This is an adaption of the current (as of 5/20/2009) Royals'  WAR leaderboard for position players  at FanGraphs:

But what does all of that really mean?

This spring, before the start of the regular season, there was some discussion about some of the newer (I hate the word "advanced" -- makes things sound more complicated than they really are) stats, requests for them to be explained with reference to Royals players. So a mini-series began with Gopherballs' post on FIP, NYRoyal's post on hitting stats, and my own compilation of some introductory sabermetric links.

Shortly after that, NYRoyal asked if I would take WAR (Wins Above Replacement). I was flattered, but a bit worried, since WAR isn't just one stat, but a bunch of them put together, and is different for position players and pitchers (and starters are different than relievers!). WAR is a "total value" stat -- it is supposed to tell us what a player is worth compared not just to other players at his position, or other hitters, or other fielders, but as a whole.

This is just an introduction and brief overview. I might come back alter and discuss individual aspects in depth (such as replacement level, etc.). For now, I'm just going to deal with position players. For an introductory piece on pitcher value, check the links above or click here.

One more thing before the concrete discussion: almost all the concepts and ideas herein are debated as to how they are implemented or if they should be used at all in the sabermetric community. So if you don't like something or disagree with it, chances are, you aren't alone. Again, this is just a way to understand what's up when someone mentions a player's "WAR."

I will simply go through the columns and explain what they mean.

Batting is runs created above what a league average player would create in the same number of plate appearances according to linear weights. While FanGraphs uses a custom version and park adjusts the numbers in the Batting column, the basic formula for this is ((wOBA-lgwOBA)/1.15)*PA.

Fielding is the number of runs above or below what an average player would have saved in the same playing time in the same position(s) the player played. FanGraphs uses a version of Mitchel Litchman's Ultimate Zone Rating  (their version is sometimes referred to as "bUZR" because it uses data from Baseball Info Solutions  rather than STATS Inc.). Fielding stats are still developing and controversial. Even moreso than batting stats, one should be very aware of sample size issues with fielding stats. A good rule of thumb is that one full season of  fielding stats is the same sort of sample as two month so of hitting stats in relation to true talent. Nonetheless, we are addressing value rather than ability here -- players can go through hot streaks and cold streaks, have up and down seasons in fielding as well as hitting. This is a huge topic on its own, and I've said too much already. Note that there are no in-seasons catcher defensive stats listed, as UZR only covers groundballs for infields, a very small part of catcher defense. Catcher defense is tough to measure in general -- there are some good ways of doingn it now with reference to SBs, blocking pitches, etc., but they are mostly done after the season when Retrosheet data is available. that's a whole 'nother discussion, though.

Let's skip over to positional. There are different ways of adjusting for positions, and how this is done is a matter about which there are many different opinions. These adjustments are Tom Tango's. In short,  we know that the group of players who can play average defense and hit like major leaguers is much small at SS than at 1B. So we prorate a different number of runs above/below "average" playes overall playing time at each position. Prorated for 162 games played (and for separate positions so that, e.g., Buck, Guillen, Jacobs, et. al. have playing time prorated acording to the time they've spent at DH as well as their regular positions), FanGraphs uses these run values:

C +12.5
SS +7.5
2B/3B/CF +2.5
LF/RF -7.5
1B -12.5
DH -17.5

Replacement is probably the toughest thing to explain, so I apologize in advance for its brevity. Major league teams want to beat other major league teams. To do this, they have to purchase talent through the draft, trades, or signing free agents with scarce resources.  While there are millions of people out there who would gladly play pro baseball for free, those who would actually help a major league team beat others are quite scarce. In short, a "replacement level" player is the term for the kind of player that a team would not have to give up talent or money over the league  minimum. Triple-A lifers, etc. This is a more useful conceptual baseline than average because not all below average players are freely available -- hence the Royals paying out more than the  minimum for two catchers most would see as below average overall players.

