A non-technical layperson's description of the science behind deflategate

Everyone,

My earlier post went through exactly how the gas law calculations are made, in full detail. I have certainly learned that a lot of people tend to freak out just when they see a math equation! This is unfortunate, but it is real. In the interest of being a communicator of science, even to people somewhat hesitant to even THINK about the science itself, I put together this lay person's description of what I did, why, and what it may mean. This might prove more useful in making people more comfortable about the science of deflategate, which is only coming to a clearer and clearer consensus (well, at least unless more sources, unnamed or otherwise, give info to contradict our assumptions). Thanks!

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Part 1

We have all heard about “deflategate” by now, the allegation that somehow footballs used by the New England Patriots must have been tampered with, because they were shown to have lost some of their pressure during the first half of the AFC championship game. There have been many varied explanations thrown out there about what it was that caused the pressure drop, though “cheating” has been the most often-heard allegation.

Last weekend I read claims that the loss of pressure in a football by natural causes alone just could not have happened, that it violated the laws of nature, and that the temperature drop, from the time when the footballs were inflated up until halftime, would have had to have been very large, even 100 degrees or more, to see the pressure drop that the referees apparently measured. The first analysis that I read online mentioned that other people had reached this same conclusion. Something about the claims bothered me, though. I grew up in the North. I remember playing basketball outside on cold days, even just slightly cold days. I remembered how the basketball noticeably cooled down and didn’t bounce as well. I am also a scientist, so I thought that I should look into this a bit more, since it just didn’t make sense to me.

Any gas or any mixture of gases, like air, that is kept in a closed container (a balloon, a football, a glass jar, or anything like that) expands when it is heated and contracts when it cools. This was first described over 400 years ago, when early scientists were using glass containers to try to make inexpensive thermometers. Over time scientists found that pressure and temperature move proportionately in the same direction: as temperature goes up, pressure goes up; as temperature goes down, pressure goes down. It became part of what we now call the “ideal gas law”, which is taught in high school and college chemistry and physics classes.

The temperature/pressure connection is something that almost all of you have likely noticed before. Have you bought balloons at the grocery store? They generally are inflated in the store, while you watch, at room temperature. If it happens to be a winter day (and Valentine’s Day is coming up), and if you take the balloons outside to your car, the balloons will shrivel up noticeably! Then when you take them home they will fill out again as they warm up. There are many YouTube videos showing this happening, and here is one:

So the idea that air inside a warm football would lose some pressure as it cools makes sense from our everyday experiences. Why were the calculations that I saw on the internet saying that the temperature had to drop enormously in order to see a significant pressure drop? I decided to look into it. One of the persons making the claim of a necessarily large temperature drop thankfully gave a link to the math that was involved. I reviewed it. Sure enough, they did use the ideal gas law. They did convert the temperatures to the Kelvin scale, which is the temperature scale that is used in the ideal gas law. They used the supposed air pressures that were measured for the footballs in units called psi, for “pounds per square inch”. But then something went badly wrong in their calculations, and it is easy to understand.

A pressure gauge measures something called “gauge pressure” or “relative pressure”. Simply put, this is the pressure inside of the football relative to the outside air. Gauge pressures are what were used in the calculations that I was critiquing. The ideal gas law, however, uses a different pressure measurement for a simple reason: even the air outside of the football is under pressure too, the atmospheric pressure, also called the barometric pressure, which is one of the pieces of information that your weatherman likely tells you every morning. Thus the air that is inside the football is really under a total pressure that is the sum of the gauge pressure and the atmospheric pressure.

Confusing the gauge pressure with the total pressure and using the wrong one in the gas law calculation turns out to be a common mistake. Even the famous astrophysicist Neil deGrasse Tyson made this same error, which he corrected a day later (yesterday)! What happens when you do the calculations the correct way? I will spare you the actual calculations and equations, though they are most definitely not a secret and I have described them in detail elsewhere. Here I instead want to give a layperson’s level description.

The first piece of information that I needed to have was the temperature of the footballs before the game, when they were inflated and inspected. We don’t know that temperature for certain, but we are told that the inflation & inspection was done inside, at room temperature. An educated guess for room temperature is 72 °F. For my calculation I converted this temperature to the Kelvin temperature scale.

