0.000012207 x^45 + 0.0000213623 x^44 + 0.0000341797 x^43 + 0.0000512695 x^42 + 0.0000732422 x^41 + 0.000215454 x^40 + 0.000476074 x^39 + 0.000853271 x^38 + 0.00134521 x^37 + 0.00195007 x^36 + 0.00266602 x^35 + 0.00349121 x^34 + 0.00442383 x^33 + 0.0107391 x^32 + 0.016814 x^31 + 0.0226501 x^30 + 0.0282495 x^29 + 0.0336139 x^28 + 0.0387451 x^27 + 0.043645 x^26 + 0.0483154 x^25 + 0.0424042 x^24 + 0.0366138 x^23 + 0.0309436 x^22 + 0.0253931 x^21 + 0.0199615 x^20 + 0.0146484 x^19 + 0.00945313 x^18 + 0.004375 x^17 + 0.0563281 x^16 + 0.0557812 x^15 + 0.0552344 x^14 + 0.0546875 x^13 + 0.0541406 x^12 + 0.0535937 x^11 + 0.0530469 x^10 + 0.0525 x^9 + 0.1225 x^0
which gives the exact probabilities of each damage amount (the exponent of a term) and the probabilities (the coefficient of the term); a 6.10352*10^-7 chance of a double-crit with max damage of 48, for example, is described by the "6.10352×10^-7 x^48" term.

Want to know what 4 turns of damage output looks like? Raise it to the power 4! You are only limited by the precision of your algebraic engine.

And, as noded, calculating mean and variance from this model is just the matter of examining derivatives. Mean = df(x)/dx evaluated at 1, Variance is a simple formula in the 2nd derivative.

You can use this technique to describe every possible event in a simulated fight, instead of "some random examples" or "average". Now, the random solution converges relatively fast to the actual chances, so this can be overkill. But "simulating" everything exactly is fun to me.

 

[tetrasodium]

I am....so confused.

65% is a commonly quoted number in monster math discussions, and its been used heavily in discussions on this thread. That's why I used it, no more no less. If you think the 65% on a hit is not accurate, that the normal to hit rate is a big deviation from that....fair enough, what to hit value do you think is more suitable for the average?

And the first row....is just the % chance that the two attacks would miss and deal 0 damage, rounded to 2 percentage places. Again, no more, no less. It is absolutely a circumstance that will happen if you attack a creature with two attacks, yes sometimes you completely miss. How is that a distraction?

View attachment 405425

What is there to be "confused" about? 65% gets thrown around regularly because it's a good rough estimate for 5e's expected hit rate, it's also a number not found anywhere on your excel snippet where it could be used to extrapolate the math used for what other entities are representing. Your "% Chance" column however is an undefined black box in what logic you are using to generate it & as a result the "DMG" extrapolated from it is equally if not more obscured behind the need to guess what math they represent individually.

 

[Stalker0]

What is there to be "confused" about? 65% gets thrown around regularly because it's a good rough estimate for 5e's expected hit rate, it's also a number not found anywhere on your excel snippet where it could be used to extrapolate the math used for what other entities are representing. Your "% Chance" column however is an undefined black box in what logic you are using to generate it & as a result the "DMG" extrapolated from it is equally if not more obscured behind the need to guess what math they represent individually.

65% is the second sentence in the original post. I didn't think a quick chart required the full mathematics of basic to hit, adv to hit, and disadv to hit probabilities.

 

[Stalker0]

Aside: If you want a full model, find an engine capable of handling polynomials.

A 1d8+5+2+1 hit is represented by 1/8 * (x+x^2+...+x^8) for the d8, times x^8 for the flat bonus damage, or x^8/8 * (x-x^9)/(1-x).

Each term of this polynomial looks like (probability)x^(damage done). Take its derivative and evaluate at 1 and you get the average damage of a hit. Its second derivative can be used to calculate variance.

You can model crits and misses and multiple swings with more math.

Let d( n )= x/n (1-x^n)/(1-x)
Then d(8) = x/8 (1-x^8)/(1-x)
(This is just shorthand for (x+...+x^n)/n without the ...s)

0.6 * d(8) * x^8 + 0.05 * d(8)^2 * x^8 is the polynomial describing the damage distribution of "5% crit chance, 65% hit chance (including crits). Two swings is just that squared:

(0.6 * d(8) * x^8 + 0.05 * d(8)^2 * x^8 + 0.35 x^0)^2
tossing it an an algebra engine it produces:
x^8 * 0.6 * (x+x^2+x^3+x^4+x^5+x^6+x^7+x^8)/8 + x^8 * 0.05 * ((x+x^2+x^3+x^4+x^5+x^6+x^7+x^8)/8)^2+0.35)^2
=
6.10352×10^-7 x^48 + 2.44141×10^-6 x^47 + 6.10352×10^-6 x^46 + 0.000012207 x^45 + 0.0000213623 x^44 + 0.0000213623 x^43 + 0.0000512695 x^42 + 0.0000732422 x^41 + 0.000215454 x^40 + 0.000476074 x^39 + 0.000853271 x^38 + 0.00134521 x^37 + 0.00195007 x^36 + 0.00266602 x^35 + 0.00349121 x^34 + 0.00442383 x^33 + 0.0107391 x^32 + 0.016814 x^31 + 0.0226501 x^30 + 0.0282495 x^29 + 0.0336139 x^28 + 0.0387451 x^27 + 0.043645 x^26 + 0.0483154 x^25 + 0.0424042 x^24 + 0.0366138 x^23 + 0.0309436 x^22 + 0.0253931 x^21 + 0.0199615 x^20 + 0.0146484 x^19 + 0.00945313 x^18 + 0.004375 x^17 + 0.0563281 x^16 + 0.0557812 x^15 + 0.0552344 x^14 + 0.0546875 x^13 + 0.0541406 x^12 + 0.0535937 x^11 + 0.0530469 x^10 + 0.0525 x^9 + 0.1225 x^0
which gives the exact probabilities of each damage amount (the exponent of a term) and the probabilities (the coefficient of the term); a 6.10352*10^-7 chance of a double-crit with max damage of 48, for example, is described by the "6.10352×10^-7 x^48" term.

Thank you, learned something new today.

That said, if your going to do all of that effort to provide superior numbers than the chart I provided for....you should provide such a chart in return

Here is the chart with these probabilities showing every possible damage probability for a scenario:

1) Character making two attacks
2) Damage is 1d8+8
3) Chance to hit is 60%, chance to crit is 5% (aka total chance to hit or crit is 65%).
4) No advantage or disadvantage

 

[tetrasodium]

65% is the second sentence in the original post. I didn't think a quick chart required the full mathematics of basic to hit, adv to hit, and disadv to hit probabilities.

Trouble is all the other questionable numbers in the %chance columns including the green "regular" one that would not involve (dis)advantage.

Figuring out your assumptions is important because the math doesn't align logically. For example: a 65% chance of a 65% chance is 42%, you have a 42% pegged as 12.5... then just below that you have a 3.5% dealing 17 damage ... You also have 12.5% dealing 0 damage and 36% dealing 25 damage. There is no
consistency or logic there