How To Increase Your Map Rewards

There are three main ways to increase the rewards earned in maps:

Character-Modifiers

Character modifiers are plain and simple the "increased rarity of items found" modifiers on your gear.

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Don't worry, you don't have to check every item and calculate the final number. However you cannot find it on your character stats. It's rather hidden in the details of your damaging skills.
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The reason it is listed there is pretty simple: This modifier only modifies the items, monster drop when you kill them. It doesn't have an effect on items found in chests and alike.

Monster modifiers

Next up is the monster modifier. Normal monster, overall, drop the least valuable items, since they're literally weak as hell. Next up are magic monsters. Magic monsters drop better loot on average then normal monsters. But they're harder to kill. That's technically a reward system working here. The higher the difficulty aka effort, the better the loot. That's why rare monsters are rewarding you with even more/better/rarer rewards. Even the item level is one level above the current area level.
Next up are unique monsters and bosses. These usually drop significantly more loot on average than a rare monster and the item levels are two levels above the current area level.

Map-Modifiers

When we're talking about map modifiers, we're talking about 3 main parts:

These are the bread and butter when trying to get rewards from maps. This is the by far, most powerful way to increase your drops in maps, since you can roll "increased quantity of items" and various versions of increased "pack size". Since rare monsters are the main source of your overall mapping rewards you want to increase the number of rare monsters, the "increased quantity of items" and "increased rarity of items" at best. You can even increase the amount of rare monster further by applying distilled_paranoia.