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This will probably be the most controversial spot in the lineup all year.
Alex Rios flourished hitting third last season, and it's easy to justify a right-left-right combo in the 3-4-5 positions to break up Rios and Paul Konerko, but bear with me, because this is also bound to change from time to time.
With a lefty on the mound, you may see Rios hitting third and Dunn fourth. However when there's a righty on the mound, you want Dunn to get an at-bat in the first inning.
Furthermore, Rios hitting third with Dunn and Konerko behind him will take away Rios' ability to cause havoc on the bases. With two outs and Rios on first, you're not going to send him with Dunn or Konerko at bat.
The big question mark with Dunn is how he will adapt to the designated hitter role. He has expressed concern about all the down time when he's not playing in the field, but he's a fun guy. I'm sure he'll find something or someone to keep him busy.
Dunn will be his usual self, hitting 35-40 home runs in a Dunn-friendly U.S. Cellular Field. He'll drive in 100 runs and strike out more than you want him to.