Tuesday, May 26, 2015

How I Trashed the Wells Report from a Swan Boat

Does anyone else find it odd that every football fan with a computer has been weighing in on “Deflategate” (a name I will not be using again) since there was still snow on the ground in Boston, yet no one actually seems to understand the details?

I knew I had to do something about a week ago, when someone posted a reply on a message board saying that 11 of 12 of the Patriots’ footballs from the AFC Championship Game were 2 PSI under the limit. This story came from an anonymous leak on ESPN four months ago, and has been completely debunked by the NFL’s own report.

People don’t get it. Perhaps they need a summary of the Wells Report, written in English. They also need to take a deep breath, relax, and learn the facts. Luckily, speaking English and breathing are my specialties!

I understand “The Patriots Cheating” is a story that no one can resist, and the American attention span is about as long as a sneeze, so the temptation is to read the headlines, form a conclusion, and run with it. But this case is complex. If we want to get it right, we have to put in some time. I’ll do my best to make this exciting for you!

This post is divided into three parts: A review of the evidence, a resolution of the logo / non-logo debate, and an explanation of the differences in pressure lost between the two teams’ balls. Feel free to skip around as needed. And please, contact me right away with any questions or concerns!

Part I: The Evidence: Balls, Pressure, and Basic Math

As we all know by now, referee Walt Anderson’s best recollection is that he used his “logo gauge” (the gauge with the Wilson logo on it) for the pre-game measurements, though he acknowledged that he could be wrong. The Wells Report concludes that Anderson must have been mistaken and that he probably used the non-logo gauge. This is a matter of some importance, because Anderson’s two gauges were not calibrated to one another, or to anything else. The logo gauge consistently read higher than the non-logo gauge, by an average of 0.38 PSI. This means that, if the logo gauge measures a football at 12.50 PSI, the non-logo gauge would read about 12.12 for the same ball. And, if the non-logo gauge measures a football at 12.50 PSI, the logo gauge would read 12.88. Think of it as having two bathroom scales, one of which reads three pounds heavier than the other. These discrepancies would have an effect on any calculations based on measurements from those gauges.

As part of its analysis, the Wells Report calculates how much pressure was lost from the Patriots’ footballs between pre-game and halftime, and compares those decreases to the amounts that were lost from the Colts’ footballs, as well as the losses that were predicted by the Ideal Gas Law.

Their method for calculating the decreases was simple:

Starting Pressure (PSI) – Halftime Pressure (PSI) = Pressure Lost

So, if a Patriot football measured 12.5 before the game, and 11.5 at halftime, the formula would look like this:

12.50 PSI – 11.50 PSI = 1.00 PSI lost

Below are the halftime measurements of the two teams’ footballs. The PSIs were measured by two officials, Clete Blakeman and Dyrol Prioleau, whose names appear on the column headers. Because Prioleau’s readings were consistently higher than Blakeman’s by about the same 0.38 PSI difference discussed earlier, the Wells Report assumed that Blakeman had the non-logo gauge, and Prioleau had the logo gauge. For each pair of readings, the larger number is highlighted in blue for ease of reference.

The Wells Report also assumed that, after the Patriots’ balls were gauged, the two officials switched gauges, because for the Colts’ balls, Blakeman’s readings are consistently higher than Prioleau’s, again by about this same 0.38 amount. All these assumptions might make you nervous, but the differences between the two gauges are very consistent throughout all measurements, no matter whose is higher, so the assumption seems logical.

NOTE: After testing 11 of the Patriots’ footballs, the officials only had time to test four of the Colts’ balls before they needed to get back out to the field for the second half.

Halftime PSI Readings by Official
(Higher readings highlighted in blue and are presumed to be from the logo gauge)

Wait a minute. Something is wrong with the measurements of the Colts’ balls, isn’t it? If we assume that the two officials switched gauges before measuring the Colts’ footballs, we would expect Blakeman’s number to be higher for all four. Instead, we see that Prioleau’s number is higher for Colts ball #3.

The Wells report concluded that this “flip” was due to a transcription error; that is, someone simply wrote the numbers in the wrong columns for that particular ball. It seems pretty clear that this is what happened, since the bigger number (12.95) is 0.45 larger than the smaller one, which is right around the average discrepancy between the gauges. But, just to be safe, the Wells Report threw out the two measurements for Colts ball #3. I’ll remove it from my calculations too, to make sure that my calculations match Wells’, but I don’t agree that we need to do so. There are plenty of footballs with a logo gauge reading that is 0.45 more than the non-logo reading. It’s a reasonable assumption that the numbers were switched, so I’ll post two versions of my tables here: With Colts ball #3, and without. I’ll place all the with tables at the end of this section.
Here are the updated halftime results:

Halftime PSI Readings by Gauge Used

Notice, not only did we remove the readings for Colts ball #3, but we also placed all the logo gauge readings in the same column, and updated both column headers accordingly. Now, finally, we have a full set of halftime readings from both gauges, for both teams’ balls.

Next, let’s calculate the amount of pressure each football lost during the first half. Referee Anderson did not write down the starting PSI measurements for any of the footballs, but the Patriots staff reported that they set their footballs to 12.50 PSI prior to the game, using a gauge belonging to the Patriots, and the Colts staff reported that they set their balls to 13.00 PSI using a gauge belonging to them. Indeed, when Anderson tested the balls before the game using one of his gauges (though he is not certain which one; more on this in a moment), he recalls that the Patriots’ balls were at or around 12.50 PSI, and the Colts’ balls were at or around 13.00. We will therefore use these values as the starting point for our calculations.

Calculation of First Half Pressure Losses by Team and Gauge

For comparison purposes, let’s look at how the Wells Report calculated those same numbers (from Appendix I, page 9):

Bingo! Our numbers match the Wells Report exactly! That must mean we were both 100% correct. Right?


Take a closer look at the starting PSIs:

Are you seeing it yet?

Think back to my analogy about the bathroom scales. The logo and non-logo gauges are not calibrated to one another, remember? A 12.50 PSI football on the logo gauge would only read 12.12 on the non-logo gauge, and a 12.50 football on the non-logo gauge would be 12.88 on the logo gauge. The two gauges never produce the same reading on the same football. There is no possible way that Anderson’s two gauges could both show 12.50 for the same ball. Our table is wrong.

Now, we have a small issue. We know that Anderson’s best recollection is that the Patriots’ and Colts’ balls were 12.50 and 13.00 PSI, respectively, but he does not recall for sure which gauge he used to determine this. His best guess was that he used the logo gauge, so let’s start there.

Calculation of First Half Pressure Losses by Team and Gauge
Scenario 1: Logo gauge used for pre-game measurements

See what happened? The numbers for the logo gauge remained the same, naturally, since we assumed that the logo gauge was used for the pre-game measurements, and we therefore did not adjust the starting PSI for that gauge. But once we corrected the starting PSIs for the non-logo gauge, the differences went down by an average of—you guessed it—0.38 PSI, the difference between the two gauges.

In hindsight, this makes sense. Yes, the logo gauge reads higher than the non-logo gauge, but after we correct for that discrepancy, the amounts lost should be the same. Going back to our scale example, if one scale says you are 153, and the other says 150, and then you lose three pounds, you would fully expect your new readings to be 150 and 147, respectively. No one would ever expect them to be the same, if they weren’t the same to begin with. They also would not take the starting weight from scale 1 (153), subtract out the ending weight from scale 2 (147) and claim to have lost six pounds. That would be silly. Yet that is exactly what the table on page 9 of the Wells Report does.

Incidentally, there is a minute difference (.02 PSI) in the amounts lost between the logo and non-logo gauges for the Colts’ balls, which is due to rounding error. We’ll use the larger value (0.35) going forward, but such a small difference wouldn’t have any impact on our calculations either way.

The table above teaches us an important lesson. Never assume something is correct just because it’s in a book or (even worse) because it came from a lawyer. Question things. Double check.

Next, let’s see what the numbers would look like if the non-logo gauge was used pre-game:

Calculation of First Half PSI Losses
Scenario 2: Non-logo gauge used for pre-game measurements

Similar to scenario 1, this table shows a consistent amount of pressure loss for each teams’ balls, whichever gauge was used, with a very small rounding error for the Colts’ balls.

To put it another way, the logo and non-logo gauges both show a loss of 1.01 PSI for the Patriots footballs (if the logo gauge was used pre-game) and they both show a loss of 1.39 (if the non-logo gauge was used pre-game). The gauges will always agree with one another, no matter which one was used pre-game.

Based on the above, the chart from Appendix I, page 9, should have looked like this:

Summary of Halftime PSI Readings

Remember, the whole purpose of this project is to determine whether a Patriots employee secretly let air out of his team’s footballs. Since no one has confessed or been caught red-handed doing so, we have to take a close look at the PSI losses and determine if they can be explained by natural causes.

