Unlike basketball, even football, having the best player in baseball can mean much less than we tend to realize.
We think it matters, except when it doesn't. There was a saying: as Mantle goes, so go the Yankees. The thinking was: the Yankees won because they had Mickey Mantle. Then why didn't the Giants win more when they had Willie Mays during the same years?
The Angels have Mike Trout but are not likely to win much in 2016. The Nationals have Bryce Harper, maybe the closest to Trout. The Nationals will probably win more than the Angels but will they win enough for Harper to be considered the most significant reason?
In the NBA add or subtract LeBron James from the starting five and that team changes dramatically. Even in the NFL, add or subtract a top quarterback and a team's playoff chances have a huge shift.
If you add or subtract Trout or Harper, the impact rests on a lot of stuff, especially the starting pitching. A team having both a player and pitcher who are at or near the top may still not be enough. In 1957 the Milwaukee Braves had MVP Hank Aaron and Cy Young winner Warren Spahn; those Braves beat the Yankees in the World Series. In 2011 Detroit Tiger Justin Verlander won both the MVP and Cy Young awards. Oops. And the Tigers also had Miguel Cabrera since 2008 and he was MVP in 2012 and 2013. Wow, that's quite a one two punch. The Tigers in those years:
2011: 95-67 first; Lost ALCS (4-2)
2012: 88-74 first; Lost WS (4-0)
2013: 93-69 first; Lost ALCS (4-2)
2014: 90-72 first; Lost LDS (3-0)
Despite not winning the championship that was quite a four year run by the Tigers. In 2016 Cabrera will be playing in his age 33 season so his impact will be diminishing each season as he ages.
But both Trout and Harper are in their prime, entering season ages 24 and 23 respectively. Their only downside is that each will be paid much more in each succeeding season for the foreseeable future. That means that less money will be available for other quality players and pitchers. So far their teams did not take advantage of their extreme value by being top players at very low cost. They cannot improve much, only cost more.
Mantle was an MVP caliber player in his second season and Mays actually won the MVP in his second season. In each of those second seasons their teams won the World Series. Mantle's Yankee teams continued to succeed but the Giant teams of Mays did not, although through no fault of his own.
In his four full seasons Trout has these MVP finishes: 2, 2, 1, 2. But his Angels qualified for the tournament only in 2014 when he was MVP: Trout had one hit, a homer, and the Royals swept the Angels in the first round 3-0.
In his first four seasons Harper won the MVP in 2015 but had no significant votes in any of the previous three. His Nationals qualified for the tournament in 2012 and 2014 but lost in round one both times. In 2012 against the Cardinals Harper had only three hits in five games: double, triple, home run; OPS .522. In 2014 in four games against the Giants Harper went wild: double, three homers, OPS 1.251.
In the 1962 World Series between the New York Yankees and San Francisco Giants, the Yankees won 4-3. It pitted Mantle, who won his third MVP, against Mays, who should have won the NL MVP. They were at the peek of their powers, the kings of their leagues. Both sucked in the World Series:
Mantle: OPS .401
Mays: OPS .597
In baseball the best player can be marginalized ... or suck.