"To answer this, I checked all postseason series -- actual series, not the Coin Flip Round -- dating to 2009, when league K/PA jumped above 18% for the first time. (All stats from Fangraphs; I did not tease out intentional walks from PAs.) Here is the series record of the team with the better offensive contact rate during the regular season:
2012: 7-0
2011: 5-2
2010: 4-3
2009: 6-1"