If we’re talking about the price of a pack of gum, there’s not a lot of difference between 1.01 and 1.39. But when we’re talking million-dollar fines and four-game suspensions, the difference becomes massive. Don’t look now, but Logo vs. Non-Logo just jumped ahead of Mary Ann vs. Ginger in the annals of all-time debates.

If Anderson used the non-logo gauge to measure the balls before the game, then the Patriots have 1.39 of PSI losses to explain. If he used the logo gauge, that number drops 27%, to just 1.01.

I will admit that it took me more than a few readings to find the error mentioned above, and it would be pretty impressive if I figured it out and this multi-million-dollar research firm didn’t. But somehow, I just can’t quite believe that it was an accident on their part. Call me cynical.

We’ll find out in just a minute what Exponent’s (the scientific research firm retained by Ted Wells) error means in the all-important calculation of unexplained PSI loss, but whether the effect is big or small, whether it was intentional or unintentional, it should concern us. A player’s legacy and a world championship are being openly questioned. If you are going to use scientific experiments to condemn a player, and a team, your logic better be airtight, and your report better be immaculate. Instead, we find a major error on page 9. A B+ isn’t good enough. Consider my confidence shaken.

So, how much of a pressure loss do we have to explain? 1.39 PSI, or 1.01? Of course, the only way to find out is to determine which gauge Anderson used.  We already know that Anderson said it was the logo gauge, which would mean we only have to explain a loss of 1.01 PSI. But the Wells report says Anderson was mistaken. Why?

Read on to see the charts from Part I revised to include the third Colts football, or feel free to jump right to the resolution of the logo / non-logo debate.

Part I B: Tables Recalculated to Include Colts’ Third Ball

As promised, here are the relevant tables from Part I recalculated to include the Colts’ third ball (am I the only one who finds that phrase disturbing?). Again, I really don’t see a valid reason to throw out the measurements from that ball, and I can’t help but wonder what the Exponent folks could have been thinking. At any rate, here are the charts. Enjoy!

Halftime PSI Readings by Gauge Used

Calculation of First Half Pressure Losses by Team and Gauge
Scenario 1: Logo gauge used for pre-game measurements

Calculation of First Half PSI Losses
Scenario 2: Non-logo gauge used for pre-game measurements

Summary of Halftime PSI Readings

PART II: Swan Boat Inspiration Strikes: A Resolution to the Logo / Non-Logo Debate

From the Wells Report, Appendix I, page 44:
According to information provided by Paul, Weiss, personnel from both the Patriots and the Colts recall gauging the footballs for their teams to pressures at or near 12.5 psig and 13.0 psig,respectively, prior to providing the balls to Walt Anderson. Each team used its own gauge to adjust the final pressures before presenting the balls to the referee, who used a gauge different from either used by the two teams to measure the pressure in the footballs. Walt Anderson recalled that according to the gauge he used (which is either the Logo or Non-Logo Gauge), all of the Patriots and Colts footballs measured at or near 12.5 psig and 13.0 psig, respectively, when he first tested them (with two Patriots balls slightly below 12.5 psig). This means that the gauges used by the Patriots and the Colts each read similarly to the gauge used by Walt Anderson during his pregame inspection.

It has been shown that the Logo Gauge consistently reads higher than all other gauges analyzed in this investigation. As a result, it is very unlikely that the Logo Gauge would have read similarly to the gauges used by each team. Therefore, it is most likely that the gauge used by Walt Anderson prior to the game was the Non-Logo Gauge, which read similarly to the Master Gauge and other gauges tested during the investigation.

Did you get all that? Don’t worry—most people don’t.

Let me break it down for you:

  1. When the Patriots prepared their footballs for the game, they set them to 12.50 PSI. This pressure was measured using a gauge that belonged to the Patriots. The Patriots did not use either of Anderson’s gauges.
  2. When Anderson tested the Patriots’ balls before the game using one of his gauges, he recalls that they were at or near 12.50 PSI, just where the Patriots set them.
  3. Based on the above, we can conclude that Anderson’s gauge (whichever one of the two he used) read similarly to the Patriots’ gauge.
  4. Exponent tested many sample gauges during this project. Anderson’s logo gauge read consistently higher than all of them, and his non-logo gauge read similarly to most of the sample gauges.
  5. Since the logo gauge read higher than so many sample gauges, it’s likely that it also read higher than the Patriots’ gauge. Also, since the non-logo gauge read similarly to the sample gauges, it probably also read similarly to the Patriots’ gauge.
(NOTE: All of the above applies to the Colts’ gauge as well, which was used to set their footballs to 13.00 PSI before the game.)


Are you as concerned about #5 as I am?

Basically, Exponent is assuming that their group of sample gauges is an accurate representation of the Patriots’ gauge. But how can they be so sure? An assumption is dangerous in any case—and it’s about to get worse.

A few questions come to mind right away:

How does Exponent know that the Patriots’ gauge reads the same as the sample gauges?

What type of gauge did the Patriots use?

What types of sample gauges were in this sample?

The Wells Report is 243 pages long. Surely I’d have no problem finding some answers! I eagerly dug around, and found this on page 13 of Appendix I:

Exemplar Gauge
A gauge that is thought to be nearly identical to the Non-Logo Gauge. Specifically, Model CJ-01 with the description “Electronic Ball Pressure Gauge.” Exponent obtained multiple
dozens of Exemplar Gauges from both Wilson Sporting Goods (via Paul, Weiss) and other sports equipment retailers.

Excuse me while I retrieve my jaw from the floor.

Exponent wanted to get some sample gauges. So what did they do? Did they obtain a variety of different brands and styles, to represent the variability of store-bought pressure gauges? Did they at least buy two different brands or styles?

Nope. “Multiple dozens” of the Exact. Same. Thing. Identical brand and model number.

Let’s say you drive a Nissan Maxima, and you want to know whether your car is faster than mine, but you have no idea what kind of car I drive. So you go out and buy several dozen Nissan Maximas and test them against yours. Surprise, surprise—the Maximas all perform at about the same speed! Based on these findings, you conclude that because your Maxima is so similar to all your test cars, it must also be similar to mine—even though you still don’t have any clue what kind of car I drive. Oh, and you also conclude that since your other car, a Toyota Celica, is faster than the Maxima, then it must also be faster than mine. Everybody okay with that?

I am sure Exponent had reasons for conducting their experiments the way they did, but that doesn’t change the facts. Essentially, all they did was compare Anderson’s non-logo gauge to dozens of other non-logo gauges. They all read similarly. So what? What does that prove about the Patriots’ gauge? Or the Colts’ gauge, for that matter?

One other thing. Anderson had two different gauges, logo and non-logo. If Exponent saw fit to go out and buy a huge pile of non-logo gauges, surely they did the same for the logo gauge, right?


Neither Exponent nor Paul, Weiss was able to procure exemplar gauges identical to the Logo Gauge. (Appendix I, page 14)

So they couldn’t find any. Another head-shaker. Apparently they don’t have access to eBay or Amazon! Look, I’m sure there’s an innocent explanation of why they couldn’t find any logo gauges. I just wish they would have shared it with us, instead of just a parenthetical comment. Again, you are accusing a four-time world champion of cheating. Your credibility must be beyond question—especially when you are relying on such shaky logic with the non-logo gauges.

Of course, all of this sample gauge stuff would be unnecessary if we could simply get our hands on the gauge that the Patriots used on the day of the game. If we had that, we could just get a few footballs, measure them with the Patriots’ gauge, then measure the same balls with the logo and non-logo gauges, and determine which one most closely matches the Patriots’ gauge (the same thing would work if we could obtain the Colts’ gauge). The actual game-day gauges used by the two teams are far more useful than a boatload of non-logo gauges with no connection to the game.

I’m no dummy, but I’m sure I am not the only one who sees the importance of the teams’ game-day gauges. Surely Ted Wells and friends put a lot of effort into finding them. Right?

I did an exhaustive search of the entire Wells Report, checking every mention of the word “gauge” (yep, I was there for a while). I found exactly one reference to the Patriots’ game-day gauge, on page 65, footnote 36:

We believe that [NFL Director of Game Operations James] Daniel located and used the pressure gauge supplied by the Patriots [to measure the football intercepted by D’Qwell Jackson]. We further believe that this is the gauge that [Patriots Equipment Manager]John Jastremski considers his normal gauge. It has not been located since the day of the AFC Championship Game. It should be noted that we have not relied upon the air pressure measurements of the intercepted ball in any respect in reaching any conclusions set forth in this Report.

