Monster Math 5th Edition

*edit* A lot of these fit log scale plots nicely. That is an artifact of how I am clumping my data. 0, .125, .25, .5, 1, 2, 3, 4 predisposes the data to fit a log scale. If I combined the first 4 categories, we would fit a more traditional linnear curve more often.
*edit 2* I realized I hadn’t included how to set DCs and Saving throws for abilities.

So I took all of the monsters from the D&D starter set, except the dragon whose CR was twice the next lower cr creature and looked at key features of them. For each creature I recorded hp, AC, movement, saves, skills, to hit bonus, average damage of their attacks, ranged hits, average damage of those, and special abilities, including immunities, resistances, perception modes, spell casting, vulnerabilities, etc

Then I treated everything but CR, AC, HP, to hit, and average damage like the * abilities from OD&D.
I broke things into benefits and penalties
Examples of things that gave benefits:

Benefits
Having a saving throw at all.
Each saving throw higher than 3.
Every 3 skill points.
Having extra movement types.
Every 10 feet above 30 movement for the fastest movement type
Having a ranged attack
Every die of damage a ranged attack does past 1.
Having a resistance
having an immunity
having a special perception mode
every 5 levels of spells a spellcaster can cast.
having a situational advantage
gaining extra dice of damage in a given situation.
any other positive ability

penalties
Any vulnerability
having a situational disadvantage
every 10 feet of movement below 20 on the fastest movement type.

Using that, there are on average 3 bonuses plus 5 bonuses per CR on a given creature. If hp or ac is higher than average, aim for fewer bonuses. If they are lower than average then give more bonuses.

For example a cr 1 creature should have a 12 ac and 25 hp and 8 bonuses.
If you give it a 16 AC, you might count that as 2 bonuses (2 AC points per bonus).
Then make it skilled at +3 in 2 skills: 2 more.
Give it a 1d6 ranged attack: 1 bonus
Give it advantage in combat when working with allies: 1 bonus
Give it dark vision (almost everything has dark vision): 1 bonus
Give it a second melee attack 1 bonus
There is a nice CR 1 creature. Some sort of trained and organized warrior, Maybe like a hobgoblin…

Here are all of the charts

CR ac hp # of creatures
0 10 4 1
0.125 13 5 3
0.25 12.25 13.25 4
0.5 15 14 3
1 14 24.8 5
2 11.8 40.6 5
3 13.5 48.75 4
4 13 40 1

The First thing we have is the average number of hit points and the average ac of creatures of a given CR. Notice that we have very small sample sizes and that ACs are falling in a very narrow band. The average AC value moves from about 12.5 to 13 between CR 0 and CR4, so if you give a creature an AC greater than 13 you might want to give it an attendant penalty, or if it has a cr below 12, you might want to give it some sort of bonus.

Approximately 12.5 +.2* CR for the base AC of a creature.

HP are 10.5*CR+9 on average

CR speed points total stat bonus average saving throw skills
0 1 0 0 0
0.125 1.666666667 -4.666666667 0 2.333333333
0.25 1.25 0 0.25 3.25
0.5 1 2.666666667 0 1.333333333
1 1.2 1.6 1 5.4
2 1.4 0.6 0.8 5.2
3 2 7 0 4.5
4 2 3 7

Speed points are based on movement modes. Notice at the lower CRs there is seldom more than 1-1.5 speed point. That means that creatures at those levels should seldom have more than one movement type and should not move more than 30 feet. At CR 3 and 4 though, extra modes of movement and higher speeds are acceptable.

Stat bonuses: I didn’t look at actual ability scores, but at the modifiers they gave. If you ignore the CR .125 and CR 4 entries, you average about 1.75 stat bonus points per CR (this is the sum of positive and negative numbers.) If you include the, it is 1.5 stat bonuses per cr. 1.75x fits the curve better though.

Saving throws are rare. Getting a save at all is worth a bonus, and then give extra saves

Skill points On average everything gets 2.5 skill points and an additional skill point per CR.

Resistances and Immunities

CR vulnerable resistance immunity
0 0 0 0
0.125 0.333333333 0 0.666666667
0.25 0.25 0 1
0.5 0 0 0
1 0 0 0.6
2 0.2 0.8 1.4
3 0.25 2 2.75
4 3 7

Vulnerabilities are something you can hand out whenever you need to balance something else out. They were rare among the set of monsters.

Resistance is pretty rare too, coming in at about 1 resistance per CR > 1

Immunities approximate 1 per CR, though that was often a bunch of creatures immune to nothing and then one or two with several immunities. Notice that the CR4 creature is immune to 7 things, which helps adjust for it having low hp for the CR.

Perception modes:

This doesn’t need a chart. Almost everything has dark vision. most of the rest have blindsight. No truesight was used in the creatures I analyzed.

