Is it because the players can see the pitch better when righties hit?
The home team dugout is on whatever side the home team wants it to be. At Dodger Stadium, the Dodgers sit on the third base side.
Usually when the stadium is built, the architects ask which side the home team wants to sit on.
There are a whole bunch of factors that may enter into this: the sun, the position of the bullpens, or whether or not a certain side has better bathrooms.
There is absolutely no hard and fast rule on this.
However, hijacking this thread, why is it in college basketball that the offensive teams shoot at the basket on the same side as their bench in the second half, but in the NBA, it’s always the reverse (i.e. you play on defense near your own bench in the second half.)
At B.O.B., the Diamondbacks dugout is on the third base line. It’s one of the few parks with home plate pointing directly south the home dugout is nearly never in the sun.
Why? Are the two sides constructed any differently? I would assume the only differences are decorational. Unless the Away dugout is purposely built with some sinister motive in mind.
The dugouts are usually the same, it’s just the amenities are nicer.
At Candlestick Park, the visitors’ dugout wasn’t connected to the locker room. The players had to walk across the field to get to it. It also meant that it was a real pain to use the john during a game.
Such constructions are frowned upon now.