So James Daniel finds the Patriots’ game-day gauge, uses it to measure the D’Qwell Jackson football, and then what? Did he leave it somewhere? Where? Did he give it to someone? Who? And why the oddly-worded “It has not been located since the day of the AFC Championship Game”? Has not been located by whom?

I searched the report again for any record of Ted Wells and his team attempting to locate the Patriots’ gauge. Nothing.

This gauge is a huge piece of evidence, crucial to anyone wanting to find out the truth—the actual truth, not a convoluted theory that guesses at it.  If the Wells team was searching for the Patriots’ gauge as earnestly as they should have been, if they were turning over every rock and seatcushion in Foxborough looking for it, they would have said so in the report—whether they ultimately found it or not. Instead, they only mention it once, and even then only in a footnote. Guess I shouldn’t complain, though—the Colts’ gauge isn’t mentioned at all.

I was disappointed, to say the least. The Patriots’ (or Colts’) gauge could have provided important insight, proof, maybe, of which gauge Anderson used before the game. In turn, we would have known exactly how much PSI was lost from the Patriots’ footballs, which would have brought us a lot closer to knowing whether or not the balls were tampered with. But no such luck. If only there was a documented measurement taken with the Patriots’ gauge that day…

At long last, I decided to put away my Wells Report hat for a while and take my family to Boston for the day. We were all contentedly gliding along in a swan boat, my mind focused only on the glorious sunshine streaming through the towering trees, the clear water, my beautiful wife and kids. And out of nowhere, it hit me.

There was a measurement taken with the Patriots’ gauge! Several, actually!

Look again at the footnote from page 65. The ball from the D’Qwell Jackson interception was tested by a gauge that Wells believes was the Patriots’ regular gauge. If we could find the readings from that test, we’d have an idea of how the Patriots’ gauge compares to the logo and non-logo gauges!

When I got home, I searched the Wells Report again. Paydirt!

From page 70:

The pressure of the Patriots ball that had been intercepted by the Colts was separately tested three times and the measurements—11.45, 11.35 and 11.75 psi, respectively-- were written on athletic tape that had been placed on the ball for identification.

With trembling fingers, I calculated the average of the three readings.


It's almost exactly the same as the Patriots' halftime logo gauge average of 11.49! The non-logo gauge average is only 11.11, significantly lower than even the lowest of the three readings of the Jackson ball. True, it’s only one football—far from an ideal sample size—but at least the ball was measured three separate times. And I’ll take three measurements with the Patriots' actual game-day gauge over Exponent’s sporting-goods-store-shopping-spree method any day.

At any rate, I don’t know what kind of gauge the Pats were using, but it sure as hell didn’t read like a non-logo gauge.

The measurements on the Jackson ball are amazingly high; seven of the 11 Patriot footballs actually measured lower than Jackson’s at halftime, even when using the logo gauge numbers. Nine Patriot footballs measured lower than Jackson’s when using the non-logo gauge figures. And I think you see where I’m going with this.

Based on the Wells Report’s own figures, and their own conclusions, the Patriots’ gauge was used to measure the Jackson football, and those measurements were, by far, more similar to the logo gauge than the non-logo gauge. Wells has the same information we do, and came to the opposite conclusion, based on logic that a middle-school student would reject. I’ve seen enough. I’m ready to call this one.

The only conclusion I, or any reasonable person, can draw is that Walt Anderson used the logo gauge for the pre-game measurements. This is based on four factors:

  1. Anderson’s own recollection is that he used the logo gauge. Yes, he agrees that he could be mistaken, but Anderson recalled many details from the period before the game, including specific measurements of certain footballs. Wells accepted all of Anderson’s recollections as accurate, except the one about which gauge he used.
    I don’t buy the story that Anderson remembered all the other major details about the pre-game gauging of the balls, but forgot what gauge he used, especially since the gauges look so different (one has a long, crooked needle and a Wilson logo; the other has neither of these features). If we’re using the “more probable than not” criteria that the Wells Report made famous, then clearly we should conclude that Anderson recalled correctly.
  2.  Measurements taken with the Patriots’ game-day gauge closely match the logo gauge. As stated above, the D’Qwell Jackson football was measured three times with the Patriots’ gauge shortly before halftime, and the average of the measurements was 11.52 PSI. The average of the other 11 Patriot footballs measured at halftime was 11.49 on the logo gauge, and 11.11 on the non-logo gauge. You don’t need a degree in math to see that the Patriots’ gauge read almost identically to the logo gauge, and not nearly as closely to the non-logo gauge. Given this similarity, if the Patriots’ pre-game measurement was 12.50 PSI, and Anderson was using the non-logo gauge to measure them, he would have found that the balls were far below 12.50. Instead, he reported that they were exactly at or near 12.50. The only way he could have gotten this result was if he was using the logo gauge.
  3. The Wells Report’s reluctance to discuss the teams’ game-day gauges. Wells goes into painstaking detail in certain parts of the report. For example (p.66):

    Blakeman sat on a chair placed against the back wall of the dressing area next to the ball bags (facing into the dressing room with the bags to his right), and Prioleau sat on a second chair to Blakeman’s left (facing the same way).
    Thanks, guys, for imparting this critical data on who was sitting next to whom, and what side the bags were on! What, aren’t you going to tell us what color shoes they had on?

    And yet, when it comes to the truly important evidence, like the gauges that each team used to prepare the footballs before the game, the report is inexcusably lacking. Had the teams’ gauges been tested as thoroughly as they should have been, we’d have ironclad insight as to what gauge Anderson used pre-game. This report was carefully written by a team of scientific experts, who work for a multi-million-dollar firm. I refuse to believe that they forgot this huge detail.

    Whether the gauges were found or not, whether they were available for testing or not, this report is grossly incomplete without a thorough discussion of them. The only motive Exponent could have for leaving the teams’ gauges out of the report is that the gauges didn’t support their theory.

    The Wells Report concluded that Anderson used the non-logo gauge. If the measurements from the teams’ gauges supported that idea, Wells and friends would have included this evidence prominently. Instead, they avoided the topic almost completely.
  4. Exponent’s logic does not support their theory. The experiments cited by Wells only prove that Anderson’s non-logo gauge is similar to other non-logo gauges. He does not prove, or even claim, that the Patriots’ gauge is a non-logo gauge. Therefore, these experiments are irrelevant.

Conclusion: Anderson used the logo gauge for the pre-game measurements. We need to explain a PSI loss of 1.01 for the Patriots’ footballs.

There is one matter left to discuss here: The Colts’ game-day gauge. I’m adding it after the conclusion, in case you want to skip directly to Part III. Read on if you’re interested.

Part II B: The Colts’ Game-Day Gauge

First and foremost, there are effectively no mentions of the Colts’ game-day gauge in the entire 243-page report. Nothing in the footnotes, nothing in the Exponent report.

In a sense, the Colts’ game-day gauge is just as important as the Patriots’ in trying to determine which gauge Anderson used for the pre-game measurements. This is because we know that the gauge Anderson used matched both teams’ gauges very closely. Take a look at this chart:

“The Similarity Effect”: Pre-Game PSI Readings from Referee Anderson and Both Teams

A 13.00 on the Colts’ gauge is a 13.00 on Anderson’s gauge. A 12.50 on the Patriots’ gauge is a 12.50 on Anderson’s gauge. In other words, both teams’ gauges read similar to Anderson’s.  And if both teams’ gauges are similar to the same thing, then they must also be similar to each other. Not to traumatize you with seventh-grade math, but:

If A = B, and B = C, then A = C.

Basically, using the above, we can conclude that the Patriots’ and Colts’ game-day gauges read similarly to each other.

Bottom line: if the Colts’ gauge matches the logo gauge, then the Patriots’ gauge matches it too. In the section above, we made a convincing case that the Patriots’ gauge matches the logo gauge, using actual measurements that were taken with each one. But look at this, from page 63:

The [Colts] intern used a digital pressure gauge similar to the gauge used by the Colts to set their footballs before the game, and reported that the pressure [of the D’Qwell Jackson football] measured approximately 11 psi.

Remember, the Patriots’ gauge was used to measure the Jackson ball just before halftime, and the three readings averaged 11.52 PSI. If the Colts’ gauge was used to measure the same ball, and only measured it at 11.00 PSI, we have a discrepancy—and a possible argument that Anderson used the non-logo gauge. After all, the average of the Patriots’ other 11 footballs at halftime was only 11.11 PSI on the non-logo gauge, and the 11.00 figure is much closer to the non-logo average than to the logo average.

