1) Tell the manager to throw away his batter/pitcher index cards, or book, or whatever it is that they use, and never look at another batter/pitcher historical result again. I’ll get to the alternative in a minute.
2) Do the same for any other small sample size of historical performance. For example, don’t ever look at how a batter is doing lately, either yours or the opponents’. That should have no bearing on any of your decisions.
3) Never spend another minute worrying about the best lineup. Use a set lineup against RHP and LHP and leave it alone unless you change players or someone is injured.
4) Along those lines (#3), I will give the manager the 2 or 3 best lineups to use against RH and LH pitchers. I can even tweak those for GB and FB pitchers (remember that there is a significant GB/FB platoon advantage - it is just that it doesn’t come up very often).
5) Along the lines of #2, I will give the manager a book or index cards of each batter/pitcher matchup. It is comprised of the batter’s current projection, adjusted for the park (maybe) and the pitcher’s current projection (again, maybe adjusted for park), combined using each player’s platoon ratio and a log5 method. I might give him several versions: one for in general, another for when he needs a K, another for when he wants to avoid a BB, another for when he wants to avoid a HR or extra base hit, etc. I would also have two numbers: one for when the batter is already in the game and has seen the pitcher several times, and another one for when the batter is a pinch hitter (includes the pinch hitter penalty). That way, the manager, if he wants to compare the batter in the lineup with a potential pinch hitter, all he has to do is to compare the two players applicable “matchup” projection. I would also have a column of each player’s projection (displayed in some manner that the manager can easily understand, like EQA or wOBA) versus a RH and LH opponent. That way, for example, he can decide between two or more players he is considering bringing in as a pinch hitter or reliever, given the likely opponent or opponents’ handedness.