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I am trying to determine if I should increase the base hit points, or the starting AC for my monsters to make them a bit more challenging for my players due to the size of the party (7-8 players).

Is there any reference anywhere as to the number of hitpoints an increase in AC is relative to?

For instance a Goblin with 7 hp's and an ac of 15, has an AC increase to 16, or hitpoint increase to 13 are these equivalent or does the increased hp mean the goblin is less or more survivable then the AC?

Please note I am ideally looking for answers based in fact and figures, not opinion.

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The monster building guidelines in the Dungeon Master's Guide talk about this.

Check out the segment on "Creating a Monster", starting on page 273 of the book.

The gist of it is that each monster has an offensive and defensive challenge rating, and their total rating is the average of the two. Raising an AC by +2 over the expected baseline for a certain challenge rating will push the monster up by 1 in defensive CR, raising their HP by about 15 points will push the monster to the next baseline (and might include a free increase in AC as well)

Since Defensive CR is half the monster's total CR, on average pushing the monster up by 2 steps in Defensive CR will increase its CR by 1 step. So a CR 5 creature with an extra 30 hp or an extra +4 AC will be roughly a CR 6 creature.

There's some more info in the chapter about things to look out for, and I should point that these rules are least reliable with things below CR 1, where adding a few points somewhere might have a big impact, especially with a low level party.

Also keep in mind that if you only increase defensive strength, many fights will take even longer than expected with such a big party, while not feeling any more deadly.

You might be better off throwing in more monsters. (This is also the advice giving in the "Building Encounters" chapter of the DMG when dealing with larger parties)

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    \$\begingroup\$ To the OP: Definitely note the "more monsters" paragraph above. Adding more monsters to an encounter increases the overall challenge and can make things much more dynamic due to action economy. I find using an online encounter builder makes working our the overall encounter CR much easier. \$\endgroup\$
    – PJRZ
    Commented Mar 30, 2021 at 11:31
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    \$\begingroup\$ I like this answer, you might also want to mention action economy as a more general encounter design cornerstone. \$\endgroup\$
    – Akixkisu
    Commented Mar 30, 2021 at 12:13

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