There’s been some recent discussion in comments on these pages, particularly those involving the Circle of Greats, about underrated and overrated players.  I don’t consider myself any more qualified to determine how individual players are “rated” than anyone else, but a few years ago on my personal blog, I tried to take an objective approach to this question.  I concluded that, from 2009 through early 2011, Michael Bourn was the game’s most underrated player and Carlos Lee was its most overrated.

This study comes with many caveats, and I’d rather send you to the original post than rehash them all here, but the basic premise is this: the average fan views a player’s value in terms of batting average, home runs, and RBI, the three stats most often available in newspapers and on TV.  The best all-encompassing value metric we have available is WAR (I’m using fangraphs’ version for this study), so a player who accumulates a lot of WAR without a high batting average and a lot of dingers and ribbies is likely to be underrated.

With 2013 in the books, it’s time to take a look at the same study for the last three years.  The chart below was assembled by pulling batting average, home run, RBI, and WAR totals for every player with at least 1,000 plate appearances between 2011 and 2013, then calculating the number of standard deviations each player is from the mean in each area.  FANdev is the total of the positive or negative STDEVs in batting average, HR, and RBI, while WARdev is three times the STDEV from the mean three-year fWAR total.  U(O) is the difference- a higher number representing a more “underrated” player- one whose WAR is better than his newspaper stats.

[table id=158 /]

So… that guy.  I don’t think anyone here underrates Trout, though MVP voters certainly have for the last two seasons.   It’s no surprise that Zobrist, a versatile defensive player with plate discipline and some speed, shows up near the top.  Speed seems to be the common attribute among the top ten, as it factors into baserunning, non-home-run extra base hits, and defense, but doesn’t show up in homers or RBI and has a very minor impact on batting average.

At the bottom of the list, we’ve got bat-first guys with little speed or defensive value.  It seems that the positional adjustment impacts O(U) more than walks, doubles/triples, avoiding double plays, or stealing bases.  This list may represent under- and overrated players to a certain type of fan with no appreciation for the defensive spectrum, but the initiated fan probably appreciates these guys at the top of the list, as does the average non-Ruben-Amaro GM.

Here’s another chart using fangraphs’ Offensive Runs Above Average, rather than WAR.  Rather than underrated players, these are underrated hitters.

*For full disclosure, I only multiplied the STDEV of Oruns by two, not for any scientific reason, but because multiplying by three gave me results heavily influenced by Oruns- basically, the best hitters at the game at the top and the worst at the bottom. Multiplying STDEV Oruns by one put all the emphasis on the newspaper stats, yielding a list of the game’s worst hitters at the top and the best at the bottom.  Had I done the same for the chart above, Brendan Ryan and Andres Torres would have jumped to the top, with Trout dropping to sixth.  Billy Butler and Paul Konerko would have been the most overrated, with Miguel Cabrera in the seventh spot.

[table id=159 /]

Just about every way I tweaked the calculation, the same name came up at the top.  Trout’s combination of plate discipline and baserunning makes him so valuable that even with solid newspaper stats- almost 2 deviations above average in batting, 3/4 of a deviation about average in home runs (despite 13 fewer PA than the average player in the sample), and a few more RBI than average- makes him difficult to “rate” as highly as he deserves without advanced metrics.

The rest of the “underrated” list is populated with leadoff men who don’t get a lot of RBI opportunities and good base runners, since fangraphs recently added baserunning runs to the offensive runs figure on their dashboard.  It’s nice to see Joey Votto crack the top ten, not with speed, but with patience, as his .438 OBP since ’11 leads both leagues, far outpacing his .314 batting average.  Of course, this doesn’t settle the argument about the value of Votto’s walks when a hit would drive in a run, since WAR is context-neutral.

At the bottom, we’ve got middle-of-the-order sluggers who don’t walk much and don’t steal many bases.  And J.J. Hardy.

I won’t conclude by claiming that Mike Trout is the most underrated player in baseball.  Rather, I’ll ask readers how you might use empirical data to measure something as esoteric as “ratedness”.  WAR vs. salary or jersey sales?  Some combination of stats that aren’t used in a typical fantasy league?  Maybe something similar to the study above, but with tweaks to the calculations?