Balanced?
They can get a free +6 bonus to all physical ability scores. That's absolutely broken for a player race. They also get a bonus feat, an extra 6 hit points, and a Fortitude save bonus on top of having a +2 Constitution.
Yeah, the OP could bring down the physical bonuses, and make sure they equal the mental minuses.
I wouldn't necessarily say that- or Zenkai as a whole- is truly in theme with the saiyan race.
It was noted throughout Dragonball that Goku had this odd quality that he would fight someone, get his ass kicked, and then later come back even stronger and whoop their ass.
Goku's ability to gain immense amounts of power both from training for a relatively short time, as well as the aforementioned "What doesn't kill you" shtick was finally brought to light as not just a coincidence but a legit aspect of Saiyan genetics in the Namek saga, especially since it became a quality used AGAINST Goku and Gohan, as Vegeta became an enormous threat literally overnight, and was the major motivation for Frieza to destroy Planet Vegeta (well, that and Beerus asked him to, and you don't say "no" to Beerus unless you're Whis).
The Beerus thing was a retcon, yes, but the fact that Frieza wasn't too keen on keeping around an entire species of psychotically-proud & angry slaves who literally became twice as strong every time they got their asses kicked in battle.
Cell made this even worse, since he was just a freaking gamebreaker: he had the regenerative powers of a Namekian, combined with the Zenkai power-up ability of a Saiyan, and the raw power of Frieza's race, among other races.
Even in the Buu arc, the fact that Gohan nearly died and was then healed helped initially bring him back up to his Cell Games level of power before becoming "Ultimate Gohan," where his base form alone is as strong as a Super Saiyan 3.
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So, yeah, "Zenkai" is a legit aspect of the characters; even if Toriyama at first didn't codify it, the fact that Goku had the ability to become stronger after a defeat existed from basically the second storyline onwards (the initial "find the dragonablls!" storyline had him being basically invincible, after all).
Regarding those who have seen my revised version, the Zenkai I modified was because the GM wants xp to be equal in my current campaign. The modified Zenkai rewards enhancement bonuses if you survive dying, and you get to a certain negative hit point value. The reason for enhancement bonus is that it is the same as magic items, thus wont stack with them, or spells that boost physical stats like Bear's Endurance.
Also, the bonus hit points and stuff is from a single bonus feat (essentially) called Tribal Scars.
Your GM is right. Screwing with the XP system is beyond the scope of what a race should do. Really, your GM should be the one making this race, not you.
Keep in mind that you can't create a fully faithful Saiyan race without breaking the game. In Pathfinder, aside from ability score adjustments, race only plays a major role in a character's power at low levels. The game works by having characters get powerful through levels whereas monsters get powerful through racial dice. As a consequence, player races need abilities appropriate for a 1st level character.
You can't do that faithfully with a Dragon Ball Z race unless (like the online DBZ video games) you make heavy compromises. In Dragon Ball, race plays a direct role in a character's potential. Even in the original Dragon Ball, Goku and Piccolo's alien heritage serves as a major contribution to why they're significantly more powerful than any other character in the story.
I'm willing to help you homebrew a Saiyan race, but I need to know what specifically about the DB race you want reflected. The result really depends on your interpretation. For example, in Xenoverse, Saiyans are glass cannons that get more powerful when low on health. But my initial thoughts are:
1) There's a lot of options with ability scores depending on how you look at Saiyans. +2 Con, +2 Cha, and -2 Wis are my initial thoughts. This represents the Saiyan race's durability, boastfulness, external willpower, and ties well with the kinetist class. Wisdom feels like an appropriate penalty because Saiyans have a reputation of lacking mental discipline. They have a track record of being easily manipulated and getting drunk with their own power. Even Vegeta, one of the most intelligent characters in the show, has been exploited time and again. It makes sense that a Pathfinder Saiyan would have a disadvantage in judgment and against effects that target Will.
2) Great Ape ability should work just like afflicted lycanthropey. When you change, the GM takes control of your character, just like the description of the curse. Only Saiyan Elites should have the power to control the transformation. This makes the ability a very situational curse that could also be a risky blessing if the entire party plans ahead of time.
3) Zenkai cannot be anything permanent. That's beyond what a race should do. A temporary buff when low on health or after surviving a mortal wound would work better. Many video games use this approach. I also played in a forum RPG that did this as well. Perhaps something like this: Once per day, when reduced to half their maximum hit points, a saiyan can invoke desperate power as an immediate action, gaining a +1 morale bonus to attack and damage rolls for 1 minute.
4) When designing a race, don't model something more than once. A few good professional designers said this. In other words, if you want to model a race having durability, don't give them a Constitution bonus AND a bonus to hit points AND a bonus to Fortitude saves. A bonus to Constitution already grants a bonus to hit points and Fortitude saves -- you don't need to give them an additional bonus on top of that.
If you think bonuses to physical ability scores are absolutely broken you should see what bonuses to mental scores can do in the right hands.
What kind of counter argument is that? "It's okay if you set your car on fire, because--boy--you should see what happens when you put some C4 on the engine block!"
I was pointing out that Zenkai gives you free permanent enhancement bonuses to physical ability scores. At the very least, that's basically a race that gets a free belt of physical perfection +6 at 1st level.
http://www.penguinrungames.com/podcast.php
Go to Penguin Games.
They made the tabletop game. Someone has made an online game based on it.
The cartoons had triage rules. Healing can stop dying to the point of keeping someone in a coma till science or even mad science can start them recovering. Also, they had Land of the Dead rules, where training in the afterlife can replace the missing class levels with even more levels of a prestige class. Ask your GM if he or she would like including some other aspects of the DBG universe.
My take on afterlife prestige classes is in the following link.
Goth’s Freakshow..