The president of Kisaragi High wants to prove that a girl can compete in baseball as well as a boy, and gets her chance thanks to young pitching ace Ryo Hayakawa. From there a team begins to form, and the journey is on as they rise through the difficult ranks of a boy-dominated league in an attempt to make it to the Koshien. Can they overcome the adversity and sexist notions of what females can do, include proving that their trials and tribulations extend beyond "boys"?
Without spoiling too much, no.
The baseball part is what the show does best; each game is almost treated like a highlight reel, showcasing only the most important plays, many of which are pretty flashy and out there (Lightning Ball anyone?), but entertaining nonetheless. The show manages to keep the games intense without drawing them out multiple episodes, with the exception of the two-parters. This allows for time to be dedicated to the players themselves.
Well, it should anyways. Despite the fact that each new member often has whole eps dedicated to them, and with it the promise of character depth, the show rarely follows through with any of it. More often than not they are shoved into the background, letting them pipe in to occasional remind you that yes, they still have speaking voices. And every time it feels like the show is going to focus on them and their relationship with each other, the ugly side of this show appears.
And that ugly side is a Love Triangle in the 2nd half between the two main characters and male lead. Thanks in large part to Ryo herself. She is both the main cause AND recipient of the problems a triangle usually shares; misunderstandings, indecisiveness, the heartbreak, depression, etc. She ends up undermining what the show was trying to prove; that a girls team can be physically and mentally able to compete in Koshien, turning her into a self-centered wangst machine that screws her team over because of her inability to think about things other than boys.
When I think of Princess Nine, I can't help but be reminded of Dai Guard. Both had, and occasionally showed, the potential to be something great and, dare I say, unique. Both however, fall back on cliched storytelling and forced drama. The show undoes itself as a result, shafting the "sports" part of a sports anime in favor of a Romantic Plot Tumor that doesn't even get resolved in the end.