When is a fly ball a line drive?

Let’s talk about parallax.

Simply put, parallax is a phenomenon in which the apparent position of an object can change based upon the location of the observer. Let’s consider a very modest change in location—moving from the driver’s seat to the passenger’s seat of a car. (Do not attempt this while the car is in motion, please.) Observe how the gas gauge looks in each position:

image

In this instance, the passenger would tend to believe that there was less gas in the car than the driver would.

Baseball fans will be most familiar with the effects of this phenomenon when it comes to calling balls and strikes off the television feed; most broadcasts use an offset camera angle that distorts our view of the strike zone. But what else could it affect?

Most of what we know about batted balls comes from stringers who score games. Typically those stringers are given a spot in the press box. Now, because of the way different stadiums are constructed, the view from the press box shifts around. This, for instance, is the view from the Wrigley Field press box:

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Compare to Citi Field:

image

It’s a bit more of a dramatic difference than simply moving over a seat in a car, isn’t it?

So let’s test a theory—that the placement of the observer has an effect on how that observer determines the trajectory of a batted ball. Let’s focus on air balls—fly balls, line drives and pop-ups. Based upon what we know, we should expect that the higher the observer, the flatter a batted ball looks and the more likely it is to be scored a line drive.

Grading the parks

Figuring out press box heights is not a simple task. I did the best I could given the tools I had. But the heights I collected are at best estimates. This is especially true for stadiums where press boxes have multiple levels. And for some parks I gave up on trying to get a decent estimate at all. I collected data on 27 parks in use from 2005-2009. The entire list, including the estimated heights, is available here. Parks are coded with Retrosheet park codes. I excluded one park from consideration, Coors Field; its inflated line drive rate caused by the high elevation makes it unsuitable for this study.

Then I calculated line drives per total air balls (flies, liners and pop-ups) as per the batted ball data available from Retrosheet from 2005-2009. Those data are based on the observations of MLB Gameday stringers. To avoid having a league bias, I removed all at-bats from pitchers. And because a team often uses the same hitters over a period of years, I looked only at the visiting team batting. Yes, there may be some persistence of pitcher line drive rates across seasons, but it’s a minor effect compared to the persistence of hitter line-drive rates.

We do in fact see a slight correlation between press box height, about .16, after weighting for the number of years a park was in use during the sample:

image

(Each park gets its own data point, but the correlation—and the linear trend line—are based on the weighted data.)

If that’s all there was to it, we could probably table the matter as perhaps real but not especially significant. But let’s focus on the extreme parks a minute—those 40 feet or lower and 70 feet or higher:

image

The blue-coded points are parks that are either extremely low (the Oakland Colliseum and Shea Stadium) or extremely high (Fenway Park, Turner Field, PNC Park and Citizens Bank Park). They don’t seem to follow the trend line at all; they actually seem pretty centered on the median. My hunch is that in those parks, scorers aren’t relying on their view from the press box. Instead, they are looking at the TV feed. If we look at the trend with those parks excluded, the relationship becomes much stronger, with a correlation of .38:

image

Running a regression analysis, we see that a change in observer height of one foot is worth nearly .002 points of line drive percentage. That’s a significant effect, for my money.

The implications

So far we’ve looked at a theory about how batted balls are observed and provided some evidence to support the claim. What are the implications, if this theory is true?

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The professional data providers, BIS and STATS, certainly should provide better data than what the Gameday stringers provide; they take more care with the data, provide cross-checking, etc. But they are still unable to provide a consistent point of observation in every ballpark. (STATS uses a primary scorer in the press box; BIS has no in-park scorers but relies on video feeds.)

The implication of this is that we could see an effect where fielders are over- or underrated by defensive metrics based upon that scoring data, even over a period of years, because of an error introduced by a persistent bias. What I can’t tell you—at least not without a lot more study—is which players, by how much or even the magnitude of the potential effect.

This isn’t a repudiation of current defensive metrics, mind you. But people get the impression that they are based on a cold, calculating computer. But all current means we have of measuring defensive impact are based on human observation. We don’t have a perfect means of evaluating anything— hitting, defense or pitching. It doesn’t mean we don’t strive for perfection, though.

References & Resources

For those who are interested, the full regression is:

LD_RATE = 0.253415 + PB_HEIGHT * 0.00157926

The standard error of the coefficient is 0.000403918, with a p-value of 0.0002. This indicates that the results are, at least, statistically significant. All graphs and regressions were done with gretl.

This article would not have been possible without the help of Greg Rybarczyk of HitTracker. He spent a lot of time helping me figure out the park measurements necessary to calculate the press box heights, and even provided some himself. I owe him a great debt.

Special thanks also to Chris Dial, Larry Mahnken, Cory Schwartz and Ben Jedlovec for their assistance in researching this article.

Also essential to the project was Google Earth and Panoramio. Admittedly it feels a bit like swatting a fly with a hand grenade—millions in taxpayer dollars, an entire space program supporting a constellation of satellites, and I’m using it to figure out scorer bias in line drives.