I reject this argument for three reasons:

  1. The passage specifically states that the intern’s gauge was “Similar to the gauge used by the Colts”, not that it was the actual Colts’ game-day gauge. If we want to get to the truth of what happened, we need the actual gauges each team used. Not “similar” ones. 
    Yes, I am aware that the “multiple dozens” of non-logo gauges read similarly to one another, according to the Wells Report. But the chart in Appendix I, page 20 (reprinted below) shows that, while
    on average the sample gauges read similarly, individual ones varied as much as 0.65 PSI from one another. Specifically, a “master gauge” was set to 13.00 PSI and was read by 50 of the sample non-logo gauges. The individual gauge readings ranged from 12.55 to 13.20 PSI. In other words, there is no guarantee that two of the exact same gauges will read closely to one another. Besides, we don’t even know that they are exactly the same, just that they are “similar”. There are no further details in the report as to what that means in this context.

  2. The intern said that the measurement was “approximately” 11 PSI. He didn’t provide an exact measurement. “Approximately 11” could mean 10.90, or 11.10, or 11.39. Apparently this intern was not interviewed by the Wells team to provide more specifics, or if he was, it wasn’t discussed in the report. And if he was asked now, I’d be wary about his recollections. We’re more than four months removed from the incident.
  3. Three precise measurements were made on the Jackson football using the Patriots’ gauge. The readings were immediately written down on a piece of tape on the football. We are not relying on approximations, guesswork or memory for these measurements, and these measurements clearly indicate a similarity between the Patriots’ gauge and the logo gauge. I see no justification in throwing this conclusion away because of an estimate taken from a “similar” gauge that wasn’t even used for the preparation of the Colts’ footballs that day.

PART III: Is There a Legitimate Explanation for the PSI Losses in the Patriots’ Footballs?

Here we are, at the dramatic conclusion of our Wells Report odyssey. So far, we’ve determined the following:

  1. Walt Anderson used the logo gauge to measure the Patriots’ footballs before the game;
  2.  The Patriots’ footballs lost an average of 1.01 PSI between pre-game and halftime, as measured by the logo gauge.

Our goal now is to review any legitimate (non-tampering) explanations for a loss of internal pressure in a football, and to determine if those explanations are enough to justify an average loss of 1.01 PSI per football.

Let’s begin by reviewing the readings from the logo gauge, which, as we’ve already established, was (all together now) more likely than not used for the pre-game measurements. Notice that I’ve sorted the pressure readings from lowest to highest:

Again, many of us are not coming to this debate with an open mind and a desire to learn the facts. Many (most?)  of us know what we want or believe the truth to be, and ignore anything that does not confirm our pre-existing point of view. No one is neutral when it comes to the New England Patriots. In a league designed for parity, they’ve been on top for far too long. For better or for worse, they’re under a microscope. I get it. But please, as I introduce a theory or explanation, do your best not to reject it out of hand just because it’s against what you initially believed. Hear me out. Okay?

A case in point is the Ideal Gas Law. Prior to the release of the Wells Report, most of us had never heard of the Ideal Gas Law. Those of us who had heard of it knew that changes in temperature and moisture could easily cause a football to lose pressure when brought from a warm, dry environment (e.g., a locker room) to a cold, wet one (e.g., a football field where it’s raining heavily). It may seem like ancient history now, but getting people to believe this was an uphill battle. There was a lot of skepticism about this law. Many people simply covered their ears and said “La-la-laaaaaa” when confronted with the idea that anything other than a fat guy with a needle could cause a football to lose pressure. Now that it’s been put in writing in the Wells Report and agreed upon by all sides, we’ve apparently cleared that hurdle. Nonetheless, it’s a useful lesson. Keep your mind open, please!

From the Wells Report, Appendix I, pages 39-40:

…using the Ideal Gas Law, or variations thereof, different calculations can be generated on the basis of different assumptions about the starting pressure, and starting and ending temperatures of a football. For example, using the most likely pressure and temperature values for the Patriots game balls on the day of the AFC Championship Game (i.e., a starting pressure of 12.5 psig, a starting temperature of between 67 and 71°F and a final temperature of 48°F prior to the balls being taken back into the Officials Locker Room), these equations predict that the Patriots balls should have measured between 11.52 and 11.32 psig at the end of the first half, just before they were brought back into the Officials Locker Room.

Ah, so now we have our target. Given what we know about the locker room and field temperatures on game day, as well as the starting PSI, the Patriots’ footballs should have measured between 11.32 and 11.52 PSI at halftime. The report goes on to say (Appendix I, p. 40):

Once the game day measurements are converted into their corresponding Master Gauge pressures (in order to provide for a direct comparison with the results predicted by the calculations), the measurements for all but three of the footballs, as measured by both gauges, were lower than the range predicted by the Ideal Gas Law.

What’s a Master Gauge, you ask? Well, according to the Wells Report, it’s simply “A calibrated pressure gauge”. Going back to our bathroom scale example, imagine the Master Gauge as a super-accurate scientific scale which can tell you exactly how much you weigh, as opposed to your regular bathroom scale, which might be off by 3/10 of a pound or so.

The Wells Report was even kind enough to provide a formula to convert logo and non-logo readings to a Master Gauge pressure. I won’t torture you by reprinting it here, but if you’d like to take a look at it, it’s on page 28 of Appendix I.

Let’s take a look at the Logo and Non-Logo (non-converted) halftime readings from both the logo and non-logo gauges, to see how many fall into the expected range predicted by the Ideal Gas Law:

Halftime PSI Readings Compared to Expected Ranges
Green = within / above expected range, Red = below expected range

How interesting is this? Using the Wells’ Reports own calculations, only three of the Patriots’ footballs are below the minimum PSI level expected by the Ideal Gas Law on the logo gauge! What’s more, the three that are below this level are only short by 0.12, 0.32, and 0.42, respectively. Are we now saying that Jim McNally only tampered with three footballs, and even then only took tiny amounts of air out of each?

We’ll get back to this in a moment, but for now, I’m getting a bit ahead of myself. If we look at the non-logo side, it is true that all but three of the balls are below the range expected per the Ideal Gas Law. However, this is really just a case of Exponent’s previous mistake coming back to haunt them.

Exponent calculated the expected PSI levels using a beginning pressure of 12.50. But, as we’ve established at length, a 12.50 on the logo gauge is not a 12.50 on the non-logo gauge; it’s only a 12.12. With this corrected value in hand, let’s go to our handy-dandy Ideal Gas Law calculator and plug in the relevant figures. Once we do this, we find an expected PSI value of 11.05. There is a margin of error of +-.10 on this calculation, which means that our actual expected range is 10.95 – 11.15. Let’s take another look at the pressure levels using this range:

Halftime PSI Readings Compared to Expected Ranges
Green = within / above expected range, Red = below expected range, Yellow = less than 0.075 below expected range

Well, well, well. What do you know? Once we correct for Exponent’s logo / non-logo error, things look a lot more consistent! Yes, there are still four balls below the expected range on the non-logo side, but the four are only off by 0.05, 0.10, 0.25, and 0.45 respectively.

I couldn’t bring myself to use red for Patriots’ ball #11. Seriously, guys, if you want to use 5/100th of a pound of air as proof of cheating, you’ve lost me. The figures that went into these calculations were estimates based on best guesses of the conditions that day. They weren’t exact, and we shouldn’t assume that these target ranges are, either.

Another thing you may have missed: The logo and non-logo gauge readings always end in multiples of .05. Look again at the chart above. Every gauge reading ends in 5 or 0. I’m not talking about the averages now, just the readings. Clearly the gauges are rounding to the nearest .05—so for all we know, Patriots ball #11 might only be off by .03 or .04 instead of .05. At any rate, anyone looking for proof of football tampering will need to look elsewhere from ball #11.

Next, let's convert the halftime PSIs to the Master Gauge values, so we can check Wells’ conclusion that all but three footballs were below range on both gauges when using Master Gauge figures. This will be especially useful since, believe it or not, Exponent did not provide a table for these calculations in their report.

Halftime PSI Readings, Converted to Master Gauge Values
Green = within expected range, Red = below expected range

Well, I’ll be dipped in doo-doo and rolled in sprinkles! It’s just like the Wells Report said! Once we convert to the Master Gauge figures, all but three Patriot footballs are below the expected range per the Ideal Gas Law! On both gauges, no less!

Everybody say it with me now: CHEATERS! CHEATERS! BELICHEAT! CHEATRIOTS!

Let’s go round up a couple hundred friends, light some torches, smoke Tom Brady out of that fancy mansion of his, and teach him what the integrity of the game is all about!

…Actually, guys, you might want to slow your lynch-mob roll for a minute. Put your nooses down and take a deep breath.

I’m afraid Exponent has screwed up again.

Look back at the quote from Appendix I, pages 39-40 of the Wells report copied above. Exponent took a starting PSI of 12.50, plugged it into the Ideal Gas Law calculator (along with the other required information), and found a target PSI range of 11.32 – 11.52. They then compared that range to the figures shown above, and found that most of the Patriots’ balls were lower than they should have been. There’s just one teensy problem with this.