The second piece of information that I needed to have was the temperature of the footballs at halftime, after they were used in the game for 90 minutes or so. We can assume that the footballs reached the temperature of the outside air, to a first approximation. At kickoff the temperature was 51 °F. Granted, it was raining very hard and the rain may have been colder than that, since raindrops form high in the sky and often reach the ground at a colder temperature than that of the air. Thus the rain may have cooled the footballs to a lower temperature than 51 °C. The temperature also likely dropped a little by halftime, by a degree or two. Since it is generally unwise to make any more assumptions than you have to when doing calculations, however, I used the 51 °F value. For the calculations I also converted this temperature to the Kelvin temperature scale.

The third piece of information that I needed was the barometric pressure during the first half in Foxboro, MA. A website called Weather Underground tracks this data. At around kickoff time, the barometric pressure was 29.75 inches. This can be converted to 14.61 psi.

The fourth piece of information that I needed was the pressure of the footballs before the game, when they were inspected. We know that the Patriots wanted their footballs to be inflated to 12.5 psi. Knowing this, we can add this gauge pressure to the barometric pressure to get the total pressure that we need to use in the gas law calculation.

After knowing those four things, the calculation of what the final pressure of the football must be is really pretty simple. Plugging in the actual values, a football inflated to 12.5 psi at 72° F that is then cooled to 51 °F will have a final gauge pressure of 11.34 psi, thus showing a pressure loss of 1.16 psi. This result made some sense to me, harkening back to my days of playing basketball out in the cold. Even a 21 degree drop would make the ball a little less fully-inflated, to my recollection.

However, rumors at the time in the press said that the Patriots footballs had lost 2 psi in pressure. The ideal gas law predicted a 1.16 psi drop. Thus not everything was lining up, for sure. Then, as we have seen often in this story, another report emerged on Monday from yet another “unnamed source”. This particular report claimed that only one of the Patriots footballs lost 2 psi of pressure, namely the football that had been intercepted late in the half. One Patriots football had also been judged to be “passing” at halftime. The other 10 Patriots footballs, the source claimed, dropped much less in pressure. In fact it was proposed that they dropped closer to 1 psi than 2 psi. So we had two outliers, or two odd Patriot footballs, one that was on the high side and one that was on the low side. The rest of them dropped closer to 1 psi in pressure, apparently, and thus the average drop may have been closer to 1 psi, which would agree with my calculations. This report that a pressure drop closer to 1 psi than to 2 psi, on average, may have occurred changed my perspective on my calculations. It seemed that science might be able to explain the drop, completely.

(see part 2)

part 2:

Late in the weekend and on Monday, warm/cold football deflation experiments began showing up on the internet. Some experiments were not well-controlled: they didn’t use NFL footballs, they didn’t use anywhere near the right beginning and ending temperatures, they didn’t use the right timeframe or method for cooling the footballs, etc. One set of experiments stood out to me, though, as being especially reasonable and well-done. Scientists at Carnegie Mellon University calling themselves “head smart labs” posted on the web a video and also a pdf description of their experiments.

In one experiment, the Carnegie Mellon folks found that footballs inflated in the lab to 12.5 psi at 75 °F and then cooled to 50 °F had a final pressure of 11.4 psi, a loss of 1.1 psi. In a second experiment, shown on their video on their web site, they found that footballs inflated to 12.50 psi at 75 °F and cooled to 50 °F that were then soaked in water had a final pressure of 10.7 psi, a loss of 1.8 psi. The soaking in water step was to mimic the game conditions, since much of the game was played in a torrential downpour.

The results of their first experiment, with no soaking of the footballs in water, match the ideal gas law prediction that I had made rather closely (1.1 psi pressure drop seen, vs. 1.16 psi pressure drop calculated). The Carnegie Mellon folks used a slightly larger temperature drop in their experiment, 25° (from 75 °F to 50 °F) rather than the 21 °F drop that I used. That doesn’t make either of us wrong, necessarily, since we do not know what was the actual temperature in the referee’s room, where the footballs were inflated and tested.

The results of their second experiment, which did include soaking the footballs in water, suggested a new factor to consider. They concluded that as a football gets wet the leather expands. When the leather expands, the elastic bladder inside of the pressurized football expands to match, making the football swell up a tiny bit as it becomes wet. A slightly swollen football has a slightly larger volume. With no air added, that would mean that a pressure drop must result. They found that the expansion of a football as it gets wet contributed 0.7 psi in pressure drop, getting them to a drop of 1.8 psi in total.

