Chalice of Harmony

The Chalice of Harmony is an advanced item in League of Legends.

Recipe

 * (390g)
 * (400g)
 * 100g

Explanation
The Unique Passive on Chalice of Harmony is commonly misunderstood. It will increase your mana regeneration from all sources based on how much mana you are missing. If you are at 0 mana, you are missing 100% of your mana and therefore your regeneration is increased by 100% (I.E the regeneration is doubled). The actual amount of additional regeneration is based on how much regeneration is already present. This is the best seen with the following examples:
 * A champion has 8 MP5 and is currently at 25% mana (missing 75%). Chalice will increase regen by 75% to yield 14 MP5 (so Chalice provides 6 additional MP5).
 * A champion has 8 MP5 and is currently at 50% mana (missing 50%). Chalice will increase regen by 50% to yield 12 MP5 (so Chalice provides 4 additional MP5).
 * A champion has 20 MP5 and is currently at 75% mana (missing 25%). Chalice will increase regen by 25% to yield 25 MP5 (so Chalice provides 5 additional MP5).
 * A champion has 10 MP5 and is currently at 75% mana (missing 25%). Chalice will increase regen by 25% to yield 12.5 MP5 (so Chalice provides 2.5 additional MP5).

So the more regen you have, the better the Unique Passive on Chalice gets. Unfortunately, the more regen you have, the less you need the Chalice. However, the more mana you have, the more this item have the time to be useful, as it will give you increased mana regen for a longer time.

Alternatives
Many players find that buying a Chalice is unnecessary to have sufficient mana. or runes for seals and/or glyphs often provide sufficient amounts of MP5 for most champions. Even without those runes, Chalice is often sold later in the game when the extra mana regen is no longer needed. Because of this, it can be preferable to avoid ever having to buy it. Both Ability Power and Attack Damage champions have damage-increasing alternatives ( and, respectively) that even provide increased levels of mana regen. Alternatively, especially for supports, a might give all the mana regen needed, while also increasing health regen and providing gold. The chalice is still somewhat useful thanks to the magic resist it gives.