A starting PSI of 12.50 is not a 12.50 on the Master Gauge. It’s 12.17, per the Wells Report’s own formula. And if we plug that number into the Ideal Gas Law calculator, we get an expected range of 11.00 – 11.20.

Of course, if Exponent made this mistake on the logo side, they must have made it on the non-logo side as well. As we know, a 12.50 on the logo gauge is only a 12.12 on the non-logo gauge. And if we convert 12.12 to the Master Gauge, we get 12.08. Plug that into the Ideal Gas Law calculator, and we’re looking for a range of 10.92 – 11.12.

Now, let’s take another look at the table, this time using the correct figures for expected PSI. I also added the converted Master Gauge figures for you, since Exponent apparently forgot to do so.

Halftime PSI Readings, Converted to Master Gauge Values
Green = within expected range, Red = below expected range, Yellow = 0.075 or less below expected range

(click for enlarged view)

How do you like them apples? Once we correct Exponent’s starting PSI errors, the Master Gauge numbers agree almost exactly with the logo / non-logo numbers!

As a matter of fact, the Master Gauge is actually a bit more favorable to the Patriots than the logo / non-logo gauges are. The three footballs that are below expected limits are only off by 0.06, 0.25, and 0.35 PSI, respectively, on the logo gauge side. Remember, the non-logo gauge really isn’t too relevant, except for comparison purposes, since we now know that Anderson used the logo gauge.

So far, all we’ve had to do is fix the mistakes in the Wells Report, and there are only two Patriot footballs left that fall more than 0.075 PSI below the expected limits per the Ideal Gas Law. But we’re not done yet: We still have to explain why, on average, the Patriots’ balls lost more pressure than the Colts’ balls did.

Recall from our PSI loss table that the Patriots’ footballs lost an average of 1.01, while the Colts’ balls lost 0.35. Subtract one from the other, and we have 0.66 in unexplained pressure loss for the Patriots’ footballs. How could it possibly be that one team’s balls lost so much more than the other team’s, assuming that all other factors are equal?

Ah, but there is the problem… assuming that all other factors are equal. According to wellsreportcontext.com:
The Patriots had the football on offense for the last 4:54 of the first half (except for the last 9 seconds when Andrew Luck took a knee) — i.e., just before the footballs came in for halftime measurements, the Patriots footballs were being used while the Colts footballs were being held in trash bags. The Patriots ball boys did not use bags, thereby exposing the footballs more to the rain. 
This one simple statement, if true (and I’ve heard no one dispute it), blows the Wells Report’s assumptions out of the water. The Wells report decided that the Colts’ footballs could be used as a “control group”, meaning that they were exactly like the Patriots’ footballs in every way. Merely being in the same stadium and on the same field does not mean that every single condition is exactly the same for all the footballs. If one team’s balls are in a bag, dry and protected from the elements, and the rain is pouring down on the other team’s footballs, then obviously, the conditions aren’t the same, and we shouldn’t assume otherwise. Lower temperatures and added moisture cause additional PSI losses, and if the other team’s footballs are not exposed to those same conditions, then yes, one team’s balls will lose more pressure than the other’s.

This is not a zero-sum game. We don’t have to find one single factor to account for the whole discrepancy. My guess is, it was a collection of small things, including, for example, the timing of the measurement of the footballs at halftime.

As we all know by now, the officials brought all the balls to the locker room at halftime, developed a procedure to measure and document each football’s PSI with both of Anderson’s gauges, tested each ball individually, then refilled any that were below 13.00 and retested them. While all this was going on, the Colts’ footballs were steadily acclimating to the higher temperature in the locker room—and gaining PSI by the minute.

Per the Wells Report, the footballs were inside the locker room for a total of about 13.5 minutes during halftime. Also per the Wells Report (p.71), the measuring, refilling and retesting of the Patriots’ balls took between eight and 14 minutes (the latter of course is not possible, since the balls were not in the locker room for that long). This estimate breaks down as follows:

2-4 minutes to develop testing procedure
4-5 minutes to test pressure on 11 Patriot footballs
2-5 minutes to inflate Patriot footballs and recheck

Since, according to the Wells Report (Appendix II) it requires a maximum of 71 seconds for a man to take 13 footballs out of a bag, deflate them with a needle, then put them back into the bag, I’d say it’s more than plausible that two officials could check the pressure on four Colts footballs in one minute. This being the case, measurement of the four Colts footballs didn’t start until about 12 minutes into halftime.

This means that, as soon as two minutes after the start of halftime, Patriots balls were being measured—a full 10 minutes before anyone even looked at the Colts’ footballs. Certainly, both teams’ footballs were gaining pressure throughout their time in the locker room. And certainly, the Colts’ footballs gained more pressure than the Patriots’ did, simply because the Colts’ balls stayed in the locker room for far longer before being measured. This is not up for debate. The Wells Report agrees, but says, (p.43):

…the timing of the measurements taken during halftime of the AFC Championship Game does not on its own completely account for the difference in the observed average pressure drops between the two teams.

“On its own”, it does not “completely account for the difference”. So this means that it does account for part of the difference! But how much? We only need to explain a difference of 0.66 PSI here, remember, and if the timing issue accounted for, say, 0.50 of that, then no, it would not technically account for the whole difference. But it would account for most of it. How interested would anyone be in dishing out major punishments over a PSI discrepancy of 0.16?

The passage above really makes me think. Here we have a clearly-identified issue which undisputedly would cause a differential in PSI losses between the two teams’ balls—the exact kind of discrepancy we are looking for—and the Wells Report effectively says, “Well, yeah, but that doesn’t explain all of the difference!” Okay, fine—so how much of the difference does it explain? No matter how hard I look, I find no answer to this question in the Wells Report. Surprised?

Now that I think of it, I also can’t find a final tally in the Wells Report which shows exactly how much pressure was lost due to all known factors, and exactly how much pressure loss is left unexplained. As we’ve come to learn, when something obvious is missing from the Wells Report, there always seems to be a reason for it. In this case, I’m thinking that, once we deduct this timing differential, once we have a complete, honest final calculation, there won’t be enough of a discrepancy to justify any punishment. So Exponent left it out.

Having said all this, I still would really like to know exactly how much of a PSI loss discrepancy there was between the teams due to the timing issue. Let’s tackle that together—but before we do, there’s a bit of a problem with the way this entire issue is framed.

When the footballs were out in the cold and the rain, they were both losing pressure. When they were brought back inside, they were both gaining pressure. Because the Colts’ footballs sat for as much as 10 minutes longer than the Patriots’ did before being measured, they gained more pressure. Why are we all so sure the differences are due to somebody reducing the pressure in the footballs manually? Couldn’t the differences be attributed to one set of footballs gaining more than another due to natural causes?

With that in mind, here’s a little exercise I devised to find out how much pressure each team’s balls gained after being brought in to the locker room during halftime.
I started with what I know:

  • The footballs were on the field, where it was approximately 48 degrees, just before halftime;
  • They were then brought to a locker room, where it was between 72 and 74 degrees;
  • The footballs warmed gradually after being brought in;
  • If I know a starting (conclusion of first half) temperature, an ending (halftime measurement) pressure, and an ending PSI, I can use the Ideal Gas Law to determine the starting pressure of a football;
  • If I know the starting and ending pressure of a football, I can find out how much pressure each football gained after being brought in for halftime.
According to Appendix I, page 44, Figure 22, Exponent determined that the Patriots' footballs would have returned to their pre-game state of 12.50 PSI by the end of the 13.5 minute halftime period. Since the balls were checked in the shower area of the officials' locker room, which was 67-71 degrees, we can split the difference and assume that the balls were at 69 degrees after 13.5 minutes, for a warming rate of 1.56 degrees per minute.

As you can see in the table below, I assumed a starting temperature of 52.68 degrees for the first Patriot football, which was calculated based on the Wells Report's finding that measurements started within 2-4 minutes of the start of halftime.

Also according to the Wells Report, the measurement of the Patriots' footballs took 4-5 minutes, so I split the difference and assumed that it was 4.5 minutes. Also, Wells' estimate was that the refilling of the Patriots' footballs required 2-5 minutes. Normally, I'd split the difference once again and go with 3.5 minutes, but that would bring us to a total of 11 minutes, and I believe that the Colts' footballs were measured at the 12 minute mark, for reasons you will understand in a moment, so I went with 4.5 minutes for the refilling.

