OT-deflategate: Thought experiment--could the balls have been inflated at artificially hot temps?

Submitted by stephenrjking on January 21st, 2015 at 10:21 AM
So this is the sports topic du jour, and this blog has a readership that tends to be well-educated. Let's try a thought experiment--gaming footballs with physics.

Let's say, hypothetically, that your football team likes footballs to be a bit under inflated. Now, you know that the balls will be in public view as soon as the refs release custody of them, and you don't want some ball boy caught doctoring the footballs on NFL Films.

It is 45 degrees outside. The balls are delivered to the referees 2.5 hours before kickoff. They are inspected at that time and must record an air pressure of between 12.5 and 13.5 PSI. They are measured in a 70 F room.

You're at home. You have your own rooms with thermostats, and possibly customized air delivery equipment.

Is it possible to deliberately inflate the balls at an artificially high temperature to measure the correct pressure (say, 15 minutes after inflation in a 70 degree room), knowing that the pressure will decrease once they spend time outside? Note that the balls are kept indoors with the refs for over two hours. By halftime they were 2lbs light, which suggests 10-10.5 PSI. Would it hold enough heat to work? How hot are we talking?


Ron Utah

January 21st, 2015 at 12:13 PM ^

This whole thing is such a joke.  If the balls were deflated to a point that would have made a difference, then the referees are the ones that are at fault here.  They handle the balls after EVERY play, and if they couldn't tell they weren't properly inflated, then they should be reprimanded, not the Patriots.

Anyone who has played any football can immediately tell--just from gripping a football--if the ball is properly inflated.

This is more about media attention and making a stroy than anything, but if there is a story, it should be the continued incompetence of NFL officials.


January 21st, 2015 at 12:27 PM ^

So if you cheat on a test it's your teacher's fault for not catching you?

Blame gets shifted if someone's paid to enforce the rules?

Drive drunk - if something goes wrong it's the police's fault?

People make the most biased arguments about Tom Brady and anything UM related in general on here. I guess that's too be expected


January 21st, 2015 at 5:11 PM ^

boom. exactly. thats the first thing that came to my mind the umpire is going to catch the ball all game long, the line judge and the head linesman are thrwing it to him, the umpire is then setting the ball. plus, like you said, they have to check them in the pre-game. i always try to support the refs/umpires point of view because ive been in their positions and know how it goes, but in this situation i have to blame the refs. it needed to be handled on the field during the game, not after the game. i dont know what exactly the NFL rule are in this situation, but maybe thats the issue.



and this part isnt a reply to blueinmilwaukee, but just my own thought, isnt it crazy how everyone always tries to call the pariots cheaters? i mean john harbaugh tried to call them cheaters for subbing eligible receivers for linemen and vice-versa.


at what point are people gonna give up and accept that belicheck is a genius? he reads the rule book front to back and knows everything he can exploit


January 21st, 2015 at 1:52 PM ^

Yes, it is the referees' jobs. Nobody is mad at the Cowboys guy (I don't even remember his name) who interfered with Pettigrew on that play in the WC game. I didn't hear anyone calling him or the Cowboys "cheaters." The players and coaches are not paid to make sure the game is fair, the officials are. Football isn't a sport with a tradition of "gentemanly play," unlike golf, sailing, tennis and others. There have always been and always will be teams that push the rules, and that's okay, as long as the officials are good there is no issue.

Ron Utah

January 21st, 2015 at 4:32 PM ^

Your comparisons are completely invalid.  First of all, no one has any idea who (if anyone) deflated the balls, or who ordered it.  It's more likely Tom Brady is guilty than Bill Belichick, but that's not the story out there.

Second, if you want to compare, let's use a valid comparison.  The Seahawks break contact and pass interference rules all the time, and don't get flagged every time.  Should they be fined and docked draft picks?  They are doing it in plain sight, same as the footballs.  This isn't cheating on a test, it's an open, obvious practice that the refs had the opportunity to stop AFTER EVERY SINGLE PLAY.  And comparing this to putting lives in danger by driving drunk?  SMH.  That's beyond ridiculous.

Finally, the balls were re-inflated at halftime, and the Pats proceeded to annihilate the Colts.  This game's outcome had NOTHING to do with deflated balls.  ZERO.

Honestly, the Dallas Cowboys and Detroit Lions were hurt by far more egregious officiating errors, and there was no recourse.  Give me a break.  If this wasn't Belichick's team that has a chance to be the most successful ever, then it wouldn't be a story.  

