I've mentioned using the concepts of energy and reach to achieve balance in a roleplaying game before, but as it was part of a series on archetypes I don't think I really had time to explain what I meant.
When I design a game, I build characters based on the notion of giving them "risk"–the ability to be destroyed by mistakes–"energy"–the ability to act–and "reach"–domains where their actions are useful.
This method is not strictly speaking mathematical, but I don't lay those things entirely by the side when I design. Rather, I find that simply balancing numbers results in an unsatisfying game for players, where they don't get the opportunity to have agency in their play.
I think of Divinity: Original Sin (and its sequel) as mastering this: there are a lot of things that get wacky and out of hand and broken using the mechanics if you're clever and willing to exploit the system, but these things don't tend to be the memorable moments of the games.
The reach that characters get narratively surpasses the impact that they may have mechanically, and special abilities and backgrounds and choices that contribute to the storytelling have a much greater impact on the game.
Each of these things is not just a number, but a force of storytelling. Characters who have limitations in at least one area are vulnerable and require assistance, while characters who are well-rounded may seem well-rounded and interesting or flat and generic. A good quality system allows for both outcomes to be enjoyable.
Let's talk about each of our forces of characterization separately, then talk about how they tie into each other.

Risk

Risk is a driving force in all good stories.
Likewise, as a game designer you can use risk to make sure that players don't mess with the stories that you want to tell.
That may sound a little heavy-handed, but it's something that you need to consider.
If you are working on a system that is to be entirely agnostic of a particular setting, then the purpose of risk is to give players something to strive against, a consequence for making poor decisions that encourages further decisions to be made from a more logical or prudent view (allowing the player and character to grow).
However, if you want your game to tell a certain type of story, build your systems of risk around this.
Spire, which I've mentioned at least four or five times now (I will have to find a new favorite reference for design), does this by having a fairly standard resource system: mind, body, social, money, but then adding a measure of how much suspicion the character has attracted to the mix (I'm abstracting the game terms here). Characters don't get in trouble for spending resources, they get in trouble at flashpoints when they've taken too much Stress and when they oppose society they are very likely to see that happen.
It rewards flamboyant risk-taking, but also punishes those who choose their friends and opportunities poorly.
Risk can also be acquired by giving players connections and responsibilities that are matched by in-game benefits or penalties. Belonging to an organization is a great way to limit a variety of options that would otherwise be very tempting. Only War, part of the Warhammer 40:000 roleplaying lineup, does this quite well by casting all its players as guardsmen in the Imperium of Man.
They have a set of assumed roles and responsibilities thrust upon them, plus a hierarchy that encourages action, without requiring too many strict mechanics (mess up and the Commissar will mess you up).
One thing to consider about risk is that characters who are entirely inured against risk will be bold and reckless, and highly active, and characters who are very prone to risk will naturally have fewer chances to use their abilities.
Get around this by making risk something that pursues the players; Paranoia does this in a stunning way by making the whole party suspects of the blame game when things go wrong. If you're passive, you're actually accruing more risk than if you're actively pointing your fingers at the party's scapegoat.
And don't let anyone be fully immune to risk. If someone reaches the point where the central threats likely to be encountered in your game no longer threaten them, you've either made a mistake, or you're playing with fire.
Superman, for instance, needs to be taking care of his friends even though he's effectively impossible to attack. Achilles is effectively immortal, except for one very specific weakness, which winds up being capitalized on.

Death of Achilles, by Peter Paul Ruben

Energy

Energy reflects a character's ability. You can have a tiered system, like D&D has, where characters have abilities that are essentially permanently available (standard attacks), things that are limited (casting spells), and things that are very limited (once-a-day abilities), or you can go for a more narrative approach to this.
It's important to think of energy not in a vacuum but as the machinery by which other things get done. Giving a character an infinite number of uses of their abilities can be appropriate in some circumstances, and entirely inappropriate in others.
Open Legend, which I was a very minor contributor to, handles this by essentially making everything infinitely accessible to characters (barring special status conditions) unless it is individually targeted as having some restrictions. It takes a very permissive approach to the whole energy system, with the default rules resulting in characters who are almost always ready to do their best.
When everyone's characters have distinct and meaningful reach apart from each other, as they tend to do in Open Legend, this works really well. There are still situations like combat where characters face limitations, but you always need to have some source of risk.
But you do want some limits in most cases. You can look at energy as belonging to two categories: furthering energy, which provides new opportunities, and sustaining energy, which protects from risk.

