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The Wizard's Companion gives some information on the various signs, stating that certain signs are stronger with certain elements and that have an advantage over other signs. However, it doesn't go into detail how this advantage applies.

Do attacks of a certain element just receive a damage boost? Do sun sign familiars receive less damage from Moon familiars? So on and so forth.

What impact does a familiar's sign have on its performance in combat?

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In this game of Rock, Paper, Scissors, you have 4 signs: Sun, Moon, Star, Planet. You also have twin versions of these signs.

Sun is stronger than Moon. Moon is stronger than Star. Star is stronger than Sun.

Stronger signs from these three deal 20% more damage against the weaker sign, while the weaker deals 20% less damage. If the attacker is a double sign, the damage modifier becomes 30%.

In other words: Sun deals 20% damage against double Moon, but double Moon deals 30% less damage against Sun.

Double Planet has a +10% damage bonus against all three, while a single Planet has a 50% damage bonus against double Planet, while doing normal damage to all other signs.

There are also resistance bonuses for Sun, Moon, and Star, and XP bonuses for Planets:

Sun: +5% to fire attacks and sleep
Double Sun: +10% to fire attack and sleep
Star: +5% to storm attacks and poison
Double Star: +10% to storm attacks and poison
Moon: +5% to water attacks and confusion
Double Moon: +10% to water attacks and confusion
Planet: +5% XP bonus
Double Planet: +10% XP bonus

Sources: GamesRadar and Prima Games

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