The simple truth is that most fiction plots aren't believable at all, once you distance yourself from your immersion and think them through.
Almost all fiction plots employ a fair amount of good luck and handwaving. Authors get away with this with two simple tricks.
1. Tell the reader that your protagonist can do X
The first trick is to posit the protagonist's superhuman abilities.
A playwright whose name I forget brilliantly illustrated this by writing the IQs of his characters on their foreheads. Thus, whatever the person with an IQ of "145" said came off as intelligent, and whatever the person with an IQ of "79" did was considered stupid.
In the same way, writers of fiction simply state that their characters are strong or clever or whatever and the reader takes this as a fact and thereby allows the writer to let the character win every fistfight or find all the clues to a murder mystery, and the reader will not notice how unlikely this would all be in real life.
Of course good writers don't just say "<PERSON> was stronger than any other person on Earth" but let the reader come to that conclusions by illustrating this. I just read one of the <PERSON> novels by <PERSON>, and in it <PERSON> writes that "in the military <PERSON> failed driving but excelled in everything else". There are other similar messages, some through backstory others through on stage interactions, that build an impression of ruthless courage combined with above average fighting ability all of which makes it believable when <PERSON> wins against all odds in the end.
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Fulfill your readers' daydreams
The second trick is to get the reader on the side of the protagonist so that even if what the protagonist achieves is somewhat unlikely the reader will be pleased to see the protagonist achieve it.
If the reader really, really wants the protagonist to win, because the reader identifies with the protagonist, shares his goals, and feels for his losses, he won't mind a little bit of suspension of disbelief to allow the hero to overcome the antagonist or get the girl.
One other thing helps, and that is the distribution of intelligence among your readers. About 98% of the population have an average or below average intelligence (IQ 130 or lower), and because of their limited cognitive ability they won't be able to distinguish real brilliance from fake brilliance.
This means that when you present something to your readers that appears brilliant, they will assume that it is.
Examples.
In The Lord of the Rings, <PERSON>'s willpower to overcome the lure of the One Ring seems superhuman. In fact many of the other characters are either shown to succumb to it or state that they would. How then can <PERSON>'s achievement be believed? Because <PERSON> has <PERSON> and the Elves continually comment on the unique strength of character of the <PERSON>. They say <PERSON> has willpower, therefore the reader believes that he has.
Why do readers accept the superhuman powers of comic book superheroes? Because they themselved would like to have similar powers. Therefore they allow their idols to have them and don't find the concept ridiculous. 190