It's not appropriate, but let's pretend for a minute that Wade Davis (-2.1 WAR, 2013) never came to KC and The Trade was a straight up Myers for Shields deal. Ahhhh... that feels a little better, doesn't it? We have a decent data set for Myers now, and Shields just pitched his last game of the year, so this seems like as good a time as any to evaluate The Trade.
Now, this seems like too-obvious a point to make, but since Nedbert Franklin Yost seems to struggle with this concept, I feel like it's worth pointing out that the game of baseball is won by the team which scores the most runs (no, not by the team who reaches 2nd base most often, Neddy). So, while it's notoriously difficult to evaluate a pitcher against a player valued primarily for his bat, and since WAR does a poor job of evaluating defensive metrics, I believe the best way to line up these players is to consider their effect on runs. In the simplest terms, Myers' job is to create runs and Shields' job is to prevent them. When you strip it down, The Trade (or any trade) isn't about trading players, it's about trading runs. The Royals traded runs to Tampa Bay and received negative opponents' runs in return, so evaluating who wins The Trade comes down to determining who received the bigger delta in runs. Let's stop philosophising and do the numbers:
James Shields finished his season with a 3.15 ERA and the AL average for starting pitchers is 4.17. Nifty! Way to go James! Since Shields pitched 228.2 innings this year, we can say he kept opponents from scoring 25.9 runs better than a league-average pitcher. Over the two years of his contract, we can expect Shields to prevent Royals' opponents from scoring 51.8 runs better than a league-average starter.
Wil Myers, with just a few left to play, has produced 10.9 wRAA (Runs Above league-Average) in 85 games this year. Let's say Myers plays 152 games a year. Sound fair? That means, at his current production level, he'll be expected to create 19.5 runs/year above a league-average batter. Add the runs from this year together with the next five years of club control, and the Royals gave the Rays 108.4 runs above league average.
Net: The Royals gave away 108.4 runs (mostly produced in the future) for preventing 51.8 runs this year and next.
Modifiers: Of course there are modifiers which are difficult to quantify. Take these as you will, but they are worth mentioning. Myers plays in the outfield, and outfielders are expected to hit better than most other position players, so you could discount his RAA a little; however, Myers is also 22 years old and most young hitters improve each year until they peak around age 27, so he projects to be better year-over-year in each of the next five years. Long contracts have more inherent risk because Myers has five more years in which he may sustain a career-ending injury, but pitchers are also inherently injury prone. Opportunity cost - Myers is cheap, but Shields earned $9 million this year. We'll never know what sort of pitcher might have been had for Shields' salary if the Royals had simply kept Myers and tried to play the market.
Why do I compare to league average instead of replacement level? One, "replacement level" is in the eye of the beholder whereas "league average" is easy to define. Also, replacement level players aren't usually every-day players for any team (Chris Getz and Houston Astros notwithstanding). I think it's more appropriate to compare a player to what a team would actually replace him with. A contender would be expected to replace an injured starter with a league-average player, because a replacement-level player would be an enormous liability to a team trying to contend for the playoffs, no matter how much grit he has.
Are the Royals a better team this year and next year for having Shields instead of Myers? Probably. But probably only a little if you assume Myers would have been the opening day starter in RF over Frenchy (19.5 runs created by a Myers in a full season vs. 25.9 prevented by Shields), and only if you assume there was nothing better than a league-average starter to be had on the free agent market last winter for Shields' salary. Or maybe a better 2B. Or SS, for that matter.
The difference between good general managers and Dayton Moore is that Dayton says, "I want that guy because he's really good," or "I want an ace." A smart GM asks, "What move can I make that will create the biggest delta for my team in terms of run creation or prevention?" That's the difference between thinking like a scout and thinking like a general manager. Dayton is a good scout, but a terrible GM, and that's why the Rays won The Trade.