On Tuesday, each NLDS game 3 featured an intentional walk that was followed by a big home run. The situations:

1. Trailing 3-1 in the bottom of the 5th, Brewers skipper Ron Roenicke ordered Shaun Marcum to walk Miguel Montero and pitch to Paul Goldschmidt with 2 out and 2 men in scoring position.
2. Tied 0-0 in the top of the 7th, Tony LaRussa had Jaime Garcia walk Carlos Ruiz to face Ben Francisco with 2 out and a man on 2nd.

I've ripped a number of IBBs throughout the season, but I don't think they're always bad. I liked walk #1; but not #2. My view of the essential differences:

• In #1, if you don't walk the guy, a single scores 2 runs. In #2, a single scores 1 run.

That's a pretty big difference right there.

• In #1, a single puts you down 4 runs with 4 batting innings left for each side. In #2, a single puts you down 1 with 3 at-bats left for you and 2 for your opponent.

Now, in scenario #2, the marginal value of the 1st run is big, because it moves you from tied to trailing. But is trailing by 1 such a bad spot when you have a 3-2 edge in remaining times up, and your next inning starts with the top of the order? That means a very good chance that Albert Pujols gets 2 more ABs; you just need to get 3 out of 11 men on, with no outs on the bases, to give Albert 2 cracks. (In the event, Albert did bat twice more ... as did Berkman, Freese, Molina and Theriot.)

An IBB is meant to lower your risk of letting in the runner(s) already on base, but it dramatically raises your risk of a big inning -- that is, letting in more than those runners. A man at bat can only score (right now) on a HR; a man put on 1st base with 2 out can score on a 2B, 3B or HR. Doubles and triples combined outnumbered HRs by more than 2 to 1 this year.

• In scenario #1, a big inning isn't much worse than just giving up a single. In #2, a big inning is far worse than allowing a single.

There's not much difference between being down 4 runs (scenario #1 with no walk and a single) and being down 5 or 6 runs (IBB blows up). But there's a huge difference between being down 1 run going into the bottom of the 7th, and being down by 2 or 3 runs.

• In #1, the difference in BA between the 2 hitters was on the order of 50 points. In #2, the difference was on the order of 35 points.

There are various ways to look at the BA issue -- this year, last 2 years, platoon splits, etc. Arbitrarily, I went with relevant platoon split for 2010-11 for the 3 veterans, and the straight 2011 figure for the rookie, who has only 177 PAs in the majors. Montero hit .300 off RHPs in 2010-11; Goldschmidt batted .250 this year; the difference is 50 pts. Ruiz hit .298 vs. LHPs in 2010-11, while Francisco hit .263; the difference is 35 pts. It's just an estimate, but I do think that there's a bigger BA gap between Montero and Goldschmidt against a RHP than between Ruiz and Francisco against a LHP. (And by the way, Francisco's career HR rate is almost twice that of Ruiz.)

• In #1, the walk gained a platoon advantage. In #2, both hitters were righties facing a lefty.

I could go into a lot more details (and I do, below; remember, nobody forced you to read it!), but these factors give an overview of why I think the walk to Montero was much more justifiable than the walk to Ruiz.

Another thing: I heard a brief interview in which LaRussa said (I'll paraphrase) that Ruiz has had many big hits against the Cardinals. I'm sure Tony doesn't use a WPA measuring stick, but ... I have no idea what he was referring to. Ruiz does have a walk-off, tie-breaking HR against the Cards. His other big WPA number came entirely from a 9th-inning, 2-out, game-tying error by the RF. His next-best WPA is .21, on 4 singles (1 RBI, 1 Run) in a 10-2 blowout. His next-best WPA is .10 (0 RBI or Runs), then .07 (ditto, and Ruiz's team lost both games). Really, it's that one HR, and little else of impact.

Ruiz does have good career numbers against the Cards overall -- .310 BA, .818 OPS, 2 HRs in 114 PAs. But other than the head-to-head matchup with Garcia, or a peculiar preference for hitting in Busch Stadium, how relevant can those numbers be? Was he more of a threat there because he got some hits off Jake Westbrook 3 months ago? As for the head-to-head, up to that point, Ruiz had a single and 4 walks in 9 PAs; Francisco was 1 for 9. It's not a meaningful sample.

