THE BOOK--Playing The Percentages In Baseball

As a physicist, I’m apalled by some of the arguments in the actual article. So much hand-waving.

My initial thought when I read the blurb on your blog was “metal cylinders that approximate bats”?!?! Why not use, you know, actual bats? The shape is actually important.

So what you actually want to do to hit a ball as far as possible is to provide the maximum possible impulse to it. How this works out is really complicated already. Let’s assume for the moment that we want to maximize the linear momentum of the bat - I believe this is what the point is they’re trying to make. So we have momentum, p = mv, and energy, KE = .5mv^2. So naturally, if you apply the same amount of energy to two different bats of different masses, the one which is lighter has less momentum. But can you deliver the same amount of energy to bats of different weights? I doubt it’s the same (don’t know which is more), and if they’re doing robot tests, they didn’t check it out. It would be interesting to have people in to study how fast/hard they can swing different bats.
But beyond this, people swinging bats is more rotational motion than linear, unless, perhaps, you’re bunting (but then we aren’t talking home runs). This helps explain why bats are shaped the way they are - you want the heavy part away from your hands so that you can rotate it faster, and it’s heavier to make the ball go farther. Of course, this would imply that hitting off of the end of the bat is best (this is where linear speed is highest, and momentum even moreso than that), and this is almost true; you only want to not hit off of the end of the bad to the extent that during the collision, the force of the ball gets distributed through the bat well enough to “make solid contact”.  So a bunch more variables get thrown in as well, and I don’t know the answers, but I’m shocked that these guys are talking so certainly. Maybe if I read the actual paper, it wouldn’t be so bad. But shape of the bat is really important, as well as where on the bat the ball hits and the motion of the swing.

Okay, furthermore, the thing about the humidor. I want to know how long those balls had outside the humidor before they were tested, and what the conditions outside the humidor were like. Obviously, the balls are going to re-equilibrate, it’s just a question of how long that takes. Furthermore, some of the Coors effect is surely based on this effect on the balls, but some of it also is on the air itself. The air is “lighter” (i.e. lower density and pressure, less moisture), and lighter air gives the ball less “bite”. The drag coefficient on things through the air actually has a pretty big effect on what happens to those things, and even small changes can have pretty big differences - big enough to change the optimal launch angle, for one, and the best distance given the same initial conditions, for another. Also, since breaking balls all work on “bite”, one would expect to see breaking stuff be less effective (i.e. have less break) in the ‘lighter’ air. I wonder if anybody has pitch f/x data on pitchers in different weather conditions and elevations to back this up. ?

As for the corked bats, I want to never underestimate the psychological factor.

#1:  May I suggest that you read the actual peer-reviewed paper I wrote rather than a reporter’s account of it.  You can access it at http://webusers.npl.illinois.edu/~a-nathan/pob/AJP-June2011.pdf.  You might also take a look at the article I wrote for BPro specifically on the humidor:  http://www.baseballprospectus.com/article.php?articleid=13057.  The latter is not peer-reviewed but does go into some detail on the calculation of the effect of the humidor in Coors and Chase (be sure to read all the comments, since the “best and final” numbers are given there). If after reading these things you believe I have not adequately addressed the issues you raise, then feel free to contact me privately and we can discuss.

Thanks a lot for the links - now I’ve wasted two more hours of my life gaining baseball knowledge, but I can’t really comlain about that!
The article is not nearly as informative as the actual paper, and I shouldn’t be surprised. I actually had a line about that above, but it probably gets lost in the middle of the long rant.
This basically clears up most of my issues fairly satisfactorily. Most of the questions I have left come from your starting points, and so I’m planning on doing some research on your sources over the next few days. Basically the only other thing is the issue of repeatability, but this is going to be difficult. I’m surprised and impressed that you were actually able to do this. I imagine it would take years for these questions to be answered to my satisfaction, and man would it be awesome if I could make a career of that.
Anyway, thanks again for the links, and for all the great work you’ve done.

Baseballs age, so how do you assume a balls properties are unchanged over a 30 year period?.

BTW, Rawlings began manufacturing MLB’s balls exclusively in 1977 .  There was significant volatility in HR rates from 1976-1980 (0.58-0.87 per team game).  If you had balls from 1977 for example, HR rates were comparable to today (a bit lower), while 1976 balls were possibly much less lively.

Also, while you proved that corked bats do not allow balls to be hit further, the question the mainstream asks is do corked bats allow more frequent HR’s (eg Sammy Sosa). 

Increased bat speed and bat control may allow more HR’s to be hit with a corked bat, even if the average HR distance remains the same or decreases a bit.  Unfortunately, the media reads this report as “corked bats to do not influence HR rates”.

