How many home games are there in an MLS season?

(depending on the federation in question)

League:

Every team plays against all other teams twice (once at home, once away).

Cup:

A random draw is made, 50-50 chances of getting a home or away game. Semi-finals are two-legged (one home game, one away). Final is on neutral ground.

"League Cups" (tournaments):

A pre-tournament knock-out can be required to level the number of teams, again with a random draw. Then a group stage, similar to a league. Then a knock-out stage, similar to a cup.

So, if there are 16 teams in a league, each team has 15 home games for the league. If there are 128 teams in a cup, there could be anywhere between 1 and 5 home cup games.