Saturday’s game, which the Cardinals won 9-4, featured a rare "team unearned run" in the bottom of the fifth inning. Our note about it on Twitter drew a few inquiries, so we’ll explain further what a team unearned run is. Actually, the Bullpen wiki at Baseball-Reference does as good a job as we might:

The accounting of earned runs is more complicated when relief pitchers are used. Each pitcher is liable for the runners he allowed on base via hit, walk, or hit by pitch even after he is pulled for a reliever. Batters who replace a previous runner on a fielder’s choice are charged to the previous pitcher. Also, when considering when the inning would be over except for errors, relief pitchers are not relieved of responsibility by errors that were committed before they were brought into the game. This means that some runs may be considered earned for an individual relief pitcher but not for the team as a whole, so team earned runs are often less than the sum of the earned runs allowed by the individual pitchers.

Here’s the actual verbiage from MLB’s official rules for Rule 10.16(i):

(i) When pitchers are changed during an inning, the relief pitcher shall not have the benefit of previous chances for outs not accepted in determining earned runs.
Rule 10.16(i) Comment: It is the intent of Rule 10.16(i) to charge a relief pitcher with earned runs for which such relief pitcher is solely responsible. In some instances, runs charged as earned against the relief pitcher can be charged as unearned against the team.

The particular scenario Saturday was this:

Basically, since the inning would have been over and the Nationals unscored upon if Christian Guzman, a former soccer player, hadn’t booted it (sorry, but how many chances do you get to make that joke?), any run that scores from that point on is unearned for Stammen and for the team. But then Ron Villone entered the game. As noted earlier, entering a game with runners on base — who may have gotten there via error — doesn’t relieve the reliever of the responsibility for the batters he faces. This makes sense: It would be silly to think that Villone could give up a bunch of home runs and not have them accounted to him as earned, simply because an inherited baserunner reached on an error. From a team standpoint, however, the inning is treated a a whole, regardless of who is pitching. Therefore, Rasmus’s run is unearned to the team.

As far as we can tell, the Cardinals have not had any team unearned runs this season.

It’s an odd rule, but it makes some sense. To us, though, it merely adds to the case for using fielding-independent pitching stats. Then no one would have to worry about this business of team unearned runs.

Do you ever wonder how much managers "manage to the stat"? We’re not talking about the decisions that managers make that are *informed* by stats, such as how a particular batter does against a particular pitcher, or whether to bunt in the first inning with the #2 hitter. We mean those times when the stat itself becomes not the means but the ends of a decision, such as whether to leave a struggling starting pitcher in so that he can get the win, or bringing in the closer when a save situation is technically in order.

It’s the latter example that is the topic of today’s graph. When the save became an official stat back in 1969, it obviously wasn’t a major bargaining tool for free agency (indeed, free agency hadn’t even happened). Even so, managers used relievers the way you might expect them to: They’d use their best reliever for the highest-leverage situations, regardless of the save rules. Today, well, it’s a different story: The following graph shows the number of saves that occurred at each number of batters faced. For example, in 1969, there were 104 saves in which the pitcher faced three batters. In 2008, that number had ballooned to more than four times that, at 480.

A few observations:

• Clearly the "start-the-ninth-inning save" (a.k.a., Robb Nen Save) is an example of the stat changing manager behavior/strategy. Dramatically.
• In 2008, there were 20 saves of nine batters or more. In 1969, there were 162!
• 41% of saves in 2008 were three-batter saves. In 1969, three-batter saves were the plurality, but they were only 14% of the total.
• Absent the save rules, we might expect the usage pattern to be more of a gradual arc around that three-batters-faced data point, as it was in 1969.

So you’re Tony La Russa, your team is up by one run heading into the ninth inning and you’re facing the Astros’ 3-4-5 men, Lance Berkman, Carlos Lee and Miguel Tejada. Whom do you summon from the bullpen?

We imagine that TLR has some numbers written down on a notecard in his back pocket. If we were him, here’s what we’d want to be looking at: A matrix of my relievers by batter, with each batter’s Gross-Production Average (plate appearances in parentheses). We’ve highlighted the actually matchups and italicized the most favorable ones (by GPA, anyway):

What really happened Wednesday night was La Russa bringing in Trever Miller to face Big Puma. It was a smart move: Though Miller had no history against Berkman, Berkman’s OBP drops about 50 points against southpaws (.426 to .370). Of course, the other LOOGy option was Reyes, who has been relatively successful against the Astros’ first baseman.

