Optimistically, it sounds like Papi's recent soreness could simply be something similar to what WMB felt last week.
From Rob Bradford:
There were some initial concerns after Ortiz postponed his scheduled baserunning exercises Sunday due to soreness. But the designated hitter was told by the team’s medical staff that the discomfort was natural, and part of the recovery process.
“To be honest with you, I did it all today and nothing gave me a hard time, which is fine,” he said. “Dan [Dyrek], our therapist, he tells me the soreness I’m getting is from things that are starting to break down, things that weren’t functioning because I wasn’t running for like six months. It’s like when you go to the gym the first time, the next day you’re going to be sore all over the place because you haven’t been working out, so that’s pretty much what happens to injuries in your shoulders, arms, knees. Once you start functioning and do all the activities you’re supposed to, you’re definitely going to get sore and you have to get used to it. Hopefully, that’s the case. I think I ran today better than I normally do.”