Obviously, I think about saves. I need to compete in the category. But we know that half the closers will either get hurt or lose their jobs. Plus, the leagues I play in allow for daily transactions, so I always have two to four talented set-up relievers in my lineup. A solid group can contribute more than 200 strikeouts per season and help in ERA/WHIP so that you can gamble on starters a bit more.
So, more often than not, I hunt for saves throughout the season. If I draft correctly and have a surplus of power hitters, I can always acquire a solid closer. But there are enough pitchers who emerge as their team’s closers that I never focus on saves during the draft. As with most positions, I focus on skills.