Did feudal Japanese samurai actually pair off into one-on-one duals in a large scale pitch battle?

Part 1

So like I mentioned below, the answer is No, with some notes.

We actually have to move outside my time period and move to the Heian to Kamakura. Let's just say with the rise of unit tactics in the Sengoku, it's pretty set that no one thinks this was the case in the Sengoku. However, that doesn't stop people from writing about paired-off duels that basically no historian believes in. For instance, many have heard about Uesugi Kenshin charging Takeda Shingen at the fourth battle of Kawanakajima, with Shingen having to deflect the blows with a fan. As unbelievable as that story from the less-than-reliable Kōyō Gunkan is, according to the Hokuetsu Gundan (which is not a Uesugi clan source as often mistakenly labelled, but tells the story from the Uesugi perspective), Kenshin actually killed Shingen's brother in single combat and engaged with Shingen in single mounted combat. At separate battles (IIRC), but it doesn't matter because Hokuetsu Gundan's timeline, and narrative in general, is messed up.

Anyways, there's long been a misconception that prior to the Sengoku, and especially in the days of Heian and Kamakura, samurai fought in this weird honorable duel. They would only fight pitched battles, during which they would ride forth, call out to each other their names, ranks, lineage etc, and then engage in an archery duel. Just on a personal note, my undergrad professor in Japanese history believed in this and tried to justify to the class how it was possible. I hope he doesn't still.

Though not directly to do with this question, I just want to blow this interpretation more out of the water by quickly mentioning that ambushes and trickery was the preferred method of battle. Of 58 engagements in the Heian period recorded in non-literary sources with enough details to be reconstructed in any way, 41 "involved ambushed and/or surprise attacks in one form or another." Even in literary sources from historical fiction (traditionally used as the source of the above interpretation), ambushes and surprised attacks are often seen and treated as just another tool in the samurai commander's belt.

Now let's talk samurai combat. The samurai were mainly mounted archers. The engagement range for the samurai though is assumed by various historians to be around 20~30m as the distance for aimed shots in mounted archery, aiming for the gaps in the armour, which it's recorded that samurai had to actively do. The estimate could be as low as 10m or lower in order to defeat the heavy samurai armor. As the engagement range was so short, it was very possible to pick out individual targets. As the samurai and his attendants were essentially private military contractors to the army, instead of being mobilized and trained as a unit, rewards for battle was very much on a individual or small unit basis (a samurai and his attendants). With such technical and cultural aspects, we find it result in the samurai regarding enemies not as units but as a group of individuals. In both literary and actual historical records (when they go into such detail), despite combat not being close-quarter, we find accounts of warriors picking out and engaging individual targets. For instance, the Azuma Kagami, the official Kamakura Bakufu record, writes of an old warrior in 1191 talking of how he survived an encounter with Minamoto no Tametomo, an archer of legendary caliber, in the Hōgen Conflict of 1156. He wasn't talking about fighting with Minamoto no Tametomo's unit, no. He was talking about how he actually found himself facing off with Minamoto no Tametomo and came out of the encountered having only taken an arrow to the knee. For real.

Jokes aside, the answer might sound very much like a yes right now, so why is it a no? Well, first, we need to remember that in a pitched battle, especially between sides of rough equal number of men in the front ranks, some form of pairing off is inevitable unless the weapon you are using is indiscriminate, like a bomb. Or rock. Or long-ranged archery (remember, samurai mounted archery is short ranged). I would say this is no different in Europe.

More importantly, there was no such thing as "pair off". A samurai can only aim at one target at once. Doesn't mean he can't be targeted by multiple opponents at once. The only thing preventing a gang-up in the case of a numerical disparity is if there was a culture which respected fights as actual duels. And such a culture did not exist. There are many reference in the records of samurai being killed by "stray arrows", in other words, arrows shot by attendants fighting on foot. So, obviously said attendants were not just standing around or fighting only among themselves while their mounted lords duked it out. If someone saw an opening, he took it. Azuma Kagami recorded two encounters during the Battle of Azugashiyama in 1189:

Amid the defenders who remained to fight was Kasuo Tarō Hidekata (thirteen years old), a son of Kongō the Intendant [bettō]. He rode forth on a black-dappled horse and, turning its bangs to the enemy, took his place in the lines; his countenance was striking. He galloped toward Kudō Jirō Yukimitsu, but as he drew near Yukimitsu’s retainer, Tō Gonan, rode between them and engaged him.... Gonan thereby killed Hidekata, yet the youth’s strength was out of proportion to his years, and it is said that they fought for some time.

So Tō Gonan had no intention of letting Hidekata just go and duel his master, and engaged and killed the young man instead.