Physics of Baseball… Ball-Bat Collision

physics of baseball

With a Rapsodo Hitting camera finally here at RPP, it’s time to start talking physics of baseball on the hitting side.  We’re going to start this series of articles by going over the point of contact, where the bat meets the ball.  We all know that a baseball hit hard at the right place can do a lot of damage.  But the art and skill of doing so can be a difficult process.  So, let’s review what happens at the point of collision, where 90 mph pitches meet 90 mph bat speeds.

Dr. Alan Nathan (Professor Emeritus of Physics at University of Illinois) has written a substantial number of studies and articles on the physics of baseball.  In an article titled “Optimizing the Swing” (published by The Hardball Times, November 11, 2015), he provides a comprehensive review of what happens when the ball meets the bat.  To summarize and “simplify” parts of his article, there are three different significant topics that determine the outcome of the collision:

    • Pitch Descent Angle – The angle at which the ball is arrives at home plate
    • Attack Angle – The angle at which the bat meets the ball
    • Offset – The vertical distance between the centers of the ball and bat

Here is a simplified side-view (recreated with some minor changes from Dr. Nathan’s article):

physics of baseball

Let’s review each in some detail:

Pitch Descent Angle: This represents the angle at which the pitch is crossing the plate.  This is a function of many things, including

    • Pitcher height
    • Pitcher arm slot
    • Type of pitch
    • Pitch-specific spin data
    • Pitch velocity

Although there aren’t any studies (believe or not) on descent angle of the pitch, there a couple of reference points available.  Dr. Nathan’s article lists fastballs crossing home plate at an average of 6 degrees downward angle, with a breaking ball crossing the plate at a 10 degree downward angle (we are assuming these are for professional pitchers).  In a somewhat related article, titled “Using Swing Plane to Coach Hitters: A Deeper Look”, Jason Ochart at Driveline Baseball refers to a descent angle range between 4 and 21 degrees for “virtually all pitchers” (we assume the wider range implies a larger population including younger pitchers).

Attack AngleAttack Angle is the angle of the bat’s path, at impact, relative to the horizontal. A positive value indicates swinging up when bat meets the ball, and a negative value indicates swinging down, and zero is perfectly level with the ground.

The Offset:  This is basically where the bat meets the ball, defining the batter’s aim.  Best way to explain it is a diagram:

So, what does this all mean?

In general, we all know pitchers are in control.  They have the ball.  They know what they’re throwing, and they control the timing.  For players, there are only two elements of control:

    • Offset (a function of the batter’s aim)
    • Attack Angle (a function of the batter’s swing path)

The interplay between the Offset, the Attack Angle and the Pitch Descent Angle play important roles in determining the Launch Angle, the Exit Velo and the distance the ball travels.

If you simply and only want the highest exit velo then just square up the bat and the ball, by matching up the Attack Angle with the center line angle (image below). In that instance you’re putting the swing path on the identical plane as the ball with a direct transfer of energy, basically a 100% level swing through the ball’s center (please note that high exit velo does not necessarily mean the farthest distance, you can hit a ball with 100 mph exit velo into the ground!).

On the other hand, if you want to generate incremental distance, you need an “offset” between the swing path and the ball and an attack angle less than the center line angle to (a) create a positive Launch Angle and (b) generate incremental “hang time” as the exit velo does its work.

Taking this analysis one step further, the charts below (from the article Optimizing the Swing) say it all.  Assuming an Attack Angle similar to the Pitch Descent Angle, by creating a level plane (bat and ball) with an offset, you can drive the ball farther by creating lift and hang time.  For example, a baseball hit on a level swing with a 6 degree Pitch Descent Angle, 100 mph exit speed and a 0.4 inch offset would travel approximately 150 feet.   On the other hand, a 1.0 inch offset on the same swing would travel 400 ft.

For clarity:

    • Top chart is Exit Velo (mph)
    • Middle chart is Distance (ft)
    • Bottom chart is Hang Time (s)

The charts demonstrate that even with a little degradation in Exit Velo (from 101 mph down to 98 mph), you can still drive the ball substantially farther with an increased offset, from 0.4 – 1.0 inch.  A lower offset behaves more like a line drive and larger offset behaves more like a deeply hit ball.


The art and skill required to hit a baseball well can be difficult.  As you can see the physics of baseball can be equally complicated.  The permutations are endless but we can draw some very practical conclusions.  Simply put, in order to drive the ball, create a “level swing” path where it coincides with the downward plane of the ball.  This will help improve your chances of a good solid contact, even if your timing is slightly off.  The combination of a level swing and an “offset”, between the two planes, will help you drive the ball harder and farther.

Now, if only it was that easy!!

By Bahram Shirazi (BSEE, MBA, Co-Owner RPP)