Homebrew GM Question: CR and Leveling Monsters

[keith battle]

Hi, All. I am about 6 sessions in to a homebrew campaign. So far, so good. This is my first campaign and all of my players are new players so we're still too ignorant to know all the things we're doing wrong. In other words, we're having a great time! :)

My PCs have recently acquired Level 2 and, although I could start throwing higher CR monsters at them, I want to zerg them with a bunch of kobolds... for narrative reasons. Yeah. It's for the narrative. Anyway, I've been building out a kobold warren complete with well-defended brood chamber and, according to the bestiary, I should be setting up a mini-society with non-combatants and sergeants and lieutenants and a leader. Sounds cool. I may just be sleep deprived but I'm having a hard time wrapping my head around:
a) calculating CR for CR 1/4 monster mobs - and -
b) calculating CR for the level 3 sergeant, level 4 lieutenants and level 6-8 leader

I've been using this CR calculator (https://juneberryjournal.weebly.com/cr-calculator.html) and I can't make sense of the formula it's using to calculate CR for these CR 1/4 critters.

1 x kobold = CR 1/4
2 x kobold = CR 1/2
3 x kobold = CR 1/2
4 x kobold = CR 1
5x kobold = CR 1
6 x kobold = CR 2
7 x kobold = CR 2
8 x kobold = CR 3 (???!!??)

Likewise, I see from this calculator that 2 x CR 2 = CR4, 2 x CR 8 = CR 10 and 3 x CR 8 = CR 11. This looks to me like CR = Monster CR + # of monsters of that CR. However, I'm sure there's more to it than that.

I found some templates for the above mentioned sergeant, lieutuenants but I would love some guidance on how to roll up a level 6-8 leader, which will be a more fleshed-out NPC that the party will have to decide to confront or convince.

My goal is to populate the warren with some nasty traps, a few CR 2-3 zerg encounters where my level 2 party is greatly outnumbered and being attacked at range from partial cover, and a mini-boss fight that'll leave the party bloodied but breathing. I've been following the general guideline of building my encounters to be CR = APL+1 so as to make them "tough". However, and this may just be some weird mix of my ignorance, good character builds on my players' part and good old lucky dice rolls, this party has cake-walked through encounters I thought would have them running (or limping) back to safety with their bodies and egos bruised. The temptation is to throw something really tough at them but I don't want a TPK. At least not yet. An help and insight y'all can provide is greatly appreciated.

[SuperJedi224]

CR is simply additive up to about CR 1. After this point, doubling the number of monsters increases the CR by about +2, and tripling the number of monsters increases the CR by +3. (This means that multiplying the number of monsters by 6 increases the CR by about +5 and multiplying the number of monsters by 8-9 increases the CR by about +6.)

Another method of calculating the CR would be based on the total XP value, in which case an encounter worth about 800 XP would be CR 3.

Typically, creatures with PC levels (and no racial hit dice) have a CR of their level - 1 (except for level 2 or higher creatures with PC-level wealth, in which case their CR should be equal to their level) while creatures with NPC levels (and no racial hit dice) have a CR of their level - 2. Note that, for some reason, the default 1st-level Kobold warrior has a listed CR of 1/4, when by these guidelines it should be 1/3. (There are a few other exceptions; for example, the sample Svirfneblin has a listed CR of 1 rather than 1/2.)

[keith battle]

Thanks, @SuperJedi224! This is super helpful!