im stupid pls point out my mistakes its been a year since i took math
since 1.8, weapons should have a range under its damage values
let's say you have a weapon with an attack value of 7000, which, after applying the damage range, you would be (for example) hitting around 4000~10,000 damage randomly based on the value that your RNGeesus selects.
if you have 0% maximize, you have equal chance of inflicting 4000 damage and 10,000 damage. illustrated by the graph below. if your RNG chooses a value that is on the left of the red bar on the left, you will automatically yield the lowest damage (4000). if RNG chooses a value that is on the right of the right bar, it will yield maximum damage (10,000)
very basically, your RNGeesus chooses a number between 0~100 which is represented by the graph. the red bars are put at 25 and 75. if RNGeesus chooses a number from 0~25, which is on the left of the red bar, you will yield the lowest damage. if RNGeesus chooses a number from 75~100 which is on the right of the red bar, you will yield maximum value
what maximize does is that it basically shifts the graph to the right so it looks like this (below).
so, in very basic terms again, RNGeesus chooses a number between 0~100, but now the red bars are at 15 and 65. if he chooses any number from 0~15, you will yield minimum damage and if he chooses any number 65~100, you will score the highest damage. basically just follow the area on the right and the left side of the bars on the graphs
as you can now see from the graph above, you have less chance of scoring minimal damage since the area on the left is smaller, while you have more chance of scoring maximum damage because the area on the right is larger. so RNGeesus has less opportunity to select a value which will yield you lowest possible damage, while he has more chances to select a value which will result in you getting maximum damage
at 50% maximization, RNGeesus can no longer yield you minimum damage, because he can no longer select a value on the left side of the red bar. however, this does not mean that maximization becomes useless after 50%. instead, socketing further maximization will increase the chance of you scoring maximum damage. i cant give you an RNGeesus values anymore because i screwed up on the values i used when explaining the top half and frankly im too lazy unless you ask if you cant catch my drift
when you reach 100% maximization, the graph will be shifted to have the right red bar at 50%. this means that you'll have a whopping 50% chance to score maximum damage. on average, you'll be doing waaaay more damage than your enhancement level is worth.
however for statistical reasons and also bc of socketing efficiency, the highest optimal level of maximization you should have is 80%.
anyway maximize is very crucial if you want to bump up your dps. especially more so than add. damage, especially on PvE. maximize will be applied on every single one of your hits, so it practically is the foundation of your damage. crit and add damage works on maximize to enhance your damage even further, so you generally will want a good spread of maximize and your other primary attacking stat (which is crit for PvE and add. damage for PvP). in PvE, i recommend trying to bump maximize to 50% first, then i start to make maxi = crit. dont really have enough PvP sets to gauge the effectiveness of add damage in pvp tho so idk about pvp