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SABR 101 - Relative and Absolute Scales (June 6, 2003)

Posted 4:13 a.m., June 26, 2003 (#11) - Sylvain(e-mail)
  Ok, I'm not very familiar with Replacement Level, so I won't add any comments, but I found this article on Prospectus very interesting and thought it might fit pretty well here.
Link: http://premium.baseballprospectus.com/article.php?articleid=2032

S

A Study of the Barrel Constructions of Baseball Bats (June 9, 2003)

Posted 8:47 a.m., June 13, 2003 (#7) - Sylvain(e-mail)
  So, as part of may grunt work, I decided to look at the advantage of using a corked bat, using very basic approaches.

Here is the first step: what is the relation between the mass of a bat and its speed? Ok, since it's a basic model it has flaws, I'll try to show them. If anybody has some ameliorations, suggestions...

Since I am bad at using html, I apologize for the formatting.

Suppositions (each is is subject to amelioration, which could be implemented more or less easily):
- the bat follows a circular trajectory around the player. The axis of rotation is vertical (imagine yourself holding a bat horizontally and turning on yourself). The center of the rotation is O. A point of the bat is M.
- The axis of the bat is orthogonal to the axe; and the distance from the bat to the axis is constant.
- the drag is negligible
- the player exerces on the bat a force F which application point is the center of gravity of the bat. I'll later make the assumption that the component horizontal and orthogonal to the bat of this force is constant. (in polar coordinates, the component of F along Utheta is constant).

I also use polar coordinates (r, theta, z, with the associated vectors Ur, Utheta, Uz). Since I don't know how to type theta or omega in HTML, I will use H for theta and w for omega.
df/dt is the derivate of f by t.
d2f/dt2 is the derivate second of f by t.

So: the bats rotates around the axis (read player) with an angular speed w (and the associated vector W). We have w = dH/dt.

The referential is in rotation around a static (galilean) referential; therefore in polar coordinates we have, with the following notations (Speed: v, vector V, Vectorial product sign: ^):

m*dV/dt = mG - 2*m*W^V - m*[dW/dt^OM] - m*[W^(W^V)] + F

The polar coordinates of the vectors are (dr/dt = 0 and dz/dt = 0)
dV/dt ( -r*w*w ; r*dw/dt ; 0)
mG (0;0;-m*g)
W^V (r*w*w)
dW/dt^OM (0; r*dw/dt; 0)
W^(W^V) (r*w*w; 0; 0)
F (Fr, FH, Fz)

Which gives:
-mrww = -2mrww - mrww + Fr
mrdw/dt = -mrdw/dt + FH
0=-mg+Fz
Or:
Fr = 2*m*r*w^2
FH = 2*m*r*dw/dt
Fz = mg

Besides the speed is V = dr/dt*Ur + r*dH/dt*UH + dz/dt*Uz = r*w*UH

So, applicating this to G, center of gravity of the bat (let's call d the distance from g to the axis of rotation):

dw/dt = FH/(2*m*d); supposing that FH is constant (in other words the player's efforts to accelerate the rotation speed of the bat are constant):

w-w(t=0) = FH/((2*m*d)* (t-0); I here suppose that t = 0 at the beginning of the swing.
Let's call w(t=0) wo. A discussion on wo will follow.

So: we now can write that:
v = [FH/(2*m)]*t + wo*d

Suppose that wo = 0; the whole swing takes place at a belt or knee or chest high level. we have v*m = constant (t), which means that a corked bat with the same FH will have a greater speed than a normal bat (decrease in m, increase in v). And in a same amount of time, a corked bat will make more way than a normal bat. Finally, a decrease of 10% of the weight of the bat will make the speed increase by exactly 10%. But the quantity of movement (momentum in English I guess; p = m*v) will stay the same at a given time, if the bat is corked or not. And momentum is important: if one considers the schock between the ball and the bat as elastic, then there is conservation of the kinetic energy of the system (bat+ball), and of its momentum as well.

So what is the advantage of a corked bat ? (based on these results) If a batter uses a corked bat knowing that while making the same effort he can have a greater bat speed: with a corked bat he can:
- hit the ball earlier on the ball's trajectory (i.e. further from the catcher); this can be useful is the batter's swing is slow.
- begin to swing later and have a little more time to recognize the pitch, but still hit it (a corked bat needs less time to make the same way as a normal bat); this can be useful if the batter doesn't lack swinging speed but doesn't see the pitches very well.

I'll add more commentaries later.

By the way some people with a better knowledge of who used corked bats and when might definitely help here.

BUT I made the assumption that wo is equal to zero. The point is that it is not: in fact a better modelisation of the swing of the batter would include the fact that at the beginning of the swing, the bat is higher than the point at where it hit (or miss) the ball; the center of the gravity of the bat goes from head high to belt high, and not belt high during the whole swing as ín my model. And during this "descending" part of the swing, the heavier the bat is, the more the speed the bat takes, and consequently the bigger wo is.
(I'll look at the wo gain during the descending part in a later post).

So the speed gain made by using a corked bat is not as easy as 10% less weight means 10% more speed, what my model would say.

Sylvain

A Study of the Barrel Constructions of Baseball Bats (June 9, 2003)

Posted 10:53 a.m., June 16, 2003 (#8) - Sylvain(e-mail) (homepage)
  See homepage: very good article on corked bats (and other stuff).

The next steps will come later this week (I hope).

S

A Study of the Barrel Constructions of Baseball Bats (June 9, 2003)

Posted 8:38 a.m., June 19, 2003 (#9) - Sylvain(e-mail)
  Looking at the advantage of using a corked bat: linking the mass of the bat and its speed.

Warning: this study is based on very simplistic approaches and approximations! Some better studies (more accurate models) have been and can be performed.

