Roxana Dior writes:
From this news article, I found out about this paper, “Global warming, home runs, and the future of America’s pastime,” by Christopher Callahan, Nathaniel Dominy, Jeremy DeSilva, and Justin Mankin, which suggests home runs in baseball have become more numerous in recent years due to climate change, and will be scored more frequently in the future as temperatures rise.
Apart from the obvious question—when will Moneyball obsessed general managers look at optimizing stadium air density when their team is at bat?—is this a statistically sound approach? I am no baseball aficionado, but air density changes due to temperature seems like it would have a miniscule affect on home runs scored, as I assume that the limiting factor in scoring one is the “cleanness of contact” with the bat, and that most batters hit the ball with sufficient power to clear the boundary when they do. There are probably a hundred other confounding variables to consider, such as PED usage etc. but the authors seem confident in their approach.
They end with:
More broadly, our findings are emblematic of the widespread influence anthropogenic global warming has already had on all aspects of life. Warming will continue to burden the poorest and most vulnerable among us, altering the risks of wildfires, heat waves, droughts, and tropical cyclones (IPCC, 2022). Our results point to the reality that even the elite billion-dollar sports industry is vulnerable to unexpected impacts.
I think I agree with the sentiment, but this feels like a bit of a reach, no?
From the abstract to the paper, which recently appeared in the Bulletin of the American Meteorological Society:
Home runs in baseball—fair balls hit out of the field of play—have risen since 1980, driving strategic shifts in gameplay. Myriad factors likely account for these trends, with some speculating that global warming has contributed via a reduction in ballpark air density. Here we use observations from 100,000 Major League Baseball games and 220,000 individual batted balls to show that higher temperatures substantially increase home runs. We isolate human-caused warming with climate models, finding that >500 home runs since 2010 are attributable to historical warming. . . .
My first thought on all this is . . . I’m not sure! As Dior writes, a change of 1 degree won’t do much—it should lower the air density by a factor 1/300, which isn’t much. The article claims that a 1 degree C rise in temperature is associated with a 2% rise in the number of home runs. On the other hand, it doesn’t take much to turn a long fly ball into a homer, so maybe a 1/300 decrease in air density is enough to do it.
OK, let’s think about this one. The ball travels a lot farther in Denver, where the air is thinner. A quick Google tells us that the air pressure in Denver is 15% lower than at sea level.
So, if it’s just air pressure, the effect of 1 degree heating would be about 1/50 of the effect of going from sea level to Denver. And what would that be? A quick Google turns up this page by physicist Alan Nathan from 2007, which informs us that:
There is a net force on the ball that is exactly opposite to its direction of motion. This force is call the drag force, although it is also commonly referred to as “air resistance”. The drag plays an extremely important role in the flight of a fly ball. For example, a fly ball that carries 400 ft would carry about 700 ft if there were no drag. The drag plays a less significant — but still important — role in the flight of a pitched baseball. Roughly speaking, a baseball loses about 10% of its speed during the flight between pitcher and catcher, so that a baseball that leaves the pitcher’s hand at 95 mph will cross the plate at about 86 mph. If the baseball is also spinning, it experiences the Magnus force, which is responsible for the curve or “break” of the baseball. . . .
Both the drag and Magnus forces . . . are proportional to the density of the air. . . . the air density in Denver (5280 ft) is about 82% of that at sea level. . . . the drag and Magnus forces in Coors will be about 82% of their values at Fenway.
What about the effect of altitude? Here’s Nathan again:
The reduced drag and Magnus forces at Coors will have opposite effects fly balls on a typical home run trajectory. The principal effect is the reduced drag, which results in longer fly balls. A secondary effect is the reduced Magnus force. Remember that the upward Magnus force on a ball hit with backspin keeps it in the air longer so that it travels farther. Reducing the Magnus force therefore reduces the distance. However, when all is said and done, the reduced drag wins out over the reduced Magnus force, so that fly balls typically travel about 5% farther at Coors than at Fenway, all other things equal. . . . Therefore a 380 ft drive at Fenway will travel nearly 400 ft at Coors. . . .
Also, Nathan says that when the ball is hotter and the air is dryer, the ball is bouncier and comes faster off the bat.
