Using ZiPS, some career stats and some wild guesses, I'll try to determine whether Jim Tracy was right to face Pujols in the ninth inning. It gets messy, and I fully recognize what they same about what happens when I assume. The executive summary is that pitching to Pujols gave the Pirates a ~20% better chance of taking the game to the 10th, roughly 55% versus 35%. Tangotiger found something similar for Bonds in a tie game with runners on first and second and one out.

Again, there are big assumptions here. I need Roberto Hernandez to be an average pitcher, for Juan Encarnacion to be better than he's looked most of the month (and for that matter, not to be a 900-OPS hitter with the bases loaded, as his career splits have been to this point), for Scott Spiezio to be horrid, for guesses about baserunning to be reasonable, no balks, no wild pitches, no passed balls, no stolen bases, yadda yadda yadda. The difference I'm computing is pretty substantial though. Somebody let me know if I got something wrong.

Here's the dirty work:

Starting off, here's ZiPS again:

Name                 AB    R    H  2B  3B  HR   BB    K  AVG   OBP   SLG 
Pujols              603  134  203  42   2  48   98   61 .337  .434  .652
Encarnacion         536   70  152  35   3  16   43   95 .284  .342  .450
Spiezio#            392   44   93  20   3  10   45   56 .237  .318  .380

(By the way, if you use ZiPS, you should probably send a thank you to Dan Szymborski.)

Here's what happens when you walk Pujols:

Tie Game, Bases Loaded, One Out, Bottom of 9th
Encarnacion
- Reaches base = 34.2% (ignores reach on error, worth roughly +10 points of OBP)
- GIDP = 9.2% (96 GDPs in 1045 career at-bats with runners on <2 outs, ignores other DPs)
- Sac fly = 12.7% (32 in 251 AB + BB + SF with R3<2O)
- Strikeout = 17.7%
- GB Productive Out = 7.1% (WAG based on G/F ratio)
- GB Force at Home = 7.1% (WAG based on G/F ratio)
- FB Non-Productive Out = 12.0% (WAG based on G/F ratio)
Meaning:
- 54.0% chance game ends there
- 9.2% chance inning ends there
- 36.8% chance it gets passed down to Spiezio

Spiezio
- Reaches base = 31.8%
- Doesn't reach base = 68.2%

In total: Chances of Cardinals winning in 9th are .540 + (.368*.318) = 65.7%. That a productive out from Encarnacion could end the game is huge if you walk Pujols.

This is what Jim Tracy chose instead:

Pujols
- Singles 18.4%
--- Eckstein scores 40% of time (WAG) = 7.4%
--- Eckstein stops at 3rd 40% of time (WAG) = 7.4%
--- Eckstein thrown out 20% of time, runners move up (WAG) = 3.6%
- Doubles, Triples, Homers = 15.3% (damn)
- GIDP = 10.3%
- Strikeout = 10.1%
- Productive out = 15.0% (WAG)
- Nonproductive other out 30.9%
Meaning:
- 22.7% chance game ends there
- 10.3% chance inning ends there
- 7.4% chance bases loaded (same as walking Pujols)
- 18.6% chance of lead runner on third, two outs
- 41.0% chance of lead runner on second, two outs

Encarnacion
Lead runner on third, two outs
- Hit = 26.3%
- Walk or HBP = 7.9%
- Ordinary Out = 65.8%
Meaning:
- 4.9% overall chance of game ending here
- 1.5% overall chance of bases loaded, two outs for Spiezio
- 12.2% overall chance inning ends here
Lead runner on second, two outs
- Singles 16.9%
--- Eckstein scores 80% of time (WAG) = 13.5%
--- Eckstein stops at 3rd 10% of time (WAG) = 1.7%
--- Eckstein thrown out 10% of time (WAG) = 1.7%
- Doubles, Triples or Homers = 9.4%
- Walk or HBP = 7.9%
- Ordinary Out = 65.8%
Meaning:
- 9.4% overall chance of game ending here
- 3.9% overall chance of bases loaded, two outs for Spiezio
- 27.7% overall chance inning ends here

Spiezio
- Reaches base = 31.8%
- Doesn't reach base = 68.2%
Meaning:
- 1.7% overall chance of game ending here
- 3.7% overall chance inning ends here

Whew!
- Total Good Stuff = .227 + .049 + .094 + .017 + .074*.657 = 43.6%
- Total Bad Stuff = .103 + .122 + .277+ .037 + .074*.343 = 56.4%