Combat values

CR melee hit bonus avgdmg points from ranged
0 2 2
0.125 3.666666667 4.333333333 0
0.25 3.75 5 1.5
0.5 4 6.333333333 2.333333333
1 3.2 8.8 1.2
2 3.8 9.4 1
3 4.75 10.75 0
4  5  18 9

So the first question is to hit modifiers. The low cr creatures have really

high to hit modifiers relative to their level. With them in place, you start at +3 and add half a point per point of CR. Without them, it is +2 with .85 points per CR. That second trend line goes almost exactly through CR 0, 1, 2, and 3 (the cr 4 monster has no melee attack.and is mostly a caster, but if you use it ranged attack number the equation is very nearly the same as not including it. (.75*CR+2.25 vs .85*CR+2.0)

So roughly, your creatures should have 2 + their cr in to hit, with a tendency to err on the side of low. If a creature has a to hit number 3 points higher than the average for its cr, that is about the same as giving it advantage and could count as a benefit. If it is 3 points too low, that is roughly the same as disadvantage and should count as a penalty.

Damage:

This has a couple of caveats: If a creature had multiple attacks, I combined their average damages. This is a little inaccurate, but good enough for the accuracy of the data I am working with. It is also balanced by undervaluing multiple attacks. If you look at damage done per round vs a given AC, a second attack is pretty close to doubling the damage if there are no attack penalties. Also, I used WOTC’s damage estimation method. Half the die plus bonuses. The CR4 creature had no melee attack, so i used its ranged attacks. What we get is 3.8 + 3.15*cr damage which is roughly 1d8+ (1d6 per CR). A CR 2 creature thus gets about 10 damage per attack. You can do that as 2d8+2 or 1d8+2d6 or 2 1d8+1 attacks. For every extra die or +3 damage bonus, count that as a benefit, and for each lost die or any minus to damage count it as a penalty.

Ranged

Since ranged attacks are secondary for most creatures, i counted them as pure bonus. The chart isn’t super useful since about 2/3rds of the creatures had no ranged attacks. I assigned them bonus value at a rate of 1 point per die of damage ignoring bonuses and 1 point per 2 points of to hit (round up). So a +5 to hit attack that does 2d8 damage is worth 5 bonus points. It may turn out that in creature creation, that is too many points, but ranged can be a powerful addition.

Other benefits

CR benefits
0 0
0.125 1
0.25 1.25
0.5 1
1 2
2 1.8
3 2.25
4 4

This is things like Poison or 5 spell levels of spell casting or shape changing or attacks with advantage when ambushing. These are the special text block benefits you can give a monster. Remember, bonuses are countered by penalties. (The number on the chart are bonuses not counted anywhere else in the accounting for a monster.)

Oops. I forgot saving throws and ability difficulty classes.

CR average save
0 10
0.125
0.25
0.5
1 11.5
2 12.33333333
3 13
4 13

There were no saving throws between CR 0 and 1. I set CR 0 to 10. There were fairly few data points in the packet. 13 abilities between fewer monsters. I also set the 0 intersect for the trend line by hand to 10 since 10 is the base number. That gives me DC = 10 + .91*CR At CR1 there are creatures with DCs between 10 and 13, so there is a lot of range. My suggestion is if you use a number above the suggested count every 2 points higher as one benefit and every 2 points below the goal as a penalty.So let’s use this system to create a couple of monsters.

 

Kobold

Small and viscous, these doglike humanoids are most comfortable working in packs.

We will start out by assigning a CR.

We’ll make them about equivalent to goblins, so CR 1/4

AC The formula sets it at just over 12, but I imagine them as nasty tenacious beasties, so lets make it 14 which means we have one benefit

HP: Kobolds are weak and easy to kill, the bottom of the food chain in a lot of places. The formula is 10.5*.25 + 9 or about 12. I think we want to go down a bit, say 5 (1d6+2 hp) That is one penalty.

Speed Small and fast, we’ll give them a 30. Great from running away from their natural predators: Everything

Stats:They are pegged at just under one total stat point.Str 6 -2Dex 16 +3Con 14 +2Int 10 +0Wis 8 -1Cha 8 -1

That gives a +1 total to their stats. I think that is fine. No boon or penalty here.

Kobolds are trap makers, and I think they need a save vs their own creations so lets give a benefit in the realm of a Dex+ 0 save.  1 benefit.

________________________________________________________________

So far we are at +2 benefits and -1 penalty.

Skills None

Senses Darkvision 60 feet, passive perception 9  (1 benefit for darkvision)

Languages Common, Kobold.

Challenge 1/4 (50xp)

______________________________________________________________

Cowardly A kobold who is not within 10 feet of another ally is at disadvantage in all to hit rolls(penalty)

Actions:

Pick Axe: Melee Weapon Attack: +2 to hit, reach 5 ft , one target. Hit 3 (1d6) piercing damage.

This is low for a cr.25 creature, 1 penalty.

Poisoned Dart +2 to hit, Range 20ft/80ft Ranged Weapon Attack Hit 1 (1d3-1) + Fortitude DC 10 or gain the poisoned condition (2 benefits)

So we are now at +5 benefits and -3 penalties. That works out to +2 benefits, which is 1 above standard for a cr 1/4.

That is well within the variation in the book, but if you want you can gvie them an extra penalty like:

Light blindness: The first 3 rounds a kobold is in torch light, they gain the blinded condition.

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