Visualization: Tracking Home Run Flight Paths
by danmerqury on Aug 30, 2011 7:00 AM PDT
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PrintAfter the doubleheader against Boston on Saturday, the A's have hit a total of 91 home runs. What do they all look like?
Click to enlarge. (Another bonus chart inside after the jump!)
What can we do with all of this? Honestly, not a whole lot, at least not in a player analytical sense. But it sure is fun to play around with. Some notes:
- The longest home run hit in an Oakland uniform in 2011 came off the bat of Josh Willingham, on July 15th. It was a 446 foot shot into the second deck of the Coliseum off of Dan Haren, above the BBQ Terrace.
- But that shot certainly wasn't as impressive as the A's home run that reached the highest altitude: Brandon Allen's now-famous moonshot into the third deck of Yankee Stadium last week against Bartolo Colon. The short RF porch in New York made it look bigger than it actually was (a "mere" 428 feet), but the ball's flight topped out at 139 feet above the ground.
- On the opposite side of things, the dinkiest home run by an Oakland Athletic belongs to Eric Sogard, in the same game as Allen's third decker. It only traveled 331 feet, at a pop fly-like 40.4 degrees above horizontal, and Hit Tracker Online calculates that the 331 foot estimate includes 20 feet of help by atmospherics. At sea level, indoors, in 70 degree weather? It would have only traveled 311 feet. The right field foul pole at the Coliseum sits at 330.
- What else is there, besides distance and altitude? Launch speed. The 2011 Oakland record, unsurprisingly, belongs to Josh Willingham, on the same home run that holds the distance record. It came off of the bat at 113.7 mph. But second place? Scott Sizemore, off of Felix Hernandez in Seattle, on August 2nd. That home run was hit at an 18.2 degree angle above horizontal, at 113.0 mph. An absolute laser that left the park in a hurry, causing Felix to turn around and say to himself, "wow".
And yes, I did promise one more chart. This one was made by averaging each player's home runs (both distance and apex altitude) and plotting them all together. Quick, without looking at the legend, guess which one's Sogard!
Again, click to enlarge.
The A's send Trevor Cahill to the mound tonight to face Jeanmar Gomez of the Indians in Game 2 of the four game series. First pitch is at 4:05 PM PDT.
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This is easily the prettiest chart you've made
and that’s saying a lot.
How did you get the data? Does HitTracker provide the path data, too?
Very nice graphs, Dan.
2011 Oakland Athletics: We have Cy Young pitchers and make yours look like it, too
Thanks!
As far as path data, I actually had to fake it a little bit. HTO provides a lot of variables, but not path data. And I could have just assumed simple symmetrical parabolas, but obviously drag is a factor. So I just looked at a few paths that HTO has on the website, and it seemed like the apex tended to sit at around 60% of the final distance. So with just two variables, the apex height and the distance, I plotted two parabolas for each HR—one on the way up to the apex, and one on the way down.
nice workaround
and I really love the aesthetics
2011 Oakland Athletics: We have Cy Young pitchers and make yours look like it, too
pfff
If you were a true bot, you would put the drag into the equation rather than pasting two halves together.
Being wrong about something you’ve worked on is a blessing, not a curse, and people are so invested in being right that that gets lost. —Graham MacAree
And it wouldn't have solved it
As you can not calculate Magnus, for you don’t know the spin
2011 Oakland Athletics: We have Cy Young pitchers and make yours look like it, too
NERDS
Official Athletics Nation Rotating Tagline Editor - Pam liked my old sig better.
My thoughtful watermelon is easily mistook for an early American catapult.
DURRRR THEY’RE TOO OLD, BABIP IS TOO HIGH, TOO MANY Ks, DURRRRRR
thank you.
The funny thing about baseball is that people will believe what they want to believe. —Joe Posnanski 8/29/09
I think they are just making up all these words to act important.
"Trying not to rec a "F**k the Giants" post is like trying not to look at boobs."
See! Another made up word!
You guys have invented your own basement-nerd language.
"Trying not to rec a "F**k the Giants" post is like trying not to look at boobs."
Magnus force, no, but drag is calculable.