Re pft (#4):

1.  Baseball age:  From our paper:

The main difficulty in any measurement of this type is finding a supply of unused baseballs from earlier years. Serendipitously
we were able to find unopened boxes of baseballs
from the late 1970s. These baseballs were provided to us by the family of Charlie Finley, then owner of the Oakland A’s, and were official American League baseballs bearing the facsimile
signature of then American League President Lee MacPhail and manufactured by Rawlings. These facts constrain the baseballs to the period 1976–1980

BTW, the baseballs were stored in a humidor at 70 deg/50% for about two weeks prior to testing. 

2.  Regarding reporters getting it wrong, we purposely used a provocative title for our paper, expecting it would receive attention in the popular press.  And it has.  Anticipating such attention, we chose the words in our paper very carefully.  In particular, we devote a whole paragraph to discussing *benefits* of using a corked bat.  We conclude that paragraph with the following:

Although the present study shows that corked bats do not result in longer home runs, it makes no statement about whether home runs might be hit more often with a corked bat.

Reporters may get it wrong, which means they are not reading carefully (or listening carefully when they talk with me).

Re Alan Nathan’s #5, reporters are more often than not under the deadline gun, and also under word count constraints (as in “All the News That Fits"); as a former practioner, I feel safe in adding that at least some professional explainers are dumb and lazy.

On a technical note, I wonder whether craftsmanship matters when corking a bat. A sloppy job would result in core material that rattles around in the bat’s bored hole, so I’d expect poor energy transfer from wood to cork (which is, I think, a “dead” material to begin with).

Re #6:  I have found that, as in baseball, the quality of their work has a broad range, from MLB quality to barely rookie league.  In fact, the article that Tango linked to at the top of this thread is really quite good.  I talked with the reporter for about a half-hour on the phone (as did my colleague Lloyd Smith) and he pretty much got things right (i.e., MLB quality).  On the opposite extreme is an interview I did last week for a reporter for the WSU newspaper, who butchered the science completely (albeit, in charming way).  I won’t even both to supply the link here, in fairness to her!

Interesting question about the quality of the corking.  The main effect of adding the cork was to increase the weight of the barrel, which improves the collision efficiency.  Indeed, the increase in collision efficiency that we observed was consistent with it being entirely due to the added weight (i.e., no additional improvement due to a trampoline effect).  If the corking had been rattling around in the cavity, then it would not be as strongly coupled to the rest of the bat, so we might not have seen as large an improvement in the collision efficiency.  Had we thought of doing it at the time, we would have investigated that.  Good question.

Alan,

What I’m interested in is if the model includes the way the batter actually uses the different bats.

For example, I remember reading when ABS came out (anti-lock brake system), that cars with it were more dangerous.  That’s because you are not supposed to pump the brakes like with a regular car when trying to avoid swerving on ice.  The ABS is supposed to take care of that for you (by pressing and holding the brakes)… but only if you let it.  (Not sure if all that is accurate, but the illustration serves the purpose.)

So, I’m wondering how “real” the experiments you run are, in terms of allowing for all the parameters involved when used in reality.  The way the bat rolls slightly in your hand, the way you move the bat up and down, or back and forth as you shift your weight, the way you would break your wrists slightly differently with the two bats, etc.

Tango: This is the bulk of the question I have left. It’s pretty clear that you can swing a lighter bat faster (technically one with less moment of inertia, but this is what we mean), but how much faster, how differently, etc. is not so clear. I’m going to try to do some research on the sources listed in the paper on that, and I’ll post back here with the gist of what I find.

Tango and WW:  In order to calculate the trade-off between higher swing speed and lower collision efficiency (the latter being easily measured in the lab), it is necessary to know something about how a batter’s swing speed depends on the inertial properties of the bat.  There is a body of data showing that it is the moment of inertia of the bat about the knob (MOI) that matters, not the weight itself.  A recently published study of college-age batters can be found here:  http://webusers.npl.illinois.edu/~a-nathan/pob/ComparativeBatStudy.pdf, see Section 3.4.  Even more recent is a study that is as yet unpublished of batters in the 13-18 year category.  Finally there was an extensive study of slow-pitch softball players from a few years ago.  These studies all come up with a very similar result on the relationship between swing speed and MOI.  It was that relationship that I used in our paper.  Actually, I did something even more creative than that.  I established limits on how that bat speed could depend on MOI based on some very simple principles.  Then I showed that at both extremes (as well as everywhere in between), the tradeoff results in lower batted ball speed.  You can see an account of that discussion in my paper.

I was also thinking of something like the point of contact being different, which, of all things, would be the most critical thing to know (I’d guess).  So, in that respect, it would seem that you would need to empirically measure where bat meets ball, and the angle of the bat, etc, with real-world batters.

