OK -- let's see if I can work this out...

With 88 wins, the most the Cardinals can lose is 74 games. Therefore, when any team reaches 75 losses, they are eliminated.

The following teams still have a chance to catch the Cardinals:

Atlanta (79-59)
Philadelphia (73-64)
Florida (72-65)
Washington (72-66)
New York (70-67)
Houston (72-64)
Milwaukee (67-70)
Chicago (66-71)
Cincinnati (63-73)
San Diego (68-68)
San Francisco (62-73)

Next, we'll assume that each teams wins every game against teams not listed (StL, Pit, Ari, LA, Col); that's the worst case for the Cardinals. Thus, here are the records:

Atlanta (82-59)
Philadelphia (73-64)
Florida (72-65)
Washington (72-66)
New York (78-67)
Houston (78-64)
Milwaukee (76-70)
Chicago (74-71)
Cincinnati (76-73)
San Diego (84-68)
San Francisco (75-73)

For the record, that gives the Cardinals a record of 88-71 (with 3 games against Pittsburgh not included).

Question 1: Can 2 Central division teams pass the Cardinals?

Answer: For that to be possible, Houston would have to win 11 more games (against listed teams), Milwaukee needs 13 wins, Chicago 15, and Cincinnati 13. Looked at another way, Houston could lose only 9 games, Milwaukee 3, Chicago 2, and Cincinnati 0. Because of games between the teams, the only combination of teams that can pass the Cardinals are (Houston & Cincinnati), (Milwaukee & Chicago), (Houston & Chicago), and (Houston & Milwaukee).

In the case of Houston & Cincinnati, the Cardinals need 1 win to tie Cincinnati, 2 to eliminate them. For the Milwaukee & Chicago comination, the Cardinals need 2 wins to tie the worse team, 3 to eliminate. For Houston & Chicago, 3 to tie and 4 to eliminate. And for Houston & Milwaukee, 4 to tie and 5 to eliminate.

Yeah, I know -- 3 of those 4 cases are elimination numbers for those teams anyway [Milwaukee 4, Chicago 3, Cincinnati 1].

Question 2: Can 2 West teams pass the Cardinals?

Answer 2: No. Since San Diego and San Francisco have 7 games between them, the best record possible for the 2nd place team is 88-74, which is the worst possible record for the Cardinals.

Question 3: Can 2 East teams (plus Houston) pass the Cardinals?

Answer 3: The Mets have 6 losses available, Washington has 7 losses to give, Florida 8 losses, Philadelphia 9 losses, and Atlanta 14. Remember that Houston has 9 losses available, as well.

Houston does not have enough games against the East to affect these calculations. Regardless of the pair of East teams, Houston will also be able to pass the Cardinals.

Based on the number of games remaining between East teams, the Cards need the following number of wins to eliminate one of the combination:
Was & NYM: 4 tie, 5 elim
Fla & NYM: 6 tie, 7 elim
Phi & NYM: 7 tie, 8 elim
Atl & NYM: 7 tie, 8 elim
Fla & Was: 5 tie, 6 elim
Phi & Was: 7 tie, 8 elim
Atl & Was: 8 tie, 9 elim
Phi & Fla: 6 tie, 7 elim
Atl & Fla: 9 tie, 10 elim
Atl & Phi: 9 tie, 10 elim

Question 4: What will it take for the Cardinals to clinch the division?

Answer 4: We already know 10 wins ties Houston, and 11 eliminates them.

I'll update these numbers as things change. Hope it makes sense.

Wow. Yeah, it makes sense, although I'm surprised that all the competitors beating up on each other has that strong of an effect this soon.

Boy, is the West bad.

Here's the RIOT analysis. It says the Cards need 8 wins to clinch a playoff spot and 10 wins to clinch the Central division.

http://riot.ieor.berkeley.edu/~baseball/national_league.html

Very cool Rob and Nick -- gotta love it when "life' boils down to set of interdependent word problems. I look forward to the updates.

TSF

Martin -- that's basically what I was trying to get at. I didn't know the numbers were out there.

Much props for the old-school Astros and Brewers logos on that site.