But moreso interesting to me then the progression mechanic is what it actually does, and what it doesn't do.
The "Power" Stat
As you can see, the "Power" stat is a combination of character level + loot level. It's specific effects-increase damage, how well you cleave through enemies, and the power of staggering enemies. On the surface, these seems pretty basic, but if you think about how games are programmed or tabletop games are designed it's actually a pretty indepth and unique method of improving the "power" of your attacks. Most games would just have a scaling damage modifier, meaning your sword swipe would be the exact same with the same hitbox but just deal a percentage more of damage. While I don't know how the Vermintide damage system is calculated, the idea of player power also increasing how well you hack through enemies, thus meaning you deal with huge swarms better, as well as single target damage for bosses, stunlocking bosses, and the like is really interesting.
However, there is something interesting here in the subtext of the game about player progression. Something the developers did not want the players to be able to gain power in; either for game balance, enforcing the idea of teamwork, and to allow for player skill. Vermintide is not just about whacking a target dummy to do maximum damage, so what things does this power stat not allow you to progress in?
- Does not reduce damage taken or increase maximum health
- Does not grant you more ammo or increase your aiming ability
- Does not make you reload, attack, or switch weapons faster
- Does not increase stamina or blocking power (though some gear can)
- Does not grant armor piercing or help you deal with armored enemies beyond more damage
- Does not protect you from Special units' ability to down or disable you
- Does not make healing items, potions, or other supplies more common
- Does not make it easier to revive your teammates or stay close to them
- Does not help you navigate the map or find secrets
These concepts were just about everything I could think of as to what an RPG "Power" stat could do in the context of a game. While some of the above mechanics do exist in the context of character talents and specific modifiers on some piece of gear; the general "stat" has a very specific application in the game. What we can gather from this is all of the above bullet points are things the developers intentionally or unintentionally did not want the players to be able to automatically scale past at some point. Being at a super high power level doesn't count every hit as a headshot nor does it create a bridge to the end of the level so you can beat it faster- certain things are still respected by the game. This means that the player's skill or teammwork are still important and demanded by the developers or game designers and aren't supposed to be necessarily trivialized by a basic progression mechanic.
D&D and DIY tabletop already have a similar concept- in the form of level. Character levels in RPGs fulfill the same function. Obviously this depends hugely on the game, but if we go with a generic tabletop RPG like D&D we can see a power progression too.
The Character Level
For most retroclones and so forth; your character's level is a jump in power across every major mechanical element of the game. You gain more HD and better saves, letting you survive better. You also advance in To-Hit and sometimes damage or multiple attacks- depending on class. Certain classes also unlock all new abilities, either directly or in the form of higher level spell slots. If your class has a resource, then that resource tends to get more plentiful allowing for more uses per day in the form of spell slots or action surges or what have you.
However we can see from this what your level does not do. It doesn't let you bypass core rules of the game- such as dungeon crawling or exploration. It doesn't let you charm every NPC you come across or bypass any skill check related activity, though modern D&D skills try their best to do so if your "build" is done a certain way. It doesn't let you bypass the need for random dice rolls- even a high level character can die on a bad save- which is perhaps one of the best things about having save or die mechanics in the first place- a way to get through an overly cautious and high HP character. An element of risk or even skill, for someone who has progressed past the point of caring about individual points of damage. It also doesn't control the magic item or monetary economy of the game. While a high level character could easily buy something expensive, they can only do so on money they've earned. Very rarely do games have a sort of just "I can afford anything under this amount of money" because of a characters level ups.
Of course, there are exceptions to these rules; new spells unlocked as you level up can bypass these things, and certain classes or races, or race-as-classes like classic Elves and Dwarves can detect secret passages or doors and the like, or gain darkvision. However, it isn't a core feature of the game that you get darkvision for free once you turn level 5 or whatever- it's an exception.
The biggest "thing" that isn't overcome by levels are rulings and the in-universe lore. Some games, like story-games or Dungeon World-esque games, allow players to carve out their niche in the world built into mechanics. However, this ability isn't really overcome by leveling up or standard progression. Your plan to chop a tree and bring it down into a dungeon through the narrow tunnels so you can use it as a bridge over a chasm is just as good player-skill to overcome a problem as it would be if the DM just said "you're all almost name level- you can just cross the gap." At least, MOST DMs don't do that. I intentionally try to be more lenient with player actions if they're higher level for a more heroic fantasy feel, but that's one thing that levels don't really fit with influencing.
So let's look at this from a different perspective; what else could character levels or progression do, if not what they do now?
Alternate Power Mechanics
Instead of character level ups, we have EXploration level uPs instead. In this theoretical example, the party may share a single level, or use the highest party members EXP instead. Maybe it's for a solo RPG session, so one universal level makes more sense there, regardless of how many party members are brought along.