So, not just the physics of the bats, which you have explained.  But the actual use of the different bats (like the ABS).

Another analogy would be throwing the knuckleball.  On the one hand, physics will tell you that it will flutter all over the place if you have a quarter turn or half turn rotation.  But, if only 4 or 5 people are able to grip the ball to be able to actually throw it in the strike zone, then throwing a knuckle ball isn’t going to help you.

One final analogy: I’ve walked a plank at school or in a park, when it was about two feet off the ground.  In no way would I ever attempt to do it 20 feet off the ground.  Even with a net, my success rate is going to be worse, the higher that plank is placed.  It’s not just the property and behaviour of that plank, but how I use that plank.

Tango:  I see your point in #11.  I have assumed that the batter’s approach does not depend on whether or not the bat is corked.  With a given force applied to the bat, it ends up moving faster for the corked bat than for an unmodified bat, all else being the same.  The last 5 words are important in my analysis (and the point you are raising).  Whether all else is really the same is not something I have investigated.  Quite frankly, I would not know how to investigate that without actually doing the experiment with live batters.

Having said that, I would speculate that all else is probably the same.  Corking the bat does not result in a bat that is markedly different than it’s unmodified sister bat.  But, that is just speculation on my part and not backed up with any kind of study, scientific or otherwise.

Re #7: Was “The main effect of adding the cork was to increase the weight of the barrel...” a typo? Either way, I’d like to suggest using foam-in-a-can, the spray insulation found at big box stores, if you’re ever looking for a lighter bat whose interior is extremely well coupled (independent of the bat doctor’s skills).

#13:  Let me clarify.  We first did measurements on an unmodified bat.  We then machined a cavity in the barrel and did measurements on that.  We then filled with cork and did measurements on that.  My earlier statement was that the only effect of the cork--relative to the bat with the cavity-- was to increase the weight of the barrel.  Of course, relative to the unmodified bat, the corked bat had a lower weight in the barrel.

After having completed the measurements on the corked bat, we removed the cork and impacted the hollowed out bat again, just to check for consistency.  We then intended to fill the cavity with ground-up superball material (a la Gregg Nettles), but unfortunately the bat broke before we could do that. 

The foam idea is a good one, but we never thought of it.

#14:  My concern with the outcome has to do with bat balance.  We take so many swings that we feel a .5 oz change in weight.  Most would say this is a good thing.  My concern has to do with the balance of the bat which gives the bat a “perceived” weight. 

In other words, hollowing out a bat make the bat lighter at the possible cost of missing the “true sweet spot” due to unfamiliarity. 

I believe it was #10 that touched on this idea. 

So what do you think?

Morgan

#15:  I see two different (albeit related) issues here:

(a) Does the actual sweet spot of the bat change as a result of hollowing or corking?

(b) Does the batter’s perception of where the sweet spot is change?

I can speak to (a), since we actually looked into that when doing our measurements.  We did a so-called “modal analysis” of the unmodified, hollowed, and corked bats to study their vibrational properties, which determines the location of the sweet spot.  I don’t have any of those results handy right now, so let me just give you my best recollection, which is that the sweet spot moved by a small amount, certainly by no more than half an inch or so.  Given that the “sweet spot” is really a “sweet spot zone” (having some finite extent of 2-3 inches), I concluded that this amount of change was probably not perceptible to a batter.  I may be wrong in that conclusion.

I can’t speak to (b) with any authority; surely you can do that better than I can.  So I can only speculate.  I suspect that any batter using a new bat with slightly less weight in the barrel would have to swing it and hit with it enough to develop a “feel” for it.

Re #14: Unless I’m missing something, boring that axial hole in the bat and then shooting a ball at it is not unlike removing some wood from a beam in a house, and then observing any subsequent structural failure.

Also, it sounds as though you were testing Nettles’ practice (using ground-up superball material, indifferently tamped), as opposed to the material’s properties (I’d have wanted to pour superball liquid into that bored hole, to elminate the craftsmanship question I raised in #6).

#17:  Although we were not able to complete the superball part of the experiment, we strongly suspected that the only effect of the superballs (whether your way or our way) would be to increase the weight of the barrel.  In particular, we did not expect to find any trampoline effect.  Which makes me wonder why Nettles used superballs.  It is our contention that he could have added anything to the cavity that had the same weight and the result would have been the same.

Obviously there are other things we could have done and many of you have had some neat suggestions.  At the time we did this work (summer of 2003), the issue was hot because of the Sosa incident in June 2003.  But, we have moved on to other things so it is not likely we would do any of that again.