Let's see what this looks like if we use Detect Balance! 4 BP = +1 to an ability score, and nonhuman PHB races vary in strength from 21 (Dragonborn) to 30 (Hill Dwarves). The target score is ~25/26 BP.
Kitsune: 16 base BP
8 = +1 dex, +1 cha
3 = Darkvision 60'
1 = 1d4 natural weapon
1 = Kitsune Shapeshift & Tails (ribbons)
2 = cantrip
2 = skill proficiency
Zenko: +10 = 26 BP
4 = +1 wis
-2 = Poor synergy between wis and cha stats
1st level domain without spells:
Arcana: 8
2 = skill proficiency
6 = choice of two cantrips
Forge: 6+?
{ERROR} = heavy armor proficiency (this allows you to get heavy armor without also getting light and medium, which doesn't really work)
6 = +1 bonus to a weapon or piece of armor (similar to +2 dex or str, but not all the value)
Life: 6+?
{ERROR} = heavy armor proficiency (this allows you to get heavy armor without also getting light and medium, which doesn't really work)
6 = improved healing
Yako: +14 = 30 BP
4 = +1 int
-2 = Poor synergy between int and cha stats
12 = add int mod to cha skill checks (this is similar to +6-10 cha, since you're not going to take this subclass if you aren't using int as a main stat, but that also means that cha bonus is worth a lot less than 24-40 BP it would be if you were using it in combat.)
Nogitsune: +13 = 28 BP
4 = +1 str
3 = necrotic resistance
5 = Life Drain (This looks similar to the Dragonborn's Breath Weapon (6 BP). You gain +1d4 damage from the initial bite attack and healing equal to the damage dealt, and you give up the choice of damage type, short range, and short rest recharge. I'm going to value it slightly less.)
The race seems mostly balanced to me, although the Yako subrace is a bit strong and Nogitsune are above average.
How do you want the Zenko domain armor proficiency to work? You shouldn't be able to get heavy armor proficiency without also getting medium and light, but getting all three would make the race OP. I would suggest getting light if you have none, medium if you have light, and heavy if you have medium, but I'm not sure it's possible to implement armor proficiency +1 like that. Also I think you have to choose your race before your class, so it technically wouldn't work.
I might do some grammar & spellcheck later, there's definitely some stuff I noticed.
It's probably not the best thing to do, but a level 17 Yako Kitsune Bard who maxes both int and cha has a static +22 to all their Charisma skill checks with no investment beyond choosing those skills for proficiency and expertise.
Very nice, it does need a bit of work. I believe this is based on a creature from Japanese folklore?
Kitsune Shapeshifting: As the DC for this ability is based on Deception, it seems only fair to give the Kitsune proficiency in Deception.
Kitsune Magic. What is the spellcasting ability for dancing lights? (Some DMs are tricky and will want a DC.)
Inari Domain: I do not like this at all. It is a lot of variety and power given too quickly especially as this is a race and a kitsune could play as a cleric, gaining two of the same or different features. I would suggest something akin to the innate spellcasting offered by the aasimar in the DMG.
Silver Tongued: I agree with SirBlackAxe here, this needs to be trimmed down. Either add half your intelligence modifier or only charisma skill checks you are proficient in or both. (It's also Intelligence modifier not Intelligence modifier bonus)
From Appearance: "Their eyes hyave vertical slit pupils." Stray y there. "They also have a tail that helps them balance." Make it clear they can get more.
From Mental Power: "They have remarkable cunning that they use solve problems in the most unlikely solutions imaginable." I find this strange. Only Yako kitsune get a bonus to intelligence yet it's something espoused of the entire race? "Due to their familiarity to illusions and enchantments, kitsune often use honeyed words or pranks to oppose their enemies instead of the sword." Try "instead of swords." "Skilled kitsune can weave illusions using this ability." This is not reflected in the traits; it would be a nice addition.
Nix Kitsune Relations. With uncommon races it is usual to talk about how they are viewed by other races.
Shapeshifting: "Some kitsune master their shapeshifing art to the point where they can shift into a fox or shift into a person they have seen recently." This is not reflected in the traits.
I suggest not talking about things that are not in the traits section, this keeps confusion to a minimum.
"The relevant equation is: Knowledge = power = energy = matter = mass; a good bookshop is just a genteel Black Hole that knows how to read." - Terry Pratchett
The Inari domain is based on the the Zenko kitsune subrace being blessed by him they will have some divine power based on Inari's portfolio. Yes I will remove the armor proficiency and remove it from the domain features.
