I'll just answer this for Gen IX and try to explain the formula in simple terms. If you don't understand, come back once you've passed Algebra!
A doozy huh.
Walking through every point, here's what that means:
- Max HP: The number of hit points the Pokemon has at full health
- Current HP: The number of hit points the Pokemon has when you throw a ball at it
- Dark Grass: Despite only being available in Gen V, dark grass mechanics are still in the game's code. You can read how this affects catch rate in Gen V here.
- Modified Rate is the standard catch rate of your Pokemon. From what I can find, the catch rate is only "modified" when you use Heavy Balls. Let me know if I'm incorrect there.
- Ball Bonus is the multiplier depending on what ball you're using
- Badge Penalty "is applied when the wild Pokemon is more than 5 levels above the player's current obedience level, and is equal to 0.8n, where n is the number of Gym Badges that would be needed for it to obey."
- Bonus Level is a multiplier added when the Pokemon is below Level 13.
- Bonus Status is applied when a Pokemon is under a status condition. (1.5x)
- Bonus Miscellaneous is added when Capture Powers are under effect. The multiplier can be 1.1, 1.25, or 2 for Powers Level 1, 2, and 3 respectively.
A simpler way to figure out catch chance of a Pokemon at 1 HP is with this formula:
Chance = CatchRate×BallBonus×StatusBonus/255
So, for example, throwing an Ultra Ball at Pokemon with a Catch rate of 45 that's at 1 HP and Paralyzed results in
45×2×1.5/255 = ~52.9% chance to catch
Source
I hope this makes sense, and please correct me if I'm wrong.