Learn Swedish: Båda lagen var trötta i förlängningen. - Both teams were tired in the extra time.

Båda means "both" and is the most common word for a pair. Grammatically, båda is followed by a definite plural noun, like båda lagen here. In contrast, the formal duals from this lesson, like vardera (each of two) or ingendera (neither of two), are usually followed by an indefinite singular noun (for example, vardera laget).

Why does lag become lagen for "the teams"? Shouldn't plural nouns usually end in -arna or -erna?

Lag (team) is an ett-word ending in a consonant. These nouns don't change in the indefinite plural (ett lag, två lag). To make them definite plural ("the teams"), you just add -en, giving us lagen. Be careful not to confuse this with en lag (a law), which becomes lagarna in the definite plural!

Could I use båda två instead of just båda in this sentence?

You wouldn't use it directly in front of the noun here. You say båda lagen, not båda två lagen. However, if you drop the noun because it is already understood from context, you could say båda två var trötta i förlängningen (both of them were tired in the extra time).