Politoed, Ferrothorn, Heliolisk, Vaporeon, Tentacruel, Volcarona
Okay, I didn't play competitively last generation, so I don't know exactly how powerful Rain teams used to be, but this team seems to be pretty powerful. It's also tremendously fun to play, to me. I'm new to competitive battling, so discovering synergies like HydrationRest made me giggle a little bit. That being said, if Volcarona is fainted, this team does not like Rain to end, and it's pitifully weak in the sun.
The Team:

Politoed (F) @ Damp Rock
Ability: Drizzle
EVs: 252 Def / 252 HP / 4 SAtk
Bold Nature
- - Scald
- - Toxic
- - Protect
- - Encore
Politoed is my lead. She is the most crucial member of the team. Switching out in time to save her last HP just to suicide one more rain dance is critical. Normally, she'll drizzle three times in a game. Encore is perfect for ruining setups and switching in with my own hazards/setups. Toxic comes in handy around mid-game after the first Rain wears out and the opponent's been made aware of Encore. Scald picks off weakened mons and attempts to burn as a last ditch effort.
Cons: She's a bit of a do-nothing. If I encore a move that deals a lot of damage, switching can be tricky. I think this will be less of a problem when I get a sense of which pokemon she outspeeds, but there were a couple times I hit Protect on a setup move and then Encored the sweeping move. Also, after Encore/Protect/Switching, there isn't a lot of time to set up. My original solution, before I tried Politoed, was Prankster Raindance Klefki, but it often died before or as it set up Rain Dance.

Ferrothorn (M) @ Rocky Helmet
Ability: Iron Barbs
EVs: 252 Def / 252 HP / 4 Atk
Relaxed Nature
IVs: 0 Spd
- - Leech Seed
- - Spikes
- - Stealth Rock
- - Gyro Ball
Not much to say about Ferrothorn. Switching it in on a physical attacker and setting up Stealth Rock is mainly what I use this set for. SR and one layer of Spikes is my realistic goal before I either Leech Seed and switch or kill with Gyro Ball. Switching out of Ferrothorn is great when they switch in a fire type to specially take it out, considering the rest of my team douses most fires very reliably.
Cons: Slow. I'm not used to running slow setters, even though he's working wonderfully for me. Also, unexpected fire attacks suck when they predict the switch. I'm not yet sure of the pros and cons vs Gyro Ball and Power Whip, and I almost want to run Leftovers instead of Rocky Helmet to improve longevity.

Heliolisk (F) @ Choice Specs
Ability: Dry Skin
EVs: 252 Spd / 252 SAtk / 4 HP
Timid Nature
- - Thunder
- - Volt Switch
- - Dark Pulse
- - Focus Blast
Heliolisk slays any opposing water types with Volt Switch/Thunder. It loves switching in for Volcarona when it's likely to take water damage, then Volt Switching right back out.
Cons: Heliolisk is fragile. It can't take hits nearly as well as the rest of my team, which makes switching him around very difficult. And this team switches A LOT. It also runs into the problem of being choice locked on Thunder vs a ground type, and a lot of my team doesn't like to switch into Earthquake.

Vaporeon (F) @ Leftovers
Ability: Hydration
EVs: 252 Def / 252 HP / 4 SAtk
Bold Nature
- - Scald
- - Ice Beam
- - Rest
- - Rain Dance
Vaporeon is my rain WALL. Her bulk allows her to take a hit while setting up Rain Dance and then Rest to full HP, often as the opponent switches out. Scald as her main attack is great. She'll survive quite a few hits, so eventually something is going to get burned. Ice Beam takes out dragon types and grass types, but is rarely used before Scald burns them. Nothing really scares me when Vaporeon's getting rained on. Toxic? Nope. Burn? Lol, nope. My only regrets are that she's a little on the weak hitting side, and she has to sacrifice a move for Rain Dance.

Tentacruel (M) @ Black Sludge
Ability: Rain Dish
EVs: 240 Def / 252 HP / 16 Spd
Bold Nature
- - Scald
- - Sludge Bomb
- - Rapid Spin
- - Toxic Spikes
I've played at least two Pokemon games from each generation and I've never given Tentacruel a second look until I built this team. Turns out Water/Poison is a great typing for a defensive pokemon. Rapid Spin is necessary to get rid of Stealth Rock for Volcarona, and its poison typing takes out Toxic Spikes, which is great. I like to wait to lay down my own Tox Spikes until I've Scalded or KOed most physical attackers, which is fine because Tentacruel likes the late game, and is one of the few pokemon I don't mind being dry. I'm trying out Sludge Bomb to hit Fairies and possibly to surprise grass type switch ins.
Cons: Like Politoed, he can be a bit of a do-nothing. He absorbs hits very well, but he can't hit back very hard. Despite that, I can't see the team without him. Rain Dish is somewhat underwhelming as well. I'm thinking of changing to Liquid Ooze, just as one more response to Leech Seed users.

Volcarona (F) @ Life Orb
Ability: Flame Body
EVs: 252 Spd / 252 SAtk / 4 Def
Timid Nature
- - Quiver Dance
- - Fiery Dance
- - Hurricane
- - Roost
It's not really news, but Volcarona is a great fire type for rain teams. She can switch in on a lot of things to set up Quiver Dance, and then Hurricane till it stops raining. Then, Fiery Dance comes out. Roost is to heal after setting up/SR/Life Orb damage puts her at risk of getting KOed.
Cons: After rain, Fiery Dance is her only reliable attack due to Hurricane's accuracy. She's also one of the more fragile pokemon on my team, as I opted for Speed EVs over defensive ones.
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Overall, I think surprise is the biggest factor in my successes. On non-rain teams, a lot of my pokemon don't hit particularly hard, so getting 2HKOed by a Politoed isn't something on their radar. Leftovers is a problem to face, though. A common scenario is not being able to KO a pokemon without dying, but also not being able to switch or they'll heal back into the green. I'd like a physical attacker somewhere on my team. The last time I won vs Blissey was because I happened to Leech Seed it after it ran out of teammates. I'd love suggestions for pokemon that would compliment the team and be able to attack physically. I'm a bit wary of Swift Swim, because most users are out sped when rain stops. I've also considered Toxicroak, but that would just be one more ground weakness, as would any of the Steel types I've considered. If there's a single one-for-one pokemon swap that will fix this team, it's evaded me, which is why I'm seeking advice. Thanks for reading all this, I'm looking forward to your comments. ^^