For more than half a decade the Cubs got a .385 wOBA out of their 1st baseman. Derrek Lee was traded midseason in 2010, but from 2004 through 2010 he posted a .385 wOBA, put up a couple MVP caliber seasons, helped the Cubs to multiple playoffs and was generally one of the better 1st basemen in baseball. Lee wasn't a great player, but he was a very good ballplayer for the Cubs and not too surprisingly, they've yet to fill those big shoes.
The Cubs are hopeful that Anthony Rizzo can do it. In 2011 Rizzo showed that he was simply overmatched. In 368 plate appearances with the Cubs in 2013, he hit .349 with a 116 wRC+. Those aren't great numbers, but for someone his age they're awfully good. However, we can't just ignore 2011.
His career wOBA is .320, which is league average (99 wRC+). He hasn't been able to figure out left-handed pitching. He has only a .265 wOBA vs lefties over 140 plate appearances. That's 38% worse than league average (62 wRC+). This can't be blamed on an awful 2011 season. He was actually better vs lefties in 2011 than he was in 2012.
He's a good candidate to beat his projections below, but he also has a couple holes in his game that will need to be fixed in order to do so.
If Rizzo hits 31 home runs like ZiPS projects, I'm going to be thrilled.
There's a rather small sample available for Rizzo's defense, but CAIRO projects +1 run saved. My guess is that he's better than that defensively and it's only +1 due to the regression. I don't know for sure, but scouts seem to rave about his defense.
ZiPS projects 3.7 offensive WAR (oWAR) while CAIRO projects 1.7. If you're curious, the Steamer projections have the same exact .362 wOBA projection as ZiPS, but I'm not sure what the league average of either system is. It's clear CAIRO is weighting the minor league seasons less than ZiPS and Steamer. It also might be because they're weighting the most recent season differently. I'm not confident in either of the WAR projections. I'd be surprised if he's as good as the 4 WAR ZiPS is projecting and I'd be equally surprised if he's only worth around 1.8 WAR like CAIRO is projecting.
Using only his CAIRO projections, the percentile forecasts for Anthony Rizzo are below.
You can see from here that ZiPS and Steamer are more comparable to the 65th percentile forecast using CAIRO.
There's a lot we don't know about Rizzo. He started off really well in 2012, but then the pitchers made some adjustments. He struggled against lefties, which could prevent him from being as good as any of the projections.