What it does
Rivalry checks the gender of the ability holder against each opposing Pokémon on the field. Same gender: Attack and Special Attack get a ×1.25 multiplier. Opposite gender: both drop to ×0.75. Genderless opponents (most legendary Pokémon and some fixed-ratio species) trigger no modifier at all.
A 25% boost is meaningful on paper. The problem is the symmetry — the 25% penalty is just as real as the bonus, and there's no way to know which one you're getting until you see the opponent's party. The ability has no stable, unconditional benefit. You're always gambling.
Legendary Pokémon and other genderless species skip the modifier entirely. Champions fields enough legendary Pokémon that Rivalry often doesn't fire at all.
Who runs it
Luxray runs Rivalry at exactly 0% in Champions. Nobody picks it.
The reason is straightforward: Luxray has access to Intimidate, which drops every opposing Pokémon's Attack the moment it enters — no conditions, no gender checks, no variance. Rivalry might give +25% against the right opponent, but it might also cost you 25% at the worst moment. Intimidate never does either of those things. The 0% figure isn't surprising.
How to use it
If you were going to use Rivalry, the only realistic window is a metagame where you know the vast majority of opponents field Pokémon of a known, matching gender — and even then, one legendary Pokémon on the opposing team wipes out the edge.
In practice, just run Intimidate on Luxray. The unconditional Attack-stage drop on entry is worth more than a coin-flip multiplier that can cut both ways.
Tips & strategy
Rivalry has no reliable competitive use case in current Champions. The boost is conditional, the penalty is symmetric, and genderless Pokémon dodge the mechanic entirely. The 0% usage on Luxray reflects that accurately.
Know the mechanic exists, but don't build around it.