Yes, if you knew about Senran Kagura before Shinovi Versus, you would see Asuka and her team of Hanzo elites at the main protagonists of this franchise.
But here, in Shinovi Versus, debuts another "good guy" team of shinobi: The Gessen Girls. It may not seem too obvious, but this game sometimes gives Yumi and her team the top billing over Asuka's team. It really helps their case that Yumi herself has become one of the most popular characters in the entire franchise (especially if you live in Japan).
Remember, each of the game's four shinobi teams have their own interpretation of the game's overall premise. Although I have completed the Hanzo storyline, everything that the Gessen Girls did in that story does not necessarily equate to what happens in their own story, here. There's actually quite a few differences from start to finish. Some minor, but others drastic. This will also apply to the Hebijo and Crimson stories once I start on them, later.
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Yumi, and the rest of her team comprised of Murakumo, Yozakura, Shiki, and Minori were all raised in their own families of good shinobi. That is... until all of their parents were killed in action by evil shinobi. Yumi's grandfather, Kurokage, took in Yumi to raise her, himself, as well as the others as his four adopted granddaughters. They would then become the elite good shinobi at Gessen, also known as Death Cram.
One day, the 5 Gessen girls were traveling up the mountains and down a hill to visit Kurokage and bring to him his favorite desert: Strawberry Daifuku. They became his only food source once he became sick and bedridden, but this is also the first time they delivered that treat to him in a long time...
Unfortunately, they were stopped by a hearty old chef. Despite his appearance, he struck the girls with a powerful aura of a legendary warrior. Indeed, it was the great Hanzo, a top shinobi, and Kurokage's greatest rival.
And... apparently, he was also one great big pervert. For some reason, he started playing with the Gessen girls, such as fondling their breasts. Although the girls fought back, Hanzo dodged them swiftly. He was amused by Murakumo hiding her face behind and ogre mask, as well as Yozakura's voice and dialect changing whenever she gets angry.
Hanzo groped all 5 of the girls, insulting their pride and humiliating them at every turn. And if that wasn't enough, he swiped and snacked on all of their strawberry daifuku that was meant for Kurokage before they even knew it! They were rightfully pissed at the dirty old man and his antics, but then Hanzo used that to his advantage as well...
Yumi wants to fight Hanzo to reclaim her honor, but Hanzo instead invites her to face Asuka, his own granddaughter. He then vanishes into the sunset, and Yumi's team was too embarrassed by his shenanigans upon them that they lost all dignity to visit Kurokage.
So they all went back into their Ninja Room, where they are greeted by their master, Wang Pai. He presented to them a letter where they must challenge a different shinobi school to a Shinobi Battle Royale. Wang Pai's first suggestion is Hebijo Clandestine Girls' Academy, but Yumi suggests Hanzo Academy, first, based on Hanzo's own invitation towards that, but despite that school being another one that trains good shinobi like Gessen, itself.
Gessen believes in a world of absolute light, and wishes to purge it all of darkness. Yumi follows this as she believes that the balance of black and white was shattered long ago.
Together, with the rest of her dear friends and comrades, Yumi follows this as her Path of the Shinobi. To make her dream, and her grandfather's dream, a reality!