For batting awards, players must average 3.1 plate appearances per team game or more in order to qualify. Pitchers must average one inning pitched per team game. Position players must appear in 50% of their team's innings played to qualify for fielding awards.
Cy Young: Innings Pitched, Earned Runs, Strikeouts, Saves, Shutouts, Wins, Losses, Team Records and Park Factor.
MVP: Runs Created, Good Plays, Poor Plays, Fielding percentage, Park Factor, Position Played (difficulty), Passed Balls (catchers only)
Fireman of the Year: Saves, Wins, Losses, and Blown Saves
Gold Glove: Fielding percentage, good plays, poor plays, Errors, and Range Factor
Silver Slugger: Runs created and park factor
Rookie of the Year: Closely mimics the formula used for MVPs for position players and Cy Young for Pitchers. In order to be eligible for the ROY, a player must either be a prospect or a first-time player in a progressive league(theme setting).
In each case, there are weights assigned to the individual components for the award calculation. While real life awards are decided by writers using the core raw stats and their personal opinion of how good/valuable players are (despite numerous objections by other esteemed writers across the land), SLB can use more appropriate statistics and accuracy to determine the best of the best.
If you think you have a player that should be up for an award but he isn't listed, be sure to evaluate all the component pieces and compare them to the players ranked ahead of them. It's hard to take sometime (like when you have a player with 55 HR, 150 RBI and a .340 AVG not in the top then), but there are always reasons why they are ranked where they are. They could be playing 1B while those ahead are SS & CF. They could be playing half their games in a hitter's park while those ahead play in pitcher's parks. Many reasons, all put together, and the best are at the top of the pack.
It's also important to note that only prospects are eligible for the ROY. For multi-season (progressive) leagues, true first year players are also eligible. That is, players from their rookie seasons.