You walk into the lounge after a hard day of scavenging in the wrecks. Despite your exhaustion, you know that you can make new friends with whom you can share your pain because they already know your name.
After you finish conversing about your day, you crash in your hotel room and grab an interesting book from your nightstand. You remember hearing that the hotel staff trusted you to keep this specific book safe because they're aware of your experience handling objects of greater importance.
The next day, you go to the gym to work out before you journey back into the wrecks. The staff at the gym knows your preferences after watching your activity there, and tailor a workout to fit them.
The thing these three events have in common is that people know and respect you, and give you opportunities that anyone less popular wouldn't have, thus helping you get more out of your training sessions. The gist of that? Having a better reputation could make your training more effective, and having a worse reputation could make them less so. I was thinking that reputation bonuses to market prices could be applied to stat increases while training them to make the people's opinion of you and your abilities matter in your training.