All you need is the velocity vector, the density of air, the cross-sectional area of a baseball, and the drag coefficient of a baseball (0.3). The only problem? Velocity is a vector that changes during flight…which would make it a differential equation. And I’m not solving a differential equation for a chart.
I actually I have a program that does this for a thrown ball, if you assume a normal spin (ie, works best for throws from an outfield). I used a standard ODE solver, it’s a fairly straightforward initial value/shooting method problem.
Children, until we have taught them better, will be perfectly happy with a seasonal round of games in which conkers succeeds hopscotch.
Oooh. Tag me in, dan.
First, a small primer for No-bots.
There are two forces^ acting on the ball in flight: gravity and aerodynamic drag. So we could write the force equation as Drag + Gravity = mass x acceleration. Obviously, mass is a scalar quantity and gravity is a constant vector. But, as Dan points out, the Drag depends on the NON-linear velocity vector. We will need two (one for vertical drag and other for horizontal) second order non-linear differential equations. The easiest way to get past this is to form four first order equations. This is really easy to do when we break them down according to their vertical and horizontal components. I will use the position and velocity variables: X, Y, Vx and Vy.
^ We are assuming zero spin on the ball. This is a fair assumption. Okay, fine, not for Jack Cust’s homers or Rafa Nadal’s forehand shots (Hi, pam). But otherwise, it’s sound. Glancing hits off the bat would have great spin. It’s why foul balls take such a curved path. But to hit the ball far, you have to square it up. Tell me if you’ve heard that before.
Our equations are:
Vx = dX/dt
Vy = dY/dt
Ax = d(vx)/dt = (1/mass) × (dragX)
Ay = d(vy)/dt = (1/mass) × (dragY + gravityY)
Note that gravityX is zero and isn’t included because… well, gravity doesn’t act on the ball in the horizontal direction.
Now we get to this Awesome source code. It was written by a guy named Ralph Carmichael who created this incredible database of relevant programs for aeronautic applications. (I can’t articulate how helpful and amazing his site is. Click the Content Page and let the good times roll.)
Some notes:
a. It will require Fortran compiler.
b. Dan, he adds a calculation for the drag coefficient using Reynold’s Number and calls it back. Since we are going to use O.3, you can skip past that part.
c. He also includes description of lower atmosphere and calculations of viscosity. Uses them to have a super accurate acceleration value.
d. Runge-Kutta method for fourth order differentiation. Hence the adjustment to the final position.
e. He even gives a calculation for a scenario where there is no air resistance!
by harensheir15 on Aug 31, 2011 2:28 AM PDT up reply actions
Hardly, brother.
Just remembered that I had that code bookmarked somewhere.
It is all sorts of cool.
by harensheir15 on Aug 31, 2011 10:23 AM PDT up reply actions
Not for a while yet but when it's time...
Together we shall RULE THE WORLD.
Muahahahahhahah.
At least until EC bitch-slaps us back into our place.
by harensheir15 on Aug 31, 2011 2:20 PM PDT up reply actions
nerd!
The funny thing about baseball is that people will believe what they want to believe. —Joe Posnanski 8/29/09
{sigh}
And to think I gave you a shoutout.
by harensheir15 on Aug 31, 2011 11:41 AM PDT up reply actions
(i liked that part!)
dan told me I have to care about magnus BECAUSE of rafa.
The funny thing about baseball is that people will believe what they want to believe. —Joe Posnanski 8/29/09
[nods]
The funny thing about baseball is that people will believe what they want to believe. —Joe Posnanski 8/29/09
ummm okay.
The funny thing about baseball is that people will believe what they want to believe. —Joe Posnanski 8/29/09
Wow! All the college lessons I haven't thought about in 16 years just came flooding back at once.
Make it stop!
Don't you realise you'll find next monday or next Tuesday/Your golden shoes day
by PDXAthleticsfan on Aug 31, 2011 12:08 PM PDT up reply actions
Actually, not altogether unpleasant
As it makes me remember the soft-spoken, New York accent of Professor Alvin Bayliss, as he concludes his first lecture with, “And that, ladies and gentlemen, is the Fortran compiler.” Which makes we want to find the first balding, white-bearded person on the street, give him a hug and say “I love you, grandpa!”
