So to improve the odds even more they should bat the 3rd hole hitter 9th so that as the game goes on....

It's hilarious how those geeks come up with so much bullcrap and their parrots go around repeating the crap thinking they sound so knowledgeable.

At UVA, I was a math major and I can tell you that with a dataset as big as baseball outcomes, regressive models to determine the best set of outcomes should be considered highly reliable. This stuff isn't just made up out of thin air. It's based on an absolute ton of data and mathematical regression which essentially "boils down" the sample set that leads to the best outcomes in the long run. Hitting your best hitter first and the pitcher 8th leads to more runs than batting him 3rd with the pitcher 9th because over a long season your best hitter gets plenty more plate appearances, as does your second best hitter in the 2 hole.

EDIT: Another way to look at it is that the mathematics say that it is better to have your best hitter hit more often than to try to manufacture more RBI opportunities for him. However, manufacturing is valuable enough to where it is worth putting a real hitter in front of your best hitter at the expense of moving your pitcher up one spot in the lineup. It's essentially a mathematical analysis of the value of getting more PA's for your best hitter versus the value of attempting to manufacture more RBI opportunities for that hitter using the lineup. There isn't 0 value in that manufacturing but it is a LOT less valuable than having your best hitters hit more often and that makes sense.