As this season goes ever-more-ridiculously into impossible badness, let's take a quick look at how much of it we can pin on bad luck.  Keep in mind that the majority of the awful comes from not enough good players--even my most optimistic pre-season calculations had us at 75 wins.

Pythagoras, call your office

The top-level look at the team's performance is the Jamesian Pythagorean Win Expectancy, the average W/L expected based on runs scored and allowed.  Through Sunday, the Nats had scored 277 runs and allowed 360.  Their Pythagorean W/L based on those totals is 23-38; their actual record is 16-45.  Based on our scoring, we're 7 wins behind where we should be.  WTH?  This boils to down to losing a lot of close games, and only winning the blowouts.  Here's a quick summary of how we've done (and how we "should" have done) as a function of how close the games are:

Extra innings: 0-8 (Pythag: 3-5)

1-run games: 6-11 (Pythag: 8-9)

2-run games: 1-11 (Pythag: 5-7)

3-run games: 3-9 (Pythag: 3-9)

4 or more: 6-14 (7-13)

And there you are--we're losing a lot of close games, more than we should be based on how many runs we score and allow.  In fact, almost that whole pile of 7 games we "should" have won is in games we've lost by 1 or 2 runs.  Maybe some of that is bad luck or questionable home run calls, maybe it's our regrettable bullpen (early season) and prolonged offensive slump (recent).  Either way, bad luck for Nats fans...

Hit 'em where they AIN'T

Beyond that team-wide luck (or lack thereof) in close games, we can look at how individual batters are doing with a stat called batting average on balls in play (BABIP).  BABIP is (# hits) divided by (# times ball put into play)--it's a measure of how many times a batter hits a ball far enough away from a fielder (or hard enough, or soft enough, or out of the park) that it goes for a hit.  This is kind of random, and league-average is about 0.300.  If a player has a BABIP much above league-average, he's probably getting a lot of seeing-eye singles and other lucky hits--expect his batting average to come down as his luck averages out over the season!  The reverse is true of a player with a low BABIP: his batting average will likely improve as he regresses toward average.

How are the Nats doing?  Well, team BABIP is .309 so far this season, compared to a league-average of .296--our luck with balls falling in for hits is about average, maybe a bit better.  Notably above league-average are Cristian Guzman (.366), Nick Johnson (.369), and Ryan Zimmerman (.339).  Notably below are Josh Willingham (.259), Ronnie Belliard (.207), Austin Kearns (.275) and Willie Harris (.259).  Should we expect the first bunch of players to hit a little worse in the second half, and the second bunch to hit better?

BABIP is something a hitter has some control over, based on how hard he hits the ball and how many line drives he can hit.  Predicting what a batter's BABIP "should" be (as opposed to assuming it should be the league-average .300 or so) is not the most reliable statistical endeavor out there, but I took at look at a simplified "expected" BABIP model based on this work at The Hardball Times.  Anyhow, according to the magic formula, we'd expect Guz, NJ, and Zimmy all to have BABIPs around .305.  They hit the ball hard, so we expect them to do better than league-average--but not as well as they've done so far.  Sadly, they're all likely to do worse as they regress back to the mean. On the flip side, Hammer's BABIP should be up around .290, TAWH's should be .310, Belliard's should be .311, and AK's should be .313!  All four stand to show significant improvement in the rest of the season--if they get enough playing time and/or don't get DFA...  On the whole, I'd say luck with batting is slightly in our favor so far this season.

Black holes

This brings us to pitching and defense.  There's a flip side to BABIP called Defensive Efficiency Ratio (DER).  DER is a measure of how often balls put into play result in outs--if a pitcher pitches to contact, this is the percentage of the time that the defense comes through for him.  The pitcher can control some of this depending on how many ground balls he gets, but mostly it's up to the defense behind him and the luck of where the ball lands.  League average DER (higher is better) is .697, but the Nats have a league-trailing .677.  Nats pitchers are the least likely in the NL to get outs behind them if batters make contact--and we wonder why they nibble and give up walks!

Starters with high DERs include John Lannan (.722), Craig Stammen (.729) and Sharion Martis (.750).  Lannan and Stammen both get a lot of ground balls (51.4% and 48.5%, respectively--tops on the rotation), so they might be able to keep that up.  Smarty, with his 40.5% ground-ball rate has probably been getting lucky.  Look for his DER to fall, meaning his ERA will climb.  In the 'Pen, Vill0.96ne has a DER of 0.800--look for his ERA to go high enough that we can no longer replace the "O" in his name with "0.xx"!  Taverez manages .729, but his GB% of 53.6 probably warrants that.  Notable on the low-DER end of things are Joel Hanrahan (.584), Jesus Colome (.559), Scott Olsen (.639), and Jordan Zimmermann (.656).  We might expect low performance from fly-ballers Olsen and Colome, although I'd expect better from poor Hanny.

Another way to look at the impact of defense is Fielding-Independent Pitching (FIP).  FIP tries to remove the effect of fielding, looking purely at things the pitcher controls (strikeouts, walks, HR, IBB, and HPB) and computing a number meant to be equivalent to ERA.  The difference between FIP and ERA tells us whether the pitcher is getting lucky or unlucky with the fielding.  Unluckiest pitcher on the team? Jesus Colome--his FIP is 2.38, lowest on the Nats!  Crazy, but it's probably because he's only pitched 9 innings and hasn't given up any HR yet.  J-Zimm and Ross Detwiler both have FIPs around 3.85, nearly 1.5 runs/game worse than their 5+ ERAs.  Martis (despite his high DER) and Tavarez are both pitching with ERAs close to their FIPs, while Villone (4.17 FIP, 0.96 ERA) and Lannan (5.09 FIP, 3.51 ERA) are doing much better.  Interestingly, Lannan's ERA has always been about a run better than his FIP over the last three seasons--maybe he's got something going on that FIP doesn't see.  Villone, though--look for him to revert, while Martis and Tavarez stay steady, and J-Zim and Rosswiler continue to improve.  Overall, the pitching has been more bad than unlucky, although it has been unlucky.

(Note: Stats through June 15, courtesy baseball-reference, The Hardball Times, and Baseball Prospectus.)