After catching the ball on strike 3, you will often see the catcher throw the ball away, like into the stands or something (from the TV camera’s perspective). This is not just a light, underhanded toss. To whom is he really throwing the ball???
Someone in the dugout, I’d guess.
The third baseman if there is noone on base.
The throw goes “around the horn” - the catcher throws it to the third baseman, who throws it to the second baseman, who throws it to the shortstop, who throws it to the pitcher. It’s a ritual that keeps the infielders involved in the game and helps keep their arms warm. For some reason the throw never goes to the first baseman. Of course, they don’t do this when there are runners on base or when the strikeout is the third out of a half-inning.
If it’s the 1st or 2nd out, he’ll toss it around the horn. If it’s the 3rd out, he’ll either toss it into the stands for a lucky fan, or just toss it towards the mound for the other team to use as they warm up.
That is my personal preference, as well, but I’ve seen it go from 3rd to short to 2nd to 1st. I consider that the lazy man’s around the horn.
My assumption has long been that no one really cares about keeping the first baseman’s arm warm, as his throwing arm is rarely a factor in the game. Baseball traditions are odd. 
Interesting! Thanks!
Doesn’t it end up back with third baseman, who then throws to the pitcher? I thought it was always the third baseman that is supposed to give it to the pitcher. As a first basemen as a kid/teen, I never liked this. Let me get involved!
Come on, how far are you going to throw it? 20 feet to the pitcher covering?
Always thought it was bad luck for anyone other than 3B to get it back to the pitcher after an strikeout around the horn (2-5-4-6-5-1) or last throw of warmup around the horn (2-4or6-6or4-5-1).
Have occasionally seen a catcher start it at first after a strikeout, thus keeping the 1B from pouting and kicking rocks (2-3-6-4-5-1).
Oh yeah, you’re right. It goes back to the third baseman, then to the pitcher.