According to Appendix II of the Wells Report, a man can enter a bathroom, open a zippered bag, dump out 13 footballs, deflate each of them using a needle, then repack the balls and leave the bathroom in as little as 61 seconds. So I figure that, if a man can do all that in a minute, then surely two officials can check the pressure on four footballs in a minute too, since halftime was ending and they were in a hurry. I therefore assumed that the measurement of the Colts' footballs began at the 12 minute mark and continued for one minute, at which point the two officials packed up the balls and sent them back on to the field. This would match the Wells Report's contention that the balls were in the locker room for 13.5 minutes.

Of course, it is true that the temperatures are estimated, and I list the balls in order by number, even though weren’t necessarily measured in that order. What I was trying to capture is that the Patriots’ footballs would have had moderate gains, while the Colts’ gains would have been much larger.

Feel free to double-check any of my calculations using the IGL Calculator, making sure to use 48 degrees as a starting temperature, and the Est. Temp at Measurement value from the table for the final temperature.

Locker Room PSI Gains – Halftime

Interesting, no? Looks like our differential is right around the 0.66 we’re looking for!

I’m sure we could debate what the most likely temperatures were at each measurement. Of course, no one took the footballs’ temperatures before they measured them. But the one point we can all agree on is that the balls’ temperatures were rising slowly. We could also debate which balls were most likely to have been measured when.

The point is, if you’re a Wells supporter, you are now the one with a huge discrepancy to explain away. Can you tweak the temperatures and order of the footballs enough to make 0.59 go away? I doubt it—but please let me know if you can. Otherwise, I’d say this mystery has been solved.


  1. Mary Ann...oh, uhhh, sorry.

    Great read.

  2. The other thing that is nasty about the Colts balls as controls is that Exponent is forced to alter their calculations in order to make their experiments match the Colts balls.

    It happens in the Time & Temperature test, but I bet most people don't catch it.

    Look at the Ref locker room temps on the Time & Temperature graphs for Logo and non-logo. The first time they run it, for the non logo gauge, they have the starting temp at 71 or so, but when they run it the second time for the logo gauge they kept running into a problem. The Colts balls all kept up hitting their pressures way too soon. How did they fix it?

    They turned the Pats into misers that only put the heat on during the first half while no one is in the ref's locker room if the logo gauge was used. Pre-game temperature in their experiments? 67 degrees for the Ref's locker room, but at halftime it's 74 degrees. They had to do this to get their graphs to match the observed Colts balls pressures with the logo gauge.

  3. The other issue that nobody talks about is the temperature of the Colts' balls when they were first filled and measured. If they had been sitting outside in the bus for some hours they could have been colder at the outset than the Patriots' balls that were all kept indoors.

    1. Very good point. Wish there were some way to check that.

    2. If you're going to assume that breaking in the balls can heat them in excess of room temperature or that it only takes 15 minutes for the colts balls to get close to room temperature after the first half (neither of which I disagree with), it won't matter where they were before they were broken in, filled, and measured in the locker room.

  4. Great work. Short of suing NFL, Wells & his firm & Exponent, how does Brady get his reputation back? "Combating bias and general stupidity since the 1980s" -- this is such a huge problem.

  5. question, why disregard the Colts reading of our gauge being 11? Wouldnt that only further corroborate our reconstruction of the events? First it dispels the myth that the patriots gauge was perfectly in line with "all" other gauges. Secondly it demonstrates something VERY important, that it was possible the colts balls were actually measured with the non logo gauge while the Pats balls were measured with the logo gauge, something that was not dismissed as a possibility in the wells report. If the officials measurement was the same as each teams measurements of their own balls, and the Colts Gauge read much lower than the Pats Gauge, then the difference between both teams balls is even further debunked as being definitive proof of cheating. Please let me know if you understand what I am saying and if it makes sense.

    1. Are you talking about when the intern read the D'Qwell Jackson ball as "approximately 11" using a gauge that was "similar to the gauge the Colts used on the day of the game"? I actually discuss that in the post.

  6. Bravo sir. Can you say Perry Mason Moment? However, let's face it, ESPN will keep spewing whatever nonsense their partner in crime DICKtator ROG wants them to. One's a cheat and liar and the other partner has the platform to cover it up by poisoning the well, consistently.

    1. ESPN is a business more than a sports company. They are feeding the news appetite of the public at large, and unfortunately, the public at large hates the Patriots.But I truly believe that when the Wells Report gets a truly neutral hearing, it will be laughed out of court and eventually won't be taken seriously.

  7. The balls start at 12.5 for both gauges because they didn't know which gauge was used, only that the balls measured 12.5. The halftime measurements showed the relative change in PSI for each gauge from 12.5.

    1. True, they did not know which gauge was used, but the proper way to handle that was to show two scenarios, one in which the logo gauge was used pre-game, and one in which non-logo gauge was used. The way they built their table, one of the gauges was automatically wrong, and they make no mention of that.

    2. They did show two scenarios. In one, the logo gauge was used and the balls measured 12.5. They then compared the halftime reading of the logo gauge to the figure of 12.5. In the other, the non-logo gauge was used and the balls measured 12.5. They then compared the halftime reading of the non-logo gauge to 12.5.

      In both scenarios the balls have to start at 12.5 because that is the measure recorded. What is unknown is which gauge was used. There was one measurement before the game, but there were two at halftime. Both of the halftime gauges have to be compared to 12.5, not an adjusted amount that you came up.

      You cannot start at any figure other than 12.5. If the logo gauge was used before, it read 12.5. If the non-log gauge was used, it read 12.5. What the other gauge might have read before the game is immaterial. What you should be interested in is the relative difference for each gauge at halftime from 12.5.

    3. No, that's incorrect. The Wells Report shows only one scenario, and assumes one of the gauges is automatically incorrect, the logo gauge, which Walt Anderson actually remembers using. The gauges are not calibrated to each other, so a 12.5 on the non-logo gauge is actually a 12.88 on the logo gauge. In other words, a 12.5 on one gauge is not a 12.5 on the other gauge, so you cannot use 12.5 as the starting point for both gauges. While it's true either gauge may have initially measured the Patriots' balls at 12.5, they are not calibrated to one another. As a result, if the logo gauge was used to initially measure the balls at 12.5, then the non-logo gauge would have initially measured those same balls at 12.12. In contrast, if the non-logo gauge was used to initially measure the balls at 12.5, then the logo-gauge would have initially measured those same balls at 12.88.

  8. "Dr. Marlow agreed with Exponent‟s conclusions"

    Can someone get this to Dr. Marlow of Princeton University to see if he would still like to have his name backing this science?.

    Seems like it would be very bad for Princeton to be associated with this.

    1. I emailed a link to Dr. Marlow at Princeton and offered to speak to him by phone if he has any questions.

  9. Fantastic article. You clearly put a lot of work into this and did a great job.

    Although I think you should probably rename it to "Patriots are filthy cheaters, more proof surfaces" if you want to get people to actually read it.

  10. Great job!
    You convinced me. It is sad that a company like Exponent just do not understand about "most likely scenario" in a scientific deduction. Instead they rely on "more probable than not".

    It is even sadder that Wells believed from the bottom of his heart that there is a culpability, when it is probably driven by 20 million dollars cash into his pocket.

  11. Nice write-up!

    re: the third Colts measurement - I feel that it more likely that the extraneous value was not switched, but rather was mis-heard and therefore mis-recorded. It is not hard to see "twelve point one five" being heard as "twelve point nine five", but I having seen anyone consider this possibility. This would have lowered the Colts' averages and reduced the differential with the Patriots' balls.

    re: the balls heating up (and increasing in pressure) while in the locker room at halftime - Exponent attempted to correct for this by doing their own experiment to measure this. See figure 22 on page 204 of the Wells report. You could use this chart with your estimate of the measurement times to come up with an adjustment, rather than just guessing each ball went up one degree. Assuming their experiment is accurate, of course.

    1. I really need a time-track of how much the temp goes up by minute for this one. I'll try to tweak it a bit.

  12. Very, very detailed and thorough. Great job. Unfortunately most people don't have the brains or the time to understand what is being researched here.

  13. I really feel like Exponent did the test of "compare the drops in the Patriots' pressures to the drops of the Colts' pressures" because they could not look at the Patriots' pressures directly and conclude very much. They can conclude that the Patriots' footballs "lost" a lot more pressure than the Colts' balls did only by pretending that they were gauged at essentially the same time at halftime (that's what they do in Appendix A, which gives the super-low p-value).

    About Colts' ball #3: I strongly feel that there's a recording error there, for two reasons. 1) I can buy that the two officials swapped gauges between sets of balls. I find it very unlikely that they swapped gauges two more times, before and after Ball #3. I also find it nearly nonsensical for somebody to argue that, for one ball only, a person recorded the pressures in the wrong columns.

