Every baseball free agent has played at least 6-7 years in the majors before their first HUGE contract (this is different from EVERY other sport). Thus, in all likelihood, they're either right at or past their primes right off the 'bat' of their new contract. Secondly, throwing a baseball overhand repeatdedly is the single-most unatural thing you could do for the human body. We were designed to throw underhand, not overhand... and not at 95mph 100 times a game. Pitchers arms are the most fragile body part in pro sports. Now, add the fact that they've already got 6-7 years worth of tread on them, and you see why they break down.
This. Most baseball players are already a little older once they finally bust into the majors, 23-26 years old. Then they are 7 years or so away from the payday. Most big free agent contracts come to players that are 30-33 years old already. Add to that that a 33 year old free agent top level pitcher already has a lot of innings under his belt, they often will break down.
Perhaps playing every 5th or so game puts more pressure on them to "overdo" it, resulting in injury. Maybe it's that when you are a starting pitcher, you pitch 100+pitches a game (or a closer who only pitches 10-20 but is trying to hit the century mark), while hitters only swing 20 times or so (of course, this ignores fielding for those that do). Or perhaps it's just that pitching is tougher on a body than hitting?
One thing I know for sure, it's not from their bodies breaking down due to overuse of illegal abusive and destructive chemicals taken to enhance, prolong, and speed recovery. Signed, <img src="http://photos.upi.com/story/w/319f78e974edfbdd361d8dda93e18639/Report_Clemens_received_drug_shipment.jpg" border="0" alt="" />