Major League Baseball could obviously never have a team go undefeated (actually, I found out it did happen in 1869, so from now on let's just go with the live-ball era forward) because of the large amount of games played each season. The best in recent history were the '01 Mariners, who won close to 75% of their games. So on any given day the worst team can, and fairly often does, beat the best team.
To me it seems like the closest a team could ever get to "undefeated" would be to win (or at least tie?) every series in the season. For example, taking 2 out of 3 games against the Red Sox, then 3 out of 4 against the Orioles, and so on. In this specific case total wins isn't relevant.
As an example I just quickly went through the wins-losses for the 2015 Cardinals. They played in 51 different series. Of those they won 32, lost 15, and tied 4. Depending on how you look at it their percentage of series won would be .638, or their percentage of series not lost (wins + ties) would be .706. In either case that percentage is not too different than the winning percentage of total games .617 (100 wins). So I'm not too surprised, because this is the type of data I would guess is pretty normal.
What I'm curious to know is about anomalies such as a team winning ~60% of their games while managing to win 90%, or more, of the series played by remaining consistent. The thought of tie-breakers sparked this curiosity.
I'm calling this "series-wins" for a lack of better term. Is there an actual statistic for this? Or better yet is there a resource that keeps track of this? I have tried searching, but can't seem to find anything.