[NB: If you ever hear or read someone saying or writing that "sure, the team overpaid for that replacement level player, but they don't already have one in the system!" they either understand replacement level to mean something completely different than what we're discussing here, or, more likely, they don't understand it at all. By definition, a replacement level player is freely available -- if a team gives up talent and/or more than the league minimum for a player, they do not see him as a replacement level player.]

For position players, replacement level about 2 wins/20 runs below average when adding up batting, fielding, and positional adjustment. This accounts for a player's playing time.  Even if a player is below the average major leaguer offensively and/or defensively at a relatively non-scarce position like LF, The time the player spends on the field is valuable (given the economic aspect of baseball) because it is the value the player provides over the theoretical Triple-A scrub a team would grab as a free agent at $400,000/year or whatever.

RAR is Runs Above Replacement -- it simply totals the batting, fielding, positional, and replacement columns to give the players "total value." Again, this is against the average/replacement level baseline, _not_ zero. A replacement level player _does_ do something -- he will field some balls, get on base at some point, etc. What teams are interested in are players who can do this at a level beyond what they and every other team can get for "free." ONe can adjust this for relative league difficulty and era, but  Fangraphs keeps is simple, prorates replacement level for position players at +20 runs/600 PAs.

WAR is Wins Above Replacement -- runs converted to marginal wins. Teams are after wins, after all. The runs-win ratio is on one hand a complex subject, but in modern baseball, it's pretty much close to 10 runs per win each season.

You can also see last season's leaderboard, but let's go with today's, as posted above. To see what is going on. WAR helps us see just why CoCo Crisp has been the most valuable position player on the team so far this season -- he doesn't have the best offensive numbers (wOBA/Batting includes steals) or even fielding numbers, but he's above average in both at a premium position (CF) and has played in almost every game. He just edges out Bert because -- and this will shock you -- Bert hasn't been great on defense this season.

Mike Jacobs has been one of the Royals best offensive players so far this season, but since he mostly plays DH (and was dreadful at first in limited time there), he's only the Royals 4th  most valuable player. While David DeJesus' struggles against LHP have been extremely frustrating so far this season, and Jose Guillen has had a surprisingly good season so far with the bat, Guillen not only missed time with injury, but has given away more marginal runs with his glove then he has produced with his bat. It's stuff like this WAR was made for.

I hope this is helpful to someone. Remember the usual "small sample size" stuff. And keep in mind that sabermetics, as I understand it, is supposed to make the game more accessible and understandable for fans like you and me, not make it more complicated. If I can understand it, you can. And it's all open for debate and discussion.

Quick Update: I should have put this in the original post. What do WAR numbers generally mean? Roughly, over a full season of play, here's a loose rubric. Remember that the following "grades" are for the whole year, we are only through only a fraction of the season so far. 

0 or lower (should be) AAA scrub, or not ready, or shouldn't be in pro baseball
1 bench player
2 average
3 above average
4 very good
5 great
6+ one of the best players in the league

Another way to look at this, from the full-season perspective, is like the grading scale in school (back when people were allowed to fail): 0 =F, 1 = D, 2 = C, 3 = B, 4 = A, 5+ = teh awesome

Some WAR numbers from last season:

Albert Pujols 8.9
Chase Utley 8.1
Chipper Jones 7.6
Hanley Ramirez 7.6
Milton Bradley 4.5
Josh Hamilton 4.0
Willie Harris 3.2
Bobby Abreu 1.2
Robinson Cano 0.5
Jason Kubel 0.4
Willie Tavares -0.1
Jeff Francoeur -1.3

Another Update: If you just want an idea of where a guy is "right now" with respect to being "good" or bad, and/or don't like the idea of replacement level," all you have to do is take his current RAR total and subtract the "replacement" amount. That will give you the player's current runs above/below average (average being 0). If the number is greater than 0, he's above average, if it's lower, he's below average. For example, take Billy Butler (as in the above chart's data, it's different by now) -- he's hitting decently, but is it enough to be an average or above average 1B when combined with his fielding? His total RAR is 5.4, subtract the 4.9 replacement runs, and you get 0.4 -- yup, so far, Billy has been an above average player.