I received an email with subject line, “Can my friend hit a homerun in infinite tries off the best pitcher in baseball”:
Hey Professor Gelman,
I’m sure this is a weird email that you probably don’t get often but if you could respond that would be awesome!! My school is having a massive debate right now. In an INFINITE amount of attempts (without the loss or gain of strength) could a 5”7, 140lb Senior hit a home run off a 100mph pitch from Paul Skenes, at PNC park (shortest dimension of 320 ft.). If you could get back to me that would be awesome, thanks!
He has no experience playing the sport of baseball, he is not very athletic, there is no wind.
In my opinion I think he can as the possibilities of infinity would eventually create a scenario where he has the perfect swing, with the perfect launch angle, making perfect contact, in the precise direction.
I replied that it’s hard to speak of infinities but my guess is no, he couldn’t ever do it because he couldn’t swing the bat fast enough. But this is just my quick guess; I haven’t done any analysis on the question lately.
It looks like the lowest exit velocity for a homerun that we know of is 85.4 mph. https://www.mlb.com/news/harold-ramirez-hits-85-4-mph-home-run But there might have been wind. OTOH the article says that he broke his bat.
This claims that that exit velocity is possible at a bat speed of 60 mph, against a batting practice fastball. https://www.patreon.com/posts/basics-of-high-120088994
The rub is that the student “has no experience playing the sport of baseball” so his swing is probably terrible. But maybe he could with some training.
I think that answer is wrong. Trying to hit the pitch isn’t necessary, I have infinite strikes. Knowing I can’t swing fast enough if I aim, I will not aim. I just need to swing early and best I can in the middle of the strike zone. Then focus on timing, based on when the ball is released. Assuming pitches are normally distributed in the strike zone, and the bat takes 1/5th of the strike zone I should hit plenty. Strength is actually a bigger problem. Also hitting a fast ball really hurts the hands. Making contact is easy.
You don’t need to swing early, you need to swing on time. The split-second timing required for that is very challenging and tends to improve in professionals until ages 28 or 29. A bat is not 1/5th of the strike zone—it’s closer to 1/10th for a player of average height. Pitches are not at all normally distributed in the strike zone—just the opposite—good pitchers live at the top or bottom of the strike zone and ideally outside of it with movement that makes it look like the ball’s in the strike zone.
I agree that given infinite swings you might eventually make contact. But making contact in baseball is anything but easy!
This answer implies that the batter can learn something from each swing to apply to the next one. In that case then by year 200, the batter might become the best home runner hitter ever.
If every bat is the first one, then it’s a different story.
Baseball physics question, does the energy to get the ball to fly come front redirecting the power of the pitch, the swing of the batter, or some combination of both?
The more power required from the swing the less this likely this is true. Likewise, I presume you need a certain musculature to effectively control the energy of the pitch and redirect the energy in the ball. The description of this kid as not particularly athletic makes me very skeptical he has either. A more interesting question (to me) is how good do you need to be? Would say a typical high varsity baseball player have enough physical ability to pull it off with perfect luck etc or is this something you need 10 years of physical conditioning to be able to do and only the low 5 figures of pro/semi pro players could pull it off?
combination of both. At the moment of impact, there is both kinetic energy of the bat, and the ball, as well as momentum of both. During impact the ball and bat deform, and then restore to their original shape. Momentum and energy are conserved, but some of the energy goes into heating the material, making a “Crack” sound, and other things. Momentum however is more obviously conserved. You need the bat to have considerably more momentum than the ball because the center of mass travels at more or less constant velocity before vs after the impact.
100+ years of natural experimentation has shown stronger players hit more home runs, as do player son steroids, if you want a more controlled experiment.
I think a good varsity high school player would be strong enough to hit a home run. It takes a long time for the hand-eye coordination and judgement to catch up with the conditioning in baseball, which is why peak batting performance is around age 28/29.
My thought was that the main determiner would be if the kid had the literal strength to get the ball that far. Doing some searches for home run calculators, it looks like you would need an exit velocity around 86 mph to travel that distance. Another search suggests that you would need a bat speed of around 55 mph with a regular wooden bat to get that exit velocity. Another search suggests that 55 mph is an average bat speed for an upper middle school or lower high school JV player. So if this is an average-strength high school senior, I would guess they’re strong enough to get the bat moving that fast and could get lucky enough to make contact at the right launch angle in infinite swings.
