A lot of people look to the demigods for Demigod's balance. However, far more imbalanced than the demigods are the items. Erebus was a bit too good, but all the demigods can be toppled and no demigod is completely useless. The balance is functional enough for the time being. The items on the other hand are severely out of whack. Some items are amazing while others exist only to fill space. The gaps between items are crazy. Yes, items have different strengths and costs. However, some items are insanely cost efficient, while other similarly priced items are a complete waste of space and money. The two places it is most visible are the boots and the helmets. I will address helmets in this post. It's somewhat long, if you have a short attention span, scroll down and skip to the summary. It is underlined.
I would highly advise anyone reading this post to refer to demigoddb: http://demigoddb.com/
Demigod DB lists the stats and prices of all items in an excellent manner as well has providing quick access to the demigod's stats. I've bolded item names so you can quickly recognize I am referring to an item and look that item up if necessary.
Now what is wrong with helmets? Most helmets fall into one of two categories, +Mana/second and +Mana Regen%. The mana/sec helmets give you a set amount of mana/second while the mana% helmets are a function of your current mana regen.
You can start by looking at the two starting helmets, the scaled helm and the plate visor. These are similar entry level helmets, for similar prices. However, out the door the scaled helm is extremely effective, while the plate visor is pretty much useless. This is because demigod's natural regen is simple not very high. A demigod's natural regen would have to be about 11.42 mana/sec for the regen of the plate visor to match that of the scaled helm. The torch bearer, the demigod with the highest natural mana regen in the game does not reach this point until he hits level 18. No other demigod ever hits the point where the plate visor outperforms the scaled helm. In fact the regen from the scaled helm outperform the regen from the plenor battlecrown on most heroes until slightly after level 10. The scaled helm is better for erebus until level 13, for the QoT until 10, and for sedna until 11. You need 5.71 natural mana regen for the plenor battlecrown to perform as well as the scaled helm. When you bring in the vlemish faceguard it isn't even a contest. In fact the vlemish faceguard is very easily the best helmet available.
So the end result is the scaled helm and vlemish faceguard are absolutely amazing helmets and vastly outperform the others, especially for their price. The plate visor is absolutely useless and should never be purchased. The plenor battlecrown should only be purchased for the increased manapool and be used in conjunction with the vlemish faceguard. The vinling helmet is really just a more expensive, mutated version of the plenor battlecrown. The hungarlings crown is only marginally better than the vlemish faceguard, but really doesn't justify the cost (that 6500 could easily be spent better elsewhere.) Finally, the theurgist's cap is the red headed stepchild of the mix. It's really out in the blue and there is no reason to ever consider it. The mana% helmets are completely reliant on the purchase of +mana/sec items to make them effective.
You can very easily get away with using only the vlemish faceguard. You probably want to purchase a scaled helm near the start of the game, which can be upgraded to plenor battlecrown later. However, these three items can meet all your mana needs very easily. Try changing your mana item habits for a few games and you'll see what I mean.
The end result is mana items (which are mostly the helmets) are dominated by a two extremely cost effective items and a number of the helmets have zero reason to exist, other than to act as filler. They can effectively be replaced with items that do nothing and have no significant impact on the game.
So, what needs to be done to improve the situation? In general +mana/sec items need nerfed and +mana% items needs buffed or repurposed. Some suggestions on an item by item basis follow.
Scaled Helm: This item simply needs nerfed, the cheap starting items being cost efficient and powerful is great. This one is a bit too good though. +2 or 3 mana/sec would be more appropriate as would reduce +mana. It should probably give more in the range of +250-350 mana.
Plate Visor: This will never be able to compete with the scaled helm as an opener for mana regeneration. However, converting it into a mana pool item could work. If this simply gave +750 to +1000 mana (and did nothing else) it could be an appealing opener. It would give the choice between mana regen or a large mana pool.
Plenor Battlecrown: Truthfully, this item seems just about right. It is just vastly overshadowed by the vlemish faceguard. Maybe the gains could slightly higher if needed.
Vlemish Faceguard: Insanely good. You gain +16 mana/sec which is greater than all demigods have naturally at 20. In fact it is around double what most demigods naturally have at 20. On top of this all your buddies get a bit of mana too. My suggestion would be to keep the aura roughly the same (maybe +3mana/sec) and roughly cut the normal bonus in half. It should give 6-8 mana/sec total. About half as effective as it currently is. It would still be a very strong item.
Theurgists Cap: This needs completely reworked. It is bad mana gains, a poor +health item, has a good trigger condition, and the minion bonus just isn't that interesting. A hybrid health/mana item is a nice idea. This one just sucks. The health can stay about the same, but it needs to either be +70% mana regen or get a pure +mana/sec bonus. In addition I think a good way to make this a general item would be to convert the bonus. Giving the player a set mana bonus (say 100 mana) every time a minion dies could make this an appealing general item.
Vinling Helmet: This could use some small buffs. I think bumping it up to +100% mana and/or tossing a small +mana/sec onto it (say 2-4 mana/sec) could help make it a bit more appealing.
Hungarlings Crown: With the proposed nerfs to vlemish faceguard and the scaled helm, the current stats would be justified. I think the key to making this an item worth 6500 is to tone down the sub-2000 items that perform nearly as well. You just never have the need to step it up to this level with the vlemish faceguard being so powerful.
Quick math formula for comparisions:
[+Mana per second] / [%mana regen] = Mana per second needed for the percent item to be as effective as the +mana/sec item
example vlemish faceguard (+16mana/sec) vs plenor battlecrown (+70% regen):
15/0.70 = 21.42 mana/sec needed for plenor battlecrown to be as effective as vlemish faceguard.
In Summary:
Helmet balance is really out of whack. You should always get a vlemish faceguard and suppliment it with either a scaled helm or plenor battlecrown if you need more mana. The other helmets really aren't prudent investments and your money can most likely be spend better elsewhere.
Every item should have a purpose and appeal. You should be able to at least consider most items. If they are fringe and somewhat situationally useful that is ok. If they are completely overshadowed by other items they have no reason to exist and should either be fixed or removed for the game. Items like the plate visor currently serve as nothing more than newbie traps, tricking players into wasting their gold on them. These items are ultimately non-existant at higher level play.