    It seems more likely to me that somebody, perhaps writing by hand, wrote a pressure we would expect for that value, i.e. 12.05 instead of 12.95. (That would be 0.45 psi less than the 12.5 value for the other gauge, a decline typical for the difference between the gauges.) And then later, when transcribing the values, somebody turned a '0' into a '9'.

    The second point is that 12.95 is way too high to be a credible pressure for a ball that was inflated to 13.0 psi before the game and had been sitting outside for two hours.

    1. I hear ya, but the reason I believed the transposing-numbers theory is because the difference between the two figures is 0.45--a difference we see frequently between the two gauges. Just seems unlikely that we'd get the exact same difference by accident.

      Very true that 12.95 is high--but remember the Colts' balls were in trash bags and it's possible that it wasn't used in the first half at all. Good evidence of how well-protected they were in that bag.

  14. Great work. Two more potential sources of uncertainty that could explain the pressure differences. First, Exponent's methodology for testing water-soaked balls lacks credibility - spray with a spray bottle and towel off. Other experimenters have seen larger differences in temps and pressures, which we explain through evaporative cooling. The second point, that no one else has made, is that the temperature that matters is that of the air inside the ball, not the outside air. The air temperatures were measured from a weather station on the top of the scoreboard. I would point out that after weeks of sub zero temperatures, the warm-up occured within 18 hours of game time. I think it is fully possible that the ground remained frozen, or at least significantly colder than the air at the top of the scoreboard, and with a bag of footballs lying on the ground, they could have cooled more. This doesn't explain the difference to the Colts footballs, but I think the timing issues - how much longer they were in the locker room in comparison to the Pat's balls, is more than adequate to explain away those issues. It is even possible that the rain was cooler than the air temperature - but some research makes me think this is somewhat less likely in the absence of strong convective air currents.

    1. Love this. Good stuff. Exponent made lots of bad assumptions that, if corrected, could explain the discrepancies.

  15. A couple comments: adjusting the starting psi for the non logo gauge is fine, you just need to be clear that it's still under the assumption that the logo guage was used pregame. All that adjustment is showing is that the non logo guage numbers also make sense if the logo guage was used pregame.

    Your tables list green as "in the expected ramge", but it is actually "above the minimum of the expected range". Several of the balls are above the maximum. That means they are not in the expected range. Though it does hurt the narrative that they were intentionally deflated: Perhaps the too high values can be explained if the assumed starting PSI for these balls was wrong and they were actually 12.7... The bad news for wells is that if something like this explains a few balls being too high, it could also explain a few being too low.

    1. You are right, I probably should have said "at or above expected range". Obviously, no one is accusing them of INflating balls above the limit, so this means we are in the margin of error and/or the balls weren't exactly 12.50 as you said. Margins of error go both ways and the phrase "Margin of error" does not appear in the Wells Report at all. Surprise...

  16. Oh, forgot one final thing: there's an error in the numbers here

    "And if we convert 12.12 to the Master Gauge, we get 12.08. Plug that into the Ideal Gas Law calculator, and we’re looking for a range of 11.92 – 12.12."

    That range should be 10.92-11.12.

  17. Replies
    1. The other "answered unanswered question" in the report (if anyone cares to look): If Wells interviewed ~65 people and took one full day for each interview (which is highly unlikely), then there were ~35 days remaining to write the report. Goodell announced that the investigation was complete, and the report was now being written. 24 hours later, the 243 page report was released to the media. In the report, the Exponent Report is dated the same day as the Wells Report. Both documents were final on the same day. Therefore, both reports must have been written in parallel during the ~35 days available to Wells, Exponent and the NFL league office. The information in the report confirms that Wells worked together with Exponent and the NFL for ~35 days prior to publishing the "independent report".

    2. Great read. The other "answered unanswered question" in the report (if anyone cares to look): If Wells interviewed ~65 people and took one full day for each interview (which is highly unlikely), then there were ~35 days remaining to write the report. Goodell announced that the investigation was complete, and the report was now being written. 24 hours later, the 243 page report was released to the media. In the report, the Exponent Report is dated the same day as the Wells Report. Both documents were final on the same day. Therefore, both reports must have been written in parallel during the ~35 days available to Wells, Exponent and the NFL league office, and the information in the Wells Report confirms that Wells must have worked together with Exponent and the NFL for ~35 days prior to publishing the "independent report".

  18. WOWZAH!! reading all the comments have pretty much covered everything I would have said. Maybe not the second checking of math but you know what I mean. Great work. You need to print this off and send a copy to 1 Patriot Place, Foxboro MA and one copy to the Law Offices of Winston & Strawn c/o Mr. Jeffery Kessler. Again, nice work!!

  19. Nice analysis. I think one thing that is highly suspicious in the Wells Report is the section on p. 26 of the Exponent part, "The Effect of Human Factors on Gauge Accuracy".
    The conclusion is that human error does not exist (last paragraph of section).

    The come to this conclusion by taking 11 balls, setting them all to the exact same pressure (as determined by the Master Gauge), and then having 5 different people measure the pressure of each ball using the non-Logo gauge. They reset the pressure of each ball between measurements.

    Now, the standard deviation of the non-Logo gauge was determined to be around 0.12 psi (see Fig. 8 of Wells report). So whatever average pressure reading these test balls gives, the result should be mean +/- standard deviation. In this case the SD is 0.12, so the result should be mean +/- SD.

    However, this is the conclusion of the Wells report:
    "All of the readings generated by all five individuals and all 11 footballs were within 0.05 psig of each other, which is equivalent to the reading resolution of the Non-Logo Gauge (as well as the Logo Gauge)."

    In short, the Wells' report experiment was able to produce 55 readings on 11 balls done by 5 different people, and each reading was within 0.05 psi of each other.
    How can this be when the equipment used in the test did not have that kind of precision?
    Remember that standard deviation has this rule:
    68.2% of readings are within 1 SD
    95% of readings are within 2 SD
    99.7% of readings are within 3 SD.

    Thus, with 55 readings, you would expect the following distribution:
    38 balls within 1 SD (+/- 0.12 psi)
    15 balls within 1 and 2 SD (between +/- 0.12 and 0.24 psi)
    2 balls within 3 SD (between +/- 0.24psi and 0.36 psi).

    Remember these ranges are +/-, so +/- 0.12 means the readings have a range of 0.24 psi. But the Wells report states that their 55 readings are all within 0.05 psi. This is impossible. I don't know how they were able to obtain such perfect data.

    You can reverse estimate the SD of the data the Wells report produced. Essentially, they came to a mean +/- 0.025 psi (range of 0.05 psi). If you assume that at least 1 or 2 balls are within 3 SD, then you can divide that 0.025 psi by 3 and get a SD of 0.008 psi. If you want to be conservative and say that by chance all 55 readings were within 2 SD, then you can drop the estimated SD fo 0.0125 psi.

    Somehow, using a gauge that has an SD of 0.12 (from their own calculation), they were able to obtain readings on 55 balls with an SD of, at worst, 0.0125 psi. It appears that suddenly, when testing for human error, not only was human error non-existent, the gauge precision increased 10-fold.

    Can anyone explain this?

  20. The whole thing is ridiculous. The Wells report tried to assign a level of accuracy and precision to this analysis that just doesn't exist. The intercepted football had a spread of 0.4 PSI on 3 measurements using the same gauge! Measurement error alone invalidates the assumption that every ball was at exactly 12.5 PSI for the Pats of 13 PSI for the Colts regardless of which gauge was used. To drag someone's name and reputation through the mud as well as levying such harsh penalties on both Brady and the team based on such shoddy science is despicable.

  21. Thanks for taking the time to write this all out. I'll have to spend some time looking it over more carefully. But skimming through it, I thought there might be a quicker route to showing that there was no tampering. In Part II, you quote p. 70 of the Wells report:

    The pressure of the Patriots ball that had been intercepted by the Colts was separately tested three times and the measurements—11.45, 11.35 and 11.75 psi, respectively-- were written on athletic tape that had been placed on the ball for identification.

    Then in Part III, you quote Appendix I, pages 39-40:

    For example, using the most likely pressure and temperature values for the Patriots game balls on the day of the AFC Championship Game (i.e., a starting pressure of 12.5 psig, a starting temperature of between 67 and 71°F and a final temperature of 48°F prior to the balls being taken back into the Officials Locker Room), these equations predict that the Patriots balls should have measured between 11.52 and 11.32 psig at the end of the first half, just before they were brought back into the Officials Locker Room.

    So doesn't this mean that the Colts measurements of between 11.34 and 11.75 were pretty much the same as what the balls should have measured with no tampering -- between 11.32 and 11.52?

  22. Great article: I had reached the same conclusion that you did in part three about the fact that the half-time measurements of the Colts and Patriots balls were reported as if they were measured at the same time and were identical as to their wet/dry factor. Some of those factors were studied by Exponent. Those references are included below.