Inasmuch as this stuff today is meant to be goofy, the phrase
“In an INFINITE amount of attempts”
should be
“In an INFINITE number of attempts”
The distinction drilled into me in grade school regarding amount vs. number is, sad to say, long gone as are other distinctions of note.
According to ESPN, Skenes has thrown 5,411 regular season pitches and given up 23 home runs (to major league hitters) and hit 14 batters. In the scenario provided, the probability of home run would be close to zero while the probability of getting hit by a pitch would remain about 14/5,411. The scenario is basically a torture device where someone is pretty regularly (for infinity) getting plunked with close to 100 MPH fastballs.
Wins thread.
Jake:
I presume the purpose of using an infinite number of attempts is to use the density estimation of these 23 home runs in order to reduce the bias enough to get a mean and a variance that can be used in a simulation of how long it would take to hit a home run.
That is, the finite values of the number of total pitches thrown, etc., is irrelevant.
1. Mariners utility infielder Leo Rivas is about the size of the kid in question, 5′ 7″ and 150 lbs. He has one of the lowest bat speeds in the majors at 65 mph. His hardest hit ball left the bat at 104 mph, and odds are that was not a 100 mph pitch.
2. The google chatbot tells me that the weakest home run in the statcast era was hit by Harold Ramirez with an 85.4 mph exit velocity, just clearing the wall down the right field line in Tropicana Field.
3. The 100 mph pitch speed matters; physics of elastic solids show that it is easier to hit a fastball over the fence than a slower pitch.
Using Alex’s number of a 55 mph swing – or even a 50 mph swing – I believe the kid can get an 85 mph exit velocity if the ball hits the sweet spot (just slightly above the middle of the barrel).
Ramirez’ homer traveled 322 feet to the right field corner in Tropicana, which is the smallest dimension in MLB. So Ramirez’ homer yields both of the numbers the kid needs to match, an 85 mph exit velocity and a distance of 322′.
https://baseball.physics.illinois.edu/trajectory-calculator-new.html
https://tangotiger.com/index.php/site/article/statcast-lab-collisions-and-the-perfect-swing
Yes, it is possible but the batter would just have to guess where the pitch is going to end up and start their swing shortly after it leaves Skenes’ (or any major league pitcher’s) hand. A pitch loses about 10% of its initial velocity by the time it reaches home plate. The maximum exit velocity off the bat is about 1.2 * swing_speed + 0.2 * 90 so a batter would have to swing the bat at least 55 miles per hour at the sweet spot to have a chance and probably a bit more because the sidespin of a ball hit down the line creates more drag.
A (wild) guess:
Let m_1 be the mass of the baseball and v_1 its velocity. It’s traveling at the batter at angle gamma. Let m_2 be the mass of the bat, theta be the angle that the baseball is hit, and v_2 the velocity of the bat. Assume also that the collision is elastic. Then, the equation is:
-((m_1*v_1)(sin_gamma) + (m_2)(v_2) = ((m_1+m+2)(v_2*cos_theta)
Solve for v_2 in meters/second.
Then, rather assume a given velocity of the bat, iteratively progress from the slowest velocity and iteratively increase it. The goal is to reach a unit value of meters/second of the baseball that reaches a minimum distance needed to hit a home run. That is, baseball (I think) is the only sport that doesn’t have standardized field dimensions but is unique for each baseball field. So, because we want to find the minimum velocity of the bat, we would only consider the minimum distance to hit a home run.
Cricket, baseball, hurling, Gaelic football, and Australian football all have variable playing surface dimensions. (I would guess there are others too, but these are the ones I found in a quick search.)
Thanks!
The dimensions of high school basketball courts vary. College basketball too, I think, but maybe there’s been a move to increase standardization in recent years.
Also, golf.
And soccer, too. In international play, fields can be 110-120 yards long by 70-80 yards wide.
Andrew, Gregory:
Thanks!
The key is *infinite* tries. In one of those, Brownian motion of the air molecules will get all the air in front of the ball out of the way, and give it a heck of a tailwind from behind. I don’t think he even needs to swing.
Eric:
Nope. It has to happen while he’s still alive. And with infinite 100 mph pitches thrown at him, eventually enough will hit him that he’ll be in no condition to swing a bat at all!
Ugh. Mortality ruins everything.