Just curious as to whether there have been any examples of this. I would imagine it would be possible if someone was doing decently well in the first half and then came on like gangbusters in the second.
I’m also a bit curious about players winning the MVP without being elected as a starter. I know there have been examples of this (I’m almost certain that Don Mattingly was not elected the year he won the MVP - if ever) but I’m curious as to how common this is.
Well, all the pre-1933 MVPs weren’t on the All-Star team… 
Zev Steinhardt
If you’re talking about starters, one example is Fred Lynn in 1975. He won both MVP and Rookie of the Year, but did not start in the AS game.
The method of fan voting has a flaw, in that it’s skewed toward better-known players. In Lynn’s case, he was unknown (and probably wasn’t even on the official ballot), so the fans didn’t vote for him.
I don’t think it likely that anyone missed the AS game entirely (unless they skipped it due to injury) and won MVP, since most of the roster is made up by the manager, who can put on anyone who’s of MVP caliber.
Just last year Barry Zito of the Oakland A’s won the Cy Young but was not on the All Star team.
Kirk Gibson won the MVP in 1988 and never made the All-star Game in his entire career.
Chipper Jones - 1999 MVP but not an All-Star.
I might spend time poring through the awards for a comprehensive list, but I bet it is more widely common than one might initially think. A person could have a pedestrian first 70 games. They would have decent stats, but nothing outstanding. A 90 game run of excellence could follow, moving them from decent year to stud year. The majority of the great play would happen after the voting was essentially over.
That is sort of what happened with Chipper. His stats were pretty good, but he really made his hay in the 2nd half of the season. He did a good job of sewing up the award with some steallar series and homers against the Mets who were hot on the Braves heels at the time.
A different example would be Rick Sutcliffe in 1984. He won the National League Cy Young with a 16-1 record but did not make the All-Star team. Why not? He started the season with Cleveland, going 4-5 pre-trade.
He wasn’t close to an AL All-Star and his NL stats wouldn’t have been remotely good enough at that point either, so a mid-season trade could also result in award but no All-Star.
Today’s cnnsi.com listed several players who seemed to have been unjustly left off the All-Star team, and three of them went on to win MVP awards:
1935 - Hank Greenberg
1956 - Don Newcombe
1999 - Chipper Jones
I came across another example: Robin Yount in 1989.
I would quibble with this. Gibson was named to the All-Star team a couple of times, including 1988, but he elected not to participate.