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@archon_silverius, thanks for your reply! Yes, realm_capital_size_500_modifier means modifier used when size is bigger than 500 and less than the next tier 1000.
As for disproportionate, I personally enable both mods the same time so kinda alleviate that problem. Imo both will be better than using only one.
If I ever make a more precise mod (or to answer your question of "best"), I would probably use a weighted combination of (monthly income of the entire realm, monthly income of the top liege, realm size, tier and maybe amount of direct vassals and even their contracts) to decide the benefit of the modifiers. But when I made the mod, I first only considered the ranks, and then size (similar to your example, a big and small empire should be different) come to me soon after.

As a side note I enjoy the embedded comments regarding the max sizes lol! Still trying to decide if I want to use just 1 or both. I think I may favor ranked because while a larger realm in theory has more potential, it could also be too dispersed, such as during the Mongol empire where the khanates were very independent and kept more wealth locally (as far as I read). On the other hand if you have a small empire ( like the late Byzantines who held that title with virtually nothing left) then ranked would be disproportionate. Does the empire title stay or diminish in this case? I feel like history supports both to some extent so maybe both would be good? I would appreciate any insight you or any others can offer on which you think is best. Thanks again for making these mods! (2/2)

Hi Kregon, sorry I forgot to explain myself again lol. So when I said formula what I meant was how the bonus was determined for each rank. For example, (this isn't what you have but just to convey what I mean) say you have an income bonus that adds +.1, for count +.2 for duke, and so on, then the formula is that each rank add +.1 to the income. But a different formula could be +.1 for count, +.2 for duke, +.4 for king, and +.8 for emperor, which means that each rank increase doubles the received bonus. Turns out I just had to check the file lol. So it seems like ranked is pretty straight forward and it looks like the numbers vary slightly in some categories but I think they make sense. Sized seems a little less straight forward but that's not a bad thing. I'm guessing that realm_capital_size_#_modifier has the # meaning the number of counties? For instance, realm_capital_size_500_modifier means having 500 counties? (1/2)

Hi @Imozan, I'm not sure if this mod need update at all beside editing the version to remove that warning mark. All this mod does is add a decision (and related scripted effects) which is probably not involved with any update in the future. However, if the mod is not working properly let me know, I haven't touch CK3 since the last DLC, so not sure.
And Hi @archon_silverius, thanks for your questions! I'm not sure what your question is? the formula for 'ranked' is the rank obviously? with each rank giving a different modifier. As for the 'sized', it's realm size 5, 10, 25 etc. You can look at them in the scripted effects and modifiers of each mod if you are interested. There's not a formula per se, but 'if' conditions.

Hi Kregon, I'm making a post on both ranked and sized in case I'm not the only one with this question (copying and pasting to save time). So what is the formula that each uses for determining bonuses? Apologies if I overlooked it.

will this get updated?

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You can use the other mod Realm Capital Sized, link above, that one allow all to take the decision. It would give you better modifier if you are strong vassal, say a duke with 30 counties would have modifier equals king in this one. I will keep this one for independent rulers, for people like to only allow independent ones. If you really would like it for all, you could go into the decision file under mod/common/decision and comment out the "is_independent_ruler = yes" under is_valid. It then should work as you like.

Can non-independent rulers also use this feature?

Yes, it's mentioned in description as well.