The 2014 Cardinals have not lit the world on fire offensively. They have been a (basically) league average offense by wRC+ and by runs scored they've been well below average. Let's look statistically at what they've gotten from their lineup so far, keeping in mind we're only talking offense.
1st hitter - .275/.370/.389/.759
2nd hitter - .259/.312/.393/.705
3rd hitter - .277/.375/.454/.829
4th hitter - .267/.306/.386/.693
5th hitter - 294/.350/.457/.808
6th hitter - .249/.304/.341/.645
7th hitter - .225/.279/.350/.630
8th hitter - .235/.301/.306/.608
9th hitter - .200/.269/.271/.539
Baseball Musings has a lineup analysis tool (http://www.baseballmusings.com/cgi-bin/LineupAnalysis.py) that you can use to see how many runs, historically, a team would score with a lineup that has the OBP and SLG listed above. That is not the best way to look at a lineup, necessarily, but it spits out a nice runs per game number at you. The 2014 Cardinals have actually scored 3.80 runs per game. Baseball Musings believes this lineup so far in the season should have scored 4.132 runs per game. The Cardinals have basically underperformed their potential runs scored by about 8.69% to this point. That would give them an additional 41-42 runs this year were they performing up to standard.
Instead of looking back, lets look forward. Here is my idea for what the Cardinals should do the remainder of the year to score the most possible runs. This may not be their best every day lineup due to defense, etc. but I won't be changing anyone's position or anything radical like that.
The Cardinals have been starting the following players each game, basically, for the last 25 games or so.
Catcher - AJP and Cruz alternating - .237/.299/.290/.589
First Base - Matt Adams* - .295/.328/.496/.823
Second Base - Kolten Wong** - .261/.289/.479/.767
Third Base - Matt Carpenter - .283/.377/.400/.777
Shortstop - Jhonny Peralta - .266/.339/.459/.798
Left Field - Matt Holliday*** - .259/.359/.456/.815
Center Field - Jon Jay - .313/.385/.407/.791
Right Field - Oscar Taveras**** - .247/.291/.321/.612
Pitcher - Pitchers - .200/.269/.271/.539
*Matt Adams' stats shown are from when he returned from injury until now.
**Kolten Wong's stats shown are from when he returned from injury until now.
***Matt Holliday's stats are shown from the beginning of July until now because he's historically been better in the second halves of seasons.
****Oscar Taveras' stats are shown from the time he got the starting role July 23rd until now (25 games played, 22 starts in that time).
While my preferred batting order using the 9 players above would be: Jay, Carpenter, Holliday, Adams, Peralta, Wong, Taveras, Pitcher, Catcher; using those numbers from above, Baseball Musings spits out an optimal lineup of:
Baseball Musings gives that lineup 4.609 runs per game, which would be an enormous improvement over the 3.80 runs per game they are currently scoring. In fact, 4.609 runs per game would be a 21.2% improvement and would place them squarely in 4th place in the entirety of Major League Baseball.
In any case, the Cardinals lineup as currently constructed should score loads more runs than their earlier season counterparts that stunk completely. Moving Jay to 2nd in the order this week was moving in a positive direction, as noted at Viva El Birdos earlier today.