The next question is how will this affect the home run total. Ignoring the bouncy-ball thing, we’d want to know how many fly balls are close enough to being a home run that an extra 20 feet would take them over the fence.
I’m guessing the answer to this question is . . . a lot! As a baseball fan, I’ve seen lots of deep fly balls.
And, indeed, at this linked post, Nathan reports the result an analysis of fly balls and concludes:
For each 1 ft reduction in the fly-ball distance, the home-run probability is reduced by 2.3 percent.
So making the air thinner so that the ball goes 20 feet farther should increase the home run rate by about 46%. Or, to go back to the global-warming thing, 1/50th of this effect should increase the home run rate by about 1%. This is not quite the 2% that was claimed in the recent paper that got all this publicity, but (a) 2% isn’t far from 1%, indeed given that 1% is the result from a simple physics-based analysis, 2% is not an unreasonable or ridiculous empirical claim; (b) the 1% just came from the reduced air pressure, not accounting for a faster speed off the bat; (c) the 1% was a quick calculation, not directly set up to answer the question at hand.
And . . . going to Nathan’s site, I see he has an updated article on the effect of temperature on home run production, responding to the new paper by Callahan et al. He writes that in 2017 he estimated that a 1 degree C increase in temperature “results in 1.8% more home runs.” Nathan’s 2017 paper did this sort of thing:
I don’t like the double y-axis, but my real point here is just that he was using actual trajectory data to get a sense of how many balls were in the window of being possibly affected by a small rise in distance traveled.
Callahan et al. don’t actually refer to Nathan’s 2017 paper or the corresponding 1.8% estimate, which is too bad because that would’ve made their paper much stronger! Callahan et al. run some regressions, which is fine, but I find the analysis based on physics and ball trajectories much more convincing. And I find the combination of analyses even more convincing. Unfortunately, Callahan et al. didn’t do as much Googling as they should’ve, so they didn’t have access to that earlier analysis! In his new article, Nathan does further analysis and continues to estimate that a 1 degree C increase in temperature results in 1.8% more home runs.
So, perhaps surprisingly, our correspondent’s intuition was wrong: a small change in air density really can have noticeable effect here. In another way, though, she’s kinda right, in that affects of warming are only a small part of what is happening in baseball.
Relevance to global warming
The home runs example is kinda goofy, but, believe it or not, I do think this example is relevant to more general concerns about global warming. Not because I care about the sanctity of baseball—if you got too many home runs, just un-juice the ball, or reduce the length of the game to 8 innings, or make them swing 50-ounce bats, or whatever—but because it illustrates how a small average change can make a big change on the margin. In this case, it’s all those balls that are close to the fence but don’t quite make it over. The ball going 5% farther corresponds to a lot more than a 5% increase of home runs.
Elasticities are typically between 0 and 1, so it’s interesting to see this example where the elasticity is much greater than 1. In the baseball example, I guess that one reason there are so many fly balls that are within 20 feet of being home runs, is that batters are trying so hard to hit it over the fence, and often they come close when they don’t succeed. The analogy to environmental problems is that much of agriculture and planning is on the edge in some way—using all the resources currently available, building right up to the coast, etc.—so that even small changes in the climate can have big effects.
I’m not saying the baseball analysis proves any of this, just that it’s a good example of the general point, an example we can all understand by thinking about those batted balls (a point that is somewhat lost in the statistical analysis in the above-linked paper).
Jim Albert just blogged about the same paper in a post titled Game time temperature and home runs (if you like baseball and the kind of analysis you see on this blog, you’ll like Albert’s blog). He goes through exactly the same kind of marginal analysis Andrew is concerned about and hits one the perennial topics on the blog—overdispersion. And he fits the model with Stan (brms, specifically). I won’t spoil his result…
Bob:
After my first look at the Callahan et al. paper, I was skeptical: it seemed a bit sus to try to use a statistical analysis to estimate such a small effect. Then I saw the thing about air density, which made me think about the Colorado Rockies, so I googled that—yup, I’m too lazy to work it out from the laws of gravity!—and then the effect seemed so much smaller than that, and then I googled some more, and it turned out that Alan Nathan had already done all the work. So convenient not to have to do it all from scratch. It’s just funny to me that Callahan et al. didn’t do that googling themselves, as it would’ve strengthened their paper.