Some other helpful resources:

Photo of Wrigley Field pressbox courtesy of pedalfreak and released under a Creative Commons license. Photo of Citi Field press box courtesy of kenyee and released under a Creative Commons license.

The information used here was obtained free of charge from and is copyrighted by Retrosheet. Interested parties may contact Retrosheet at “www.retrosheet.org.”

For those curious—the pictures of the gas gauge come from my car, an ’07 VW Rabbit.


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Sean Smith
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Sean Smith

Good job Colin.  This is top notch investigative journalism.  I knew there were differences specific to park but I never thought of press box location as being a factor.

Nick Steiner
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Nick Steiner

I agree with Sean.  Great job Colin, I would never have thought of this.

Pip
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Pip

The professional data providers, BIS and STATS, certainly should provide better data than what the Gameday stringers provide; they take more care with the data, provide cross-checking, etc.

I’m not sure on what basis this claim is made. As someone who actually does datacasting for MLBAM, I can assure you that MLB takes as much (if not more) care with the data, cross-checking, etc.

On a separate note, is it possible to see the identity of all of the parks on the graphs?

dzop
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dzop

So if you make a scatter plot, then remove the points that don’t fit the correlation you want to find, you find a correlation with an R^2 so low that you don’t report it!

Brilliant! Where can I order the book!?

Jeff Lewis
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Jeff Lewis

I’m not understanding, dzop.  By my reading, the R^2 with all the data was 0.18, and 0.38 with the extremes removed.  The reasoning for removing the outliers seems plausible.  It’s probably worthwhile to ask some observers at those parks whether they really do rely on TV feeds.

Colin Wyers
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Colin Wyers
dzop, I report the R in the article. The equation to compute R-squared from R is: R^2 Since I don’t want to strain you any more than I already have, I’ll report that: .38^2 = .14 If instead you want the adjusted R-squared, it’s 0.135696. And I expressely said why I excluded the data points that I did. And I showed it both ways, so that you could make your own determination whether or not I was right to do so. I don’t mind criticism of my work, and I do everything I can to enable criticism of my work… Read more »
Colin Wyers
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Colin Wyers

Pip – STATS will assign multiple scorers per game. BIS randomizes the assignment of scorers per game, which should eliminate individual scorer biases. Neither has to publish data in real time. Probably the best study of the differences is Peter Jensen’s.

And Gretl doesn’t let me label the data plots as you suggest. R or Excel probably would – I’ll see what I can do about that.

Peter
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Peter
I think we’re missing something really important here – When do stringers move between parks? If stringer A only scores at Wrigley field, then his perspective/parallax never changes. So he should always be judging under the same conditions. If the ballpark moves the press box in the middle of a season, or if a stringer scores consecutive seasons in different stadiums with different perspectives (like shea/citi, oys/nys), then you might have a year-to-year issue. but I hardly doubt there’s a contingent of mobile stringers hopping from stadium to stadium and having different judgements. Now announcers who do jump from stadium… Read more »
BenJ
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BenJ
Colin, I’m still not convinced by the 20 point sample size.  There are three influential points that basically determine the entire equation (not sure which parks they are, but the one in the bottom left and the two on the far right of your final plot).  I also think it’s a bit arbitrary how you removed press boxes at 70 feet but not at 68.  The 90+ ft press boxes and those below 40 are clear outliers, but why discard the 70s and not the 68s?  Even if you leave them in (the first plot), the two or three x-axis… Read more »
Joe
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Joe
Colin, I am also a datacaster for MLBAM.  I work in Pittsburgh and have done at least half of the games during the period you referenced although I have had two different partners during that same period.  I was intrigued to see we sit in the highest press box in MLB.  I knew it was high but wow!  If it helps, we have an assigned seat for PC connection purposes in the top row of the press box so if your measurement is to the start of the press box we are probably another 15 feet higher. I second Cory’s… Read more »
Cory Schwartz
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Cory Schwartz
Colin, interesting work, but this statement is entirely untrue on two points: “The professional data providers, BIS and STATS, certainly should provide better data than what the Gameday stringers provide; they take more care with the data, provide cross-checking, etc.” First, MLBAM is very much a “professional data provider”, in that our data is used not only in premium products on our own site, but is also distributed in real time to several major media partners. That the Gameday .xml is freely available via the Internet doesn’t make us any less professional than either STATS or BIS. Second, our trajectory… Read more »
Erich
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Erich

I agree with BenJ. Also, since you’ve already identified denver as being an outlier due to altitude, perhaps other park related factors need to be factored as well. What are the other outlier parks?