Silver Tongue: that is a typo it should be charisma skill checks. So no intelligence on charisma saving throws and attack rolls. I'm also debating whether i remove the intelligence and give it charisma and give it proficiency in deception and double its proficiency bonus.
Kitsune foxfire is Dancing Lights. It can make a ghostly shape.
Shapeshifting: there is a feat that augment their shapeshifting abilities but that are being playtested right now.
I thank you for the input and put into consideration for my latest revision.
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After a play-test with my players I added and modified the kitsune race I posted on the forms and published it on D&D beyond for the world to see.
I'm currently play testing it with a DM who has DMed since 1st edition. I would love any feedback such as grammar and possibly any balance issues.
You can view the base race here along with the Zenko Kitsune, Yako Kitsune, and Nogitsune.
Also don't be afraid to ask questions.
Let's see what this looks like if we use Detect Balance! 4 BP = +1 to an ability score, and nonhuman PHB races vary in strength from 21 (Dragonborn) to 30 (Hill Dwarves). The target score is ~25/26 BP.
Kitsune: 16 base BP
Zenko: +10 = 26 BP
Yako: +14 = 30 BP
Nogitsune: +13 = 28 BP
The race seems mostly balanced to me, although the Yako subrace is a bit strong and Nogitsune are above average.
How do you want the Zenko domain armor proficiency to work? You shouldn't be able to get heavy armor proficiency without also getting medium and light, but getting all three would make the race OP. I would suggest getting light if you have none, medium if you have light, and heavy if you have medium, but I'm not sure it's possible to implement armor proficiency +1 like that. Also I think you have to choose your race before your class, so it technically wouldn't work.
I might do some grammar & spellcheck later, there's definitely some stuff I noticed.
It's probably not the best thing to do, but a level 17 Yako Kitsune Bard who maxes both int and cha has a static +22 to all their Charisma skill checks with no investment beyond choosing those skills for proficiency and expertise.
Very nice, it does need a bit of work. I believe this is based on a creature from Japanese folklore?
Kitsune Shapeshifting: As the DC for this ability is based on Deception, it seems only fair to give the Kitsune proficiency in Deception.
Kitsune Magic. What is the spellcasting ability for dancing lights? (Some DMs are tricky and will want a DC.)
Inari Domain: I do not like this at all. It is a lot of variety and power given too quickly especially as this is a race and a kitsune could play as a cleric, gaining two of the same or different features. I would suggest something akin to the innate spellcasting offered by the aasimar in the DMG.
Silver Tongued: I agree with SirBlackAxe here, this needs to be trimmed down. Either add half your intelligence modifier or only charisma skill checks you are proficient in or both. (It's also Intelligence modifier not Intelligence modifier bonus)
From Appearance: "Their eyes hyave vertical slit pupils." Stray y there. "They also have a tail that helps them balance." Make it clear they can get more.
From Mental Power: "They have remarkable cunning that they use solve problems in the most unlikely solutions imaginable." I find this strange. Only Yako kitsune get a bonus to intelligence yet it's something espoused of the entire race? "Due to their familiarity to illusions and enchantments, kitsune often use honeyed words or pranks to oppose their enemies instead of the sword." Try "instead of swords." "Skilled kitsune can weave illusions using this ability." This is not reflected in the traits; it would be a nice addition.
Nix Kitsune Relations. With uncommon races it is usual to talk about how they are viewed by other races.
Shapeshifting: "Some kitsune master their shapeshifing art to the point where they can shift into a fox or shift into a person they have seen recently." This is not reflected in the traits.
I suggest not talking about things that are not in the traits section, this keeps confusion to a minimum.
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"The relevant equation is: Knowledge = power = energy = matter = mass; a good bookshop is just a genteel Black Hole that knows how to read." - Terry Pratchett
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The Inari domain is based on the the Zenko kitsune subrace being blessed by him they will have some divine power based on Inari's portfolio. Yes I will remove the armor proficiency and remove it from the domain features.
Silver Tongue: that is a typo it should be charisma skill checks. So no intelligence on charisma saving throws and attack rolls. I'm also debating whether i remove the intelligence and give it charisma and give it proficiency in deception and double its proficiency bonus.
Kitsune foxfire is Dancing Lights. It can make a ghostly shape.
Shapeshifting: there is a feat that augment their shapeshifting abilities but that are being playtested right now.
I thank you for the input and put into consideration for my latest revision.