Step #2: in post #7 I considered a swing that was purely lateral. This step is an improvement as I added a vertical component to the swing in order to find out the effect of gravity on a swing. The notations I am going to use are same ones.

First a correction (oups...): instead of Fr = 2*m*r*w^2, once projected on Ur, the principle of Newton gives: Fr = 0 ( in fact Fr = m*d2r/dt2 but d2r/dt2 = 0). My bad.

The centre of gravity (G) of the ball is supposed to be in rotation around a vertical axis (z), with the distance from G to the axis being constant and equal to R. O is the projection of G on the axis.

The coordinates are still polar coordinates: r, theta = H, z. The corresponding vectors are Ur, UH and UZ,

The swing is decomposed in two phases:
1) from H = Ho to H = H1, a descending and rotating one, z varying from zo to z1;
2) a rotating one, H varying from H1 to ? and with z = z1. For this phase I will use the results from post #7.

Ho, H1, zo, z1 are function of:
- the player: how he swings (I'd say that if a hitter is a ground ball hitter than it would imply that the second phase is almost non-existant, Line drive hitter would have a big second phase, and a fly ball hitter would also have a third ascending phase).
- where he wants to swing (low, high in the strike zone).

I also pose that at t = 0, H = Ho and both dz/dt and dH/dt = 0.
I define t1 as the instant when H = H1 and z = z1.

So, in the general case, the equations give:
- on Ur: m*(d2r/dt2 - r*(dH/dt)^2) = -2*m*r*(dH/dt)^2 + m*r*(dH/dt)^2 + Fr
- on UH: m*(r*d2h/dt2 + 2*dr/dt*dh*dt) = - 2*m*dH/dt*dr/dt - m*r*d2H/dt2 + FH
- on Uz: m*d2z/dt2 = -m*g + Fz

Since I supposed that R = constant, dr/dt = d2r/dt2 = 0. Which gives:
- Fr = 0
- 2*m*r*d2H/dt2 = FH
- d2z/dt2 = -m*g + Fz

I now suppose that FH and Fz are constant. Since the first part of the swing was a descending one, it implies dz/dt negative. Or dz/dt = Vz = (-g + Fz/m) * t + Voz, with t positive and Voz = 0 => Fz - mg has to be negative.
It makes sense, Fz has to be inferior to the weight.

And I also have dH/dt = (FH/(2*m*R))*t + dH/dt (at t = 0).
So that dH/dt = w can be written w = constant/m*t
Let's integrate this:
- z(t)-zo = 1/2*(-g + Fz/m)*t^2
- H(t) - Ho = 1/2*A/m*t^2
This two equations can also give z as a function of H .

Remember t1: we have:
- z1 - zo = 1/2*(-g+Fz/m)*(t1)^2
- H1 - Ho = 1/2*A/m*(t1)^2
=> (z1 - zo)/(H1-Ho) = (-g + Fz/m)/(A/m)
This equation gives the relation between the force to apply and the swing chosen/type of swing.

After t = t1, we find ourselves in the case I exposed in post #7. In post #7 I looked at wo; since I changed the origin of time, the wo in post #7 is now w1 or w (t = t1) or dH/dt (t = t1).
Rewritting it gives:
w1 = dH/dt (t = t1) = FH/(2*m*R)*SquareRoot[2*(H1-Ho)*m*2*R/FH]
=> w1 = SquareRoot[FH * (H1 - Ho) / ( m * R )] = B/SquareRoot[m*R]
By replacing t1 by its expression obtained in the z(t) equation, you can also obtain w1 as a function of zo - z1 .

In post #7 we had w(t) = FH/((2*m*d)*t + wo. Using the new notations give, for the second phase:
w(t) = FH/(2*m*R)*t + B/SquareRoot(m*R); since the velocity v in the second phase is equal to w*R we can write:
V = A*t/m + B/SquareRoot(m)
W don't have m*v = constant (t) any more !

What does this mean ?
- If a batter uses a corked bat, the impact of the corked bat will depend on his swing and this advantage is bigger for line drive hitters than for a ground ball hitter.
- the relation between the loss of mass of the bat and the speed is not linear. A gain of mass of 10% will produce a gain of speed inferior to 10%, the factor of "speed restitution" depending on the swing (player + where in the zone).

Further comments and questions are wel(l?)come, as usual.

Sylvain

A Study of the Barrel Constructions of Baseball Bats (June 9, 2003)

Posted 5:35 a.m., June 20, 2003 (#10) - Sylvain(e-mail)
  Another link that, well, explains it all:
http://www.kettering.edu/~drussell/bats.html

See the article concerning corked bats.

He does everything I did, but better.

Sylvain

A Study of the Barrel Constructions of Baseball Bats (June 9, 2003)

Posted 7:58 a.m., June 20, 2003 (#11) - Sylvain(e-mail)
  So, let's go to step 3 (the last but most exciting one): the collision between the bat and the ball. The homepage links says it all, but I still have some points to add. There will also be less equations.

As noted in the link posted in #10 (article on bat weight, swing speed and ball velocity), the speed of the batted ball depends on:
- the weight of the bat,
- the speed of the bat,
- the speed of the ball before the collision,
- where the ball has been hit on the bat.

These parameters and the speed of the batted ball are all linked by the following equation, derived from the conservation of the momentum for the system (ball + bat) and introducing a "speed restitution" coefficient e:

V(batted ball)*(mbat + mball) = (mball - e*mbat)*V(pitched ball) + (mbat - e*mbat)*V(bat before collision)

with e = - (V(batted ball)-V(bat after))/(V(pitched ball)-V(bat before))
e depends on the speed of the incoming ball and is about 0.55 for a pitched ball velocity of 90 mph; it actually is a consequence of the conservation of the enery of the whole system bat+ball. The article doesn't precise it but I am pretty sure it also depends on the point of impact between the ball and the bat; see the article on bending modes and the sweet spot.