I hadn’t really thought of the effect of water on the ball at first, but it does make some sense. In their experiment they dunked their footballs completely in a tub of water for awhile. Is that analogous to a heavy rain, or would it be overkill? That issue concerned me a bit. One other thing that the Carnegie Mellon folks did also was curious: they used brand new NFL footballs. New footballs apparently come from the factory with a waxy coating on them that makes them very slippery. Quarterbacks hate it. That in large part is why footballs are “prepped” for use: to get rid of this coating. I don’t know what this coating is, from a chemical point of view, but might the waxy film repel water, just like wax on your car? If that were true, maybe a prepped football (like those used in a game) would waterlog more easily than the new ones that were used at Carnegie Mellon. So it is hard to say whether their second experiment is valid or not. It probably has some importance, but to err on the side of caution, in my analysis here I place more emphasis on their dry football experimental result, where they found a 1.1 psi pressure drop, in general agreement with the 1.16 psi calculated result that I obtained, which also doesn’t take football wetness into account.

My conclusion is simply that it would be reasonable to expect, based on both experimental results and gas law calculations, for a pressure drop of at least 1.1 psi to have occurred within the Patriots footballs in the first half of the AFC championship game, based on the known game time weather conditions and the observation that the footballs were (likely) inflated to 12.5 psi (gauge pressure) at room temperature (72 °F) before the game. A larger drop would be expected if the “expanding wet ball theory” is valid.

Then we face a huge issue: what about the Colts footballs? Don’t they have to obey the laws of nature? Yes they do. Do they? To find out, we just need to have the same pieces of information. Since we know all of the weather information, we just need to know the starting pressure of the Colts footballs. Unfortunately, we don’t know that. But, it may be reasonable to assume that their footballs were inflated up to the maximum legal pressure of 13.5 psi gauge pressure. Why? Well, this assumption relies on still more reports from still more unnamed sources, but it is claimed that the Colts went into this game with a concern that the Patriots has used under-inflated footballs in the past. If they indeed knew that football pressure loss would be monitored, and if in fact if they were planning to ask the referees to do halftime or postgame tests, then it stands to reason that they would want their footballs to be as far from being under-inflated as possible, yet legal. That would be a pressure of 13.5 psi.

I plugged in the numbers for the Colts footballs into the gas law equation. The finding: Colts footballs should have been at a final pressure of 12.3 psi if they started at 13.5 psi and at 72 °C. The legal lower limit is 12.5 psi. The Colts footballs should have measured low in pressure at halftime by 0.2 psi, with these assumptions.

Well, there you have it, the Colts footballs would not have passed, technically. You have to ask yourself, though, would a referee call a reading of 12.3 rather than 12.5 clearly out of specifications and illegal? How about a reading of 12.4 rather than 12.5, or a reading of 13.6 rather than 13.5? It is hard to tell for sure, I think. It certainly depends on both the accuracy and precision of the pressure gauge. A digital readout (the kind most often used today) often shows significant drift or fluctuation in the last digit. If in real time the referee saw values on that last digit fluctuating between 12.4 and 12.5, for example, he might say “It looks to be about 12.5; good enough!” Similarly at the beginning measurement, if he saw values on that last digit fluctuate between 13.5 and 13.6, for example, he might say “It looks to be about 13.5, good enough! He could instead say, for example if the 13.6 value were there for longer, “It looks more like 13.6, which is illegal”. Similarly in making the call at halftime he could say “It looks more like 12.4, which is illegal”, of course. But is he really likely to be that confident in trusting that shaky last digit on the pressure gauge, so confident to make him declare something illegal? That would be like the cop who writes you a ticket for going 71 mph in a 70 mph zone. In the real world and for most cops, 1 mph too fast is not a big deal. The referee probably doesn’t think that being 0.1 psi off specs is a big deal, either, while he is in the middle of checking and inflating or deflating as many as 60 footballs in about 15 minutes (24 from each team and also 12 kicking balls).

(see part 3)

Part 3:

Do we know that the Colts footballs were at 72 °C when they were tested pre-game? No. If they were colder for some reason (maybe they had just come off of an equipment truck shortly before inspection?) the pressure drop during the game would have been less, since they would have cooled down less to reach 51 °F by halftime. For the Colts footballs it is not unreasonable to predict that they would (barely) pass, based upon what we expect of inflation levels, inflation temperatures, temperature-related gas expansion, and the human-element (the referee deciding he isn’t confident in calling something illegal that appears to be off by only 0.1 or 0.2 psi).

