I've noticed that when a work of fiction focuses on a group of four characters, the roles those characters play within the group fall into a pattern. It seems to be more or less the same regardless of the gender of the group, although these are almost always same-sex groups. The roles are:
There seems to be something about these particular archetypes that form a stable and satisfying group dynamic. A functioning group can't have four leaders or four goofballs, nothing would get done. These characters balance each other out and support each other. When one's overarching modus operandi is harmful to the situation, the others unite to compensate. When the leader pushes the group too hard, the goofball lightens the mood. The Brain comes up with the plans, but needs the others to execute. The Hothead is passionate and fires the group up, inspiring them to drive forward towards their goal (Though sometimes the Hothead can go too far. If they perceive the group isn't caring enough and they'll try to go off on their own, requiring rescue from the rest of the group).
I'm focusing here on stories where the group is united in a quest towards some common goal, which seems to often be the case. If the story is a Hero's Journey, the leader is often the hero, with the rest of the group as support. The same character types are also evident in more open ended formats where there isn't necessarily a quest - examples below.
The first place I noticed this was in the movie Stand By Me, as it seems particularly pronounced there:
Stand By Me is interesting because it's about (so to speak) The Brain, in that he's the narrator. Usually if there's a main character, it's The Leader, but much of the time all four characters share the focus equally. Some other four character ensembles where this dynamic plays out:
Also very obvious, and probably a better canonical example than Stand By Me.
I've heard tell that some people consider Raphael the leader. Unfortunately, those people are wrong.
This is a less than perfect example. Winston is The Hothead mostly by the process of elmination. If Ghostbusters has a failing, it's how underdeveloped the character of Winston is, compared to the other three. It will be interesting to see how the new Ghostbusters handles the Winston-equivalent character. Speaking of groups of women, they hold to more or less the same dynamic.
To be honest, I haven't seen a whole lot of this show and I'm not sure I have this right. One could make an argument for switching Charlotte and Miranda. Samantha is much more on the "Free Spirit" side of Goofball / Free Spirit type. The Goofball's role is to push the group to lighten up and take things less seriously and sometimes provide comic relief. A lot of the time this is accomplished by The Goofball character being naive and innocent, almost childlike. Samantha is an interesting departure in that she accomplishes this purpose while being decidedly not innocent.
This one puzzled me for a bit. I wanted Jessa to be the free spirit, since that is the way she seems to view herself. By season 2 though, it becomes obvious that Jessa isn't as carefree as she appears, and that is mostly an act to cover up her personal struggles. Shoshanna, on the other hand, is charmingly naive sometimes, dispensing wisdom in a from-the-mouths-of-babes type way. She plays The Fool, who, because of her innocence, can get away with acknowledging truths the other characters know, but delude themselves into ignoring.
Seinfeld fits so well I have to think it's deliberate. George flies off the handle on the regular. A whole episode is devoted to Elaine retaking an IQ test to prove how smart she is. Kramer is, well, Kramer. It's also a somewhat rare example of a mixed-gender group. Way to be progressive, Seinfeld!
This seems to be a remarkably robust dynamic. It holds true even in larger groups, where more than one character may combine to fill the same role. Take Lord of the Rings, for example - many more than four characters, yet they fit the same archetypes.
As a variation, The Hothead is sometimes optional. If the characters are sufficiently motivated by their situation and/or if the story is too light-hearted to support someone who's dark and brooding, it's not necessary to embody that aspect in a character. Harry Potter is the most obvious example of a three person dynamic.
I don't think the story would have been improved by the addition of a fourth Hothead character to the main group. The direness of the impending doom of Voldemort taking over the world is sufficient to inspire the characters to move forward. Harry also does some double-duty by having brooding, troubled episodes at times.
Clearly, I could go on indefinitely analyzing how various different character groups fit into this mold, as it's a lot of fun to me. I doubt it's perfect and probably someone will be able to point out an example where it doesn't hold. Still, I think it provides a good framework for how characters can interact with each other in a way that is satisfying to watch. Definitely something to keep in mind and play with if I ever write something about a group of characters.