And see this comment for my quick thoughts on how it is that the statistical analysis worked so well in this example, considering how poorly such models work in various policy analysis settings.
Ok, so what you did above is a fun analysis and makes for a great blog post. The fact that the underlying article is in the Bulletin of the American Meteorological Society is bonkers (esp. because instead of a physics based approach they econometrically try to identify the effect – do we think that AMS is going to have good peer review process for causal identification?)
On the identification side, the warming trend seems to correspond to both the steroids era and the increase launch angle era from moneyball type insights. It would’ve been interesting to see their results if you take out the top-X home run hitters of each year from the sample. If I take their problem seriously, the more interesting effect is not on the Barry Bonds and Aaron Judge’s (I can see the headline now – Aaron Judge’s HR record due to climate change, Roger Maris still the king! [insert eyeroll]) but on the average batter who just gets an extra HR a year or two and maybe gets more $ bc of it.
Ignoring the statistical questions, which I may be wrong about, why is this study dressed up in a suit and tie and being sent around to all these media outlets? I can’t even work through the identification stuff without thinking why am I wasting time on this? Climate change will affect most things. It’s more important to adapt to heat stress in open air stadiums than homeruns, which people love. I don’t get this stuff at all. Fun blog post, yes please. This blog post, loved reading it. I’m all for a fun research paper every once in a while, but this one did not do it for me. Curious what others think.
> . In another way, though, she’s kinda right, in that affects of warning are only a small part of what is happening in baseball.
I wonder if there wouldn’t be an associated interaction effect with among air currents (as a mediator or moderator) and warming/density changes and distance traveled (whether increasing it or decreasing it with warning).
Andrew wrote:
“affects of warNing are only a small part of what is happening in baseball.” And then, Joshua repeated the phrase. I suppose, because I do not follow the minutia of baseball, each really means “warMing” and not “warNing.”
Typo fixed; thanks.
It’s plausible that home runs are decided on a razor thin margin; in competitive activities, this is often by design to make things exciting. So it is plausible that small changes in air density can have a noticeable effect on home runs, but global warming affects more than just air density. It also makes small or large changes humidity, when crops start harvesting, the length of the ideal practice season in the northern hemisphere, the wood that goes into new bats and the leather that goes into new balls, so I would put pretty even odds on the sign of the effect of global warming on home runs. It may not even be monotonic with temperature changes, it might be positive for the next degree and negative for the one after.
Not that I expect this data, or any data we can realistically collect, to be able to resolve this either.
I saw this paper when it came out – and the premise seemed reasonable to me, although there have been many things that have changed that also influence the number of home runs. But I haven’t read the paper, so I don’t know if they included these 2 factors:
1. A natural experiment might be to compare indoor stadiums with outdoor stadiums. There have been more an more of the former and they have been built at different times, so it may be possible to screen out some of the other influences on home runs (such as the ball density, pitching prowess, etc.).
2. Stadiums differ considerably in park dimensions. Presumably this should permit some modeling of the variability of warming impacts on home runs. It might be reasonable to specify a distribution of fly ball lengths which could then be matched to stadium dimensions for an expected impact on home runs that would vary across those stadiums.
Perhaps they considered such things, but I haven’t read the paper so I have no idea.
Poor Barry Bonds, he had to play six seasons in Candlestick Park, an icy venue. For instance, he hit only 33 homers in 1995. His fantastic production in 2000, 2001, and 2002 which some have attributed to anabolic drugs can now be properly understood as moving to what is now called Oracle Field. Thank you for posting this article that exonerates Barry.
BTW, Oracle Field is a great venue for watching a game.
Oncodoc:
As discussed in the above post, the effect of a small changes in temperature is not zero but it’s much less than variations among ballparks, not to mention variation among players.
UHI?? :)
The UHI effect in many cities is **dramatically** larger than the global warming effect. One group claims that Seattle is on *average* 5°f warmer than the surrounding rural areas during the summer (e.g., UHI is *on average* about 2.5x AGW), and can be as high as 17°f locally. Another recent study also measured a peak difference of 17°f between urban and rural locations in the Houston area.
