Baseball's back in 2020, but which Olympic sports could baseball players dominate right now?

Unless you live in an underground bunker or an Obi-Wan-style cave, you know that the Olympics are currently going on in Brazil. As some of the world's greatest athletes compete in a variety of tantalizing competitions, the men of Major League Baseball continue to battle through the dog days of summer.
Earlier this month, the IOC announced that baseball will return to the Olympics in Tokyo in 2020 after a 12-year absence. As excited as we are to see the Mike Trouts and Efren Navarros of the world compete on the diamond in four years, we're more curious about which current Olympic events would best suit the MLB stars of today.
In a baseball-less Olympic landscape, which sports could these athletes excel at?
Archery: Fernando Rodney
Who else? The veteran reliever known for his post-save celebrations, Rodney is the obvious candidate for this competition. The only question is this -- does Rodney actually know how to use a bow and arrow?
His trademark celebration doesn't exactly mirror what we've seen in Rio this summer from some of the top competitors, but you'd have to assume the eccentric closer drew his inspiration from somewhere. The other issue here is that he always seems to be aiming his arrow upward -- far higher than where the targets are set in competition. We're confident Rodney could correct his aim enough to compete for a medal the next Olympic cycle. Wait, hold on a second ...

Weightlifting: Miguel Cabrera and Jose Altuve
Venezuela has never won a gold medal in Olympic weightlifting or Olympic getting weight lifted. This clip of Cabrera and Altuve shows that the South American country might have a future in both of those very real events. Miggy's form leaves much to be desired (too much strain on the back), but the ease with which he lifts another human being above his head is encouraging.

Though the undersized second baseman packs a punch, you have to think Altuve would work better as the lifted and not the lifter. We already measure height in Altuves, so why not weight?
Diving:Yasiel Puig
After winning the 2013 NL West, the Dodgers took a little swim in the D-backs' pool. This ruffled some feathers in Arizona, but we were blessed with this outstanding clip of the one and only Yasiel Puig belly-flopping into the swimming pool:

Now, usually the goal is to minimize splash, but who are we to criticize a legend of the diving world like Puig? Extremely impressive form on the bellyflop as well -- doesn't bend his arms or move his head. Just takes it full force in the dome. Who knows, a flop like that might get Puig some Wendy Peffercorn smooches.
Dressage: Yoenis Céspedes and Noah Syndergaard
Duh:

Haters gonna say the Mets tandem is too big to ride a horse at the Olympic level, but to that we say: poppycock (which is something that must be said in dressage all the time). 
Synchronized swimming:Elvis Andrus and Adrián Beltré (also Rougned Odor)
These two forever:

Odor arguably even more impressive: 

Andrus and Beltre have a long-documented history of performing baseball tasks in unison. They have clearly developed a level of chemistry necessary to compete at the highest level of Doing Things At The Same Time. While Andrus and Beltre are both impressive individual fielders, these two seem to excel in tandem. This makes synchronized swimming or diving the perfect event for these guys. One can only imagine what other levels of synchronization they could reach with further practice outside a live MLB game.
Gymnastics: Matt Carpenter  
If the Cardinals All-Star can pull off this advanced tumble with a rather enormous catcher in the way, think of the complicated floor routines he could attempt with no obstacles and more training:

Should he compete in the Olympics, he'd likely have to add some more complex elements to his routine than merely a somersault. On the plus side, any athlete that has to deal with no-nonsense umpires on a daily basis should be able to handle the stern intensity of international gymnastics judges.
Javelin throw: José Bautista
Here's a realm where Bautista can throw a stick really far and not make anybody mad while doing so. But in order for him to really get a good javelin throw, Bautista is gonna need to crush a wiffleball with the javelin first. Joey Bats is no more. Say hello to Joey Javs.