Things that break my stall team (Walrein + Hail):
1. Powerful Toxic spike absorbers
After spending 2 turns setting up toxic spikes, nothing is like watching a Toxicroak come in, swords dance on the switch, and start sucker-punching my sweepers, and using close combat on anything weak to it.
2. Momentum
When I'm fully set-up to stall, I can take Choice Banded Garchomp outrages and then outstall the Garchomp. However, if you get a guy setup that I cannot phaze out for whatever reason (OHKOs my phazer, you've weakened my phazer, etc. etc.), then my team is done for.
3. Friggen Taunt
Funny thing: so many pokemon can do the taunt / setup routine. Weavile can swords dance / taunt + sweep with double-stab Night Slash / Ice Punch. Infernape can Swords Dance or Nasty Plot and Taunt, as can Gliscor. Do I need to mention taunt gyarados?
Taunt stops healing attacks, status attacks, and... well... everything. And walls don't exactly hurt some of the bulky taunters like Gyarados that much.
4. Outstalling the stall
There are a few pokemon that outstall my team, but I think that is because every stall team has a weakness to a counter-stall. Clefable has much less defenses than my stall team, however the defenses are "good enough" to survive the hits from... everything, and sit around for the rest of the game.
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Things I noticed that may hurt other stall teams
1. Subsitute
All stall teams have a phazer. So don't sub unless you're ready to deal with the phazer in some sort of way. They get as bulky as Swampert and Hippowdon, and have many types like Skarm, Suicune and even Articuno gave me trouble once.
But sub up, and they can't toxic you, they can't status you, they can't do anything to you really. If you're bulky enough, they can't even break your sub.