It’s hard to find a compilation of actual measurements, but Climate Central’s heat index – which is not a direct measurement, but a model – of UHI effects ranks Aaron Judge’s NYC 3rd in the US, with an average model UHI effect of 7.6°f – nearly FOUR TIMES the effect of global warming. Major League cities of Houston, San Fran, Boston, Chicago, and Baltimore round out the top nine, all of which have a heat index value of over 7.0°f or about 3.5x AGW effects.
I couldn’t find an ungated copy of the paper to find out of they controlled for UHI, but something tells me they didn’t….
So I guess when you take UHI into account, we’re missing **alot** of home runs!
Chipmunk:
The physics analysis looked at changes in temperature, and the statistical analysis compared daily temperatures, so there’d be no need to control for urban/rural differences.
Does UHI create a trend, or is it a constant offset?
Another question: How has the increase in temperature affected pitching?
Victor:
Follow the above links; in his posts, Nathan discusses effects on pitching.
Anyone who commits the atrocity of 2 y-axis plots is already fighting an uphill battle to earn credibility.
An interesting read. Air temp impacts football, soccer, etc because the ball itself is inflated of course. It would stand to reason that thinner air would impact baseball, but I’m more curious how it impacts pitching than hitting!
According to their theory, the atmosphere on Venus should be extremely thin since it is so hot. Instead we observe that denser atmospheres are hot and thin atmospheres are cold.
Atmospheres have a tropopause wherever the pressure is ~ 100 mBar[1], and then the temperature and density typically monotonically increase (if we ignore inversion layers, which could also become more/less frequent) according to the lapse rate as the air gets closer to the surface.
For warming, the altitude of the tropopause rises and air gets *denser* and hotter at the surface.
[1] https://www.nature.com/articles/ngeo2020
Anon:
Nobody here’s talking about Venus. They’re talking about small changes in Earth surface temperature. If you want to argue about one, go at it with Alan Nathan.
I don’t think you understand, here is their calculation:
https://github.com/ccallahan45/Callahan-et-al_ClimateBaseball_2023/blob/main/Scripts/Temp_HR_Regression.R
There are a number of issues. First, they use sea-level pressure. That is not the actual pressure at the ballpark. For a place like Denver the calculated density will be much higher than the actual. It may or may not affect their regression coefficients, idk. But that is not what I am concerned with.
You can see that density is directly related to pressure and inversely to temperature. Fine. But this is not what we see in real life atmospheres. They are assuming (if you average over local, short-term fluctuations to get an approximate equilibrium) that the temperature and pressure of an atmosphere are independent.
In a real atmosphere the volume, pressure, temperature, and albedo all feed back on each other. You couldn’t increase the temperature of the earth without also affecting the other properties of the atmosphere. In particular, it appears the pressure at the surface must also increase.
Peter wrote:
Less insolation of course. You can approximate the surface temperature of Titan (and Venus, which are the only other two rocky objects with atmospheres that exceed the 100 mBar threshold) thus:
It gives ~95 K.
Eg:
https://www.ncei.noaa.gov/access/monitoring/monthly-report/global/202201
Increasing the temperature should be expected to also increase the pressure. They assume reduced air density as a result of warming. It is key to the entire argument, and it looks wrong.
Anoneuoid:
The time-averaged pressure at the surface of the earth in Pa is more or less the mass of the column of air molecules above a region 1m^2 times the acceleration of gravity g. Technically this changes as you go up in the atmosphere but the atmosphere is actually quite thin and there’s some effective g that’s probably like 9.77 m/s^2 that gives the right value and is just slightly lower than g at the surface of the earth which might be more like 9.79 or 9.80 m/s^2.
Increasing and decreasing the temperature slightly, even globally, is going to affect this approximately by changing more water molecules to gas and then increasing the mass of the atmosphere overall, so yeah you’d expect slight increase in average pressure with slight increase in temperature maybe.
But time-averaged pressure (averaged over say 1 year) might not be so relevant. If it gets hotter in a certain region, say where there’s some dark soils experiencing solar heating, then the gas expands resulting in lower density, and rises due to buoyancy, this causes air to move in towards the center of the region, and the coriolis effect eventually balances that approximately, causing the air to circulate around that heated region. The column of air above the hot region weighs less because of lower density… at some radius with the circulating air, that stuff weighs more. So if the hot region is at the ballpark, it’ll have slightly lower pressure. If the hot region is hundreds of miles away, maybe the ballpark will be windy and have higher pressure.
