As a Varsity baseball head coach for a local High School team, I use 2 visual aides to determine whether to keep a pitch in in a close game and my pitcher has a shutout:
1) Location of pitches. If he is starting to leave his ball up in the zone consistantly, that's a clear cut indicater that he is tiring.
2) Are the opposing hitters starting to lock in on his stuff. If the other team is smoking the ball hitter after hitter whether we get outs or not, the pitcher is losing his effectiveness.
The easiest way is pitch count and knowing how far a pitcher can usually go before his legs start to go. It's not the arm that goes first, it's the legs. Soon after the legs go, the arm won't be far behind.
It's not as easy as asking the pitcher if he is getting tired. 90% of the time, they will say they are fine even though they know they are lying.
I think the same general principles go into the MLB pitchers.