The “Vengeance Driven” fight scene: This technique is like a mini Mel Gibson revenge thriller and the scene is generally superfluous to the primary plot-line. It is a direct, no-nonsense fight, usually for the side of good, or at least to destroy evil, that is cathartic for the reader. This fight has no real benefit to the plot, but it shows the protagonist accomplishing something that is beneficial for himself or humanity as a whole and establishes his prowess in battle.
Example: The Complete Chronicles Of The Jerusalem Man (1996) by David Gemmell
Shannow fought to hold the surging anger, but it engulfed him and he pushed himself to his feet, his hands curling around the butts of his pistols. He stepped into sight and the men scrambled to their feet, dragging knives and hatchets from their belts of rope and hide. Shannow's guns came up and then he spoke.
"Thou shall be visited by the Lord of Hosts with thunder and with earthquake and great noise . . ."
He triggered the pistols and two men flew backwards. The other five screamed and charged. One went down with a bullet in the brain, a second fell clutching his belly. A third reached Shannow and the man's hatchet flashed for his head, but Shannow blocked the blow with his right arm and thrust the left-hand pistol under the attacker's chin. The top of his head flowered like a scarlet bloom. A club caught Shannow on the side of the head and he fell awkwardly; his pistol fired, shattering a man's knee. As a knife-blade rose above his face, Shannow rolled and shot the wielder in the chest. The man fell across him, but Shannow pushed the body clear and lurched to his feet. The man with the shattered knee was crawling backwards.
". . . and great noise, with storm and tempest and the flame of devouring fire."
The cannibal raised his arms against the pistols, covering his eyes. Shannow fired twice, the shells smashing through the outstretched hands and into the face beyond, and the man pitched back. Shannow staggered and fell to his knees; his head was pounding and his vision blurred and swam. He took a deep breath, pushing back the nausea that threatened to swamp him. A movement to his right! He pointed his pistol and a child screamed.
"It's all right." said Shannow groggily. "I'll not harm you. 'Suffer little children to come unto me.' Just give me a moment."
He sat back and felt his head. The skin was split at the temple and blood was drenching his face and shirt. He sheathed his guns and crawled to the children, cutting them free.
What makes it work:
This type of scene helps establish the protagonist’s character. In the example above we see that humans who have become cannibals in Gemmel’s post-apocalyptic world create a righteous anger in the protagonist, and that the protagonist is driven to destroy them without mercy for their evil. In other words, the quick fight serves as a form of character description, not as part of a plot movement. David Gemmel used this technique in several of his works.
Why it doesn’t always work:
Because it is not central to the plotline, the reader knows with 100% confidence that the protagonist will survive and win, so there is no risk for the reader. While this is generally true of all fight scenes involving the protagonist, it is especially true on a “random encounter” that the reader knows the author will not use to sacrifice his king or queen.
The protagonist almost always suffers a minor wound that will have no bearing later. This is an attempt heighten the low stakes of the battle.