Increasing the temperature should be expected to also increase the pressure. They assume reduced air density as a result of warming. It is key to the entire argument, and it looks wrong.
No, I think they’re correct. On a terrestrial planet, like the Earth or Venus, the pressure at the base of the atmosphere is essentially determined by the weight of the atmosphere, which is constant. If the temperature changes, then the pressure at the base of the atmosphere doesn’t change, but the scale height of the atmosphere changes. This determines how the gas density varies with altitude. If the temperature goes up, the scale height increases, the atmosphere essentially becomes thicker, and – given that the total mass is the same – the density goes down.
Increasing the temperature should be expected to also increase the pressure. They assume reduced air density as a result of warming. It is key to the entire argument, and it looks wrong.
This is pretty basic physics. If you keep the surface gravity of the Earth and the mass of the atmosphere the same — which is of course the case — then increasing the temperature increases the pressure, leading to expansion of the atmosphere, which reduces the density, until the pressure returns to its equilibrium value.
Daniel Lakeland:
aTTP:
Peter Erwin:
I agree with Daniel that increased temperature will increase the mass of the atmosphere as more volatile molecules evaporate from the surface (eg, water). It is most definitely not constant, although is probably of the order 0.1-1% for a rise of 1 degree K. When it comes to baseball, that is swamped by measurement error along with local and short term fluctuations.
Now, the atmosphere (in particular the troposphere) will also expand so more molecules will escape into space. I don’t know how this works out dynamically. But (without inputting more energy) I don’t see how the average temperature can rise over the long-term without also increasing the pressure at the surface.
Anoneuid:
I agree with Daniel that increased temperature will increase the mass of the atmosphere as more volatile molecules evaporate from the surface (eg, water).
OK, let’s see what effect that would have. An increase in temperature of 1 degree (C or K) increases the integrated water vapor (IWV) by about 7% according to the Clausius-Capeyron relationship, though some studies suggest it may in practice be closer to 4% for the Earth system. IWV has units of kg/m^2, which is the total mass of water vapor in a column of the atmosphere with an area of 1 m^2, integrated out to the edge of the atmosphere. The current global mean value of the IWV is about 25 kg/m^2 (e.g., this figure). Given a surface area of about 5 x 10^14 m^2 for the Earth, this translates to about 1.3 x 10^16 kg of H2O vapor. Thus, a 4-7% increase means about 5-9 x 10^14 kg of H2O added to the atmosphere. Since the atmosphere has a mass of about 5 x 10^18 kg, the increase is about a factor of 0.00010-0.00018 in the total mass of the atmosphere (in other words, 0.01 to 0.018%, not “0.1-1%”).
Increasing the temperature by 1 degree will multiply the pressure by (288 + 1)/288 (assuming a mean surface temperature of 15 C = 288 K) = 1.0035. So you’re increasing the upwards force on the atmosphere by a factor of 0.0035, while increasing the mass of the atmosphere by a factor of 0.0001 to 0.00018. In other words, the increase in pressure is about 20 to 35 times the increase in atmospheric mass.
So the atmosphere will definitely expand and get less dense.
I don’t see how the average temperature can rise over the long-term without also increasing the pressure at the surface.
If the atmospheric mass changes minimally (as we’ve seen is the case), then increasing the pressure pushes (rather literally) the system out of equilibrium. The atmosphere will expand until the product of the increased temperature and the lowered density returns the pressure to its previous (equilibrium) value.
Increase in capacity to hold water vapor != increase in mass.
But we have moved on from calling me stupid to now acknowledging the mass will increase. Next account for lower solubility of oxygen/nitrogen and if the topic comes up again we can start from there.
But we don’t need to figure out the exact source of the mass, to know it must increase. An atmosphere cannot just keep expanding in response to temperature. The volume, temperature, and pressure must all increase together or else it would be too unstable. Just imagine increasing the temperature to that of Venus.
