Steve's Lineup Toy  
To use the Lineup Toy:

The Lineup Toy uses OnBase Percentage (OBP), Slugging Percentage (Slg) and OnBase plus Slugging Percentage (OPS) to come up with a suggested lineup.
In baseball, runs are generally scored by players getting on base and other players knocking them in. So it makes sense to put the best players at getting on base in front of the players who are best at getting them home.
The players at the top of the batting order get more plate appearances than the players lower in the order. The higher a player's OBP, the fewer outs that player makes. Since the length of your game is limited by 27 outs, putting high OBP guys on top of a lineup gives your team more plate appearances as a whole, and more chances to score runs.
This suggests a fairly simpleminded strategy for constructing a reasonable lineup:
1. Put the best OPS in 3rd
2. Put the best remaining Slg in 4th
3. Put the best remaining OBP's in 1st and 2nd (with the better Slg in 2nd)
4. Arrange the remaining players in order of descending Slg
Now, this might lead to some pretty strangelooking creations. But like I said, it's a simpleminded method. The Lineup Toy doesn't take into account factors like speed and stolen bases. Take the Lineup Toy's suggestion and use some common sense to tweak it.
RC27 is the estimated runs scored for 27 outs of the given lineup. It's computed by figuring out how many plate appearances each player will get on average; scaling the player's stats to that number of plate appearances; adding the stats up to produce a team's total bases and onbase percentage; and multiplying those to come up with a simple Runs Created figure.
This is Version 2 of the Lineup Toy. You can find Version 1 here.
If you'd like to discuss the Lineup Toy, leave a comment on my Lineup Toy blog entry or Email me, please.
Thanks for stopping by,
Steve