Remember that all values are algebric ones!

The batter has control on:
- V(bat before),
- mbat, linked to V(bat before) (see step 1 and 2),
- where the ball is hit.

Now we have to make some suppositions: if the ball hits the bat on the very same point whether the bat is corked or not (thus supposing e = constant), Then:

As we've seen, the relation between the speed of the bat and its weight can be written V = constant*t/m + constant/SquareRoot(m).
With t = time spent since the beginning of the swing.
First case: the batter begins to swing at the same time, whether the bat is corked or not. Then V(corked is bigger), then the corked bat will hit the ball earlier. Therefore, even without considering the second term, the momentum of the corked bat will be smaller for the collision ! But, on the other hand, the speed of the pitched ball will be higher (very very slighty) at the time of the collision (for more infos on this, see the thread on loss of velocity of a pitched ball) thus increasing the speed of the batted ball.
All in all, I'd say that the speed of batted in such a case in about the same if the bat is corked or not, the gain of power is therefore negligible, if there is any.

Now case #2: knowing that he has a bat speed advantage, the batter begins to swing later, but the contact with the ball happens after a same rotation of Theta (or in other words the point of contact bat-ball has the same spatial coordinates).
Then during the contact the corked bat will have a higher speed. However the momentum of the bat will also be lower (momentum = constant(t) but here tcorked inferior to tnoncorked and constant is growing with t). No gain at all, a loss I'd even say.

BUT remember that I supposed e = constant. Part of the aim of the batter is to maximize e by optimizing the point of contact. He can do it by lowering his swing, effect on z, or extending R. The equations (posted in previsous posts) show that with a similar force, the deviation will be higher if using a corked bat (m*d2r/dt2 = Fr and m*d2z/dt2 = -m*g + Fz). What happens in our two cases?
Case 1: both swings begin at the same time
Then of course the batter can deviate the bat using the same force. However because of the bat speed, these modifications will take place also "further" in space, at a theta bigger. The batter won't be able to play that much on the point of contact.

Case 2: corked bat swing begins later
The batter will be able to better recognize the pitch, optimize the point of contact, e, and still hit the ball, compared to a normal bat. The gain of speed of the batted ball depends on this optimization. So that there might be a gain in batted ball speed, depending on the point of contact .

So, why use a corked bat? I'd say:
- don't use a corked bat if you're in a power slump, unless you begin to swing later and can hit the ball really better (big e difference) and don't get caught.
- in a hitting slump due to lack of swing speed: by beginning the swing at the same time, a corked bat will help have more contact, more times on base due to errors, and perhaps more hits, but you won't have more power. Still, don't get caught.
- in a hitting slump because of bad pitch recognition: a corked bat will allow you begin to swing later and help you make a better contact, if any. But, just as in the other two cases, don't get caught.

These were my thoughts.
For comments, questions....

Thanks to those courageous and brave who took the time to read, thou shall go back to your castle, find and kill the dragon, and marry the princess.

Sylvain

Velocity loss of a pitched baseball (June 10, 2003)

Posted 11:21 a.m., June 11, 2003 (#1) - Sylvain(e-mail)
  If someones here enjoys physics:
http://farside.ph.utexas.edu/teaching/329/lectures/node58.html

It is worth looking at: it explains the curve, screwball, knuckleball.

SC

Velocity loss of a pitched baseball (June 10, 2003)

Posted 6:13 a.m., June 13, 2003 (#4) - Sylvain(e-mail)
  There are other limits to the model:
- it doesn't take the gravity into account, i.e. the ball is supposed to follow an horizontal course; the gravity will increase the ball's speed.
- the drag coefficient is not constant. A graph in the link I posted (I pretty much guess it comes from Adair's book, but I don't have the book).

Here is a small improvement of the model presented in Tango's link (so my grunt work):
- we neglect the spin of the ball force; the trajectory of the ball can therefore be described by two variables, x and z, x horizontal, z vertical (no side variations)(with x increasing when going from the pitcher to the plate, z increasing when going up)
- As for the horizontal course, one can suppose that when the pitcher releases the ball (instant t=0), the original speed Vo is purely horitontal (Vox = Vo, Voz = 0)(sorry for the formatting).
Neglecting the vertical drag and the spin, we have: Vz(t) = -g*t (g gravity)
Since the ball needs about 0.4 sec to reach the plate, it gives a maximum vertical speed of 0,5*9,8 # 5 m/s or 11.2 mph. Since there is drag, the actual vertical component of the speed of the ball at the plate will be lower. On the other hand, the horizontal speed will be between 80 and 90 mph, considering the drag or between 42.5 and 35.7 m/s. Vz(plate) is not negligeable, but "small" compared to Vx(plate) (I will consider Vz/Vx <= 1/4)

And the drag can be written: Fd = -a*v^2, with a direction opposed to the speed. Its axial component will be (considering a constant drag coefficient):
Fx = -a*Vx*square_root(Vz^2+Vx^2)
Fz = -a*Vz*square_root(Vx^2+Vz^2)
There fore Fz/Fx <=1/4; considering that at the release of the ball, the vertical drag is 0 (Vo horizontal), the vertical drag is small.
And Fx = -a*Vx^2*square_root(1+Vz^2/Vx^2) can be approximated by
Fx= -a*Vx^2; on a side note Fz = -a*Vz^2*square_root(1+Vx^2/Vz^2)can be approximated by Fz = - a * Vx * Vz

