Arod makes around 40,000$ per at bat and 120 to 140k per inning. I'm not sure exactly how to answer the why part but his past achievements hold great significance in why Rodriguez makes as much as he does. The Yankees signed him to one of the biggest contracts in Baseball history. The contract also includes incentives for breaking the home run record.
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You can do this in a few ways.
Career: 618 home runs, total salary:264,416,252
$427,858.01 per home run in his career.
You can do it season wise as well.
In 2010 A-Rod was paid $33 million and played in 137 games. That's equivalent to about $240,875.91 per game
In the year 2013, Alex Rodriguez, also known as A-Rod, made $29 million. He averaged 500 at bats which would average out to be about $58,000 each time he went up to bat.