At this point, the Runge-Kutta method is nothing but a familiar, but meaningless phrase.
There’s a reason I ended up doing policy work and not engineering.
Don't you realise you'll find next monday or next Tuesday/Your golden shoes day
by PDXAthleticsfan on Aug 31, 2011 2:32 PM PDT up reply actions
Exactly what a professor preached.
“You don’t know just which parts you’re going to end up needing so you have to learn all of it. You may never have to hear the words LeGrange Multipliers ever again but until you’re sure of that, you’ll do well to understand them.”
I’m not too thrilled with numerical processing either. It’s why I could never do computer sciences. It’s a means to end;I I used it in analysis for aeronautics only. But some of them are kinda nifty. Especially seeing how people first derived some of those algorithms.
If you don’t mind my asking, where do you use your talents in policy work?
by harensheir15 on Aug 31, 2011 2:50 PM PDT up reply actions
Yeah
I’m sure if I tried, I could remember diff. eq. I had to re-learn them once in grad school, but that’s now more than 10 years past. Just like a foreign language – once you live in that world, it all comes flooding back.
As to your question, my current position is developing statewide water quality standards.
Don't you realise you'll find next monday or next Tuesday/Your golden shoes day
by PDXAthleticsfan on Aug 31, 2011 2:53 PM PDT up reply actions
Foreign language is a very good metaphor. Dead ringer.
And wow, development?
That’s really neat. Public sector is such a great, direct way to have meaningful input in that regard.
by harensheir15 on Aug 31, 2011 3:31 PM PDT up reply actions
See, Lagrange multipliers rings a bell.
I vaguely remember what that is. Eigenvalues/functions, right? But like PDX, I just recognize the name Runge-Kutta, and nothing more.
Eigenvalues is used with matrices in linear algebra.
LeGrange is used more in Calc for in optimization problems with constraints.
But your point is very well taken. You’re much farther along than I am. PDX has us both beat by a long mile. To a point where these specific applications are a small part of your comprehensive repertoire. So they’re not at all urgent knowledge.
by harensheir15 on Aug 31, 2011 3:41 PM PDT up reply actions
Not sure I think of them as part of my repertoire
just a hazy memory.
As I’ve gone through my career, I’ve un-learned certain things, while adding others. Statistics is currently a much more useful skill then calculus/ differential equations, and, at that, mostly enough knowledge to understand what I’m reading and sift through the BS. Fortunately, I can rely on others to do the heavy lifting in that regard.
Don't you realise you'll find next monday or next Tuesday/Your golden shoes day
by PDXAthleticsfan on Aug 31, 2011 4:03 PM PDT up reply actions
Heh, hazy memory.
Nice to have colleagues do their share.
Thank you, this has been an helpful discussion.
by harensheir15 on Aug 31, 2011 6:14 PM PDT up reply actions
"But to hit the ball far, you have to square it up"
I disagree with this, btw. Home runs and fly balls can have significant backspin, which provides quite a bit of upwards force that keeps them flying. Torii Hunter, supposedly, was famous for training himself to hit with backspin (supposedly accounting for his age 24-25 power spike).
The good news is that modeling it is probably not too difficult, since for home runs and fly balls you can assume pure backspin, and I would guess that the range of backspins is small (could be wrong on the last part).
Children, until we have taught them better, will be perfectly happy with a seasonal round of games in which conkers succeeds hopscotch.
I wasn't actually suggesting you do it perfectly.
Just that you apply that compression of the horizontal across the whole parabola instead of splitting in two halves.
Being wrong about something you’ve worked on is a blessing, not a curse, and people are so invested in being right that that gets lost. —Graham MacAree
That would have been possible, I think.
But it was far easier to make the path fit a parabola (or two) than try to pull a non-parabolic equation out.
meh
I prefer a nice Fast Fourier Transform.
And yes, I use it at work. In ActionScript.
That's really cool!
I vibrated with joy that join A's. -- Kim Seong-min
by WaddellCanseco on Aug 30, 2011 11:23 AM PDT up reply actions
I was going to comment on the non-parabolic paths homeruns take, as gravity becomes a factor after the ball reaches its apex.