So considering an almost horizontal problem we can write
m*dVx/dt=-a*Vx^2 (1) (and mdVz/dt = -m*g-a*Vx*Vz)
(1) gives m*(1/Vx-1/Vox)= a * (t-to) = a*t (with to= moment of release = 0 and Vox = Vo)
Or: Vx = 1/(a/m*t+1/Vo) = m/a*[(t+m/(a*Vo))^(-1)] = dX/dt
Integrating it one more time:
X-Xo = m/a * (ln(t+m/(a*Vo))-ln(to+m/(a*Vo))
Or X - Xo = m/a*ln(1+a*Vo*t/m)
Considering Xo=0 (origin of the axes = point of release of the ball):
X = m/a*ln(1+a*Vo*t/m)
and t = m/(a*Vo)*[Exp(a*x/m)-1]

Numerical application:
m=145g=0,145 kg
Distance point of release - plate = 17 m (or 55.75 feet)
a=dragcoefficient*cross section area*1/2*density of the air
a=0.3*pi*0.037^2*1,225=0.0006448

With a release speed of 95 mph or 42.5 m/s,
t (ball reaches plate) = 0.416 sec
Horizontal speed (ball reaches plate) = 39.4 m/s = 88 mph

With a release speed of 90 mph or 40.2 m/s
t (ball reaches plate) = 0.439 sec
Horizontal speed (ball reaches plate) = 37.3 m/s = 83.4 mph

Velocity loss of a pitched baseball (June 10, 2003)

Posted 6:18 a.m., June 13, 2003 (#5) - Sylvain(e-mail)
  Oups, some incomplete sentences:
"A graph in the link I posted (I pretty much guess it comes from Adair's book, but I don't have the book)" would tend to show that the drag coefficient can be considered as almost constant.

The formatting is bad, so here are the main formulas, if one wants to play with them:
Vx = 1/(a/m*t+1/Vo)
X = m/a*ln(1+a*Vo*t/m)
t = m/(a*Vo)*[Exp(a*x/m)-1]

Sylvain

Velocity loss of a pitched baseball (June 10, 2003)

Posted 4:48 a.m., June 17, 2003 (#6) - Sylvain(e-mail) (homepage)
  From Jayson Stark's latest column:
"The Yankees, of course, had last been officially no-hit on Sept. 20, 1958, by a knuckleballer (Hoyt Wilhelm). So they clearly set one more record Wednesday -- greatest difference in miles per hour of a final pitch of consecutive no-hitters. The Little Unit, Billy Wagner, threw the final pitch of this one -- at about 147 mph. Wilhelm's was more like 57 mph, give or take 20."

147 mph!!!! That seems a lot to me, especially based on the data of the homepage link. Can someone confirm this? Or is this just a typo?

S

Velocity loss of a pitched baseball (June 10, 2003)

Posted 10:24 a.m., June 17, 2003 (#8) - Sylvain(e-mail)
  Based on the spreadsheet I also used for the relay thread:
Suppositions:
* distance home - point of release = 55 feet
* Vo is purely horizontal
* pitch = fastball, no lateral magnus force, rotation = 1800 rpm

Speeds are in mph, distances in feet, time in seconds

OriginalSpeed_SpeedatthePlate_Timeneeded_VerticalDeviation
106__98.4__0.37__-1.4
104__96.4__0.375__-1.45
102__94.5__0.38__-1.5
100__92.4__0.39__-1.6
98__90.3__0.40__-1.7
96__88.2__0.41__-1.8
94__86.1__0.42__-1.9
92__84.0__0.43__-2.0
90__81.9__0.44__-2.1
88__79.8__0.45__-2.2
86__77.7__0.46__-2.3
84__75.6__0.47__-2.5

A loss of 4 mph for a pitcher represents 0.02 seconds more for the batter. I don't think that is negligible. A swing takes about 0.3 seconds to travel between 90 and 120 degres. Supposing that this speed is constant, 0.02 seconds represents a bit less than 10%. But since w the angular speed is growing, it could represent around 10% more rotation! (supposing that the batter begins to swing at both pitches at the same time). And a higher bat speed, meaning more power!
This is of course a very basic view. But a loss of speed of 4 mph is a lot.

This result can also interpret the change represented by an offspeed pitch compared to a fastball.

Sylvain

Velocity loss of a pitched baseball (June 10, 2003)

Posted 3:00 a.m., June 18, 2003 (#9) - Sylvain(e-mail)
  As for: "But since w the angular speed is growing, it could represent around 10% more rotation! (supposing that the batter begins to swing at both pitches at the same time). And a higher bat speed, meaning more power!" ,
I should have said: "it could represent around 10% more rotation! (supposing that the batter begins to swing at both pitches at the same time). And a higher bat speed; however one has to consider the loss of momentum of the ball (less speed) as well."

S

Velocity loss of a pitched baseball (June 10, 2003)

Posted 11:34 a.m., July 30, 2003 (#10) - Sylvain(e-mail) (homepage)
  A very interesting link, follow the homepage

Sylvain

Hitting the cutoff man (June 13, 2003)

Posted 7:33 a.m., June 16, 2003 (#1) - Sylvain(e-mail) (homepage)
  Ok, I'll take my shot on this issue.

Suppositions:
- 3 players considered (OF, IF, C); all 3 are aligned, the infielder is between the outfielder and the catcher.
- spin and magnus force negliged
- drag negliged (for this model)

Initial conditions at t=0 : we suppose the following coordinates:
OF (x=0; y=0), IF (L1; 0), C (L2; 0), the OF has the ball, and the initial vector speed Vo makes with Ox an angle alpha (noted a).

The methodology is not that long and already explained in the homepage link, so I'll begin with the results:
x = Vo*cos(a)*t
z = -1/2*g*t^2 + Vo*sin(a)*t

I also pose a belongs to ]0; Pi/2[ (z has to be >= 0 and x growing, the level z = 0 corresponds to the "altitude" of the shoulder. Generally speaking, the ball will reach the following player (IF/C; coordinates (x = L, z = 0) at a time T if:
z = 0 = -1/2*g*T^2 + Vo*sin(a)*T (1) and x = Vo*cos(a)*T = L (2)

First result : the maximum distance (without rebound) that can be reached by a player that throws a ball with a speed Vo is: Lmax = Vo^2/g. This maximum distance will be reached if a = Pi/4 or a = 45°.