Certainly it was wise to wait to bring in Ryan Franklin until Lee, who has a dismal .228 GPA against him (mostly from their American League days). So far, so good. Things got interesting, though, after Lee’s double (and subsequent pinch-runner brought in). Though Tejada doesn’t hit Franklin particular well for power, his .261 GPA is based mostly on his .368 OBP –and since the Astros needed only a base hit (and not power), the Franklin-Tejada matchup wasn’t as favorable. Still, TLR didn’t have many other options vs. the Astros’ performance-reduced (?) shortstop: Only Motte and Reyes have had any success, and that was in a very small sample. Hawksworth shuts down righties (.150 GPA), but La Russa probably preferred his veteran in such a high-leverage situation.

Keppinger was another matter, with a .420 GPA against Franklin. We don’t expect La Russa to pull his closer for the final out, but if it were us, we would’ve considered McClellan. Again, all the Astros needed was a single (and, with a runner on third after Tejada’s at-bat, an infield single at that), and Keppinger had had three singles in five plate appearances against Franklin. Some may call it overmanaging, but we’ve seen a lot more acute examples from TLR over the years.

As the bard wrote, though, all’s well that ends well. Indeed, the Cardinals go for a sweep Thursday afternoon, up nine games on the Cubs and with a magic number of 28.

The Cardinals and Astros hooked up in a pitchers’ duel last night that was more reminiscent of low-scoring affairs at old Busch Stadium and the Astrodome back in the 1980s than of the bandbox ball of the new millennium. The principle proponents, Adam Wainwright and Wandy Rodriguez, were both so sharp that we wondered if their duel was the best combined pitching performance of the Cardinals’ season. According to FIGS (the newer version), here’s where they rank:

Wainwright, who is having a career year (he is now fifth in the majors in Pitching Runs Created with 106), is all over the list of best games. For his part, Rodriguez made the top 20 twice. And tonight’s Astro starter, Roy Oswalt ranks 19th with his tete-a-tete with Chris Carpenter, who pitches in tomorrow’s series-ending matinee. Here’s hoping that if Oswalt repeats WRod’s performance, Joel Pineiro makes like Wainwright did last night, too. Or like he himself has done a lot this season.

Update: Acting on the sage suggestion of reader DaveBug (@_) to determine the best games by the highest lower FIGS of the two pitchers ("
81/45 doesn’t feel like much of a duel to me, but 60/58 is amazing"), we’ve re-ranked the best games accordingly. We agree with DaveBug: These are better "pitchers’ duels." The Waino-Wandy tilt moves up to seventh place:

Heading into tonight’s action, the Cardinals have opened up an eight-game lead over the Cubs. Their magic number stands at 31. Without taking anything for granted, when might they clinch the Central Division title? If you’re interested in speculatively buying a ticket to see the clinching game, let’s figure it out.

For the season, the Cardinals have won games at a .571 clip. Another way to look at winning percentage is to say that for every game, the team accrues about .57 of a win. Ceteris parabus, over a period of, say 10 games, they usually have won 5.7 games (over 100 games, 57 wins). On the other hand, the Cubs, the next-closest rival in the Central, lose at a rate of .49; that is, for every 10 games, they’ll have 4.9 losses.

In case you’re not familiar with the idea of the magic number, Wikipedia defines it thusly:

A magic number is a number used to indicate how close a front-running team is to clinching a season title. It represents the total of additional wins by the front-running team or additional losses by the rival team after which it is mathematically impossible for the rival team to capture the title in the remaining games. This assumes that each game results in a win or a loss, but not a tie.

So if we project the number of Cardinal wins and Cub losses at some point in the future that will accrue to 31 (today’s magic number), we’ll know the celebration date. We’re actually going to use the teams’ Pythagorean Win% instead of actual, since it tends to factor out some luck. The Cardinals’ PyW% is slightly worse than their acutal (.556, .571 actual), while the Cubs’ is slightly better (.525, .508 actual).

In the following chart, W is the number of accrued wins for the Cardinals at the end of the day; L is the accrued losses for the Cubs.

Interestingly enought, the teams’ head-to-head series occurs in the middle of the countdown. Obviously, the teams can’t accrue part of a win (or loss) in each of those games, but since this exercise assumes a constant rate of either winning or losing, we’ve treated the games as any others.

At any rate, if you want to witness the clincher, it looks like you’ll have to take a trip to Colorado. And for all of you optimists out there who would prefer to use the teams’ actual winning percentages, the big day would still occur at Colorado — just the night before.