THE BOOK--Playing The Percentages In Baseball

"Challenge to Alan: how about a throw from the outfield, with one hop to the catcher?”

What’s so challenging? Just point a radar gun at Johnny Damon.

I separated my shoulder a few years ago, and my already slow “fastball” has suffered dramatically.  I was clocked at 35mph about a year ago, which seemed surprisingly slow (and I’m certain I could throw from home to second in the air, though not much farther).  So I’m guessing the gun was aimed more towards the plate than my release point.  Good to know I can still likely bring the heat in the mid 40’s

I guess that is one way to measure your throwing speed if you don’t have a gun: see how far you can throw it at various angles.

I used to throw a softball with accuracy at 150ft.  Probably means I could throw a baseball at 175ft?  That puts my speed at around 55mph or so.  Sounds about right. When I’ve thrown in pitching machines, the radar would be low 50s.

Answering the “on one hop” part is a little more complex, but to throw the ball 300 feet on the fly, you would need to launch it at 83.4 mph at a 30-degree angle.

My impression from playing with the numbers a bit is that the answer for a throw on one hop from 300 feet is also going to be a launch speed in the 80-85 mph range, but at a much lower angle, around 10 degrees or less.  It will hop once somewhere on the infield around or just before the pitcher’s mound.  That kind of trajectory lowers the time of the throw from around 4.5 seconds on the fly to around 2.5 seconds on one hop.  I’m just guesstimating what will happen on the bounce, so those are ballpark figures.

A throw from less than 300 feet will not need to have as much speed.

Mike,

How about the record throw of 445 feet by Glen Gorbous in the 1950’s?  I remember reading about other players throwing 400 feet or more in competitions, I think Honus Wagner did it, and I remember a story about Satchel Paige doing it when he was pretty old.

I see the link to the calculator.  If Gorbous had no wind he was throwing 112 MPH (Didn’t mess with the angel, I assume it is set for optimal?)

With a 30 MPH wind he would be throwing 99 MPH.  Records are generally set in favorable conditions, but his arm was probably as strong as any of the top pitchers we’ve seen.

Rob Dibble once threw a ball from pitcher’s mound to the CF bleachers when he was upset about being removed from a game.  He was usually clocked around 100, so that ball must have still had some distance left after the first 350 feet.

Dave Righetti did something similar.

Rally, with no wind, I find the optimal angle to be about 24 degrees with a throw of 106 mph.  I set the backspin at 3000 rpm.  The high temperature on August 1, 1957 in Omaha was 96 degrees, so I used that.  The elevation of Rosenblatt Stadium is about 1100 feet.

Gorbous got a running start on flat ground, so it’s feasible that he could maybe throw a few mph harder than a pitcher striding down a pitching mound from a set position.

A 10-mph tailwind drops the required speed to 102 mph while increasing the optimal angle to 30 degrees.

Byung-Hyun Kim threw one from the mound into Monument Park against the Yankees after he got the save after blowing two heart-breakers in the ‘01 world series. I always thought that was impressive as he basically threw flat footed.

Thats a fun calculation to make...but one assumption made my “is that right?!?” meter spike.  I’m not yet convinced that any human could throw a baseball at 27 mph and 3000 rpm.  At the very least, it seems to contradict what I think I am seeing when I play catch, which is that below some threshold velocity (~50-60mph or so is just my guess), the angular velocity of the baseball is linearly proportional to the linear velocity of the ball.

But I’m not fully convinced of that...it’s just something that is twiddling around in my head.  I may have to see if this can be explored with pitchf/x…

Ike, you may be right to some extent.  There is some portion of the angular velocity which is provided by the velocity of the arm.  The rest is provided by the snap of the fingers. 

My thought was that you could get quite a bit from the finger snap/roll if you were specifically trying to emphasize that.  A major league pitcher can get about 1000 rpm more from the finger snap on a fastball relative to the changeup which is seated deep into his palm, and he’s doing that while trying to make the two pitches look as much the same as he can.  You do, in fact, see that in the PITCHf/x data.