There are some factors that I have not taken into account at all in this analysis. One of them is the football preparation (football rubbing) procedure. Bill Belichick says that in a reenactment of their game day procedures, the Patriots footballs gained about 1 psi in pressure during football preparation. Mr. Bill Nye considered that number to be unreasonable. A 1 psi pressure rise would be substantial, and it would have to arise by friction. The footballs would have had to have been rubbed so vigorously that the friction made their internal air temperature rise by about 20 °F, in fact. That seems like a lot, even if some type of mechanical football buffering machine were used. For now I am assuming that the football preparation procedure does not affect psi in the least, which is Mr. Bill Nye’s assertion. In reality I disagree a little bit with him, though, in that he seems to suggest that the effect of friction would be zero. It is probably non-zero. But whatever it is, it is unknown and even unknowable without learning of the exact football preparation procedure that the Patriots used. Importantly, though, special football preparation is not even needed to explain a significant pressure drop (one of over 1 psi).

I also ignore the “wet footballs swell up” argument, since it is a bit harder to model by any quick and obviously valid calculation. It does seem logical to me, though, that wet footballs swell up at least a little and therefore lose some pressure, based on the Carnegie Mellon (headsmartlabs) experiment #2. Other factors ignored here include the possibility of the rainfall being colder than 51 °F, the possibility of the referee’s room being hotter than 72 °F, the possibility of the Colts footballs being at a temperature lower than 72 °F when they were first tested, and maybe other factors as well. Key pieces of the puzzle that we do not have include the actual ref-recorded data for the Colts’ footballs, which is clearly very important. We’d also like to have real sources rather than unnamed ones, so that we would also know, for example, if the Patriots footballs dropped by 2 psi, by 1.5 psi, by 1.0 psi, or by some other amount.

One final thought: pressure in a football simply is not everything! How often do you hear as you tune into a cold weather game “Catching the football today is going to be like catching a rock”? Guess what: those rock-hard footballs likely have a low pressure, if they were pumped up to legal pressure at room temperature! How can cold footballs feel as hard as a rock despite having a low pressure? Likely it is because the leather gets much stiffer (inelastic) as it gets colder. The stiffness of the leather covering a cold football, in fact, apparently more than makes up for its low pressure and makes it harder for the quarterback to squeeze and harder for a receiver to catch. And this is why the cold football game pressure issue has really never been important at all in the past: footballs just simply do not turn into mush when they get cold! It only seems to be an issue because the NFL rules tell the referees to look at just one thing: the gauge pressure of the football, and further, they fail to clarify for the referees that what is REALLY important is the gauge pressure of the football at room temperature.

1/28/2015

I wish the mediots could read (unlikely), and understand (less likely) this.

Great post, I had not thought about the football possibly becoming less elastic when getting colder. So many factors, so many unknowns, it's difficult to precisely know the magnitude of them all except in totality through experiment.

One thing I thought about, in the Peter King article the footballs were in a bag that looked mostly water resistant. I would imagine they try to keep the footballs dry before their use.

Now you may have several footballs that are wet to varying degrees, depending on use, and some dry. By assuming the Headsmart labs experimental numbers that means that on to of the 1.1 or so, you have an additional 0-.7 dependent on use.

I doubt anyone thought to track varying degrees of wetness when they did the half-time measurement. They probably have 12 balls, and 12 measurements, and almost assuredly the dry balls would have a different reading than the wet. Maybe that's part of what they found suspicious? Plus the fry balls may have been slightly warmer. The balls with same initial conditions could have had a variation of 1psi just based off that. And we haven't even got into gauge error and human accuracy during inflation.

It seems like a very poorly thought out investigation to go into this thing without knowing these factors. Now, we can't go back and look at which balls were wet etc. and record. Without having a good deal of data to make conclusions it was a stupid decision to even try measuring balls at half time that have a near inperceptible difference in feel and start drawing conclusions, and beginning investigations.

How quickly do you think a cold ball would warm up? IE if the colts balls were right off the truck and pressure tested within 30 minutes, I wonder if they'd still be cold. I would think so.

I thought I read the Colts balls pressure tested at not much more than 12.5PSI which would be strange that they didn't lose at least some PSI in the rain and thus measure under.

Palm Beach Pats Fan said:

part 2:

Late in the weekend and on Monday, warm/cold football deflation experiments began showing up on the internet. Some experiments were not well-controlled: they didn’t use NFL footballs, they didn’t use anywhere near the right beginning and ending temperatures, they didn’t use the right timeframe or method for cooling the footballs, etc. One set of experiments stood out to me, though, as being especially reasonable and well-done. Scientists at Carnegie Mellon University calling themselves “head smart labs” posted on the web a video and also a pdf description of their experiments.
(see part 3)

Click to expand...