In this alternate timeline, we'll say that the DMs of old never figured out or thought of how to improve characters in combat- no extra attacks or to-hit bonuses, nor more HP. Instead, characters at 1st level and max level fight at pretty much the same strength. Perhaps equipment plays a bigger roll, or combat is decided in a more skill based way; something like a game of risk-reward blackjack or a mathematical puzzle. We'll just say for the sake of simplicity that in this example, everyone fights with 1d6 weapons and 1d6 hit points regardless of their "level". What would this mean for the game? Since progression isn't tied to characters combat power, monsters remain as dangerous as ever, minus things like magic items or spells that may give an advantage. Monsters naturally must remain on a roughly human approachable scale of threat- so no giant elder dragons with 100+ HP or eldritch deities.
So then, how DO players advance mechanically? They advance in the more gamified part of this game; which in this alternate universe is in exploration mechanics.
Exploration as normal.
Map is always accurate / DM checks over map and corrects one mistake per session.
You always have a basic light source (lantern)
Party automatically marks places they have been. Slopes are identified.
Always find secret doors. Traps are disarmed after they are triggered once.
Always find hidden walls. Immune to pit traps.
You always have dark vision / no longer need light source. (Stealth?)
Doors no longer automatically close. Party can request map directions to hoard / stairs.
Hirelings will now do any action requested. Teleporters have exits marked.
No longer roll random encounters. Free exit to/from dungeon (Fast travel?)
Alternate Class Progressions
Slightly less unusual, the concept of class-based gameplay and progression fits more naturally into an OSR/DIY playstyle. But how do the classes actually progress?
Instead of every class getting a generalized power boost- their specific role in the party is what is increased instead. Similar ideas do exist in other games; imagine a game where no class gets any To-Hit bonus or more hit points as they level EXCEPT for the fighter, because that's the fighter's role. Thieves only get better at thief skills and stealth, but probably don't get sneak attack bonuses since they're more focused here. Wizards would probably be the same, except with more specific spells- no more combat or creature-avoiding spells, just spells to influence and travel the dungeon environment. (MUs already don't have a "clear" gameplay role, which is why I sort of cut them out in my homebrew.) Clerics on the other hand are simple enough, just more spells and resource management, but get no combat ability as they level up. Turning undead would probably remain their specialty.
Other Forms of Progression?
Depending on the nature and primary goal of a game, other forms of RPG like progression could be chosen. I really like the idea of highly specific bonuses that scale with level, or are unlocked based on role- a classic example are saving throws or the elf immunity to ghoul paralysis in oldschool D&D- it's specific because the game and world are specific. However, with a more stimulationist or "game world" oriented style, tying progression to generalized stats, skills, or power progression tends to work better and be more immersive for players overall.
So here's a list of 20 types of player progression- based on my list of 20 alternatives for gold to xp list.
20 Alternate Player-Power Progression Systems
 You get better at tracking elephants. Strength score increases to better wrangle them with rope.
 Combat power increases- though specifically through dueling or single target actions.
 Increased ability to pacify natives; savages must make a morale check to stand against you.
 This is just Wolf-packs & Winter Snow.
 Load up a Harry Potter RPG homebrew- I'm sure there are least a dozen of them.
 Progression is based on memories found in the otherspace- you get level ups and class benefits from random classes from other games. So one memory you get a GLOG Acrobat template A, another and you get the saving throw table from an 6th level Dwarf, etc.
 You already get XP for murdering stuff and being evil- just reincarnate to level up.
 Better gang fighting skills, tagging skills, and avoiding the law. Maybe lets you have more gang members in your posse.
 You get stronger against the specific kind of monster your group hunts. Eventually you have acidic blood and the ability to force bats to land if you kill a strong enough Dracula.
 Getting better stats = progression. Makes sense to me.
 Get better prices from the shops, or get an Appraisal skill that you can use in the dungeon to compare item stats.
 Increased knife skills, heat resistance, and ingredients you collect stay fresh longer. Chef powers.
 Highly combat focused clan warfare- advance as barbarian. As you level up, you become more and more revered and have mythical feats attributed to you. (If you did them or not- Finn Mccool style)
 More powerful angels can call upon more miracles; and keep watch on mortals. You can guide good people on the path to becoming more heavenly-guardians when they die, or perhaps become your replacement after guarding the gate for a thousand years.
 It's another Fighter-progression for caravan guards- except your abilities are mostly defensive. When you get to 6th level, you can use your action to corral 6 camels who ran away from the ambush- that kind of thing.
 You are farmers defending your crop. You aren't just getting better at fighting goblins, but you also get bonuses to rabbits, foxes, snails, and all other vermin. When you reach name level you get a cat that kills all of your rats for free.
 Dark cultists get spell slots. To keep with the theme- you still have to bleed out hit points or sacrifice virgins or whatever as you get stronger- just don't give away too many or else you won't be able to complete the BIG ritual that matters.
 Every player advances as thief. You can still pick cool thief knacks though- maybe it's like Payday where you have classes but all the classes are still "thief" classes. Like one guy is the muscle who gets all the health and armor and the other guy is the mastermind who can accurately predict where the next guard patrol is gonna go and so on.
 Megadungeon- unlock shortcuts as you level up too. Maybe add the EXploration level uPs system from above; but for your highest level character. If they die- oh well- all those little chalk marks and secret paths they knew are gone now.
 Increase your saving throws to magic shard dust addiction.