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The St. Louis Cardinals Lead the NL Central Despite Unlucky Run Distribution

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After beating the Chicago Cubs yesterday afternoon at the now LED-infested Wrigley Field, the St. Louis Cardinals find themselves with an 12-7 record, which is good for a .627 win percentage. Without Chris Carpenter having thrown a single pitch, with Allen Craig having not played a single Major League game, with Lance Berkman having taken a mere 30 plate appearances (PA), and with Jon Jay having missed the last six games due to a separated shoulder, the Cardinals have a .627 win percentage. The thing is, their win percentage should be better.

The Cardinals have shown themselves to be a balanced team: good starting pitching and a good offense. Even with their Berk-less and Jay-less lineup failing to score many runs against the Pirates and Cubs, St. Louis is second in the National League with 91 runs scored. Their pitching staff has posted a 2.65 cumulative ERA that ranks third and a 3.16 FIP that ranks second in the NL. Because of their well-rounded offense and solid pitching, the Cards' +38 run differential is head and shoulders above the rest of the NL. (Atlanta has the second-best run differential at +23.)

Despite the Cardinals' gaudy run differential, they have only the third-best record in the NL. The Nationals, with their +20 run differential, are 14-4, which is good for a .778 win percentage. The Dodgers have league's second-best record at 13-6 (.684 win percentage) with a +12 run differential.

What's to blame for the Cards' record not matching their run differential? Run distribution.

The Cardinals have won a rather large share of their early games by a wide margin. Five of their twelve wins have been by five or more runs. On the flip side of the won/lost column, there is a much different story. The Cards have lost quite a few close games. Three of their seven losses have come by one run. Given these outcomes, it's no surprise that their Pythagorean record is better than their actual results.

Pythagorean record is a Bill James invention that attempts to relate how many runs a club has scored and allowed to its win total. Baseball Prospectus has a wonderful page that contains expected wins and losses as well as adjusted standings. It has taken the James idea of Pythagorean record to the next level (er, actually, the next two levels). Baseball Prospectus has First Order, Second Order, and Third Order win percentages.

The First Order record is based on a Pythagorean record formula "based on actual runs scored and runs allowed to determine how often a team "should have" won based on their run differential." Second Order record is based on a Pythagorean record formula that "substitutes projected runs scored for actual runs scored. This calculates, based on a team's underlying stats, how many runs they "should have" scored and uses that in the Pythagenpat method." Third Order record is "based on underlying statistics and adjusted for quality of opponents."

The following chart contains the Pythagorean records for the Cardinals as posted on Baseball Prospectus for the various orders.



1st Order

2nd Order

3rd Order






Win Pct.





As difficult as it is to believe, no matter which Pythagorean formula one uses, the Cardinals have been unlucky in terms of run distribution. As the season progresses, hopefully their luck changes for the better.

Writer's Note: I apologize. For some reason, my table wasn't publishing, but the problem has been corrected.