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The last time the Red Sox opened a new ballpark, John Phillip Sousa’s marching band opened the festivities at Yankee Stadium and Babe Ruth christened his new home with a home run.

This time around, the Red Sox were victimized by Jason Kubel in Target Field’s debut. The result was the same: a three-run loss.


* Albert Pujols, through seven games, has outslugged the Astros lineup by himself. He has more home runs and RBI than all the Astros hitters combined.



* And speaking of the Astros, let’s show them some pity. Of the starting pitchers they’ve faced so far, three got Cy Young votes as recently as last year. That trio of Tim Lincecum, Roy Halladay and Adam Wainwright, have combined for 24 innings pitched without allowing an earned run.

Should we really expect the Twins to win six fewer games because of Joe Nathan's season-ending injury? Not at all -- the number is actually less than half that.

Even if you believe Nathan's more than six wins better than a Triple-A scrub, that number overstates the actual effect on the Twins bullpen. Why? Because the scrub won't directly replace Nathan. He'll be replaced by one of the better relievers already on the team, and everyone else will move up one rung. This is known as bullpen chaining. And it matters because, in general, the innings pitched by a closer are more important than those pitched by a setup man, which in turn are more important than those pitched by relievers lower on the ladder. By leveraging their bullpens to allow runs when they matter less and prevent runs when it matters more, teams can win more games without giving up fewer runs.

Thanks to Tom Tango, FanGraphs provides a statistic that measures the importance of every situation, called leverage index (LI for short). Here's what you need to know:

• The average situation (think of the starting pitcher's role) has an LI of 1.
• Closers appear in situations with an LI of about 2, meaning runs allowed by closers are typically twice as harmful as the average run.
• Setup men will see LIs in the 1.3 to 1.5 range.

What can we do with leverage index? Well, combined with bullpen chaining, we can compare the Twins' bullpen with and without Nathan. First, here's a simplified view of what the Twins bullpen would have looked like with Nathan:


Note: RAR is runs above replacement, which compares a pitcher's ERA to the replacement level ERA for relievers (about 4.75), converts that to runs saved based on the number of innings pitched, and then multiplies by leverage index to account for the importance of the runs saved.

That's a good-but-not-great bullpen, and is definitely carried by Nathan's superstar talent. Now here's the situation if I remove his innings, bump everyone else's leverage index up a bit, and hand the least important innings to the scrub:


Yikes. That bullpen will only strike fear into the hearts of Giants hitters. Quantitatively, the Nathan-less group is expected to allow 26 additional leveraged runs, or about 2.6 wins worth.

More important to my main point, notice that Nathan's RAR total from the first table implies a value of 33 runs compared to a replacement closer. That 33 number would hold if the scrub took over the closer's role, but because of bullpen chaining, the loss of Nathan is mitigated by three-quarters of a win. That might not sound like much, but the Twins' bullpen is set up to feel the loss of its closer more than most bullpens. If Nathan were a less dominant reliever or if there were a backup option who could post an ERA in the low 3.00s, losing Nathan might only have cost around two wins. Six wins? No way.

Epilogue: I'm not married to the IP and ERA numbers in the table (they're roughly adapted from the CHONE projection system), so feel free to mess around with your own bullpen setups below. Here are some tips:

• Change the green cells, but don't touch the orange cells -- they're calculations.
• The average bullpen throws around 490 innings, but that's not set in stone
• The average LI for the whole bullpen should be around 1
• Good LI's to use: closer = 1.8, setup = 1.4, a few around 1 and the rest at 0.7 or less
• For good, objective projections, check out CHONE and ZiPS at baseballprojection.com, baseballthinkfactory.org, and fangraphs.com
• RAR is runs above replacement, which is (4.75 - ERA) * IP/9 * LI [4.75 is the approximate ERA of a replacement level scrub reliever]
• LI is leverage index, the average importance of the situations a pitcher faces. One is average. More at fangraphs.com.

Feel free to distribute and modify the spreadsheet. Please keep all credits intact and don't sell it. Much thanks to Tom Tango and the insidethebook.com/ee community for their help understanding bullpen chaining. For more on bullpen chaining, go here.

Sky Kalkman writes for Beyond the Box Score.

Most of the baseball talk in Minnesota these days revolves around Joe Mauer's contract extension saga, and for good reason: He is the best catcher in baseball and the face of a franchise with hopes of contending. The Twinkies potential to make the playoffs does not rest squarely on Mauer’s shoulders, however, as GM Bill Smith made sure to improve what was arguably the team's most glaring weakness a season ago.

By trading for shortstop J.J. Hardy and signing second baseman Orlando Hudson, Smith not only brought in two of the better defenders at their respective positions, but solid hitters who look extra tasty when compared to who they will be replacing.

The Twins managed to rally back to a tie for the AL Central at the end of last season and went onto win a one-game playoff to qualify for the playoffs, but that was in spite of the awful performance they got from the men in the middle of the diamond. Orlando Cabrera, Alexi Casilla, Nick Punto and Matt Tolbert each saw their fare share of time at shortstop and second base, and their overall True Average (TAv) amounted to a pathetic .229 mark. Hardy and Hudson, although on different teams, combined for a .262 TAv that vastly exceeded the Twins in-house options. So what does the new keystone combo for the Twins project to produce this season?

Baseball Prospectus’ PECOTA projection system sees Hudson as capable of putting up a .271 TAv with Hardy coming in at .261. Weighted together, their .266 TAv would rank sixth amongst middle-infield combos in the junior circuit:

The acquisitions of Hudson and Hardy represent a very important point in the world of statistical analysis: A team does not need to acquire a superstar at one position to improve more than marginally. The Twins brought in two solid players who might not get picked first in a sandlot game, but are certainly above average, and being above average is Ruth-ian compared to who they penciled in at those spots last year. If Gardenhire’s gang once again plays meaningful baseball into October, Joe Mauer is likely to be a big reason why, but do not underestimate the contributions of Hudson and Hardy and the upgrade they will provide.

Eric Seidman is an author of Baseball Prospectus