What a hero card does
Heroes are companions from a world card banner. You equip up to three. The published bonus is flat Energy, not a damage move. Gold pays for the spins. Each world has its own pool. A pity exists for the mythic hero, and the count changes by world. Those pity numbers were not published.
Broken is a seventh tier above Secret on the energy tables for worlds 1 through 6. An older wiki page said six heroes per world and stopped before Broken. Use the seven-row tables when both exist.
How the numbers grow
Epic Energy doubles from world to world: 1, 2, 4, 8, 16, 32. Secret and Broken follow the same doubling. A world 6 common (Cat Burglar, +8) does not beat a world 1 secret (Saiyan Prince, +30). Compare the Energy number, not the rarity label, when two worlds are both available.
Within one world, roll until the next rarity is a large jump, then move on. Hidden Potential at +6 is the mythic on Alien Planet. Saiyan Prince at +30 is the secret. Broken Super Saiyan at +180 is the top of that banner. Gear Fifth at +5,760 is the top printed card on Pirate Village.
Two tables disagree
An incomplete September heroes page listed Ace Captain at +32, Akimichi Titan at +14, and Slug Sannin at +20, with no rarity column and no Broken row. The later rarity tables list Ace Captain as Secret +60, Akimichi Titan as Legendary +8, and Slug Sannin as Mythic +24, and they match the doubling pattern. This wiki uses the later table. If your card shows a different number, trust the card.
The Update 2 banner text also called Cat Burglar Rare and Sniper King Epic. The energy table calls them Common +8 and Rare +16. Both labels are on the hero pages.
Clover cards
Update 3 added seven Clover Card heroes. Their names and Energy values were not in the patch notes used here, so they are not in the hero catalog yet.
Passives are separate
World Breaker at 3x Energy is a passive roll, not a hero card. Update 3.5 lets you roll three passive slots, with the third slot at 5,000 Emeralds. Keep a high flat-Energy card equipped even when the passive is the thing you are rolling for.