Finally ... what about going after Ruiz with a fresh RH reliever? Garcia finished 7 innings in 10 of 32 starts this year; he went 6 IP or less 21 times. His pitch count in the game wasn't high -- Francisco hit the 88th pitch -- but Garcia's 2011 and career numbers in pitches #76-100 are notably worse than in prior segments, particularly in the HR rate.

The bullpen was rested; they had Monday off. And when did Tony ever meet a mid-inning pitching change he didn't like?

I don't think that any of this proves that LaRussa made a mistake. But I think it's a legitimate area of inquiry. And I do have to wonder if LaRussa's determination to nurse Garcia through the 7th had its seeds in having allowed him to bat (and strike out) with 2 on and 2 out in the previous inning.

More, for the Obsessive and the Insomniac

How many runs might the Cards have expected to score in their last 3 times up? What was their chance of scoring at least 1 run?

In the 7th through 9th innings this year, St. Louis averaged 0.49 runs per inning, while the Phils allowed 0.38 runs per inning. That suggests an expectation of about 1.3 runs in the Cardinals' last 3 raps combined.

The regular-season totals can only give a rough estimate, since they cover all kinds of game situations, not just a close and crucial game when they start the 7th with the top of the order. But it's better than nothing.

But the total run expectation is of more interest if they give the IBB and it leads to a big inning. If they eschew the IBB and Ruiz drives in the run, we're more interested in their chances of getting at least 1 run in the 7th-9th to stay alive.

We don't have that number directly, but we can make a reasonable estimate from the ones we do have. I'll put the math work at the bottom and cut to the conclusion: I estimate the Cards' chance of scoring 1 run or more, over the last 3 innings combined, at 55%.

Of course, that's only half the picture; the Phillies also have 2 chances to score. But I'm only trying to establish that going into the last of the 7th down by 1 run is not an enormous obstacle.

But in light of that 1.3 run expectation for innings 7-9, falling behind by 2 or 3 runs is pretty bad news.

_________________

The Math

With the caveat that my higher math is limited....

From the team scoring summary, we know that the Cards scored at least 1 run in 27% of their the 7th innings, 27% of their 8ths, and 30% of their 9ths, for a base total of 84%. The challenge is to avoid double-counting the games where they scored at least 1 run in more than 1 of those innings.

Chance of scoring 1+ in the 7th and 8th = 27% x 27% x 70% = 5.1%

Chance of scoring 1+ in the 7th and 9th = 27% x 73% x 30% = 5.9%

Chance of scoring 1+ in the 8th and 9th = same as 7th and 9th = 5.9%

Chance of scoring 1+ in all 3 innings = 27% x 27% x 30% = 2.2%

Total of "overlap" games: 19.1%

• Subtracting 19.1% from the base total of 84%, I estimate that the Cards scored at least 1 run from the 7th through 9th innings in about 65% of their games.

The corresponding numbers for the Phillies (allowed) are 24% in the 7th and the 8th, and 17% in the 9th, for a base total of 65%.

Chance of allowing 1+ in the 7th and 8th = 24% x 24% x 83% = 4.8%

Chance of allowing 1+ in the 7th and 9th = 24% x 76% x 17% = 3.1%

Chance of allowing 1+ in the 8th and 9th = same as 7th and 9th = 3.1%

Chance of allowing 1+ in all 3 innings = 24% x 24% x 17% = 0.9%

Total of "overlap" games = 11.9%

• Estimated rate at which the Phils allowed at least 1 run from the 7th through 9th = 53%.

• Average of the 2 teams' figures: 59%.

Adjustments: Philly would be going all-out to prevent that 1 run, which tends to decrease the number. But St. Louis would start with the top of the order and could play for 1 run, which tends to increase the number. I can only guess at the size of either effect, but since they work against each other, I would conservatively conclude that the Cards would have a 55% chance of getting 1 run over the last 3 innings.

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