Discusssion starts here.
In the manga, Musashi is a genius and the reason is because he uses his attraction to Otsu to improve his sword techniques. For most people, the direction works in the other way (they use their fighting skills to attract women).
There was this one chapter where Takuan hit Musashi on the head with a stick after tricking him into becoming distracted by thoughts of Otsu. But Musashi learned very quickly from that experience that the correct way to deal with these distractions is not to fight them, but to go with the flow so that his attraction to Otsu will not hamper his fighting abilities.
In other words, Musashi is internally motivated at getting better at fighting for the sake of getting better at fighting, and this trait is something that all geniuses have. Unlike others, Musashi is not fighting for women or glory. Musashi’s friend, Otsu’s former fiancee, notes this on multiple occasions in his musings on why Musashi always seemed to be progressing faster and further than himself.
The other necessary trait for genius is talent, of which Musashi has an abundance of. The most successful fighters in Vagabond are all extremely talented and internally motivated (Kojiro, Musashi, Yagyu, and Ittosai). The second tier of fighters are extremely talented but are not particularly interested in fighting for the sake of fighting (Yoshioka Seijiro, and Inshun). Musashi improves the most from his fights with the second tier. The third tier are the characters are interested in fighting, but lack the talent (Yoshioka Denchischiro, Matahachi, and Gion Toji). These characters suffer terribly in the manga because they are never able to attain the genius-level of fighting they see in their colleagues despite their desperate, and frantic efforts. In the end, these third-tier fighters fall apart psychologically from the strain, or get chopped to pieces, or both.
Ueda Ryohei and Tsukihaje Kohei (the only character to survive a death match with both Musashi and Kojiro) are special cases. Ueda Ryohei has the desire and the talent to match Musashi, but he is hampered by his sense of comradeship and responsibility to the Yoshioka clan. This is why he loses. Kohei is special because he has first-tier fighting talent and the desire too. However, unlike Musashi or Kojiro who fights for the sake of fighting, Kohei fights for the sake of killing. In the end he loses too because clarity of genius (as expressed through Musashi and Kojiro) is stronger than clarity of malice.
And continues here.
Most of the enjoyment in Musashi comes from watching the second and third-tier fighters fall apart over the course of the story.
Matahachi finally learned, after losing everything precious to him, that trying to copy genius, when you’re not a genius, is a bad idea, but by then it’s too late for him and he’s already an old man.
Toji learned that his power was a the reflection of Seijuro’s genius, and that without Seijuro, he is nothing.
Denshichiro learned that he’s simply not up to par with people like Musashi or his younger brother. Not enough talent. Bad genetic luck.
Ueda learned in his final moments that his sense of responsibility kept him back as a fighter.
Kohei learned the hard way that there is always someone stronger than you.
Seijiro never learned anything. He was… beat. The only thing he may have regretted at the end was not killing Musashi when he had the chance.
Inshun learned that he never really wanted to fight at all.