Furthering Energy

The furthering energy is typically what you need to balance the most carefully, though not always. I suggest that characters have a high amount of this sort of ability in the majority of cases.
Why?
Furthering energy is how the character achieves their fullest reach.
People who are playing your game want to be able to accomplish things. They do not want to be sitting around doing nothing.
If you build a magician who only gets to gain the benefits of spellcasting every third session, how are you different from the noble, rogue, or warrior except for the fact that you may be inferior in regards to them in their own spheres while being pathetic in your own?
This isn't to say that every character in your game needs to have constant access to world-altering abilities. Rather, they need to be able to do what makes them stand out quite frequently. In Open Legend, which does this quite well, a character can almost always do whatever they are supposed to be doing as their specialty: inflicting damage, controlling the battlefield, healing allies, hindering opponents.
All of these characters can afford to have high furthering energy because their reach is distinct.
This is true in the narrative sense as well: someone will be good with technology, another with people, yet another with stealth, and a last person with survival. When you build a party this way, everyone has a clearly defined role: class-based systems like D&D do this quite well, but you don't need a class system for this to work. In fact, D&D often is heavily restrictive with furthering energy, making it so that characters run out of spells or abilities: nominally this is to ensure balance, so that no one character can hog the spotlight, but it can also mean that a character who has poor luck or a player with poor decision making simply doesn't get to have an impact in the story like they normally would.
A good storyteller can compensate for this flaw in design, but it requires them to be aware of it and consciously seek to correct it.

Sustaining Energy

Sustaining energy is a character's resistance to the negative impacts of risk.
Sustaining energy is more important to keep steady, since it measures how long characters can pursue goals that are deleterious to the story. Note that sustaining energy is not simply something like health points or an armor level, though these are both examples.
The best example of raw sustaining energy are reroll mechanics that allow characters to actively change the results of bad rolls, effectively making risk disappear. This can be used sparingly (and in many schools of design, the argument is that it should or must be used) to make it so that players don't feel that the world is out of their hands.
Because it tends to slow down play, I consider sustaining energy to be risky. It should only be given as a resource to a character when doing so allows them to play a protective role to the other players' characters (e.g. as a "tank" character). One of my biggest concerns with D&D as a player is how mired in mathematics the higher-level play gets, with raw inflation as opposed to meaningful development.'

Reach

The way that reach works is a little simpler to explain: reach is what characters can do.
As with energy, it comes in multiple levels: you might have things that a character can do, and things a character can do well, and things a character can do best.
When designing Hammercalled, we explicitly make characters have statements of ability written into who they are: "I am able to..."
This means that they have a defined set of aptitudes and abilities. On top of this we layer more traditional attributes and bonuses, so that characters can have a certain amount of compatibility at a glance (e.g. physically strong characters look like they are strong with simple numbers, without requiring you to look over their IAATs).
Reach is the balance problem that most people think of. If your game is not meant for adversarial play, and rather focuses on a cooperative method, then the reach solution is simple: give everyone their own distinct role.
This is something that works well for Open Legend, as I mentioned before, because of the flexibility of the system. D&D's strength is managing reaches, especially in Fifth Edition where they took an incredibly nuanced look at design principles.
However, one cautionary tale about managing reach is the likes of Shadowrun.
Shadowrun is an incredible game. It's the first game I ever ran for a large group (which has a certain element of danger to it), and I even liked the "bad" editions in their own ways.
But it has one thing I always hated: Cyberspace.
I love the concept of it. Cyberpunk wouldn't be cyberpunk without cyberspace.
But there were certain builds of hackers and magicians who would spend a lot of time in cyberspace or on an alternate plane (and riggers, who operated vehicles, could occasionally fall prone to this as well).
This meant that instead of having a balanced reach, they had overreach. They were the sole masters of a significant portion of any session where their characters were highly important, to the point that many people just out-and-out suggested doing separate one-on-one sessions for their players.
Solo sessions was an additional time investment for the players and wasn't really satisfying for anyone involved as much as a large group session would be in the majority of instances.
So reach needs to be unique, but not overpowering, for each member of a party. You don't need to force this as a designer, though storytellers should be reminded that they potentially could, but you should strongly encourage it by building a rich ecosystem of opportunities: maybe you even give characters multiple specialties, but have furthering and sustaining energy levels that make it necessary for them to seek help from others. Alternatively, consider a single strong specialty with low baseline levels of proficiency in many other areas to encourage specialization without limiting characters from interacting with other things.
A final note on reach: reach is not necessarily something that has to be broad, but you should make sure that characters with a needle's focus still get a chance to do things regularly.

Tie-In and Wrap-Up

Risk, energy, and reach all serve as means to accomplish balance. If your game is designed in such a way that you can't point to successes and limitations in each of these areas for every character, you might be setting storytellers up for failure.
As a designer, you can assign risk and energy universally, but reach will be separated by character. Each character's reach needs to be meaningful, giving them a series of abilities that other characters are likely to lack.