Batting Order Substitutions
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from Scoresheet:

1)  Lineup Juggling:  Our computer sometimes juggles your batting order when one of your bench players has to start a game for you. The reason we don't simply put the sub in the same spot as the starter is because often the sub is a far weaker hitter than your starter.  For instance, you may have Mike Piazza batting third, but if Jason LaRue is your backup catcher you certainly don't want him hitting third if he starts a game. Before we do any lineup juggling we figure out who your starters are; the juggling procedures occur after your starters are determined.  Here are the rules we follow when juggling lineups. 

A)  A starter never moves down in the order. 

B)  A starter batting leadoff, 2nd, or 3rd never moves at all.

C)  A starter who is in your 3, 4, 5 or 6 slot never moves higher than the third slot.

D)  Since we never move a 3 thru 6 hitter above the 3rd slot, your new leadoff and 2nd batter (if either is subbed for) comes from either a sub or your 7th or 8th hitter (and/or 9th hitter in the AL.) If your leadoff or second batter is out we first look for a batter who has a Y in his steal column to fill that spot.  If more than one batter has a Y we put the batters with the better PH rank (the lower the number the better - #1 is best) at the top of the order.  Also, a catcher will not be moved to the leadoff spot.

E)  In the 3 thru 8 (or 9) spots, we put the guy with the best pinch hit number highest in the batting order.  (We never move a starter down in the order.  But when a sub comes in the decision of whether to move other guys up, or to bat the sub higher than a starter, is based on PH rank.)  Lineup juggling is another reason that ranking your hitters in the PH column is important, as we do put the hitters with the better rank higher up in the order. 
[A substitute without a rank for pinch hitting against the handedness of the starting pitcher will bat behind all players in the batting order with PH rankings, but ahead of any remaining guys at the end of your order who do not.]

I believe this was written by Cory Watson of Scoresheet Canada in 2002, but it may have originated from either Dave or Jeff Barton founders and operators of Scoresheet Sports.
- John Carter