We now suppose that every distance will be in accordance with the condition LIF) = Vo(OF)*sin(1/2*arcsin(g*L1/Vo(OF)^2))*2/g
+ time for the infielder to catch and throw
+ T(IF->C) = Vo(IF)*sin(1/2*arcsin(g*L2/Vo(IF)^2))*2/g

Second Result : It will be faster to relay if the sum of the 3 terms above is bigger than the time needed to throw directly .
But:
- for the direct throw, we need one very accurate throw (because y, the deviation will equal to Voy*time of flight, and Voy will be the measure of the accuracy)
- for the relay, we need 2 accurate throws; the accuracy of the first throw will also influence the time neede by the IF to catch and throw.

Numerical Application
Max distance
Remember: the drag is not considered! The real distances will be shorter (I don't know by how much, but I'd say mimimum 10%)!
Original Velocity (MPH)__Max Distance (FT)
89__536
84__471
78__410
73__354
67__301

Relay or Direct ?
I suppose that both the IF and OF can throw at the same speed (75 mpH)and that the IF is midway between the C and the OF
Distance(OF-C, in FT)___Time Direct(Sec)___Time Relay(Sec)
(the max distance for a speed of 75 mpH is 376 feet)
360__4,1__3,4 + time for the IF to catch and throw
330__3,5__3,1 + ...
300__3,1__2,8 + ...
270__2,7__2,5 + ...

The break even (considering an IF catching + throwing time of 0,4 sec) is at 330 feet distance between C and OF.

I once read the max distance ever thrown at was 180 meters or 590 fee. This corresponds to a speed of 94 mph not considering drag and supposing the original angle was 45°. The real speed might have reached 100 mph.

Sylvain

Hitting the cutoff man (June 13, 2003)

Posted 10:49 a.m., June 16, 2003 (#3) - Sylvain(e-mail)
  Tango,

The problem I have with drag is that integrating it gives some very heavy equations that can't be solve easily. I haven't had time yet to really give a look at it, and every time I found a paper on the web it implied (if my memory is correct) a computed solution using maple/mathematica or another software in case of a non vertical movement. Even vertical, still if my memory is correct, the solutions are functions like cosh, sinh.. (cosh = 1/2*(exp(x)+exp(-x), sinh = 1/2*(exp(x)-exp(-x)).

The differential equations actually look like
dx/dt = x*rootsquare(x^2+y^2) and
dy/dt = constant + y*rootsquare(x^2+y^2)

So, if there's any differential equations specialist here, don't hesitate to contact me.

Still, based on the homepage link, tim raines could throw at about 243 feet (angle a = 35°); give me 20 minutes and based on this site I'll try to build a basic rule linking my results to the "real" ones.

As for the deciphering, I'll try to find the time to type everything and make a .pdf out of it. I know it's hard to read.

Sylvain

Hitting the cutoff man (June 13, 2003)

Posted 11:17 a.m., June 16, 2003 (#5) - Sylvain(e-mail)
  So, based on 15 points (small sample size...) between 101 and 67 mph, a basic rule seems to be:
Max Distance (feet) = 3.4 * speed (mph)
Or
Max Distance (feet) = -119.5 + 4,481 * speed (mph)

The angle is always around 35°

SC

Hitting the cutoff man (June 13, 2003)

Posted 5:52 a.m., June 17, 2003 (#6) - Sylvain(e-mail)
  I gotta make such an idiot: here is the homepage link I refer to in post#3:
http://www.npl.uiuc.edu/~a-nathan/pob/

the sim I used to "generate" the 2 formulas:
http://www.scri.fsu.edu/~jac/Java/baseball.html

S

Hitting the cutoff man (June 13, 2003)

Posted 9:09 a.m., June 17, 2003 (#7) - Sylvain(e-mail) (homepage)
  So, some better results.

Methodology
Based on the equations (and the notations) given in the homepage link, and neglecting the lateral magnus force (phi = 0), I ran a step method (constant step = 0.01 second):
vx(step n+1) - vx (step n) = - vx(step n)* step * Drag_Coefficient(vx(step n);vz(step n)) - step * B * rotation * vz(step n)
B is a constant and corresponds to the magnus force; the drag coefficient depends on the speed, and both formulas and values given already include m.
Add g (gravity) and do the same along the z axis and you will obtain the equation for vz(step n+1).
For x and z:
x(step n+1) = x (step n) + step * 1/2 * (v(step n+1) + v (step n))
Same for z...

BTW, for the magnus force I supposed a rotation of the ball of 1800 rpm (like a fastball). The results I obtain are similar to the ones given in the sim (93 mph and 35° give me 328 feet instead of 330; 98 mph and 20° give me 323 feet instead of 312; 75 mph and 10° give me 133 feet instead of 141).

By the way, the magnus force has a big impact on the distance travelled: if one takes a rotation equal to zero with a speed of 75 mph and an angle of 35°, the ball will travel

Results
Supposing that the IF needs 1 sec to catch and rethrow the ball, here are some estimations:
ArmeSpeed (mph; OF and IF)___ BreakevenDistance (feet)__MaxDistance (feet)
65__187__193
70__210__216
75__230__240
80__245__262
85__275__286
90__295__312
Distance between C and OF shorter than breakeven => direct throw fastest.

Conclusion
Unless and OF is close to his maximal throwing distance, a direct throw seems faster, based on this model. However some elements here haven't been taken into account such as lateral spin, accuracy of the throw, weather conditions, and all the throws are supposed optimized. Rebounds haven't been considered as well.