PBPF, Can you email this guy http://physics.columbia.edu/people/profile/383

His email address is there. He flapped his gums today in the NYT that it was a person not weather in his opinion. It is troubling as he is speaking as a representative of Columbia which the NFL has charged with doing the science investigation.

Dr Pain said:

PBPF, Can you email this guy http://physics.columbia.edu/people/profile/383

His email address is there. He flapped his gums today in the NYT that it was a person not weather in his opinion. It is troubling as he is speaking as a representative of Columbia which the NFL has charged with doing the science investigation.

Click to expand...

The fix is in.

I cannot understand how anyone can reject (or even accept for that matter) the science without knowing the measurements.
The biggest screw up in this debacle is to have discussion, "reporting" and opinion go on for 10 days based on an unconfirmed (and now contradicted) explanation of what the pressure of the footballs was.

AndyJohnson said:

I cannot understand how anyone can reject (or even accept for that matter) the science without knowing the measurements.
The biggest screw up in this debacle is to have discussion, "reporting" and opinion go on for 10 days based on an unconfirmed (and now contradicted) explanation of what the pressure of the footballs was.

Click to expand...

This is what gets me wicked pissed at the NFL.
They have issued leak after leak of information unfavorable to the NEP but not one utterance describing actual pressure measurement data. Such data IF THEY HAVE IT would go a long way to moving the discussion into more productive discourse.

PatsWickedPissah said:

This is what gets me wicked pissed at the NFL.
They have issued leak after leak of information unfavorable to the NEP but not one utterance describing actual pressure measurement data. Such data IF THEY HAVE IT would go a long way to moving the discussion into more productive discourse.

Click to expand...

Even worse they allowed a leak about the pressure that led to people forming opinions, and 3-4 days later a conflicting measurement rumor was leaked.

So I'm still kinda confused, sorry for being dumb but it's the weather and NOT the temperature that is the reason they deflate? Because some people are saying temperature other people are saying climate or weather.

Froob said:

So I'm still kinda confused, sorry for being dumb but it's the weather and NOT the temperature that is the reason they deflate? Because some people are saying temperature other people are so climate or weather.

Click to expand...

Just go watch HeadSmart Labs video of it. It's pretty much all you need to see that weather and temperature can cause a drop.

Froob said:

So I'm still kinda confused, sorry for being dumb but it's the weather and NOT the temperature that is the reason they deflate? Because some people are saying temperature other people are saying climate or weather.

Click to expand...

Temperature changes pressure by the ideal gas law. That much is not arguable. The rain COULD have expanded the balls slightly which would lower the PSI by about .3 for every 1% increase in volume. I've also read that water vapor in the air could raise the effective atmospheric pressure which would lower guage pressures slightly, not sure.

One place, CMU, did a study and they measured both effects. I think they got 1.2PSI for temperature alone, which is about what the equation says.

There are always little confounding variables in reality.

Keep beating this dead blood splotch(formerly a horse) into the concrete. It's exactly what this damnable league wants. The Pats won the game ...won it big...the ball was the ball...period. No one has ever tried to use THIS idiotic, moronic and utterly stupid excuse to exacerbate plain fact in NFL history. Another first.

It is interesting that they've never measured PSI in a ball mid game or post game as far as I know. So for those who say "other cold weather games didn't have balls that deflated", they simply don't know that to be the case.

kennyb said:

It is interesting that they've never measured PSI in a ball mid game or post game as far as I know. So for those who say "other cold weather games didn't have balls that deflated", they simply don't know that to be the case.

Click to expand...

You're forgetting something. Other games were played during a suspension of the laws of physics as a result of divine intervention, what is otherwise known as Tebow rules.

Dr Pain said:

PBPF, Can you email this guy

Click to expand...

done!

Palm Beach Pats Fan said:

done!

Click to expand...

Awesome. We can only try Thank you so much for at least getting King to use a brain cell.

The problem is cognitive dissonance. They believe that the Patriots are cheaters - Science shows they didn't cheat. In a mental bind such as this emotion usually beats reason.

One other factor that no experiment or calulationm can duplicate what happened.

What was the resolution of the gauge used by Head Smart Labs? the NFL official?and so on what does inserting the measurement device allow air to escape the football.

Too many variable that will never be know.

However the key point remains. The footballs used in an NFL Game will and indeed must respond to the weather in which the game is played. Further the conditions the night of the Colts game seem to strongly indicate that the temp will drop from 1-2 psi.

Well will have to deal with what King referred to as the forensic evidence. Which tends to exonerate the Pats.