To most Reds fans, today was the day we shed our greatest problem from last year.  I like to describe Taveras's disastrous 2009 season as "Corey Patterson, but without the power."  Come to think of it, given Junior's disastrous career in Cincinnati, you have to start worrying about curses on our center fielders....  The Reds haven't done will by their CF in a while...  

The question is, however, whether Miles is any kind of improvement over Taveras.  Let's break down the deal, starting with what we got: Aaron Miles and his $2.7 M salary, plus a player to be named later.

SHB INF Aaron Miles Offense (thanks to FanGraphs)

Prior to last season, Miles had been somewhere between a replacement player and a decent reserve guy over the previous several years.  He peaked in 2008 with a season that was within striking distance of being league average.  Offensively, he actually reminds me a lot of a poor man's Orlando Cabrera: decent contact, very low walk rate, and not much power.  He lacks Cabrera's speed, though.

Obviously, he was a complete disaster last year.  I think it's interesting to see how the different projections treat that The Fans are the most optimistic that he will bounce back with modestly respectable performance...but then Fans tend to be an optimistic lot.  CHONE seems to pay a lot of attention to his apparent 2009 downturn season, whereas Marcel is more or less in the middle.  Overall, I'll just go with the average of the Marcel and Fans projections (though I'll use the Fans' PT estimates) and put him at roughly 9 runs below average in 303 PA's.

Fielding

At first, things looked ok here.  Jeff Zimmerman's UZR projections put Miles as a -1 run per season 2B.  CHONE has him as a -1 run at 2B.  But the Fan Scouting Report has him as a terrible 2B, 22 runs below average per season. Maybe some of this was spillover anger over his awful offensive performance, but my feeling is that we shouldn't ignore it.  An average of all three estimates puts Miles as a -8 run fielder at 2B.

So, overall, using 43% playing time:
Batting: -9 runs
Fielding: -8 * 0.43 = -3 runs
Position (2B): +2.5 * 0.43 = +1 run
Replacement: +22.5 * 0.43 = +10 runs
Total: -1 run above replacement--essentially dead on replacement level.

Miles will make $2.7 M next season, but is worth league-minimum, or ~$400k.  That makes him a $2.2 M liability.

What about Taveras and Rosales?

Here are their projections, using the same methods as above:

Taveras (52% playing time per Fans)
Batting: -10 runs
Fielding: [+7 (TZ) +2 (UZR) -8 (Fans)] / 3 = +0 runs
Position (CF): +2.5 * 0.52 = +1 run
Replacement: +22.5 * 0.52 = +12 runs
Total: +3 runs above replacement, or ~0.3 WAR

Taveras is essentially a replacement player too (maybe slightly above replacement by these projections), who probably at best worth $1 M.  He will make $4 M, however, which means he is a $3 M liability.

Rosales (53% playing time, based on CHONE & Marcel)
Batting: -4 runs
Fielding (3B): [-2 runs (TZ) + -4 runs (Fans)]/2 = -3 runs * 0.53 = -2 runs
Position (3B): +2.5 * 0.53 = +1 run
Replacement: +22.5 * 0.53 = +12 runs
Total: +7 runs above replacement, or 0.7 WAR

Replacing Rosales's projected production with a free agent would cost ~$2.5 M, and yet he will likely make right about league minimum of $400K.  This gives Rosales as a "property" a surplus value of ~$2.1 M.

Trade values

So, the trade can be written as:

Miles ($2.2 liability) + PTBNL = Taveras ($3 M liability) + Rosales ($2.1 surplus)

So, for the Reds to get market even value on this deal of bad parts, they'll need to get somewhere on the order of $1.3 M in surplus value with this unnamed PTBNL.  That's not a particularly tall order, so I'd guess that this deal is going to turn out to be pretty close to even.  But we'll have to wait and see who ultimately gets tapped to complete the transaction before rendering a final verdict.  

Update (update was updated again at 9pm): as several have noted (esp sidnancy), the playing time estimates I give to all of these players--typically around 50% of a season--may be overly optimistic, as none of these guys is a starter anymore.  If you drop them down to 25% playing time (~175 PA's), Miles and Taveras barely change (essentially replacement players...Taveras sees his slight positive cut, which makes him even more of a liability), but Rosales sees his surplus value cut in half.  However, this is countered somewhat by the fact that Rosales's value should have been calculated across the remainder of his foreseeable career in the majors.  That's the value shown below.

Miles ($2.2 liability) + PTBNL = Taveras ($3.5 M liability) + Rosales ($2.5 surplus)

So we're more or less back where we started, with the Reds needing a player who provides roughly $1.2 M in surplus to break even on the deal.