THE BOOK--Playing The Percentages In Baseball

I wouldn’t read anything into the first two charts.  Sample sizes are so small they are highly likely to be biased by which pitchers are in the “at Colorado” sample.  The author seems to indicate he did not correct for that effect, which would render the tables meaningless, IMO.

The last one is inaccurate according to physics; I suspect it suffers from the same problem.  Air density in Denver is about 81% of what it is at sea level, so pitches thrown with the same spin will be deflected 81% of what they would at sea level.  In a physical accurate graph, all the point would move about 19% toward the origin.  (Small caveat: many people lump drag and spin effects together on spin deflection charts, in which case the points would move about 19% toward a location about an inch above the origin.)

It’s interesting that although non-Rockies pitchers throw fewer “sinkers” at Colorado, they throw a few more “two-seam fastballs” and Rockies pitchers throw more “sinkers” and fewer “two-seam fastballs.”

However. . . adding the two-seamers and sinkers together as a category makes the results more statistically significant than just the sinkers alone.  The home/away split for Rockies pitchers (still not controlled for pitcher identity) is 1.8 sigmas for just the sinkers, 2.1 for both types together.

For non-Rockies pitchers, the difference rounds up to 1.0 sigma for just sinkers, but is 1.3 for both types together.

Assuming there isn’t a bias from pitcher identity, the chances for both variations on (only) the sinkers happening by chance is about half a percent (5.6 x 10^-3).

However. . . we should apply an “anywhere factor” of 28 (7 pitch types x 4 high/low combinations) because (unless I’m missing something) we didn’t have an a priori reason to expect this particular split in this particular pitch type.  The probability of at least one pitch type having at least this level of variation from normal at Colorado is more than one in 7 (14.6%).

I would need more information to be suspicious that this is a real effect.

#1
Thanks for your inputs Mike, appreciated.

Regarding the chart - yes, this is not calculated but taken from the Pitch F/X data in a combination of comparisons (Rockies staff in Denver as opposed to what they threw in the away games and single Rockies’ pitchers for their home/away pitch movement). As I state, it is a rough estimate and you are right - calculating it instead of looking at the results would have probably been a better way to go about it.

As for your last comment, I am not sure I understand it completely:
“Small caveat: many people lump drag and spin effects together on spin deflection charts, in which case the points would move about 19% toward a location about an inch above the origin.”
(emphasis mine).

Are you saying that the effect of drag force in Colorado (or the relative lack of it) would be for the balls to finish their trajectory higher than in the sea level parks?

Isn’t the Z-component of drag force positive (pointing above) and reduced with reduced air viscosity? Shouldn’t that mean that reduced air density leads to reduced drag lifting the ball and effectively make the ball land lower? Am I missing something here?

Thanks in advance for your input.

Isn’t it possible that that last chart is accurate, based on how the pitchers actually throw?

That is, knowing that the curve won’t bite as much at Coors, then either:
a. disproportionately really good curveball pitchers are in the Coors sample

and/or

b. they throw their curveballs even slower to try to get an even bigger bite to cancel out the Coors effect?

More support for the a. is that the fastball shows the biggest change, so that perhaps “bad” fastball pitchers appear more here.

Bojan/3, I assume you took the pfx_x and pfx_z numbers from the data, which are spin + drag.  You are correct that the Z component of the drag force points up since the ball is falling.  This effect is usually around a magnitude of one inch of break in pfx_z.  So the true “origin” for a spinless ball is not 0,0.  It’s something closer to 0,1.  (And if you have more right-handed or left-handed pitchers in the sample, it may be a little left or right of zero in the horizontal dimension, too.)

In Colorado the drag would be reduced to 81% of sea level, too, as you note.  So if the spinless “origin” was [0,1] at sea level, it would be [0,0.81] in Colorado.

I generally like to remove drag from spin deflection charts altogether, but that’s not something most people do since it requires recalculating pfx_x and pfx_z without drag effects.

Tango/4,

I would expect that the last chart is accurate based upon the pitches that were actually thrown.  I’m not saying Bojan did his work wrong.  I’m saying you have to be very careful how you interpret something like that.

I suspect that the difference in the amount that the various pitch types moved toward the center is due to the difference in the identity of the pitchers in the two samples being compared.  Now whether that is purposeful or random, I don’t know.  I’d lean toward random without any evidence to the contrary.  You’re free to speculate, of course.  I generally don’t have much success with that sort of speculation, but maybe you’re a much better speculator than I am.

I’m not going to speculate.  I’d rather ask questions so we can have a discussion, so that researchers can look for biases in data.

Regarding Mike Fast’s point about mixing drag and Magnus, I wrote extensively about that back in 2007 (see http://webusers.npl.illinois.edu/~a-nathan/pob/Magnus.pdf).  Mike in #5 has the explanation exactly right.  At the time, I was advocating that pfx_x and pfx_z be calculated with the drag component removed.  But no one adopted the idea.

Is it a decision made before or during a game? My guess is that some pitchers try to throw it early in a game and realize it isn’t working so they stop throwing it. Is there a way to check if the numbers are more normal in early innings?

Will #9, I suspect something like that might be part of the picture. For one thing, I don’t know if we can expect away pitchers to drastically alter their style of pitching while in Coors. They’ve been working on their game for years, know what pitches work for them, would probably not feel comfortable taking a different approach to pitching, so I wouldn’t think they would consciously alter what they throw in any drastic manner when pitching to batters in Coors. They rely on certain pitches and a certain approach that they feel best works for them. But hearing and reading many post-game interviews with pitchers about how a game progressed, you quite often hear them saying that “this pitch wasn’t working, so I went with more of this pitch”.

