The Physics of Batting Practice

How different is batting practice from the actual game? (via Andy Rusch)

Another great season is almost in the books and it is time for the players to rest, recover, and heal. Not for long, however. For professional athletes, it is always time to prepare for next season – back to the cages.

Despite “The New Science of Hitting” created by the Statcast data set, hitting practice seems to have changed little. Of course, I’m not a hitting instructor nor a player so I don’t know for sure. Nonetheless, I can and will take a stab at discussing the physics of the three most common methods; tee work, traditional batting practice where the pitcher throws slow pitches from in front of the mound, and hitting off a machine that fire balls at near game speed.

The difference, from a scientific point-of-view, is the incoming speed of the ball. For tee work, the ball isn’t moving. Traditional batting practice uses pitch speeds around 60 miles per hour thrown from about 40 feet, while pitching machines can fire the ball at game speeds in the 90 miles per hour range from closer to 55 feet.

The variation in incoming speed creates two scientifically and, perhaps, athletically relevant issues. First, the ball-bat collision is distinctly different in that the exit velocity off the bat is dependent upon the pitch speed to some extent. Second, the batter’s timing abilities are essentially unchallenged with tee work and strongly challenged by the pitching machine.

Let’s start with the exit velocity issue. If you wish to deeply understand the physics of the ball-bat collision, you’ll need to spend some quality time with Alan Nathan’s classic paper, “Characterizing the Performance of Baseball Bats.” Here, we’ll have to settle for a far more simplified discussion.

When all the physics is done, the exit speed of the ball depends upon the speed of the pitch and the speed of the bat, but you already knew that. The detailed physics tells us the relationship and it appears to be surprisingly simple:

vexit = q vpitch + (1 + q) vbat.

Of course, all the complex physics is hidden inside q, often called the “collision efficiency.” The collision efficiency depends upon all sorts of messy stuff like the bounciness of the ball, the mass of the ball, the mass of the bat, the shape of the bat, and point along the bat where the ball collides. None of these things will matter to us if I just tell you the value of q for a well hit ball using a common type of bat.

Before I tell you the typical value of q, make a guess. Think about whether the speed of the pitch or the speed of the bat makes more difference to the exit speed. Compare a bunt to a blast. It turns out, the speed of the bat is about six times more important than the speed of the pitch, so q is around 0.2.

vexit = 0.2 vpitch + 1.2 vbat.

Assuming a bat speed of about 75 mph, we now have the answer to our first question. The exit speed for each of the three methods of hitting practice is listed in the table below.

Table 1
Method Pitch Speed Exit Speed
Tee work  0 mph  90 mph
Traditional BP 60 mph 102 mph
Pitching Machine 90 mph 108 mph

These results clearly show the pitch speed doesn’t make a dramatic difference in exit velocity. In addition, they bring up the second issue. In BP, there are way more home runs than in a game. Yet the data above indicates the exit velocity should be higher for a 90 mph pitch than for a 60 mph pitch. The timing issue is the explanation.

“Hitting is timing. Pitching is upsetting timing” – Warren Spahn

Here’s a table showing the time to home for the three methods.

Table 2
Method Distance Time to Home
Tee work  0 feet        ?
Traditional BP 40 feet 0.45 sec
Pitching Machine 55 feet 0.42 sec

Notice the time to home plate for traditional BP and the pitching machine are within 10 percent of each other, less than the variation in game values with different pitch types. Now, let me suggest that the time to home plate is not as relevant as the time the ball spends in the hitting zone.

The hitting zone can be estimated by assuming the sweet spot of the bat is about 30 inches from the hands and swings through a bit less than 45˚. This gives a distance of about 20 inches where contact with the bat results in a fair ball. The table below shows the time the ball is in the hitting zone for each method.

Table 3
Method Time in Hitting Zone
Tee work   Forever
Traditional BP 0.019 sec
Pitching Machine 0.013 sec

Look at how small those numbers are! Even in traditional BP the hitter has less than two one hundredths of a second within which the collision must occur to result in a fair ball. Yet, they accomplish this feat with apparent ease – amazing. The time in the hitting zone is one-third shorter with the pitching machine, a distinct difference compared to traditional BP.

In summary, tee work has a maximum exit speed much less than the other two methods. However, the hitter need not worry about timing the incoming pitch. Traditional BP has slightly higher exit speeds and the time for the ball to reach the batter is roughly the same time as game speed. The difference is the time the ball spends in the hitting zone is much longer for traditional BP than at game speed.

The pitching machine set to game speed results in game type exit velocities. In addition, timing the ball’s flight to the plate and the time the ball spends in the hitting zone are also consistent with game conditions.

Here’s the part where I’m less confident – where I’ve blown it, comment below. The best type of hitting practice depends on which of the many pieces of an effective swing a particular batter needs to improve. If one is working on the shape and structure of a swing perhaps tee work is most effective.

With my untrained eyes, it would seem that the pitching machine would be the best way to work on timing the collision with the ball. The traditional BP is perhaps useful in reacting to timing a pitcher’s release and dealing with less consistent pitches than those associated with a pitching machine.

That said, anecdotally I’ve heard rumors that players are starting to complain that traditional BP is just a show for the fans and not as helpful as going under the stands to the pitching machines. As more teams move toward selling fans the opportunity to be on the field during BP, maybe the hitters have a point.

By now, you may agree with Tris Speaker when he once said, “It would be useless for any player to attempt to explain successful batting.” However, I may have I’ve just proven the same may be said with even more emphasis about a physicist! If so, the comment section is open for business.

References & Resources

David Kagan is a physics professor at CSU Chico, and the self-proclaimed "Einstein of the National Pastime." Visit his website, Major League Physics, and follow him on Twitter @DrBaseballPhD.
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Can pitching machines crank it up higher than 90 miles an hour? I often think that if hitters are trained at that speed, yet modern relievers all throw in the high nineties or even triple digits, then hitters are setting themselves up for failure.

Brad Johnson

Yes, and the most advanced ones can even throw breaking balls while simulating arm action (to some extent). However, I mainly view BP as a way to get loose. It’s much simpler to get all of my moving parts synced up and comfortable against “easy” pitching. It also helps to wake up all the muscles I’ll need for the real thing. I do often wonder why teams don’t have journeymen type pitchers who throw a couple dozen bonus AB to the Byron Buxtons of the world every week. Full disclosure, I barely hit in college and rarely face 90+ mph… Read more »

Jetsy Extrano
Jetsy Extrano

I’ve wondered why they don’t get a final tune-up to machines that can throw the actual speed and spin of that night’s pitchers.


I am curious if part of the messiness of the value of q includes the batters strength. Would a stronger batter be able to influence more force at point of contact when the ball compresses and the bat flexes? Also how long is the time when bat and ball are in contact?


And how far do bat and ball travel in contact before the ball separates?