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Teching is a technique in the
Super Smash Bros. games, introduced first in
Super Smash Bros. Melee. When a character is launched into a wall, if they dodge quickly enough, they will not bounce off the wall, but be in the normal falling position. This can help prevent KOs in stages like
Shadow Moses Island. But if the knockback is extremely high, the character will not be able to jump until the knockback wears off, but the character will not
tumble. If the player uses their triple jump and rises over the wall, they will still be sent flying during this time. This can be prevented by
Air dodging right when they hit the wall."
Teching is basically bouncing off of a wall, ceiling, floor or ledge. It's a lifesaver for every smash player if they perform it. It also helps you be less predicable during matches.
A great example of teching is Ken vs. Bombsoldier JGT GrandFinals.
What Bombsoldier did was a wall tech. When Ken hit Bombsoldier with the Dolphin Slash, Bombsoldier immediately jumped right when he came in contact with the wall which caused him to jump in the opposite direction and gain vertical an horizontal direction. After that he used a his side-B to get the ledge. Had Bombsoldier not done that, he would have lost his stock. This is just one example on how teching works.
There are also different types of teching such as: Ledge Teching, Standard Tech, Rolling Tech and Ceiling Tech. You can find information on those techs and the usefullness of teching on this Wiki page
http://www.ssbwiki.com/tech