I read a little bit about baseball physics. Excellent job on the graphs, Dan. A lot of hard work went into this. ANcyclopedia worthy.
by player20 on Aug 30, 2011 7:42 PM PDT via mobile up reply actions
non-symmetrical parabolic paths, I meant
by player20 on Aug 30, 2011 7:46 PM PDT via mobile up reply actions
Thanks!
But total nerd tangent: gravity’s always a factor, regardless of whether it’s at the apex, before it, or after it. The force is constant. You can plot the path of anything using a parabola, as long as the acceleration is constant. And if drag was a constant, then it’d work with a single parabola. But since drag changes based on the speed of the ball, acceleration is no longer constant, and it’s no longer parabolic.
I also find it cool that
Greg Rybarczyk has a category “In how many ballparks would that ball be out under normal circumstances”. Both Brandon Allen shots in NY had the value of 30. Sogard? 0.
2011 Oakland Athletics: We have Cy Young pitchers and make yours look like it, too
In normal circumstances.
As in, without the wind and the temperature as they were on that day. Indoors, in 70 degree weather at sea level, it would have lost 20 feet.
ah. the “ugliest hooker” award. (ie., not even in the bronx.)
by AV on Aug 30, 2011 9:18 AM PDT up reply actions
no, what i tried to say was, that’s weird that indoors is considered the norm. but i know what you mean.
by AV on Aug 30, 2011 9:20 AM PDT up reply actions
Heh, fun
But definitely interesting to get the path data, not just the distance and the apex.
Last of the Ninth - Photography
The path data of BRANDON ALLEN'S shots
would show where they made contact with alien life forms before descending
A Kouzmanoff for the rest of us!
by OptimistPrime on Aug 30, 2011 8:55 AM PDT up reply actions
excellent graphs, Danbot
I’d like to think that Sogard’s might have made it out in Boston… but who am I kidding.
"Once you go Bed....everything else is dead." - Bed
"So you're saying we should skin the Rangers and wear them as uniforms? I’m down." - Kyli
Also, I would have liked to see where Allen's HR would have hit at the Coli
Reached the flagpoles, maybe?
"Once you go Bed....everything else is dead." - Bed
"So you're saying we should skin the Rangers and wear them as uniforms? I’m down." - Kyli
Bart Bridge
A Kouzmanoff for the rest of us!
by OptimistPrime on Aug 30, 2011 8:42 AM PDT up reply actions
Bay Point BART, that is.
Official Athletics Nation Rotating Tagline Editor - Pam liked my old sig better.
My thoughtful watermelon is easily mistook for an early American catapult.
DURRRR THEY’RE TOO OLD, BABIP IS TOO HIGH, TOO MANY Ks, DURRRRRR
by mikev on Aug 30, 2011 8:47 AM PDT up reply actions 1 recs
Not far enough... Allen's dinger would have gone all the way to the E-Tran hub in Elk Grove.
"OK, Recker is starting, that’ll mean a rain delay, 12 grand slams, a hurricane, a US Airways flight landing in the outfield and the toilet backing up."- WhizDad
by Gaijin_Suketto on Aug 30, 2011 11:24 AM PDT up reply actions
Come on guys, lets be realistic.
If he hit the homerun at the Coli, it still would have landed in the third deck. At Yankee stadium.
"Even if the plane is on autopilot, I don't want a monkey in the cockpit" - ilikeike
We need a chart of Dan's Greatness
A Kouzmanoff for the rest of us!
by OptimistPrime on Aug 30, 2011 8:53 AM PDT reply actions 6 recs
I wish I had done this! Love love love!
"A man makes a bad decision and he's an idiot for a day / teach a man to make bad decisions and he’s an idiot for life." - B-E-D
In all due respect
Brandon Allens greatness surpasses all pie chart figures…
"The Most Interesting Man in the World is Brandon Allen" - the World
"Brandon Allen is what I'm talking about" - Willis
by jemilesathletics on Aug 30, 2011 9:50 AM PDT up reply actions
The chart does say "mortal world"
Don't you realise you'll find next monday or next Tuesday/Your golden shoes day
by PDXAthleticsfan on Aug 30, 2011 9:54 AM PDT up reply actions
yeah, duh!
