Off memory, only 5 clubs with the best regular season record have won the World Series in the Wild Card era (since '95).
1998 Yankees
2007 Red Sox
2009 Yankees
2013 Red Sox
2016 Cubs
Losing in the WS were
1995 Indians
1999 Braves
2003 Yankees
2004 Cardinals
2013 Cardinals
11 Teams lost in the LDS, don't have me guess, what the heck, Cardinals, Angels, Nats, Phillies, Mariners, Angels again, Yankees, Yankees again, A's, Braves, Giants and the Indians I'm pretty sure in 96.