For this calculations I used an Excel spreadsheet. If anyone is interested, wants to know how far he can throw, send me a mail or leave a message on the thread. The spreadsheet can also be easily updated in order to include curve, slider, sinkers and screwball.

Sylvain

Hitting the cutoff man (June 13, 2003)

Posted 3:04 a.m., June 19, 2003 (#11) - Sylvain(e-mail)
  Thanks a lot for posting it Tango!

Sylvain

Hitting the cutoff man (June 13, 2003)

Posted 9:08 a.m., June 23, 2003 (#13) - Sylvain(e-mail)
  Steve (I guess): the max distance a throw can reach (given an initial speed Vo depending on the player) seems to be 35 degrees. Ok, I didn't purely demonstrated it... But this has nothing to do with runners being thrown out. The best application of the 35 degrees is hitting.

As for the fielding applications you are right, the relevant issue is time. For your calculations: supposing that Gonzo can throw at 300 feet with an angle of 35 degrees, that makes a speed of about 87-88 mph and 4.6 seconds. And the max distance Gonzo can throw at within 4.5 seconds is about 295 feet.
However a relay with a cutoff man (arm speed also 87.5 mph situated between Gonzo and the Catcher) would take 2*1.36 seconds plus time for the IF to catch and throw (est. 1 sec) = 3.7 seconds. A gain of almost 1 second.
The relevant issues are: given a flyball (as a distance to the catcher) and a runner (time to reach home):
- can Gonzo throw directly to the catcher? If yes, how much time does it take: will he throw the runner out?
- is a relay faster?
The second issue becomes important as soon as the time for the runner to reach home and the time for the direct throw to reach the C become close. However in "live action" it's very difficult to assess all those parameters: is the cutoff man in position, will the throw be accurate enough in order not to lose time, windy conditions. There are a lot of other parameters.

As for your question on the 300 feet as a good sac distance: it depends on the fielders and the runner: as pointed ou above, a relay needs about 3.7 seconds, but a direct throw 4.5 seconds. If one considers a time of 4 seconds for the runner, you have the answer: will the OF go for the relay or not?

Sylvain

Hitting the cutoff man (June 13, 2003)

Posted 7:20 a.m., June 24, 2003 (#15) - Sylvain(e-mail)
  Steve,
Concerning the bounce, well, I don't really know how to look at it. I'd say the loss of energy during the ball-ground collision depends on:
1) speed of the ball (norme)
2) direction of the ball/ground (angle + if grass field, then how the grass grows)
3) nature of the ground: turf/wet grass/sand/dry grass... One could suppose, as you mentioned, that turf might better restitute the speed (harder, different friction coefficient, etc.)

BTW, if the relays aren't used that often, it's because, based on the numbers given in post#7, unless the fielder is really close to his maximal range (nothing to do with RF), a relay would actually cost time. A bounce might even increase this advantage. So the relay is (seems to be barely a viable option). Another point to consider is that when the OF throws the ball, he is running, adding an horizontal initial velocity. I haven't considered this point is my calculations.

Concerning the 250 feet throw in 4 seconds: 82 mph 35 degrees give 3.7 seconds, so that a throw with less speed will reach 250 feet after a rebound and more time, a throw with more speed in less time (85 mph, 250 feet = 3.2 seconds, 28 degrees).

Concerning the vertical component and the may height, I'd say this is correct when neglecting drag, since drag depends on the speed as a whole. But when looking at a throw, it is advantageous to throw with the lowest angle possible: the speed increase due to gravity (also limited by the drag) isn't enought to compensate the difference in distance.

I don't know if I answered your questions.

Sylvain

Estimating Pitch Counts (July 2, 2003)

Posted 8:03 a.m., July 2, 2003 (#1) - Sylvain(e-mail)
  I don't know if anybody saw this estimator, I fell on it a few weeks ago; it requires more data though (BFP), and is based on college pitchers data:

http://www.boydsworld.com/breadcrumbs/epcintro.html

Jim Boyd writes for Prospectus as well I think...

Sylvain

Sabermetric Site to Visit - ESPN (July 25, 2003)

Posted 3:05 p.m., July 29, 2003 (#2) - Sylvain(e-mail)
  Hijack.... I looked for a similar discussion but coulnd't find one.

I discovered sabermetrics through this website, and discovered this website thanks to baseball reference. However what I haven't found yet is a site cataloging all the sabermetrics concept developed here, on prospectus, fanhome, or any other place, and organizing them, saying who developed them, linking to discussions, data, etc. For example Global Evaluation Tool > Win Shares, tool developed by Bill James> the 2003 Win Shares can be found on Baseball Graph > and Tangotiger and Rob Wood propose a critic (clink to have access to the Pdf). Does such a site exist ? Skilton's Baseball links does a good work of linking to as many sites as possible however it isn't organized based on the ideas/stats. I think such a site might be very useful especially for newcomers (what does RC mean? Is it a good stat?) and I'd be willing to develop such a site or help. The categories would be subject to discussion (offence/defense/etc).

Thanks for your comments/links/ideas/whatever

Sylvain

Sabermetric Site to Visit - ESPN (July 25, 2003)

Posted 8:18 a.m., July 30, 2003 (#4) - Sylvain(e-mail)
  Thanks for the info. It actually been a long time since I hadn't visited the baseballstuff site and I highly recommend it(even though I haven't read every article yet).
Though my idea would not consist in hosting articles, but just in providing links and organizing them. A kind of baseball links, with a mix of baseball reference (I don't know if everybody understands what I mean...). Or like the Prospectus Glossary, but organized by themes (and more exhaustive).
If this is what you meant with your suggestion (although it seems complicated; it's not as if I was a website development god and had fully understood what you said), well, then I'm interested in participating/doing it, even alone if the people here think it is worth it (but then lower your expectations).

