Under the new rules which have been promulgated by the Hall of Fame, recently retired players will no longer stay on the ballot for a maximum of fifteen years. Now, players will drop off the ballot after ten years, although Lee Smith, Alan Trammell and Don Mattingly (in their 13th, 14th and 15th years, respectively, of eligibility on the next ballot) will be grandfathered in, rather than immediately dropped.
In recent years, Bert Blyleven and Jim Rice have made it in very late in their eligibility period, and neither of those players would have been elected under the ten year rule being implemented.
Once a player drops off the BBWAA ballot, he is eligible for consideration by the "Era Committee." While in the past, very liberal standards for being picked for the Hall of Fame have been applied by the Veterans Committee -- peaking in the "did you play with Frankie Frisch" Veterans Committee in the late-60s and early-70s that inducted marginal candidates such as Jesse Haines and Jim Bottomley -- the recent trend has been that, if the BBWAA doesn't vote you in, you probably aren't getting in.