There are four teams from each league that make the playoffs. Each league is divided into three divisions. Each division winner gets an automatic bid to the playoffs. There is a fourth team from each league that makes the playoffs and this team is called the 'wildcard' team. The wildcard team is the team that has the best overall win loss record of those teams that did not win their division.
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162 and then playoffs
The MLB team that has gone undefeated in the playoffs were the 1976 Cincinatti Reds swept the Phillies 3-0 in the NLCS and then swept the Yankees 4-0.
2005 Padres, 82-80 (.506)
Through the 2008 season, the last season both the Cubs and White Sox were in the MLB playoffs was 1906. The White Sox defeated the Cubs, 4 games to 2, in the World Series. This is the only season both Chicago teams made the MLB playoffs in the same season.
.800 ... Myers had 4 hits in 5 at bats in the 2008 MLB playoffs (1 for 2 in the NLDS and 3 for 3 in the NLCS).