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In my opinion, a naturally gifted athlete is what the scouts call a five-tool player—someone who can hit for average, hit for power, run the bases and field his position. (That's only four tools, but I'm combining throwing ability and fielding ability into one bucket.)
With that in mind, these are the criteria I used to whittle the playing field down to the final 30 players.
1. No pitchers
With all due respect to guys like Clayton Kershaw and Felix Hernandez who can paint a 97 MPH fastball on the outside corner, there's no great way to measure how athletically gifted a pitcher is. For the most part, they don't hit or run, and they rarely have to field their position.
Considering we've seen pitchers with the physique of David Wells and Bartolo Colon make it to multiple All-Star Games, and the greatest relief pitcher of all time has torn his ACL while shagging fly balls, you're not convincing me that anyone on the mound deserves to be in the same discussion as Andrew McCutchen for athletic prowess.
2. Must be on an active roster with a minimum of 600 career plate appearances
Here's a link for those 345 players (there are 351 in the link, but six are pitchers). I exported that file and narrowed the rest of the field offline.
3. Must have a positive Fld + BsR total (192 players remaining)
This one knocked out nearly half of the field, but it's also more than half of the tools.
In case you're unfamiliar with those sabermetrics abbreviations, Fld is "fielding runs above average" and BsR is "baserunning runs above average." In each case, a zero means the player is league average, as is the case with Jed Lowrie in fielding and Josh Donaldson in baserunning.
A negative number means you are worse than average in that aspect of the game. If the sum of the two numbers is negative, that means that with the possible exception of your time spent in the batter's box, you're actually a detriment to your team.
One of the biggest casualties here was Miguel Cabrera, whose -83.3 score is the seventh-worst in all of baseball, and a testament to why Mike Trout should have been the 2012 AL MVP. As great as he is at hitting the ball, he's not a five-tool athlete.
(Criteria continued on next slide.)