Thanks,

Sylvain

Sabermetric Site to Visit - ESPN (July 25, 2003)

Posted 11:26 a.m., July 30, 2003 (#6) - Sylvain(e-mail)
  Ok, then we agree on the idea.

Now I'm gonna think the technical details and specifications. Yet, if you know any links, post them here.

Thanks a lot.

Sylvain

Competitive Balance (July 25, 2003)

Posted 9:27 a.m., July 26, 2003 (#2) - Sylvain(e-mail)
  Excellent stuff, as usual....

S

Tippett's DIPS study (July 29, 2003)

Posted 7:35 a.m., August 1, 2003 (#2) - Sylvain(e-mail) (homepage)
  I also pointed it out in the Clutch thread, but since the "hot topics" frame in clutch hits doesn't seem to work properly (victim of its success, too many posts or threads?) whereas the Primate Studies one seems to work better:
Tom Tippett provided an answer to remarks made in the original clutch hits thread on his diamond mind weblog (link in homepage address).

Sylvain

Open Directory Project - Sabermetrics (July 30, 2003)

Posted 12:07 p.m., July 30, 2003 (#1) - Sylvain(e-mail)
  Thanks Tango.

I posted my ideas om the thread "ESPN - Sabermetric website". The site I want to develop is as of now just a vague project. The technical details remain to be defined. However the concept would be the following: enable people to have an easier access to metrics and concepts developed. For example if in a discussion something like "hey, he's got an OWP of .547 and his VORP this year is.." appears, some people might not understand and thus be scared by sabermetrics.
The site (a sabermetrics glossary, or catalogue) would provide links to pages providing:
1) the definition of OWP and VORP (source) and possibly how to calculate it
2) data (VORP this year, past years) and
3) point out some relevant discussion about these metrics (why OWP is bad, what is the relevance of OWP...)

The long-term goal would be to provide a complete and exhaustive list of different metrics and concepts or discussions used in most saber discussions.
If anybody is interested or finds this idea interesting, do not hesitate to comment, give ideas, on this thread or directly per mail.

Thanks a lot,

Sylvain

Open Directory Project - Sabermetrics (July 30, 2003)

Posted 9:35 a.m., July 31, 2003 (#4) - Sylvain(e-mail)
  Trantor, Tango: thanks for the ideas. I'll give some updates as soon as I'll have made (time?) any significant step.

Sylvain

DIPS year-to-year correlations, 1972-1992 (August 5, 2003)

Posted 5:46 a.m., August 14, 2003 (#98) - Sylvain(e-mail)
  Excellent, tremendous stuff, congrats to every participant.
Should automatically deserve the primey for best thread.

Sylvain

Advances in Sabermetrics (August 18, 2003)

Posted 12:10 p.m., August 25, 2003 (#41) - Sylvain(e-mail)
  So, back from holiday, on top of my head:

Major improvements (and a great thanks to those who contributed):
DIPS, LI, PAP and pitch counts, Replacement Level; as the DIPS Solved thread showed, better "usage" or "understanding" (from me at least) of stats (regression to the mean...) (which implies I'll have to go find back my college books); pbp data usage...

Future improvements (on top of my dreams):
Linking PAP and biomechanics (delivery type, pitch thrown...), DIPS and pitch by pitch data, catcher's influence on the game, protection and hustle, and who deserves the ROY award? (I hop I'll be among those who participate)

Sylvain

Pitchers, MVP, Quality of opposing hitters (September 19, 2003)

Posted 8:11 a.m., September 20, 2003 (#4) - Sylvain(e-mail) (homepage)
  As for "adjusting to the opposition faced" the homepage links to a post I wrote for a Halladay thread: I tried to factor the difference of IP pitched agaisnt same teams between Loaiza and Halladay in order to arrive to an ERA that would be more "representative".
BTW Prospectus does a similar thing in taking into account the fact that over a season a pitcher doesn´t face his own team (see Team Pitching Adjustment http://www.baseballprospectus.com/cards/glossary.shtml)

But as Kurt points out, a major problem I faced is sample size. Are the 8 IP by Loaiza against BOS for real? Are the 26 IP pitched by Halladay against DET for real? How to regress these performances? I remember (David Smyth or Patriot) provided a chart saying by how much one should regress towards the mean depending on the PA. Can I do the same for ERA against one team: regress it towards the season ERA after taking into account the opposition faced?

For example: suppose Loaiza pitched 12 innings with 1 ER against DET (OPS 650) but has en era of 2.5 for the season (avg OPS 750)? Or do I have to do an odds ratio method first (what would be Loaiza´s season ERA had he faced a 650 OPS) and then regress the 1 ER in 12 IP towards this "mean"?
This would (I think) give a better estimation, even if a second problem would be to assess the OPS of the teams faced (hot month/injuries: one could take the OPS of the team during the week of the start considered, regress it as well...).

Please correct me if I´m wrong.

Any other ideas? Or is an odds ratio method at the end of the season in order to adjust to the OPS faced enough?

THEN would come the point of the teams that a pitched faced and not the other (interleague games/schedule).

Thank you

Sylvain

Sabermetrics >WIN SHARES bibliography (September 19, 2003)

Posted 7:40 a.m., September 20, 2003 (#5) - Sylvain(e-mail)
  Thanks for the link.

By the way if anyone sees an error or wants to suggest a link that we missed or has a specific wish (seeing a particular bibliography), send me an email:
s_cognet@yahoo.fr

Sylvain

Results of the Forecast Experiment, Part 2 (October 27, 2003)

Posted 3:35 a.m., October 28, 2003 (#37) - Sylvain(e-mail)
  Thanks a lot Alan and Tango.

Sylvain

Results of the Forecast Experiment, Part 2 (October 27, 2003)

Posted 10:19 a.m., October 28, 2003 (#45) - Sylvain(e-mail)
  Thanks one more time Alan and Tango.

