Battle Institute

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Battle Institute

Access to:
Exit: Mauville City

The Battle Institute is a facility, accessible in X, Y, Omega Ruby, and Alpha Sapphire, where the goal is to defeat five Trainers in a row and get a high score. The player can choose to enter the challenge in either Singles, where they will pick three Pokémon, or Doubles, where they will pick four.

Battles conducted in the Institute are subject to restrictions.

Enemy Pokémon are always level 50. The player's Pokémon above or below level 50 will be set to level 50.
Set Mode is enforced.
Items cannot be used in battle.
The moves Return and Frustration, when used by the opponent, will always have their maximum power.
If the player loses the battle, the Battle Test challenge will still continue; the player will just not receive points for winning that battle.
Pokémon encountered in battles will not be added to the Pokédex.
Enemy Pokémon will always take their Nature, Item, moves, and EVs from predetermined 'sets'.
Enemy Pokémon that can have multiple Abilities, including Hidden Abilities, will always have a random Ability. Enemy Pokémon that can be male or female will have their gender randomly determined.
The player cannot enter two Pokémon of the same species or holding the same held item.
Any Pokémon holding a Soul Dew cannot enter.
Some Pokémon cannot be entered altogether, and will never be encountered on an opponent's team:

Mewtwo	Mew	Lugia	Ho-Oh	Celebi
Kyogre	Groudon	Rayquaza	Jirachi	Deoxys
Dialga	Palkia	Giratina	Phione	Manaphy
Darkrai	Shaymin	Arceus	Victini	Reshiram
Zekrom	Kyurem	Keldeo	Meloetta	Genesect
Xerneas	Yveltal	Zygarde	Diancie	Hoopa
Volcanion	Eggs

The enemy Trainers and their Pokémon are pulled from the same lists that are used to determine opponents in the Battle Maison, located here for Pokémon and here for Trainers. Each Trainer faced during the challenge is limited to a specific range of Trainer numbers, and will have a specific IV value, shown in the table below.

Battle	Trainer Number	IV
1	51-70	7
2	111-160	19
3	161-180	23
4	241-270	31
5	271-300	31

Scoring

At the end of the five battles, the player will receive BP (which can be used as a currency at the Battle Maison), a rank, an item reward, and a number of stars added to their Trainer Card (such that only the best result is saved to the Trainer Card). The ranks are as follows:

Points	Rank	Stars	BP	Item
0-999	Beginner	1	3	Random Wing, except for Pretty Wing
1000-1999	Novice	2	5	Random Wing, except for Pretty Wing
2000-2999	Normal	3	7	Random Wing, except for Pretty Wing
3000-3999	Super	4	9	Random Vitamin
4000-4999	Hyper	5	11	Random Vitamin
5000-5999	Elite	6	13	Random Vitamin
6000-9999	Master	7	15	PP Up

The highest score the player can get is 9999.

The scoring logic works as follows:

Action	Score
Player wins the battle	+1000
Each opposing Pokémon that faints	+80 per Pokémon
Each move used by the player's Pokémon that hasn't already been used in the same battle	+15 per move
Each time the player switches Pokémon (without using Volt Switch, etc.)	+5 per switch
Each opponent's attack that the player's Pokémon is immune to based on their type or Levitate	+5 per attack
Each opponent's attack that is not very effective	+2 per attack
Each player's attack that is super-effective	+1 per attack
Each player's attack that is not very effective	-2 per attack
Each player's attack that the opponent's Pokémon is immune to based on their type or Levitate	-10 per attack
Every turn that passes	-10 per turn
The amount of missing HP that the player's Pokémon have at the end of the battle	The HP of all of the player's Pokémon is added up. Then, the percentage of HP missing is converted to points and subtracted. For example, if all Pokémon have a combined remaining HP of 70%, then 30 points will be subtracted.
Each of player's Pokémon that faints	-80 per Pokémon

Resources:

turskain's damage calculator, with the possible opposing movesets built in

Credits & sources

The Battle Maison records topic on Smogon, for the collected resources of many players (notably Team Rocket Elite / R Inanimate, NoCheese, and turskain) including Pokémon movesets, Trainer information, and all the collective team-building knowledge.
Bulbapedia, for the Trainers used by this challenge, the item rewards, and scoring details.