From economist Cy Morong.
The correlation between the change in strikeout rate and the change in contact rate was .142. So if a batter’s strikeout rate increased, his batting average while making contact also increased. Looking at the changes from 2005 to 2006 gave a .18 correlation.
Maybe this makes sense. If you swing harder, you strike out more. But a harder swing means the ball is hit harder, which should mean more hits. So combined with the earlier study, a player should be careful if he thinks he should make a big effort to strikeout less.