To answer your one reasonable question: YES.  Blame does get shifted if someone is paid to enforce the rules.  As my other examples above indicate, it is the referee's job to make sure the rules are followed.  That's why we have refs.  That's why you don't call your own fouls in professional sports.  If you were ever an athlete or coach in a terribly officiated game, then you understand that bad officiating tilts the scales, and, if properly enforced, rules are broken far, far less often.

Have you ever played a sport and broken a rule?  Ever fouled someone in basketball and not had the foul called?  What did you do?  Did you tell the ref to stop the game and give the guy some free throws?

The self-righteousness of our society is staggering.


January 21st, 2015 at 10:28 AM ^

Did they remeasure the Colt's balls too?  You can't just assume only the Patriot's ball deflated due to the cold.

Damn, I don't think I've used the word "balls" so many times in a post other than those involving Michael Rosenberg.


January 21st, 2015 at 10:28 AM ^

and I agree with your theory, but it falls apart when you consider that the Colts footballs were all at the right pressure.  They would have suffered the same effect as the Pats footballs due to the cold. 


January 21st, 2015 at 10:58 AM ^

Maybe New England shoots for the bottom range while Indianapolis goes for the top range. They could have an equal loss of pressure but Indianapolis would register ok while New England wouldn't.

There is also no word on how underinfalted the other balls were. The referee handles these balls constantly and evidently didn't notice a problem. It tells me we are not talking about a major difference.


January 21st, 2015 at 11:22 AM ^

Exactly, hot air would cause the pressure to register anomolously high when inspected by the officials, then, as the inside heated air cools to ambient temps, the pressure would greatly decrease. This is analogous to your vehicle tires registering low psi on the first really cold day of winter.


January 21st, 2015 at 10:57 AM ^

I'll have to find something to that effect.  I recall hearing something on the radio this morning, but I'd have to be sure.

On a related note, anyone see a reminder about Brad Johnson shelling out $7500 to have the Buccaneers footballs scuffed up before their Super Bowl years ago?

I Like Burgers

January 21st, 2015 at 10:28 AM ^

That's something that I'm wondering too. If they are measured indoors at a warm temp, what's a normal expectation for deflation when they are outside and cold? And if you bring them back inside after the game, what's a normal expectation for PSI loss during the course of the game? Feels like there's a lot of science missing in this whole thing.

I Like Burgers

January 21st, 2015 at 11:43 AM ^

Would like to see the math and science behind this.  A simple "no" doesn't do anything for anyone.  Seems like the perfect Sports Science segment.  Like if you fill a ball to 12.5 psi inside a 70 degree room, and then go play with it outside in 40 degree weather for 4 hours, what PSI should you expect the ball to be at when you read the PSI back inside the 70 degree room after the game?  Or even the next day depending on when they rechecked these balls.

I'd even like to see some variations on this.  Like what if you filled the ball with 100 or 120 degree air?


January 21st, 2015 at 2:15 PM ^

Pressure's proportional to temperature for an ideal gas (a good-enough approximation for our purposes). A drop from 12.5 to 10.5 psi is a 16% drop; we'd need a 16% drop in temperature to explain it. 40 degrees Fahrenheit is 278K, which would be a 16% drop if the temperature of the gas when the pressure was measured was 331K, or 136 degrees Fahrenheit.

Edit: Never mind--like countless before me (I should have read the thread, or just known, that I wouldn't be the first to do the calculation) I forgot about the difference between air pressure and gauge pressure.


January 21st, 2015 at 1:29 PM ^

No numbers are needed to know that the footballs were tampered with. Every football found to be deflated was deflated the exact same amount. This scientifically makes no sense because each football was put under a different set of conditions. Some were used in warmups, some were kept in a warmer bag throughout the game, some were used for the majority of the gametime, etc. In any scientific experiment you need to keep all outside variables controlled in order to have any validity in your test, and even then alot of times you will still get a range of values. The fact that they all lost the same exact amount of PSI shows that they deflated the ball to an exact psi, and temperature/science had nothing to do with it. Also, the fact that the Colts did not have this issue proves this further. 


January 21st, 2015 at 6:32 PM ^

I would actually prefer that they report that they were all the exact same pressure. That would point more towards a scientific explanation and less to manipulation. As you pointed out, without whipping out a pressure gauge in the middle of Gillette, it'd be nearly impossible to deflate them all the same.

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January 21st, 2015 at 10:28 AM ^

I'm no physicist, but I have to think that to make the balls hot enough to make a difference, the refs would note that they were scalding their hands.

