Sure, you just gotta go around the bases without any fielder committing an error for it to be a home run. It doesn't actually have to leave the field of play.

Now is it possible to hit the ball over the outfield wall on a bunt with a wooden bat? No. There just isn't enough energy in that interaction.

If you mean just a run, then sure, you just need to be a phenomenally fast runner or have infielders who can't grip the ball. But I think you mean a home run that goes out of the park.

For all intents and purposes, a bunt is just a bounce. That means that it will always leave the bat moving slower than it was being pitched; even with ideal materials and no air resistance, the best a bunt can do is bounce the ball as fast as the pitch. So the first question is, could a sufficiently fast fastball go over the wall?

A professional baseball player can throw a baseball about 100 meters, which also happens to be about the same distance from the batter to the outfield wall on most fields; so just on the face of it the answer is "no," because even in an ideal scenario it's already traveled 18 meters from the pitcher's mound to the plate before it starts moving toward the wall, meaning that an ideal pitch of a perfect ball bouncing as efficiently as possible off a perfectly-bouncy bat would fall 18 meters short of the wall at best.

So what would it take to make this work?

Well, let's consider location. For an out-of-the-park homer, pure distance isn't enough; we don't just want to hit the wall, we want the ball to go over it. Assuming MLB stadiums, you might think our best bet is to send it over the right field wall in Fenway Park in Boston, which is only a meter tall; but the Pesky Pole that's 92 meters away is 4 meters and it doesn't come down until it's 115 meters from the plate. So we should go for Yankee Stadium, which has a 2-meter wall in the right field at 96 meters.

And obviously we're going to need an amazing pitcher here, which we'll talk about in a minute, but the batter is actually important too. Specifically his height; we need him to be as tall as possible, so that the top of his strike zone is as close to the height of the wall as we can get (or taller, if we can manage). Plus, he needs to be a southpaw, as a right-handed batter would have to contend with the taller left field wall. He'll also have to focus on hitting the ball at an ideal angle (30°) and imparting whatever backspin he can to give it a little bit of aerodynamic lift.

What we need from a pitcher is just speed (and I guess a tendency to pitch to the very top of the strike zone). The ball is going to lose a good deal of speed in the bunt, so it needs way more coming off the mound. In a normal hit, the batter puts a ton of energy into the ball, but in our bunt, it's all up to the physics. The bat-ball coefficient of restitution in the MLB is usually around 0.5, so the best we can realistically hope for is that it's going to lose about half of its speed to heat, sound, and vibration. It'll actually lose even more to the fact that the BBCoR is measured against a perfectly stationary bat (so even the most sturdy human bunting would decrease that number as their muscles and bones absorbed the impact), but the batter could try to push the bat and give it a little bit more power at that point, which could compensate for that loss. We'll call that part a wash.

But here we are into a realm where we can start putting some actual speed numbers on stuff. The slowest speed-off-the-bat of an over-the-wall home run is about 42 meters per second, and since we're effectively not going to get any help from the batter, x/2 has to equal 42. So the pitcher needs to be able to throw at 84 meters per second, which is a 188mph fastball; interestingly, that's exactly double the average MLB fastball speed (94mph), and about 178% of the speed of the fastest fastball ever recorded. (Actually it'd need to be 89 m/s to account for the speed it would lose to drag from the pitcher's mound to the plate, but at that point we're just being pedantic.)

Unfortunately, unlike human running speed, the fastest a human can throw a fastball seems to be pretty much optimized, and in fact biomechanical models suggest that any human throwing faster than about 108mph would probably tear the ligament in their elbow from the torque. A 188mph fastball thrown by a human would certainly be career-ending and maybe even dismembering. So not only do we need a superhuman baseball pitcher, we also need them to be willing to throw their entire pro baseball livelihood away on our stunt. And we only get one shot at it.

So let's talk through this crazy situation, second-by-second (with apologies to Randall Munroe). I'll treat the moment of the bunt as T0.

T - 10.00s: The most powerful pitcher in all of human history stands atop the pitching mound at Yankee Stadium. The catcher gives him the sign, which in this case I can only assume would be showing him a picture of the pitcher's family, whom he's kidnapped and threatened in order to get the pitcher to do this.

T - 5.00s: The pitcher sheds a tear and nods. The catcher probably moves out of the way, knowing as he does what's about to happen.

T - 1.75s: The pitcher winds up for the pitch. The batter begins to move the bat into position for the bunt, right at the top of his strike zone; he has to do it now, even though the pitcher will see it, or else it won't be in position in time. Any other pitcher would switch up his throw, seeing this, but the catcher has his kids, man.

T - 0.25s: Our ball leaves the pitcher's mound, traveling at 89 meters per second about a meter off the ground, at about a 10° downward angle with significant backspin. Close behind it is the pitcher's lower right arm, severed at the elbow from the rotational torque severing the UCL, muscles, and skin. Luckily the pitcher managed to release the pitch at the optimal angle before he threw his arm.

T - 0.125s: Our ball is halfway to the plate, and it's now 0.9 meters above the ground.