Colin Wyers
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Colin Wyers
Ben: Of course this isn’t meant to be the end of the discussion but the start of it. You surely have better access to the data than I do (presumably BIS keeps tracks of what games were scored by which video scout) and could do a more in-depth analysis than I’ve presented here. Cory: I’m sorry if my remark offended you. My impression of the Gameday data was based upon this article, which says in part: “MLB’s Gameday also tracks hit balls for use in its Gameday graphics and hit ball charts. It, too, uses a contract employee in the… Read more »
Nick Steiner
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Nick Steiner
Colin – This really is an original and awesome piece, and I appreciate all the work that it took to figure out press box height; however, like BenJ, I’m just not that by convinced by the results.  An R^2 of .14 is really, really, low and can be affected by a few extreme data points.  Also, <blockquote>Then I calculated line drives per total air balls (flies, liners and pop-ups) as per the batted ball data available from Retrosheet from 2005-2009. Those data are based on the observations of MLB Gameday stringers.<blockqoute> I assume you mean GameDay right?  Or does Retrosheet… Read more »
Colin Wyers
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Colin Wyers
Nick – There are obviously a lot of factors affecting how many line drives are scored by stringers, not least of which being the actual number of line drives hit. There is still plenty of research left to be done here; consider it the start of the conversation, not the end of it. I’m very glad to have the participation of people like Ben and Cory in this discussion and hope that they can put their resources (more substantial than mine, presumably) toward looking into this issue. One thing I want to emphasize here, though, is that we can empirically… Read more »
Nick Steiner
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Nick Steiner

Oh, I agree.  I think that there is definitely validity to your theory; however, given the limited (max of 30 samples) data that we are dealing with here, and one that is expected to have a bunch of other factors obfuscating the picture, I’m not sure if a regression approach is the right way to go given the data we have now. 

Do you know of another way we could test the theory?

Nick Steiner
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Nick Steiner

Or, if you think a regression is the right way to go (which it probably is), you should do as much as you can to normalize line drives by other possible factors that you can think of before you run the regression.

Peter Jensen
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Peter Jensen
Brian – The comparison that I did of the hit ball locations from STATS, BIS, and Gameday were done a year before I normalized the Gameday data for my BZM fielding metric.  The normalized Gameday data should be even closer to the pay services.  Most of the problems with hit locations in the Gameday data have to do with input field diagrams that are not drawn to scale and are way too small for accurate positioning of the hit ball, not the lack of diligence of the stringer or an insufficient review process.  As I mentioned at The Book blog,… Read more »
Brian Cartwright
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Brian Cartwright
Re Colin’s statement about the quality of the Gameday data in comparison to BIS and Stats, and Cory’s reaction. I believe that it was a common perception that teams, writer and analysts were willing to pay for the BIS and Stats data because it was more precise than the freely available Gameday data. Why pay for something that I can get for free elsewhere? However, in Peter Jensen’s work in comparing the batted ball positions of the different systems, he concluded that none are as accurate in xy position and thus also horizontal angle as we might like for detailed… Read more »
Nick Steiner
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Nick Steiner

Brian – I believe that Mike Fast has said that the data is corrected for errors the day after the game.  When I downloaded that data, I waited several days until the games had been played before I downloaded it.

Will
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Will

While this may not be “a repudiation of current defensive metrics”, it is a very significant criticism. Contrary to many who advocate their definitive use, defensive metrics are still along way from reliability, especially when evaluating fielders who aren’t on either extreme.

Beege
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Beege

Interesting stuff.  Someone should explain parallax to Chip Caray so he doesn’t call every fly ball as if it’s going to be a 450 foot home run.

Bill P
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Bill P
Colin, Although I agree with some of the caveats pointed out by others, this was a fascinating first look at a topic that I had never considered before.  I have one additional suggestion, which might be too much work to implement.  You say this: “And because a team often uses the same hitters over a period of years, I looked only at the visiting team batting. Yes, there may be some persistence of pitcher line drive rates across seasons, but it’s a minor effect compared to the persistence of hitter line-drive rates.” Would it be feasible to instead look at… Read more »
Colin Wyers
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Colin Wyers

A lot of very good comments here that deserve a response. Unfortunately I’m rushing to get ready to leave town for a few days (going to the Winter Meetings in Indy.) I’ll to my best to get back to some of these concerns and suggestions later on in the week.

Jeremiah
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Jeremiah

This is an interesting problem, but it seems to me that the answer to identifying line drives and fly balls will soon be available, if not already.  The pitch f/x data is widely used, but can’t the hit f/x data be used for exactly this purpose?  If you know the speed and angle of the ball off the bat, it should be easy to categorize a ball in play.  On a related note, it seems as if this data would be useful to the various fielding metrics as well.

BenJ
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BenJ

Jeremiah,

Ideally, yes.  Realistically, no.  A couple studies from this summer illustrate that the spin of the batted ball has a great impact on where it ends up, and spin is something Hit F/x won’t pick up.  I forget the exact numbers, but a ball with backspin can go dozens of feet further than a ball with top spin even when they have the same initial trajectory.  We still need to know the landing point, or at least an approximation of it.

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