After many carefully controlled collisions and hours of video of bats striking balls, a group of physicists at Washington State University came to the conclusion that the relationship between a baseball and a bat was inelastic.
It was not an earth-shattering revelation, but it did debunk a few assumptions. Elasticity is the ability of an object to regain its shape when it is deformed in some way. During a collision, elasticity causes the object to "push off" the surface that deformed it. An elastic rubber ball will bounce off the floor when it's dropped; it gets smushed down when it strikes the floor and the force it uses to regain its shape pushes it up. An inelastic ball, like a beanbag, will hit the floor and stay there. It has no ability to regain its original shape.
Baseball players looking at a rubber ball and a bean bag knew which one they'd rather have bouncing off their bats. One player was caught using a bat with cork in it, supposedly to give the collisions elasticity. That may have been the goal, but it wasn't the result. The corked bat may have made it easier to swing a bat, but there was no greater elasticity in the collision.
There have also been plenty of rumors that balls have been changes, surreptitiously, to become more elastic. As people expected greater and greater feats from their sports stars, companies, teams, and players changed the balls in order to deliver — or so the story goes. Physics, stern but fair, came to the rescue again, showing that the elasticity of baseballs hasn't changed much since the 1970s. Players may be getting a little help, but it's from the realm of biochemistry, not physics.
There is one thing that changes the elasticity of this collision, but it isn't for the better. Higher humidity takes what little elasticity there is in the collision, resulting in less impressive hits and presumably more dented balls. Conclude the researchers:
[There] is no measurable trampoline effect with a corked bat and that it is unlikely that a batter can hit a baseball harder by using a corked bat. We have found no evidence that baseballs of today are more or less lively than baseballs used in the late 1970s. Finally, we have shown that storing baseballs in humidors at 50% relative humidity in Denver can lead to a marked reduction in home run production. A similar effect can be achieved by storing the baseballs at a temperature of 35 ° F.