As for pitchers, starting pitchers had to amass 100 IP in a season while relievers needed 45 IP to qualify.
The idea came to fruition based on one of my favorite pastimes of going back and forth with a good friend of mine rattling off role players from the early 90's (i.e Andy Stankiewicz, Mike Gallego, Hensley Muelens, Eric Plunk, Steve Howe, Melido Perez, etc.).
Some statistics used in this analysis that you may not be familiar with: wRC+, OW%, ERA+, and FIP.
Note: Some positions, most notably SS and Closer didn't really have a bad season at all but I had to choose the "worst" within the minimum amount of time played.
|C||Jose Molina '08||.216||.263||.313||52||.214|
|C||Jorge Posada '05||.262||.352||.430||111||.555|
|1B||Tino Martinez '00||.258||.322||.428||92||.422|
|1B||Andy Phillips '06||.240||.281||.394||72||.306|
|2B||Alfonso Soriano '01||.268||.304||.432||98||.450|
|2B||Robinson Cano '08 ||.271||.305||.410||86||.402|
|SS||Derek Jeter '03||.324||.393||.450||131||.631|
|SS||Derek Jeter '08||.300||.363||.408||110||.502|
|3B||Scott Brosius '00||.230||.299||.374||73||.292|
|3B||Robin Ventura '03||.251||.344||.392||100||.466|
|LF||Rondell White '02||.240||.288||.378||77||.349|
|LF||Chuck Knoblauch '01||.250||.339||.351||96||.440|
|CF||Melky Cabrera '08||.249||.301||.341||71||.333|
|CF||Bernie Williams '05||.249||.321||.367||86||.390|
|RF||Shane Spencer '01||.258||.315||.428||99||.475|
|RF||Shane Spencer '02||.247||.324||.375||85||.422|
|DH||Jason Giambi '04||.208||.342||.379||96||.440|
|DH||Ruben Sierra '04||.244||.296||.456||92||.448|
|BN||Tony Womack 05'||.249||.276||.280||57||.250|
|BN||Enrique Wilson '04||.213||.254||.325||49||.209|
|SP||David Cone '00||155||6.91||1.768||70||5.44|
|SP||Jeff Weaver '03||169.1||5.99||1.619||73||4.26|
|SP||Darrell Rasner '08||113.1||5.40||1.535||82||4.72|
|SP||Ted Lilly '01||120||5.37||1.467||83||4.79|
|SP||Carl Pavano '05||100||4.77||1.470||89||4.89|
|SP||Javier Vazquez '04||198||4.91||1.288||92||4.78|
|SP||Joba Chamberlain '08||157.1||4.75||1.544||90||4.82|
|BN||Jose Contreras '04||95.2||5.64||1.411||80||5.83|
|BN||Kevin Brown '05||73.1||6.50||1.718||65||3.61|
|BN||Kei Igawa '07||67.2||6.25||1.670||72||6.37|
|RP||Sterling Hitchcock '03||49.2||5.44||1.510||81||4.24|
|RP||Tanyon Sturtze '04||77.1||5.47||1.397||82||4.63|
|RP||Scott Proctor '05||44.2||6.04||1.410||70||5.59|
|RP ||Scott Proctor '07||54.1||3.81||1.510||119||5.56|
|CL||Mariano Rivera '00||75.2||2.85||1.087||169||3.28|
|CL||Mariano Rivera '02||46.0||2.74||1.00||161||2.88|
No surprise here, the worst offensive seasons go to Jose Molina in 2008, Enrique Wilson in 2004 and Tony Womack in 2005. On the pitching side it'd be hard to argue that David Cone's season in 2000 was downright awful. Kei Igawa did give him a run for his money in 2007, but with half the innings pitched he ultimately would have had an opportunity to bring that ERA down if he had pitched the same number of innings.
The Yankees have had a pretty successful decade by all standards. All in all they've amassed 9 playoff berths, 4 Pennants and 2 WS Championships. The only team to win as many World Series as the Yankees over the decade is the Red Sox. Even a greater testament to the AL East is that 7 out of the past 10 years have sent an AL East team to the World Series.
The Yankees have been lucky to have that stable of players from the late 90's in Posada, Jeter, Rivera and Pettitte (since he's been in pinstripes for a majority of this decade). Here's to another successful decade with a stable of players the likes of Alex Rodriguez, CC Sabathia, Mark Teixeira and Robinson Cano to keep the dynasty going.