Very brief and entertaining video clip
It takes a couple viewings to see exactly what's going on here: the ball flew straight into the pitcher's glove (and he then had to manage his body’s reaction).
I'm curious about the odds of a ball reaching a 11cm x 11cm target from a distance of 18m. Maybe assume, for simplicity, that it's equally likely to be hit anywhere within a 90° horizontal angle (let's discount foul balls), and at any vertical angle of 0  45°. Pitcher's mound is about 18m from home plate.
Can anyone help?
Geometry of a Fluke

 Vacationer at Tralfamadore
 Posts: 16150
 Joined: Mon Jan 21, 2008 1:57 pm
 Location: Alexandria, Virginia
Re: Geometry of a Fluke
To first order (for a ball traveling that fast) it must be something like 2 in (1800 cm/11 cm)^{2}.Jim Leff wrote: ↑Tue May 28, 2019 7:35 pmVery brief and entertaining video clip
It takes a couple viewings to see exactly what's going on here: the ball flew straight into the pitcher's glove (and he then had to manage his body’s reaction).
I'm curious about the odds of a ball reaching a 11cm x 11cm target from a distance of 18m. Maybe assume, for simplicity, that it's equally likely to be hit anywhere within a 90° horizontal angle (let's discount foul balls), and at any vertical angle of 0  45°. Pitcher's mound is about 18m from home plate.
Can anyone help?
Art Neuendorffer

 Science Officer
 Posts: 161
 Joined: Thu Dec 09, 2010 2:00 pm
Re: Geometry of a Fluke
Thanks! 163.6 squared is 26765. So the odds are something like 2 in 26765, or 1 in 13382?

 Apathetic Retiree
 Posts: 18682
 Joined: Mon Aug 28, 2006 2:06 pm
 Location: Oklahoma
Re: Geometry of a Fluke
Did he throw out the guy on second? He didn't tag up.
Know the quiet place within your heart and touch the rainbow of possibility; be
alive to the gentle breeze of communication, and please stop being such a jerk. — Garrison Keillor
alive to the gentle breeze of communication, and please stop being such a jerk. — Garrison Keillor

 Science Officer
 Posts: 161
 Joined: Thu Dec 09, 2010 2:00 pm
Re: Geometry of a Fluke
Good point. Not sure.

 Vacationer at Tralfamadore
 Posts: 16150
 Joined: Mon Jan 21, 2008 1:57 pm
 Location: Alexandria, Virginia
Re: Geometry of a Fluke
It is an absolute fact that the probability of
 1) hitting a 22 cm x 22 cm square in the vicinity of the pitcher is 4 times the
probability of hitting a 11 cm x 11 cm square in the vicinity of the pitcher
and that the probability of
2) hitting a 33 cm x 33 cm square in the vicinity of the pitcher is 9 times the
probability of hitting a 11 cm x 11 cm square in the vicinity of the pitcher
does the probability of hitting any given 11 cm x 11 cm square drop off from that of
the stated perfect backscatter 11 cm x 11 cm square situation.
Art Neuendorffer

 Science Officer
 Posts: 161
 Joined: Thu Dec 09, 2010 2:00 pm
Re: Geometry of a Fluke
If I understand your question correctly, it was addressed when I suggested we assume, for simplicity, that it's equally likely to be hit anywhere within a 90° horizontal angle and at any vertical angle of 0  45°.
However I’m still not sure if I’ve translated your previous reply into the correct “1 in xx” statement of odds.
However I’m still not sure if I’ve translated your previous reply into the correct “1 in xx” statement of odds.

 Vacationer at Tralfamadore
 Posts: 16150
 Joined: Mon Jan 21, 2008 1:57 pm
 Location: Alexandria, Virginia
Re: Geometry of a Fluke
I was actually just trying to explain my logic in responseJim Leff wrote: ↑Wed May 29, 2019 4:26 pm
If I understand your question correctly, it was addressed when I suggested we assume, for simplicity, that it's equally likely to be hit anywhere within a 90° horizontal angle and at any vertical angle of 0  45°.
However I’m still not sure if I’ve translated your previous reply into the correct “1 in xx” statement of odds.
to your immediate reply (which you have since deleted).
If, in fact,
"it's equally likely to be hit anywhere within
a 90° horizontal angle and at any vertical angle of 0  45°" = 1.11 steradians
as compared to the target area of (11 cm/1800 cm)^{2} steradians,
then the answer (for a very fast ball) is ~1 in 29,750.
One should consider pop up flies & ground balls as other nonfoul playable hits
but ~1 in 29,750 is probably in the right ballpark.
Art Neuendorffer

 Science Officer
 Posts: 161
 Joined: Thu Dec 09, 2010 2:00 pm
Re: Geometry of a Fluke
I haven’t deleted anything.
Thanks.
Thanks.