Some people want Joe Mauer batting second? That's a great idea, he is by far the best number two hitter on the Twins. He would also be the best leadoff hitter, the best number 9,8,7,6,5 hitters. In fact, he would be the Twins best cleanup hitter. In short, no matter where you put Joe Mauer in the batting order, he will outshine whoever is hitting there now. But that is the wrong question.
The question is where does Joe Mauer help the Twins the most? And the answer to that is batting third, the traditional spot for a team's best hitter. There are good reasons for that tradition. But lets look at what happens with Mauer batting second.
The general argument for Mauer batting second is that he gets on base a lot, something generally valued in number two hitters. The other argument is that batting second he will get more plate appearances. Based on last year, he will get 17 additional plate appearances by moving from the number 3 spot to the number 2 spot in the order. These extra 17 at bats would all come at the end of the game when the number two batter on the Twins made their last out of that game. So these extra at bats will come with two out. If you substitute his OBP of .400 for a different player with a .300 OBP, the Twins will get 1.7 (round it up to 2) more base runners with two outs over the course of the season by moving Mauer up in the order.
While this evaluates the effect of putting Mauer in the second spot, it fails to consider the effect of moving the number two batter to the end of the order. Last year the Twins number two hitter got 741 plate appearances, the number nine batter got 619. So moving the number two hitter to number nine shifts 122 plate appearances to the rest of the order, including the 17 that would go to Mauer. The value of those extra plate appearances depends on the extent to which the number two hitter is better or worse than the average player in the rest of the order. Its likely this year that would provide some additional marginal benefit to Mauer batting second.
The first inning is the only time there is any real difference between batting second or third. In subsequent innings, the nine hitter will in essence be in same spot related to the number two hitter that the leadoff hitter is to the number nine hitter. So the beginning of the game is where you see the downside of batting second.
In the first inning, batting second Mauer will see about half as many base runners as he would batting third. If the number two hitter ahead of him batting third would have had a .300 OBP, it will be about 48 fewer base runners (.300*162 game) when Mauer bats second. But, its not only Mauer who will see fewer base runners. So will whoever was batting cleanup and is moved up to the number 3 spot. For the Twins that probably means Willingham (or Morneau).
One beneficiary of this is the number five hitter. By moving to the cleanup spot he will be more likely to hit with Mauer and other base runners ahead of him. About 30% (.300) of the times a runner is on base, the cleanup hitter would have made the last out, preventing the number five hitter from getting a shot at those base runners. Most of the other 70% of those extra RBI opportunities would go to the current number 6 hitter(Ryan Doumit) moving to number 5 and the number 7 hitter (Chris Parmelee/Trevor Plouffe) moving to number 6. There would likely be a few extra chances for the number 8 hitter who moved up to the 7 spot as well.
In short, the result of moving Mauer to the second spot, is to move a bunch of RBI opportunities to lesser hitters lower in the order. All for the benefit of an extra couple base runners with two out at the end of the game. Of course if Parmelee and Plouffe suddenly turn into allstar hitters, then you can make the case for giving them more RBI opportunities at Mauer's expense. But that doesn't seem like a very likely starting point this season.