Anoneuoid,
As Peter has already pointed out, the change in mass is almost certainly negligible. In equilibrium, the pressure at the surface is simply due to the weight of the atmosphere. You can work this out yourself. Mass of the atmosphere (5 x 10^18 kg) times g (10 m/s/s) divided by the surface area of the Earth. If the temperature were to instantaneously increase, then the pressure would increase, but this would mean that the atmosphere would be out of equilibrium and it would then return to equilibrium by expanding. Hence, the density would go down, since the mass is essentially constant.
This assumed the two main components of the atmosphere will not increase (N2/O2), that the amount of *liquid* H20 in the atmosphere will not increase, and that the distribution of relative humidity will remain constant.
Also, all these values we are talking about are negligible compared to local variations. I can step in and out of the shade and experience a 10 K difference in temperature within a second.
According to their theory, the atmosphere on Venus should be extremely thin since it is so hot. Instead we observe that denser atmospheres are hot and thin atmospheres are cold.
And the density of Titan’s atmosphere at the surface is about 4 or 5 times that of the Earth, even though its temperature is -180 C. What? How is that possible???
(In other words: that’s a really stupid argument.)
“…And Then There’s Physics” has it right.
It’s kind of funny to see adults arguing about what happens to the density of air when you heat it. Ask a 4th- through 6th-grader! https://www.grc.nasa.gov/www/k-12/Summer_Training/FranktonES/Convection_main_page.html
Anon:
Yes, please stop. Raising questions is fine—if nothing else, it motivated some instructive replies—but this sort of stubbornness is just ridiculous. Physics is a well-studied subject and is well understood. Not by me—there’s a reason I stopped studying physics!—but by lots of others in the comments here. Your series of comments is demonstrating that people can have strong and incorrect intuitions and be unreasonably confident in their errors, but we already knew that!
Ok, but the funny thing is I’m not even saying anything controversial. Here is even the BBC talking about a huge amount of oxygen leaving the oceans (and obviously entering the atmosphere):
https://www.bbc.com/news/science-environment-50690995
That is happening for all dissolved gases, and not only in the oceans. I wonder why the constant atmospheric mass assumption is so important that it triggers the ridicule response, since it defies basic physics and observation.
But yea, the discussion is done now.
Nobody is claiming that the mass of the atmosphere is exactly constant. It’s simply that the changes are small enough so as to be negligible, in this context at least. Have you actually worked out how much this huge amount of oxygen leaving the oceans will change the mass of the atmosphere? I have. It’s not by very much. It’s not enough to change the basic point that warming of the atmosphere will lead to expansion and a reduction in density.
The 2% estimate, ceteris paribus, is (to pardon the pun) in the ballpark. But there are a lot more factors, as everybody recognizes. Home runs in Coors Field, for example have been greatly reduced through both changes in the dimensions of the park and humidors to change the ball’s characteristics. Changes in sticky substances that pitchers could use have effects. More parks being built indoors have effects. Changes in batting styles that emphasize “three true outcomes” have effects.
Last year, there were 5215 home runs in 2,430 games, or about 2.2 per game, 1 little over one per team. An extra 2% is a couple of extra home runs per team per season. I’m not saying the ceteris paribus effect of temperature and humidity and air pressure can’t be estimated, but teams today play some guy who is expected to hit 5 fewer home runs per season than some other guy because his defense is better — that’s bigger than this effect.
Jonathan:
Given all these confounders, it’s actually kind of impressive that the statistical analysis did so well, in the sense of giving a reasonable answer. I think the reason why it worked is that the treatment effect really is close to a constant here—higher temperature on any particular day makes the ball travel farther, increasing the chance of a home run.
I agree with you that in baseball terms, the increase in average temperature has a very minor effect, compared to all the other changes in the game.
This is probably a correct analysis but it would be interesting to do some CFD calculations to check that there aren’t other factors such as level of separation which could change drag quite a bit. Likewise, surface roughness of the ball could make a bigger difference than a small change in air temperature. There are lots of effects such as transition to turbulence that are quite sensitive but could make a significant different. As Andrew says, there are many other factors that have a bigger effect than temperature.
But, I don’t think this tells us much about global warming’s effects generally. Home runs are defined by an artificial boundary. Generally in nature there can be tipping points but that’s the exception. A glacier will usually melt slowly over time and not catastrophically disappear. The boundaries of tornado “severity” are artificial ways of categorizing very complex phenomena.