Ouch! Tied for 31st as far as the hitting goes, but tied for 162nd for the pitching.

What will be interesting is how the primates will behave next year (if the Primer Chiefs decide to reconduct this forecast, of course): since they know the baseline is better than (most of) them, will they just go for the baseline plus 1/10th of personal adjusments in order to get an edge, or 2/3rd baseline 1/3rd forecasters, or another solution? Are the forecasters for real? Are the best Primates forecasters for real?

Sylvain

For Aging Runners, a Formula Makes Time Stand Still (October 29, 2003)

Posted 10:48 a.m., October 29, 2003 (#2) - Sylvain(e-mail) (homepage)
  Studes: your links didn't work with me, I could read the article but no graphic (perhaps some IE stuff).

In the homepage: link to the Health-Fitness and Nutrition section of the times; the article is the one above, click on the link "Graphic: running the numbers". It's a pop-up.

I think this is the graphic Studes is refering to.

Sylvain

Gleeman - Jeter - Clutch (October 30, 2003)

Posted 12:18 p.m., October 30, 2003 (#1) - Sylvain(e-mail)
  Speaking about clutch hitting, here is a list of articles on the web:
(name of the article, author, URL)

Clutch Hitting Study David Grabiner http://www.baseball1.com/bb-data/grabiner/fullclutch.html
Clutch Hitting Leaders, 1987-2001 Cyril Morong
http://hometown.aol.com/cyrilmorong/myhomepage/clutch.htm
Clutch Hitting and Experience Cyril Morong http://hometown.aol.com/cyrilmorong/myhomepage/Clutch-experience.htm
Looking for Clutch Performance in One-Run Games Tom Ruane http://www.baseballstuff.com/btf/scholars/ruane/articles/onerun.htm
Situational Hitting Tom Ruane http://www.baseballstuff.com/btf/scholars/ruane/articles/situational_hitting.htm
Clutch Hitting Rob Neyer http://www.diamond-mind.com/articles/neyerclutch.htm
Hitting with Runners in Scoring Position Jim Albert http://bayes.bgsu.edu/papers/situation_paper3.pdf
Does experience help in the post-season? Tom Hanrahan http://www.philbirnbaum.com/btn2002-11.pdf
What makes a clutch situation Tom Hanrahan http://www.philbirnbaum.com/btn2001-02.pdf

Sylvain

Fun with Win Shares (November 5, 2003)

Posted 11:53 a.m., November 5, 2003 (#1) - Sylvain(e-mail)
  Studes and Pete,

congrats and thanks for your site.

Sylvain

Win and Loss Advancements (November 13, 2003)

Posted 10:52 a.m., November 13, 2003 (#2) - Sylvain(e-mail)
  Tango: Great Great stuff, as usual.

As for the BIP, how did you do?
- Situation 1, WE = x
- BIP by the batter
- Situation 2, WE = y

and WA/LA (assigned to the pitcher) = (x-y)/2, this for every kind of BIP, or do you have some "classification" (infield fly goes 90% to the pitcher as in DRA, other)?

Interesting point and questions, if you have the time: the best starters lead the way, then come the best relievers with the very good starters... How do the populations "Starters" and "Relievers" compare? One could expect over time to have the same average WAA = 0, but the deviation?

I was also surprised by the gap between Pedro, RJ, and the rest of the pack. It seems a very good starter/exceptionnal reliever season is worth about 13-10/4 = 2.5-3 WAA or 5-6 Mio.US$, and exceptionnal one about 5 WAA for 10 Mio. US$, right? you must have said it before, but the gap is huge.

And finally, if this can be used for forecasting, what is the year to year correlation?

Sylvain

Win and Loss Advancements (November 13, 2003)

Posted 11:36 a.m., November 13, 2003 (#4) - Sylvain(e-mail) (homepage)
  Thanks Tango. Your calculations must have taken you a lot of time. Thanks for sharing them.

The homepage links to the "Anatomy of a collapse" thread, for those who like me might want to look back at it.

Sylvain

ABB# (November 24, 2003)

Posted 11:04 a.m., November 25, 2003 (#27) - Sylvain(e-mail)
  Hey Aaron,

Great idea and nice picture on your website ;-)
Hope the use of the GPA will spread on the web.

Sylvain

The Problem With "Total Clutch" Hitting Statistics (December 1, 2003)

Posted 11:47 a.m., December 1, 2003 (#3) - Sylvain(e-mail)
  2 quick comments:
- concerning the linear regression with PWV/PA, the equation gives PWV/PA = -.024 + .00015*OBP + .000095*SLG which leads to weight OBP /weight OPS = 1.58. In the OPS Begone series Tango you used Base Runs, in this article it seems to be a historical approach, so is it the 3rd time that the 1.6-2.0 coefficient is "confirmed"?

- Cyril, you used only the top100 in PA, therefore only very good players or Luis Sojo are considered; isn't it possible that the regression coefficients are valid just for the "above 100 of OPS+" players? Can't one suppose the "clutch ability" is present but at a somewhat constant level between ML Players? This must have been mentioned before; it just reminds me of the different paths and reflexions during the DIPS debates (BABIP bad measure? Not ability at all or no ability compared to league average? etc)

Sylvain

The Problem With "Total Clutch" Hitting Statistics (December 1, 2003)

Posted 11:50 a.m., December 1, 2003 (#5) - Sylvain(e-mail)
  Concerning the 1st point, it is very possible that I missed an article looking at Win Prob and OPS/OBP and SLG....

Sylvain

DRA Addendum (Excel) (January 16, 2004)

Posted 11:03 a.m., January 19, 2004 (#11) - Sylvain(e-mail)
  As DW said:

Thanks a lot Michael for your DRA articles and the amount of work put into it and the sharing of the results.

Sylvain