T + 0: Our ball reaches the bat traveling 84 m/s, right at the top of the batter's strike zone, and compresses both itself and the bat before rebounding at 42 m/s at a 30° angle toward the right wall of the outfield. A very loud crack is made from the contact. The leather cover of the ball is torn during the impact, and it's very possible that it could've exploded entirely into a tangle of yarn and cork. Good thing for us it didn't.

T + 0.05s: The crack of the bat reaches the pitcher's mound, though the pitcher is a little bit preoccupied to think about it right now.

T + 0.20s: The pitcher's right forearm hits the ground, a few meters in front of him, having reached its terminal velocity much sooner than the ball did.

T + 0.25s: The batter drops his bat and begins to run toward first base.

T + 0.30s: A very loud crack of the bat reaches the outfield wall.

T + 0.48s: If the ball were bunted straight down the middle, it'd probably hit the pitcher in the head, as it's only about a meter and a half off the ground. But he's probably suffered enough, and we're aiming to the right anyway.

T + 0.53s: The bat dropped by the batter hits the ground.

T + 1.21s: The ball is halfway to the outfield wall, and it's reached the apex of its trajectory, about ten meters off the ground. It's also slowed down to 32 m/s.

T + 2.42s: The ball just barely clears the outfield wall (it's a good thing the right fielder was so concerned about the pitcher pitching his arm off that he decided to run in to help the pitcher rather than running after the ball, or he could've easily caught it).

T + 3.00s: The pitcher has lost about 32ml of blood (not counting what was in his arm) and while the blood loss isn't critical yet, he's certainly going into psychogenic shock.

T + 4.50s: The runner makes it to first base.

From that point on, I suppose you could probably guess pretty easily as to what happens. The runner rounds the rest of the bases, but nobody really pays attention to him anymore. Medics swarm the pitcher's mound. The catcher tries to sneak away, but is caught by stadium security and later arrested for kidnapping and reckless endangerment. The pitcher's family is rescued as the pitcher himself is taken to the hospital for emergency arm-reattachment surgery. The batter is questioned extensively about his involvement in the scheme. The pitcher becomes famous for accomplishing a feat that no one can ever repeat.

I think I get what you're asking, basically want to see a brick wall of a player holding the bat perfectly steady while a pitcher throws it 500mph and hits the bat at a perfect angle?

Not really mechanics or speed, you can do it with something as simple as incompetance, or bad teamwork. Plenty of examples on youtube watch some.

https://youtu.be/XjQTHDDob-k

it's not that the ball gets hit out of the park, it's that the hitter is able to run home.

If you just want the batter to run to all the bases and reach home and score a point (or a run, by baseball jargon) with no regard for on field ruling, then yes by a series of errors being committed by the fielders.

For example if a fielder throws to first to get an out, but throws it out of reach from any fielder. However, in this case the ball MUST NOT leave the field of play (e.g., get thrown into the stands), otherwise the ball is dead, and the runner will be placed on a base at the umpire's discretion.

This however is not a home run by rule, but rather a fielding error(s) that results in a run.

Another option is that none of the fielders try to get the ball. They just stand around after the batter bunts the ball. There's no real reason this would happen, unless something extraordinary happens (aliens land on the stands, that sort of thing). This would probably be ruled a home run, but again, astronomically unlikely.

If you're allowing swinging bunts, you could potentially have a batter "doink" the ball over the in fielders but outside the reach of an outfielder and have the fielder run past the ball without touching it (if they touch it, it's an error). If the batter runs fast enough as all of this happens you can conceivably have a home run this way.

The "I'm trying to break physics" version of this may have been covered by XKCD at some point.

I have bunted a baseball over a little league fence. Me and some friends tried all day long.

My technique was to push the bunt while turning into the pitch.

Getting it to the outfield is trivial. Home run is very hard. The fence was less than 200 ft.

I guess if you just round first base instead of running through it, beat the inevitable pickle between first and second, round second, beat the pickle between second and third, round third, and then jump over the catcher à la Willie Mays Hayes in Major League, it’s possible 🤷‍♂️

If the opposing team really fucks up then maybe.

Assuming you mean turning the bat perpendicular to the pitch and stopping it so that the ball just bounces off the bat, then no. The bat has to impart enough momentum to the ball to carry it over the wall. There is some elasticity to both the bat and the ball such that a fraction of the pitch speed is rebounded, but it is a low fraction. The pitcher would have to be pitching up near the speed of sound for the rebound to carry the ball very far.

That said, I can imagine a bunt where enough errors are made in the infield that the batter makes it all the way around without being thrown or tagged out.

Someone might be along to do the actual math, but the base answer is that there really isn't a way for a true, over the wall, home run to occur from a bunt.

The pitcher would have to throw one hell of a fast/curve ball, but yeah. It should technically be possible, but you might need a machine not a human to pitch the ball. The material of the bat would also be important. You'd want as much of the force of the ball to be bounced back into the ball after colliding with the bat. You'd also probably not want the ball to just destroy whatever it hits.

Someone really good at math could probably figure out exactly how fast and with what materials this could be done with. I am not that person tho.

Sure, just don't get tagged.

A little league homer might be possible, but neither a traditional homer nor an inside the park homer could happen off a bunt.