In terms of impacts on humans, generally engineering structures are designed with wide safety margins. An airplane wing is designed to withstand a load 50% greater than the maximum load within the “flight envelop.” Even if for example atmospheric turbulence increases a little (which I doubt will happen), there will be no impact on the safety of air travel. The exception that comes to mind is building in flood plains and on the coast. There has been a huge increase in this risky development over the last century. We are pretty confident sea level will continue to increase even though in many Northern hemisphere locations the land is rising in rebound from the last Ice Age so that relative sea level is actually falling.
Generally, if you want to talk weather and severe weather, there is a good reason to expect a warmer world to have less severe weather. The Navier-Stokes equations have forcing terms involving the gradient of temperature. The temperature itself does not appear except indirectly in the state equation constraint. Because of polar amplification, the equator to pole temperature gradient will decrease significantly and its this gradient that drives mid-lattitude weather. Similarly its the vertical temperature gradient in the tropics that drives hurricanes. It seems based on weather balloon and satellite measurements, this gradient has not increased much contrary to the “moist adiabat theory”. Perhaps that’s because tropical convection is nowhere close to adiabatic. Like a lot of things in climate science, there is not a lot of valid theory here to go on and CFD simulations are mostly worthless.
Thanks for this writeup! (I’m the first author of the paper.) Long time, first time, etc.
It looks the physics of air density are already being hashed out in other comments, so I won’t retread that ground here. This paper is ultimately a fun analysis but not the most important thing about climate change, of course. And I’d like to think we emphasize in the paper that while climate change has a discernible effect on home runs, it has been outweighed (to date) by other factors like changes in the construction of the baseball.
It is worth saying that we were quite familiar with Alan Nathan’s work before writing the paper. His physical analysis — and that of folks like Robert Adair (“The Physics of Baseball”) — was really foundational to our perspective. But given that he had already done that work, we believed a statistical perspective would add another line of evidence. It’s encouraging that his physics-based calculations and our empirical estimates yield extremely similar estimates (~1% more home runs per degree Fahrenheit).
Thanks for posting this Andrew, I appreciate your response and those of the commenters as always. I actually have a background in physics, though not experimental — and the kinds of experiments I am more familiar with aren’t of this “natural” type and are in a certain sense much simpler, and it’s possible to give a fuller account of backgrounds and systematic errors (though these aren’t always undisputed).
It didn’t occur to me to look for a reference on the relevant aerodynamics here, as my intuition suggested that the effect due to (entirely plausible) changes in the viscosity and density of air would be swamped by human effects such as changes in playing style — would pitchers be able to throw sufficiently fast and accurately on hot sunny days compared to cooler nights, different pitching and hitting techniques come into and fall out of fashion — but I have no real sense for the game.
From your statement about “being on the edge”, and comments like somebody’s about “razor-thin margins” in sport, I guess that the “pitch-swing-hit” process in baseball is sufficiently well-honed as to have minimized “aleatory uncertainty” — i.e. more like your example of flipping a pickle jar than tossing an ideal coin — such that the signal of climate change can be cleanly identified. Though this “econometric” style analysis (as Anonymous puts it above) always troubles my inner physicist.
I should add that they partially address some of my concerns about the human-level effects in this para:
> Higher temperatures may affect home runs through multiple complex pathways beyond
air density, such as heat stress on pitchers (Howe & Boden, 2007). To clarify the mechanism, we perform two additional analyses. First, we directly allow air density to enter the regression
alongside temperature (Table S5). Independently, both air density and temperature have
significant effects with comparable magnitudes. When both are included in the model, however,
the effect of temperature becomes small and not significant, while the effect of air density remains (Table S5). These results imply that temperature’s effect on home run occurs primarily
by modifying air density.
Roxana:
Yes, I had the same initial take that you had. I was skeptical because it seemed that any small effect of a 1 degree change in average temperature would be swamped by the much larger effects of changes in playing styles, game conditions, and indeed the large changes in temperature from day to day. But then the physics-style analysis seemed convincing to me, and I reflected that the effect of higher temperature increasing the travel of fly balls would have a very consistent effect from game to game and over time. So this is one of the rare settings where a statistical or “econometric” analysis of a constant treatment effect will be reasonable!
I think there’s more to be said here, something like, “When do reduced-form estimates work in practice?”