It makes sense statistically that postseason stats across time will look like career averages. One problem is defining a "significant" sample of post-season at bats. It's easier for modern players because there are three rounds. It's hard to find guys with a lot of postseason at bats the further back you go in history. Ruth only had 129, Gehrig 119, Mays 89, Jackie Robinson 137 and so on.
For the A-Rod thing, I think it's interesting to look at Manny Ramirez. Man-Ram (seriously, do people call him this or is baseball-reference making it up?) had a few terrible postseasons and then did well, bringing his postseason numbers more in line with his career ones (though still quite low). Who's to say A-Rod won't have a similar path? Another fun guy to look at is Mickey Mantle.
Other players with similar postseason vs. career numbers (minimum 200 postseason ABs, arbitrary yet effective):
Code:
Javy Lopez (205 postseason AB) .278/.324/.493 vs. .287/.337/.491
Yogi Berra (259) .274/.359/.452 vs. .285/.348/.482
Bernie Williams (465) .275/.371/.480 vs. .297/.381/.477
Chipper Jones (333) .288/.411/.459 vs. .304/.402/.542
Andruw Jones (238) .273/.364/.433 vs. .267/.345/.505
Omar Vizquel (228) .250/.327/.316 vs. .276/.342/.360
Reggie Jackson (281) .278/.358/.527 vs. .262/.356/.490
Pete Rose (268) .321/.388/.440 vs. .303/.375/.409
Paul O'Neill (299) .284/.363/.465 vs. .288/.363/.470
Rickey Henderson (222) .284/.389/.441 vs. .279/.401/.419
Roberto Alomar (230) .313/.381/.448 vs. .300/.371/.443
Lonnie Smith (205) .278/.341/.424 vs. .288/.371/.420
Mark Lemke (232) .272/.335/.353 vs. .246/.317/.324
Derek Jeter (478) .314/.384/.479 vs. .317/.388/.463
Sorry if the list's slanted towards more recent players but they have more AB's and they're who I thought of off the top of my head.
Other things I noticed:
There were a few players who consistently underperformed in the postseason including Kenny Lofton, Reggie Sanders, Tino Martinez, David Justice, Joe Morgan and Terry Pendleton.
There were also a couple players who overperformed, namely, Steve Garvey and Marquis Grissom.
I know there's more in the top category and probably also in the bottom but I wouldn't know where to start looking.
To conclude, there's a number of players who underperform and possibly an equal amount who overperform over 200+ ABs but I couldn't find as many. It seems that the more postseason AB you get, the more in line your postseason averages get with your career averages though one or two good series could change it one way or another (see Lemke).