Using a linear regression model with data dating back to 2005, there appears to be a statistically insignificant relationship between the number of homeruns a player hits during the regular season and the homerun derby.
However, with the addition of a second round in 2014 and then completely overhauling the format in 2015, we might see a shift in the type of people who win the derby. Batters only have 5 minutes to swing per round. This means batters will be swinging as hard as they can and as many times as they can. We might even see some players break a sweat. My prediction: the 2016 rule change will require contestants to juice up #letbarryplay