Plate Appearances and fWAR: Position Players

If you need a primer on fWAR, please visit the FanGraphs' Sabermetric Library entry for fWAR.  I highly recommend FanGraphs, as their Sabermetric Library contains detailed information on many other advanced baseball statistics. 

Listed below is the latest data I pulled from FanGraphs for the Orioles active position players (for games played through August 30, 2011): 

Player	PA	OBP	OPS	wOBA	wRC+	fWAR	fWAR(e): (PA/fWAR)*2
J.J. Hardy	453	0.315	0.831	0.355	121	3.6	252
Matt Wieters	456	0.329	0.760	0.333	106	3.4	268
Adam Jones	546	0.327	0.805	0.349	117	2.9	377
Nick Markakis	597	0.342	0.742	0.328	103	2.0	597
Nolan Reimold	221	0.308	0.728	0.316	95	0.6	737
Robert Andino	389	0.327	0.652	0.299	83	0.7	1111
Mark Reynolds	522	0.326	0.815	0.350	118	0.8	1305
Craig Tatum	72	0.286	0.567	0.260	56	0.1	1440
Matt Angle	21	0.190	0.348	0.181	2	-0.1	N/A
Vladimir Guerrero	471	0.306	0.695	0.304	86	-0.4	N/A
Jake Fox	58	0.276	0.683	0.299	83	-0.3	N/A
Ryan Adams	60	0.333	0.690	0.309	90	0.0	N/A

As if it wasn't apparent in my past posts, I'm a big fan/supporter of the fWAR statistic as a measurement for player production.  I wanted to take the statistic one level further though.  It may be a simple misunderstanding on my part, but fWAR does not appear to distinguish between a player with 600 plate appearance and one with 100 plate appearances.  I read the literature on fWAR and number of plate appearances seems to be inconsequential in the calculation, since it measures a player's contribution/production, not the quality/efficiency level of their play.

I developed a simple calculation that uses Plate Appearances in conjunction with fWAR to determine the quality/efficiency of a player's fWAR.  This metric, fWAR(e), determines how many plate appearances it takes for a player to achieve a league average fWAR of 2.0*.  As you can see from below (and in the table above), the equation is not complex and quite elementary: 

Equation Formula (abbreviated):   fWAR(e) = (PA/fWAR)*2   or 

Equation Formula (extended):  To calculate fWAR(e), divide the player's Plate Appearances by their fWAR, then multiple that number by league average fWAR (2)

Be advised, I'm not trying to change fWAR or create some great new statistic.  I'm not a math guru either, so take this all with a grain of salt.  Just trying to find new ways to look at the Orioles disappointing season and maybe find a silver lining for next season. 

Results:

• J.J. Hardy is the highest producing and most efficient position player on the Orioles roster.  His fWAR of 3.6 leads the team and his 252 fWAR(e) is the lowest/best.  To put his fWAR(e) in perspective, J.J. Hardy can contribute league average production to a team in about 252 plate appearances.
• Andino and Reynolds have not been efficient players in 2011.  They require over a season's worth of plate appearances to achieve league average production.
• Hardy, Wieters, and Jones are the only highly efficient position players on the Orioles roster.  Highly efficient meaning they will produce over league average in one season's worth of plate appearances (650 PA).
• Markakis is just barely above league average (required 600 PA to achieve league average fWAR of 2.0) and Reimold is just below the league average number.
• Vladimir Guerrero does not even contribute at a replacement level of 0.0 fWAR, so his fWAR(e) cannot be calculated.  His fWAR of -0.4 is pathetic and NEGATIVE!!**  Vlad was a waste of 8 million dollars. 

*League Average for fWAR varies by season, but 2.0 is a good standard for this simple experiment.  

**One of the fallacies of fWAR(e) is negative fWAR.  It destroys the equation - a real statistics guru could probably remedy this situation.  Bottom line though, if a player has a negative fWAR after at least 100 plate appearances, the player is unlikely to reach a league average 2.0 fWAR.