But then we leave the realm of the PITCHf/x data to the realm of my guesstimates.  I guessed that a person really trying to emphasize backspin above all else could maybe could get 1500-2000 rpm from the finger snap/roll.  That’s equivalent to a 13-17 mph difference between fastball and changeup due to grip/release, which doesn’t seem outlandish for someone trying to emphasize that with no regard for deception. 

I further guessed that the translational arm motion would provide another 1500-2000 rpm or so.  That’s the portion which will be linearly proportional to the velocity of the ball.  Looking at it now, that estimate is probably too high by a factor of 3.

So an estimate of backspin in the 2000-2500 rpm range is probably more realistic.  That would bump the minimum release speed up to 27.4 mph.

Wouldn’t that translational arm motion cause top spin and not back spin? Or am I bass-ackwards?

Matt/13, the arm is moving underneath the ball, or more accurately, the arm moves the fingers which go underneath the ball on release, which will cause backspin.

Mike/12, I agree that we are fully into the realm of guesstimates here. (and I know at this point it doesn’t change the final answer much).  I’d add one point for consideration...and that is that the wrist snap that emphasizes backspin also adds velocity.

I’ll take your estimate of 13-17 mph as being reasonable for such a throw...meaning that the translational arm movement would have to be responsible for 10-14 mph.  I would *guess* that the arm movement is less efficient at putting spin on the ball than the wrist, (and by efficiency, I mean the relationship between mph added and rpm added), and therefore, I would further guess that you are still a bit high in your estimate of backspin.  At such low arm speeds, I would guess only a few hundred rpm are added at best from the movement of the arm...which would put my estimate at somewhere between say 1600-2200.

Not that it matters a whole lot though in the final answer...it was just something I enjoyed thinking about.  Going down that far may add another whole 0.2-0.4 mph....if that much.

Curiously, pitchf/x may be able to say something too about how much backspin the arm motion does add to the ball, and it’s relationship to velocity.  If one makes the assumption a changeup as having backspin related purely to the motion of the arm (which may not be the greatest assumption, but it would be a start), one can look at changeup backspin vs velocity of the changeup...with the slight tweak that ‘backspin’ would probably need to be defined with relation to the pitchers natural arm angle, rather than the surface of the field.  It may be possible to use such a relationship to extrapolate back to a reasonable value of rpm added for a very low velocity toss.

Ike#15:  Probably the best way to examine this with pitchf/x is to look at the total break rather than the upward break due to backspin. Actually this issue came up in a recent discussion I had with Mike Fast regarding Strasburg’s changeup, which appears to have less total break than his fastball.  I was trying to use that information to estimate how much additional spin is generated from the finger flick upon release (which would presumably be absent from the changeup).  I wanted to see if the ball is rolling off the fingers.  If so, then the extra spin is simply related to the extra speed.  However, I don’t have a satisfactory answer yet.

Since the Celtics were getting blown out last night, I let my mind wander a bit and starting thinking about why the exact amount of backspin does not matter in the result.  And it is because the speed of the ball is so slow.  In the latest version of my trajectory calculator, the Magnus force is proportional to the speed to the nth power, where n is a number between 1 and 2.  At the low v in this problem, n is closer to 2.  As a result, the upward acceleration due to the backspin is only a small fraction of gravity, even with a backspin as high as 3000 rpm.  In fact, drag does not matter a great deal either.  Again, the reason is that the speed is so slow (and drag is proportional to the square of the speed).

I won’t get around to working on Tango’s challenge for a while.

Oh I know the amount doesn’t really matter much here...it accounts for less than a foot of the total range.  It was just a fun thought experiment.

As to determining spin/speed generated from a finger flick or the arm, I wasn’t really proposing that you just look at upward break, but spin relative to the arm angle.  Using myself as an example, my changeup has a slightly different axis of rotation than my fastball (~20 degrees or so).  mainly because my wrist is actually doing something different than the fastball, and a little different than just staying totally stiff.  I suspect that there are many pitchers that are similar in that regard.

At 63 I’m fortunate enough to play adult baseball.  The score board at Lee County Sports Complex in Ft. Myers the spring-training home of the Minnesota Twins showed my pitches as fast as 57 mph.  Since some x major leaguers don’t seem to be able to throw as far as the plate I must conclude that I can ...........Oh you get it.  Yes, I know, I pitch slow for my league.