With Orlando Hudson hurt, we are hearing the talk of moving Mauer to the number two spot in the order. The basic argument is that he will get more plate appearances (about 20 more over the course of the year) and he gets on base at a .400 rate. Most of the people advocating this also want to move everyone else up, putting whoever is hitting number two now toward the bottom of the order. The other alternative is to move someone else into the 3 spot, Kubel, Cuddyer and Young would be the likely candidates. In any case, other players will also get some of the number two hitter's at bats - if he drops 6 spots to 8th in the order it would be about 120 plate appearances in all.
There are two problems with this, the benefits are not as great as you would expect and the costs are a lot greater. Mauer with a .400 OBP will get on base 8 times in those 20 extra plate appearances, while a guy with a very low .300 OBP will get on base 6 times. Over those 120 plate appearances for all players, the average is likely going to be closer to .350, which means they will get on base 42 times compared to 36 times for players with a .300 OBP. In other words, you are gaining about 6 base runners over the course of the season by moving Mauer into the number two spot and everyone else up. Of course, there is more to the issue than just getting on base. Presumably getting on base will include a variety of hits, including some for extra bases.
So what are the costs? The major issue, the reason your best hitter is usually batting third, is Mauer will come to the plate with a lot fewer base runners on base. Lets look at the impact just on the first inning. If Span gets on base at a .400 rate, Mauer batting number two will have a runner on base 64 times over the course of a season. With a .300 guy in the number two spot, he will come to the plate with two runners on 19 times (.3*64) and one runner an additional 29 times for a total of 93 plate appearances with 102 base runners. Of course that is assuming neither runner scores, but for the rough purposes here I think we can ignore that.
However Mauer isn't the only one who loses RBI opportunities with a shift. Morneau, now batting third, will also have fewer base runners. Those opportunities shift to the number 4, 5 and 6 hitters. Presumably Cuddyer, Kubel and Young. I am not sure that is a great new strategy to shift RBI opportunities to those three from Morneau and Mauer. Its hard for me to see how shifting those 48 base runners away from both Mauer and Morneau is offset by an extra 6 base runners over the course of the season.
Those impacts are from the first time through the order. After that, if you just shift everyone up, the number nine hitter essentially takes over Span's role in the current lineup. Span is now hitting directly in front of Mauer where the number two hitter was before. And, of course, this all assumes that players do not change their approach based on the new situations they are in. That is undoubtedly not true.
There are a lot of good reasons for the tradition of putting your best hitter number three. Before proposing to change it, you need to consider what they are.