Simple Damage Comparison

Disclaimer: I'm pretty new to competitive Pokémon, and that includes this forum. If this post should be in any other subforum don't hesitate to tell me.

I've been looking at this site's resources, including the amazing damage simulator and the complete damage formula. I couldn't manage to find an easy-to-read guide to damage calculations for estimation and especially comparison purposes. I studied the formula a bit and here is something I came up with. This is intended mostly for people like me, who currently lack extensive battling experience, and perhaps haven't been properly introduced to the base concepts. I still recommend the damage calculator for accurate responses. If you think this could be useful to other people, don't hesitate to share this. You can find the reasoning in a separate section below.

Damage Comparison
In order to estimate the relative damage of one move used by pokemon A with one move used by pokemon B you want to compare the following numbers. These act like multiplicative constants to the damage dealt by the pokemons. This means that, for example, if option A has a number that is twice the number of option B, then A will deal (roughly) twice the damage of option B.

DAMAGE ESTIMATOR: (Base Power) * (STAB) * (Ability) * (Nature) * (Item) * (Effectiveness) * (Base Stat + 34)

Base Power is the base power of the move you are using.
STAB is 1.5 if you are using a move with the same type as your pokemon.
Ability is a multiplier due to your ability. A few common multipliers would be: Huge Power / Pure Power (x2), Technician (x1.5), Analytic (x1.3), Aerilate (x1.3), Adaptability (effectively x1.33).
Nature is 1.1 if you are using an attack-boosting nature.
Item is a multiplier due to your item. A few common multipliers would be: Choice Band/Specs (x1.5), Life Orb (x1.3), *** Plate (x1.2).
Effectiveness is type effectiveness (x4, x2, x1/2, x1/4, x0).
Base Stat is the base attack (or special attack) stat of the pokemon. This is the tricky part (and the part that prompted me to write this post). You shouldn't evaluate the formula with just the base stat you find on the smogon's pokemon description. There is a constant +2.5 adjustment. Perfect IVs add 15.5 to the base stat, for a total of +18. Full EVs also add another 15.75 (which gets rounded to 16 because it's an estimate). The above formula assumes full EVs: if you aren't using full EVs you need to change that 34 to 18. I think most people run full EVs on the offensive stat of choice anyway. Unless it's a defensive pokemon, I guess. Whatever.
(You can add a multiplicator for weather and burn if you wish, but that's just gravy)

Common Misconceptions:
1) STAB is not additive. If you have Water-type STAB, then Hydro Pump vs Scald is like comparing 180 Base Power to 120, not 170 to 130. It's 1.5x, not +50. This is the reason moves with low base power are so weak compared to moves with higher base power.
2) The base stat indicated in the pokemon description is generally 34 points off of what you should be using in these calculations.

BULK ESTIMATOR: (Base HP + 86) * (Base Defense + 34)

This is to estimate the bulk of a pokemon relative to the bulk of another pokemon.
You may need to add further multipliers for a few modifications, in particular Assault Vest comes to mind. However, the formula is significantly simpler than the damage estimator above because there are few defensive modifiers.

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The formula I used is here: https://www.smogon.com/bw/articles/bw_complete_damage_formula
I don't think there's been significant changes in the last generation (I might be wrong on this, if so I'll gladly change the math).
The key factor is that basically everything in the formula is multiplicative, with a few exceptions. However, the first +2 factor is absorbed into a multiplicative constant (42) and the second +2 in the formula isn't really significant for anything you want to make calculations about anyway. It probably counts more in LC but that's another story.
With everything being multiplicative, you can compare two attacks of the same type (special or physical) pretty easily. This is something many people normally do, factoring in STAB, weather, base power and the like. The above method takes the stat generation formula from Bulbapedia and applies it to get a consistent method of estimation between different pokemons. Also, understanding how to estimate defensive bulk is important too.
The base stats (or stat growth rates if you will) alone aren't really representative of the whole picture. You could be tempted to think of base stats the same way you think about base power - as a multiplicative constant. However, that's just false, and it's especially false for estimating the bulk of low hp / high defense pokemons.
I actually think Base Stat + 34, or Base Stat + 86 in HPs' case, is a more telling number than just Base Stat. Or Base Stat + 18 / Base HP + 70 if you want to exclude EVs from the initial number. There's kind of a huge difference if you think about it. For example, if you compare the bulk of a Bastiodon to a Suicune, you should compare 130|186|156 to 170|133|133. Since bulk is multiplicative, you end up having pretty similar bulk. If you try to do the same with the base stats of 60|168|138 vs 100|115|115, Suicune seemingly ends up with a better physical bulk than Bastiodon, which under closer inspection is false.
 

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