Chapter -1 - Clarification of Mechanics
Parameters in Danmachi~! Everyone wants Vahn to be strong, but the 'laws' of the world restrict everything regardless of their race. The only exception to this rule are 'monsters' who are able to break the restrictions a bit, but it is at a heavy cost~!
LEVEL: The purpose of level is to act as a container for the exilia(experience). The bigger the container, the more experience it can hold. BUT, each level only increases the size of the container the same amount as Level 1, they don't get progressively larger with each increase. That means a person can gain experience to increase the boon of their falna by a MAXIMUM amount based on their potential. For most people, this is around 3000 total parameters(the stats listed below). For prodigies or people that want to strengthen their foundation, they typically push themselves to earn upwards of 4300-4500 total parameters before leveling up. When a person levels up, ALL of their parameters go to what is referred to as a 'hidden' board which is the culmination of all the parameters they have gained from their levels EXCLUDING the current level. All parameters for the current level can be viewed by anyone that sees the Familia Crest on the back.
POWER: This is not only raw strength but also allows the person to influence the physical 'laws' of the world. That means people with enough power can generate shockwaves and stuff with their punches and perform other superhuman feats. A big misconception about power is that it is additive, but that is not the case. A person with 200 Power is not simply twice as strong as a person with 100 Power. Due to skills, proficiency, and mastery of the worlds 'laws', the more power a person has the more they are able to tap into their strength beyond their limits.
ENDURANCE: Endurance is the ability to resist not only physical blows, but also allows them to disperse some of the physical 'laws' of the world. That means people become shock resistant and also able to disperse blows away from their body without taking a lot of internal damage. That means people can get blown into walls and stuff, but instead of experiencing the full impact it would disperse into the wall (which is what causes the circular cracks you'd expect to see). Endurance also determines how much stamina a person has and how quickly they can recover. People with high endurance don't get tired as easily and require much less sleep than normal people.
DEXTERITY: Dexterity doesn't make you good with a bow or anything like that, but if you have high dexterity you CAN be good with a bow. Dexterity is technical prowess and control of your body. That means if you have very high agility, but low dexterity, you would be incredibly clumsy and even smash into stuff if your perception and awareness are low. The most practical means to increase dex is to increase your actual technical skills and prowess. That means you'd have to learn combat techniques and apply them into your fighting style instead of just relying on instincts. A Samurai or a Knight would have VERY high dex, whereas a brawler or a berserker would have relatively low dex (though they usually make up for it with their intensity and perception).
AGILITY: Agility isn't just raw speed, but also allows the body to adapt to rapid changes in direction. It increases everything about movement capabilities including spacial awareness and body control, which is why it has a synergistic relationship with Dexterity. Same as a Power, a person with 200 Agility isn't simply twice as fast as someone with 100. The person with 200 agility can make greater use of speed 'laws' which allow their body to almost ignore things like spontaneous acceleration and rapid changes in direction (which would make a normal person's organs slam into their own skeleton). Even without high endurance/power, a person's resilience against speed is determined by how much they can use the 'laws' and not their body's physical restrictions~! (Normally if a person could break the sound barrier, but had a mortal body, they would literally die. But in a world like Danmachi, a person can have low Power/Endurance but still move at supersonic speeds at higher Agility Levels. It is because they can ignore the effects of the speed on their body.)
MAGIC: This is inarguably the hardest stat to increase in Danmachi unless you're some kind of genius, elf, or spirit. It influences a person's understanding of magic 'laws' which allows them to increase the mana they can contain in their bodies. At higher levels, they can even use the elements in the air to supplement their own reserves. Magic also enhances a persons perception and mental clarity. People with incredibly high perception AND magic are even able to communicate with spirits as well as sense hidden/invisible objects. At the extremes, it even allows a person to sense the structure of magical objects/constructs and break them down.
EXTRA INFO: SOUL TIER's influence on stats.
As I said previously, a person is restricted by their level for how much total stats/parameters they can possess. For most people (Soul Tier 1), they are restricted to 3000-3500 total parameters per level. If they don't level up immediately, they can push themselves to obtain over 4k stats, but it will start to burden their body and can even cause physical/mental disability. Prodigies/Heroes are people that have (Soul Tier 2) or very close to it. They are able to exceed the limit even further and reach around 4500+ parameters, while people like Bell Cranel (original MC) can get even higher stats due to the influence of his skill [Liaris Freese] and the fact he has a modified soul. Vahn had Soul Tier 2 when he was still Level 1, which is the ONLY REASON he was able to get 5500+ stats with the support of [Will of the Emperor] and [Rakshasa Body]. He is far more durable than normal people his level and has higher potential because of the strength of his soul. Once he gets to (Soul Tier 3) he would have around 6000-6300 limit on parameters per level without obtaining any new skills. You have to keep in mind though, this is the MAXIMUM if he pushes himself to his limits over and over. Even getting over 5k stats is very difficult, much less reaching the 5500+ mark. In the original anime/manga, even Bell Cranel faced this issue (even though his skill is busted). He typically levels up around 5200+ points while only his first level was a bit higher (remember he had fought and exceeded his limits against the Minotaur and even entered mind-down after the battle).
I hope this clears things up a bit.