A Kouzmanoff for the rest of us!
by OptimistPrime on Aug 30, 2011 9:57 AM PDT up reply actions
WHERE ARE YOU GETTING YOUR NUMBERS
by Rebuilding Season on Aug 30, 2011 10:33 AM PDT up reply actions
Source: Obviousness
A Kouzmanoff for the rest of us!
by OptimistPrime on Aug 30, 2011 12:56 PM PDT up reply actions
Imma gonna click on dan's name and see if he recommended this
We yet enjoy little to be envied, but endure much to be pitied.-Thomas Dudley
Which one is the 113 mph Sizemore one?
Is it the light blue one that lands near Brandon Allen’s moonshot?
Being wrong about something you’ve worked on is a blessing, not a curse, and people are so invested in being right that that gets lost. —Graham MacAree
Nope
It must be the purple one just to the left of it. Don’t ask, I just know these things
P.S. The light blue one must be Kouz
2011 Oakland Athletics: We have Cy Young pitchers and make yours look like it, too
except that when daddy tries to take the T-Bird away, we're gonna choloroform him and lock the bastard in the trunk!
"OK, Recker is starting, that’ll mean a rain delay, 12 grand slams, a hurricane, a US Airways flight landing in the outfield and the toilet backing up."- WhizDad
by Gaijin_Suketto on Aug 30, 2011 11:26 AM PDT up reply actions
chloroform is so 80's
get GMBH or get lost.
by MobiusKlein on Aug 30, 2011 12:11 PM PDT up reply actions
Gesellschaft mit begrenzter Haftung?
2011 Oakland Athletics: We have Cy Young pitchers and make yours look like it, too
that’s so 2010s… financial psychedelics. i dropped some LLC yesterday and i’m still seeing trails on my excel graphs…
by AV on Aug 30, 2011 1:11 PM PDT up reply actions
go by my house?
Being wrong about something you’ve worked on is a blessing, not a curse, and people are so invested in being right that that gets lost. —Graham MacAree
oh crap, I transposed.
Faux acronym fail by Iglew.
Being wrong about something you’ve worked on is a blessing, not a curse, and people are so invested in being right that that gets lost. —Graham MacAree
GBH
or whatever that stuff is that can make you pass out and forget.
great big hangover?
Being wrong about something you’ve worked on is a blessing, not a curse, and people are so invested in being right that that gets lost. —Graham MacAree
Very pretty!
The funny thing about baseball is that people will believe what they want to believe. —Joe Posnanski 8/29/09
Really interesting stuff.
And fantastic graphs!
You're remarkable in a funny way. Or funny in a remarkable way.
how about home run efficiency?
I would say sogard got the most out of his homer. They all count the same…so maybe batters shouldn’t be wasting calories hitting them any further than the first row.
2 home run hitters who I read were famous for NOT hitting them very far were Hank Aaron and Ken Griffey Jr. I like those guys, and in the steroid era Griffey had a funny quote where he lamented that no one ever thought he juiced cause he never looked big enough. The guys who hit moonshots I think are all a little more suspect. Mcgwire and Bonds come to mind. Of course I love the long homer as much as the next guy, I’m just pointing out there is something kinda cool about the one that just makes it over the wall.
by barryzitoforever on Aug 30, 2011 1:10 PM PDT reply actions
seems to me, hr hitters will hit their share of just-barelys
If you take every fly ball hit, and push it 10 ft farther back, warning track outs become just-barely HRs
And on the flip side
if you think just-barely is cool and try to get a just-barely hitter on the theory that he is underpriced or whatever, one puff of wind and he hits a whole bunch of warning-track fly-outs.
Being wrong about something you’ve worked on is a blessing, not a curse, and people are so invested in being right that that gets lost. —Graham MacAree
.
Melissa Lockard
#Athletics sending Grant Green, Michael Choice, Dusty Coleman, Ryan Ortiz, Tyson Ross & Ethan Hollingsworth to Arizona Fall League.
Melissa Lockard
Green was on the Phoenix squad last fall, but missed much of the AFL season with a calf strain. More time to work on his new position.
Last of the Ninth - Photography
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