If we're thinking conspiracy, couldn't they alter the balls so that they had a slow leak?


January 21st, 2015 at 11:00 AM ^

here:  Just before the half, the refs didn't call three pass interferences, defensive holds, etc, resulting in the Pats having to kick a field goal. The refs set, threw, exchanged, ect. the Pats footballs all day. They didn't question the inflation without prompting from the Colts, and apparently even then didn't intervene during the game.

What is so different between not calling an interference call that impacts the score of a game, and not calling illegal ball inflation during the progress of a game? Why would one be acceptable to question and fine afterward, and the other not?

Both were non-calls by referees during the game for intentional acts that were outside the rules.

Also: did they measure the Colts footballs too? What is the pressure loss expectation for a football during a professional game in inclement weather?


January 21st, 2015 at 12:01 PM ^

Like I said, the advantage gained was likely minimal.

The difference between cheating and refs blowing calls should be obvious. Not sure what you're trying to prove.

I'll agree that this issue is totally overblown in the media, but that doesn't mean the Patriots should avoid any sort of punishment for cheating. 

Edit - I just want to add, if there was no manipulation of their balls after the refs checked them pre-game, then this is just worthy of a tiny fine, and this is the most overblown "scandal" of all-time. The difference could be explained a poorly calibrated pressure gauge. If the Pats were sticking needles in them afterwords, then that's pretty damn shady and the NFL should hammer them. 



January 21st, 2015 at 4:02 PM ^

isn't breaking the rules?

If you listen to the Mike and Mike segment down on the page, it appears the balls were checked at half time and must've been re-inflated by the refs checking them.

So - DB interferes with receiver - which is a rule violation - and the ref doesn't flag it. Game goes on.

Balls get checked at half time, are found to be 2 lbs under - which is a rule violation - and the ref re-inflates the balls and sends them back out no in game "flag".

Both are rule violations done to get a slight advantage - what is the difference?


January 21st, 2015 at 12:07 PM ^

The Patriots haven't been "caught" doing anything.  All evidence is circumstantial.  Short of a video clip of a ball boy on the Patriot sideline with a needle letting air out of the ball, there is no way for the league to prove the Patriots deliberately deflated their footballs to gain some kind of advantage.  Certainly not an advantage that would explain a 38 point score differential.

This is just a smoke screen being thrown up by the Colts to deflect attention away from the fact that they got their asses handed to them on Sunday by a better football team.


January 21st, 2015 at 10:32 AM ^

I'm not gonna go as in depth with this as I have before, but if we use PV=nRT or even Van der Waals equation for this shit (Air is a real gas not ideal etc etc). Using cursory calculations with PV=nRT and converting psi to atmospheres and back... assuming .5 moles of air... 


2.87 atmospheres (41.58) at 294 K

2.73 atmospheres (39.67 psi) 281 K 


This is a 1.91 difference in Psi... So yes theoretically this could have been done. But this is using ideal gas law... so numbers are slightly off when talking about air which is real. 


January 21st, 2015 at 10:36 AM ^

Take this with a grain of salt. I'm too lazy atm to look up the Bolzman/attraction forces constants to actually do a calculation using Van der Waals for more accurate estimation for real gases. 

Oh and the American system is a bitch to convert back and forth from. 


January 21st, 2015 at 11:02 AM ^

You're overthinking - none of that really matters in this context. You don't have to assume any particular number of moles, since n will stay constant (assuming no air loss). R is a universal constant, so throw that out too. And you don't have to worry about converting units, as long as you use absolute values (psi is fine, for temp you'd need Rankine).

The final relevant equation is just:

T1 = P1/P2 * T2

So all that matters is ratios. Solve for T1 and you know how warm the balls needed to be.

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January 21st, 2015 at 10:56 AM ^

Your math is right but I think your numbers are wrong - shouldn't the initial pressure be more like 27.2 psi (gauge pressure of 12.5 plus sea level air pressure of ~14.7 psi)?

Using 27.2 psi as the initial pressure, and 281K as your final temp, you need an initial temp of 303K, or 85.73F. This still strikes me as pretty reasonable - at that temp I don't think you'd notice the football was unusually warm.

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January 21st, 2015 at 11:03 AM ^

Yeah I just kinda winged it so my numbers may not be ideal. The differences between the pressures should be close enough tho for our purposes. Never really thought I would be pulling out the chem/physics equations for a question pertaining to the AFC Championship game lol.

That U of M tuition going to practical use!