Statistics only lie when they are either inaccurate,not a valid comparison or meaningless but presented as being insightful.
Source of the following:
Head-to-Head Records
http://www.baseball-reference.com/games/head2head.shtml
and
Major league Standings-Google
https://www.google.com/search?q=mlb+standings&ie=utf-8&oe=utf-8
KC versus NL Central
Cubs season.579 1W KC 1W total 2g 1postponed
Reds season .413 0W KC 4W total 4g
Brewers season .417 0W KC 4W total 4g
Pirates season .611 1W KC 2W total 3g
Cards season .646 4W KC 2W total 6g
NL Central 6 Wins Royals 13 Wins/19 Games =.684 win pct
Obviously the bottom of the NL Central Barrel isn't even close to KC.(KC 8 and 0)
Cards vs AL Central
Royals season .614 2W Cards 4W total 6g
Twins season .512 2W Cards 2W total 4g
W Sox season .476 2W Cards 2W total 4g
Indians season.476 1W Cards 2W total 3g
Tigers season .472 1W Cards 2W total 3g
AL Central 8 Wins Cards 12 Wins/20 games =.600
Tigers and the Padres are the ONLY team that the Cardinals have a losing record against.
Royals have losing record against Boston,Houston,Yankees,Cards,Rangers,Blue Jays.
I believe the numbers speak for themselves
So you are correct with the .684 vs .600
As far as you counting the correct number of games.......
Willis......please 
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