Perhaps pitchers and the pitching coaches that advise them are more cognizant of how Coors Field might affect certain pitches than I realize, but I doubt if many pitchers would take a different approach for the 2 to 3 times they pitch there a year. Most people are creatures of habit, and go with what has proved successful for them in the past, until that fails for them.

Most likely, they throw what they usually throw, unless they find that it’s not working for them in a certain game, and then start throwing more of other pitches.

Mike/5
Thanks for clarifying.

So would you agree with me then in saying that a fastball is the pitch that most loses its movement in Colorado?

Compared to sea level all pitches will lose 19% of their sea level spin related deflection and on top of that 19% of the drag. However, while deflection reduction will bring pitches closer to the center, drag reduction will bring all pitches down.

So, in case of the curve ball the two reductions will be in the opposite directions on the Z-axis, while in the case of the four-seam fastball they will be cumulative (reduced spin deflection effects will bring the ball down and so will the reduced drag effect, right?

I mean, we are talking about half an inch difference tops (+/- 19% of 1"), but still, in absolute terms fastball gets flattened more than a curve ball, right?

So, all pitch deflections (from the origin) at Coors would be diminished by roughly 20%.  But, their distance from the “eye” won’t be reduced by that much.

For FF, Coors has the unfortunate effect of brining movement very close to the “eye”.  For cutters and sliders, however, the movement is orthogonal to the eye so I might speculate that these pitches aren’t harmed by Coors nearly as much.  Also, with the curve, 20% less distance to the origin, would only be something like 10% less distance from the eye.  Then again, maybe this isn’t the right way to think about things.  Maybe every thing else is being compared to FF (not to playing catch) and so all differences are reduced by 20%.

Re Bojan (#19):  The difference in speed in Denver is not very large.  Since a typical pitch loses 10% of it speed (at sea level) between release and home plate, it will lose only 8% at Coors.  What matters for the movement is the average speed, which is 95% of the release speed at sea level and 96% at Coors.  So, there is only a 1% difference in movement due to the drag (less than 1 mph).  If a typical 4S fastball drops 36” at sea level, it will drop 1% less at Coors, or 0.4” less.  Not a big effect compared to the difference in spin deflection.

Alan/13
Shouldn’t it drop more, not less in Colorado? If there is reduced drag, and drag pushes the ball upward, shouldn’t such ball end up lower?

Bojan:  The drag is primarily in the -x direction (your notation).  With less drag in Denver, the pitch gets to home plate quicker, so there is less time for the combined effects of gravity and Magnus to act.  So the effect of the reduced drag is to make the ball drop *less* than it otherwise would.
For a 4S fastball, the reduced Magnus force makes the ball drop more than it otherwise would.  So, the effects go in the opposite direction (although totally dominated by the reduced Magnus force).

So, to stick with my notation, reduced drag affects the drop in two ways:

1) The ball drops more due to the reduced Y Component of the drag force
2) The ball drops less due to the reduced -X Component of the drag force, leading to reduced time of flight in which gravity (stronger) and Magnus (weaker) affect the ball

-and-

The effects of 2) outweigh the effects of 1), so that overall, the ball drops less.

Would that be about right?

Bojan...I am not sure you have said it right.  But, rather than go through another iteration, let me suggest you investigate these things yourself using my “trajectory calculator”: 
go.illinois.edu/physicsofbaseball/TrajectoryCalculator.xls.  It is more or less self-explanatory.  In particular, you can enter the elevation and see how that affects the trajectory.

Just to get back to your specific question:  The reduces X component of drag makes the ball drop less.  The reduced Y component of drag makes the ball drop more (since Y component is up).  I haven’t bother to compare the relative sizes of these two effects, which tend to cancel.  However both of these changes pale in comparision to the effect of the reduced upward Magnus force (assuming backspin).  Reducing that force makes the ball drop more in Coors than at sea level.

Alan, thanks.

I am aware that reduced spin affects the trajectory significantly more than reduced drag, but I was curious what your findings are on the effects of drag itself and in which proportion are 1) and 2) from the above.

Thanks for your time.

P.S. Your link redirects me to http://webusers.npl.illinois.edu/~a-nathan/pob//trajectorycalculator.xls and ends with a 404

http://webusers.npl.illinois.edu/~a-nathan/pob/TrajectoryCalculator.xls

Link is dangerous and you will lose a few hours from your day messing with it.  For pitching i like to go in and set z0 to 7ft, theta 0±, phi to 90, then start messing with speed, spin, and elevation.  I also find it helpful to adjust the limits in the graph to 1.6 - 8 on the y and 0 to 55 on the x.

As to your question about proportion, i think the best you are going to wind up with is a “more than” or “less than” type situation as the formula itself is fairly complicated.  A ball thrown at altitude will have a tendency to drop more than one at sea level as the ball is not able to generate as much “lift” to compensate for gravity.

Here is a link to another spreadsheet that takes the PITCHf/x 9 parameter description of the trajectory and calculates the x,y,z components of both the drag and the Magnus force.  The temperature and elevation can be entered to see how those affect the results.  The time from 50 ft to the front of home plate is calculated.  The deflection due to whatever component of the acceleration interests you is 0.5*a*t^2, where “a” is the the acceleration.

http://webusers.npl.illinois.edu/~a-nathan/pob/Template-for-drag-and-spin.xls

Thanks Alan, good stuff