There's zero reason to think the offense will be meaningfully better than 2012 - which means it'll be awful.
Well, let's go position-by-position:
- First Base: Rizzo is a year older and should be better. 2013 > 2012.
- Second Base: Barney is Barney. Push.
- Shortstop: Castro is a year older and should be better. 2013 > 2012.
- Third base: Still likely to be awful. Valbuena was the best performer of the group last year, so you could see a little improvement just by not giving ABs to Mather or Vitters. Still, this is a push.
- Outfield #1: Soriano is a year older and should be declining. 2013 < 2012.
- Outfield #2: DeJesus is a year older and should be declining. 2013 < 2012.
- Outfield #3: Schierholtz and Hairston aren't exciting, but are competent...possibly good enough to be roughly league average in RF. They're taking the ABs given to mainly awful players last year: Mather, Byrd, LaHair after the league had figured him out, Baker, and Campana, with a few league average-ish PAs turned in by Reed Johnson. This is a massive upgrade, 2013 >>> 2012.
- Catcher: Castillo can reasonably be expected to be a .250/.320/.400 hitter this year, and has a little bit of upside. With a little luck, he'll be around a league average starter. Navarro is a perfectly capable backup, who should ensure that the Cubs at least get anti-awful performance out of the position if Castillo bombs. Soto/Clevenger/Hill/Lalli/Recker provided nothing resembling anti-awful performance. Another big upgrade, 2013 >> 2012.
So two positions that should be major upgrades (just because the names aren't exciting doesn't mean the upgrades aren't huge), and two that are a push. The improvements from Rizzo and Castro should cancel out the declines of Soriano and DeJesus, although there is a significant chance that one or both of the young players could really break out as true stars. The lineup is better. Not good by any stretch of the imagination...but good enough to move up to 11th or 12th in the league instead of dead last.
Garza is out at least a month, and after that is anyone's guess. Baker? Pray it's a month, but it could be the season. Feldman stinks but at least he's healthy and doesn't stink as bad as the likes of Raley and Rusin. Maybe Samardzija proves 2012 wasn't a career year, maybe he doesn't.
The big thing with the rotation is that a full one third of the schedule was started by the following group last year: Volstad, Germano, Rusin, Raley, Coleman, Wells, Berken. That is one third of the schedule pitched by guys who didn't belong in the major leagues. If that caliber of pitcher starts that many games again in 2013, then yes, they're going to be 95+ loss bad again. But that's not likely. Limit that group to 5-10 starts (or less) in 2013, and you're adding 5 wins easily.
It's worth noting that this team was on pace for ~70 wins last year through the deadline, and stayed roughly on that same pace in games started by Samardzija and Wood. But Samardzija and Wood only pitched about 25% of the games after July 31...so it was the 40ish win pace from the other 75% of games killed them.
The only area that looks like it could be significantly improved is the bullpen - but that gets you improvement into the two-digit loss column, and maybe to 70 wins.
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By most measures, the Cubs' bullpen was the worst in the majors in 2012. Take Fangraphs, which has the bullpen at 1.5 wins below replacement, #30 in MLB. #29 was the Mets, at 0.1 win below replacement. #28 was the Angels at 0.9 win above replacement. So by just improving to 28th in the league, the Cubs could add 2-3 wins (and that's assuming that WAR is somewhat accurate for bullpens...given the number of high leverage innings they pitch, it probably isn't accurate, and the 2-3 win estimate is low). Getting to average/slightly below adds 5+ wins to the team in 2013.
Bottom line: there was a lot of low-hanging fruit for the front office this offseason. The rotation, bullpen, third outfield spot, catcher, and third base were all so bad last year that just improving to ~20th in the majors is a massive improvement. And except for third base, they succeeded in getting respectable at all positions. That should add a lot of wins.