    The Difference in PSIs at Halftime

    It has been reported in several outlets that the league considered the “smoking gun” in this case to be the difference between the Patriots balls and Colts balls at half-time of the game. If you accept as true the Wells Report conclusion that the gauges were switched between measuring the Patriots and Colts balls, and that one of the readings for the Colts balls was reported backwards then the non-logo gauge (which the Wells Report treats as the more accurate (and lower) gauge), the average PSI for the Patriots balls was 11.1 (or 1.4 below the assumed 12.5 starting point), and the average PSI for the Colts balls at 12.325 (or approximately .7 below the assumed 13.0 starting point). This difference (a 1.4 drop for the Patriots, as compared to the .7 of the “control group” Colts balls), as I understand it, is the basis for the conclusion that science cannot explain the drop in pressure for the Patriots balls.

    (continued below)

  23. (continued from above)

    The 10 Minute Difference in Measuring

    One of the interesting facts that came out in the Wells Report in Context rebuttal that is not accounted for in the above comparison is that there was an approximately 10 minute delay between when the Patriots balls were measured at half-time and when the Colts balls were measured at half-time. Of note, despite carefully laying out the timeline of half-time events, the Wells Report is very ambiguous about the timing of events. One might even conclude that he is misleading as to the order of events since when he discusses the amount of time each event took since he references measuring of the Colts balls before referencing inflation of the Patriots balls despite the fact that it now appears that the Patriots balls were inflated before the Colts balls were checked (see page 70 of the Wells Report). The important part here is that the Patriots balls were measured in the first 2-6 minutes of entering the Locker Room while the Colts balls were tested at the very end (recall that the officials ran out of time so only checked four Colts balls).

    The Wells Report ran game day simulations that took this supposed timing into effect. Using the non-logo gauge assumptions so as to be consistent (and to keep with Wells’ assumptions), these tests showed that the Colts balls would be expected to be around 12.38 at the end of half time. This is quite close to the actual 12.325 average for the Colts balls. As to the Patriots balls, under the Exponent game day simulation, measurements in the first 3:00-7:00 minutes for the Patriots showed an expected PSI of approximately 11.5. This amount is approximately .4 PSI above where the Patriots balls were based on the actual game-day measurement average of 11.1. See pages 57-59 of the Exponent report for these calculations.

    The Wet/Dry Condition of the Balls

    The timing test run by Exponent, however, did not take into account the relative wetness of the Colts and Patriots balls. The Wells Report in Context rebuttal pointed out that the Colts balls were being kept in bags while the Patriots ball boys were not keeping the Patriots’ balls in bags. In addition, with the exception of an Andrew Luck knee at the end of the half, the Patriots controlled the ball for the last 4:54 of the first half, a time that included three time-outs and the two minute warning (as I understand it approximately 15 minutes in real time). Thus, it would be expected that the Patriots balls were largely in use during this period and getting wet, while the Colts balls were not. The Exponent report addressed the effect that a wet ball has on PSI and determined that it has an effect of about .3 PSI. See pages 60-62 of the Exponent report. This would reduce the expected PSI for the Patriots balls from the 11.5 reference in the section above, to 11.2, or only .1 above the actual game-day measurement average of 11.1.

    1. Exactly--pages 68-9 of the Wells Report has three paragraphs on the timing of the halftime events. Paragraph 1 begins "the Patriots' balls were measured first". Paragraph 2 begins "The Colts' balls were ALSO measured" (emphasis added). Paragraph 3 beings "The officials ALSO reinflated the Patriots' balls". They write the events in that order which clearly implies that that is the order in which they happened. But they were very careful not to say, "after they measured the Patriots' balls, they measure the Colts' balls. Instead we get this "also" crap.

      How's this:
      "I went to grad school."
      "I also went to middle school."
      "I also went to nursery school."

      Does that mean I went to nursery school at age 24? :D

    2. Good call on the moisture issue. None of those Ideal Gas Law predictions should be taken as exact, because they don't take moisture into account whatsoever, and it was pouring down rain that day. Exponent assumes that the Colts' balls are a "control group", as I mentioned, which assumes that all conditions are 100% equal between the two groups. That is far from true. The mere fact that you're using three (or even four) Colts balls vs. 11 Patriots balls blows that theory up.

      This sample size business is an important point. We aren't looking at a full set of Colt footballs. We're looking at THREE of them. If that's the case, I could pick, oh, say, Patriots' footballs 1, 6 and 7 and get an average pressure loss of 0.48 (0.47 on the non-logo). Compare that to the Colts' pressure loss of 0.35 and we're off by 0.13, and not having this conversation.

      Also a fail for Exponent using the non-logo gauge for their experiments. We proved here it was logo.

    3. This comment has been removed by the author.

    4. Exponent's report is filled with this kind of crap... they estimate the conditions that existed that day, assume that everything between both sets of balls is completely equal, then they find a tiny fraction of a PSI that they can't explain, and they assume cheating. It's utter BS.

  24. Brady and the Pats were punished for "conduct detrimental to the integrity of the NFL" by plotting to circumvent league rules, apparently over a long period of time. Brady might have cleared this up by cooperating with the investigation, but he chose not to. The NFL was left with a preponderance of evidence - "it more likely occurred than did not" - of a conspiracy to defraud.

    Said the NFL: "The evidence gathered during the investigation and reviewed in the report more than satisfy this standard (a preponderance of the evidence) and demonstrate an ongoing plan by at least certain Patriots' employees to deflate footballs, to do so in a secretive manner after the game officials have certified the footballs as suitable for play, and to hide these activities even from their own supervisors."

    This post is completely beside the point. The punishment is warranted regardless of whether the infraction occurred or did not occur by small fractions of psi. As a Miami Heat fan might say, "Good job, good effort."

    1. How exactly is it beside the point that the Wells Report commits major errors and uses faulty logic to arrive at erroneous conclusions? On what planet does that not matter? Need I even say it: The NFL has no case! So no, a crime did not "probably occur". Quite the opposite.

      Because there is no credible scientific evidence of wrongdoing, there is ipso facto no crime. Would you accuse someone of arson if you were unable to find the burned building?

      Oh, but wait, the NFL says that the "evidence more than satisfies the standard"! Oh, really? Why didn't you say so? In that case, by all means let's hang 'em high!

      Because the NFL says it's true, it must be so. The NFL, which brought you "No one here saw the Ray Rice video"... is that the NFL you're referring to? The one whose commissioner was found by a Federal judge to have abused his authority in the Rice matter, and who was found by former commissioner Paul Tagliabue to have selectively enforced league rules in the Bountygate case? THAT NFL?

    2. Oh and btw, as to Brady not handing over his cell phone--I support this 100%. Brady is an active figure in the players' union. It's easy to believe that there was some union business being discussed his phone, by text or otherwise. So yeah, I'm sure the league would love to get their hands on it.

      "But we offered to have Brady give us just the relevant text messages," Wells says. "He could have excluded whatever he didn't want us to see."

      Sure, because this would have silenced the critics. If Brady had, say, 100 text messages on his phone, and offered to show messages 1-50 to Wells, Wells (and anyone else) would just switch their rallying cry from "What is Brady hiding on his cell phone?" to "What is Brady hiding in those last 50 messages?". Suddenly, we'd all be focused on those 50 messages, convinced they contained the smoking gun. Nothing short of full disclosure would satisfy the angry mob, no matter how unfair or unprecedented such disclosure would be.

      Secondly, why should Tom Brady or anyone else trust the NFL, when one unauthorized leak after another was coming from the NFL offices during this investigation? What level of confidence should Brady have that his information would be kept confidential? Not only did the NFL not keep this investigation confidential; they leaked incorrect stories to the media! Once they got hold of Brady's phone, they could say pretty much whatever they wanted. They could say they found evidence that Brady killed Tupac, and to the scandal-hungry public, it would instantly become truth. So no, neither Tom Brady, nor anyone in his right mind, would have turned over a private cell phone, or any of the information contained therein, to Ted Wells.

      By the by, Brett Favre refused to turn his cell phone over to the NFL when he was being investigated. He was fined $50,000. No suspension, no draft picks. And no one thought that was too lenient.

      Oh and lastly, when Robert Mueller was investigating whether anyone at the NFL had seen the Rice tape, many NFL employees turned over their cell phones to be examined. Their WORK cell phones. Because, you know, if you were conspiring to obtain evidence illegally from law enforcement agencies, of course you'd use your office phone to do that. Guess how many PERSONAL cell phones Mueller examined during his investigation. No really, I want you to guess.

      Hint: It's less than one. And it's not a negative number.

    3. That before getting into the absurdity of the use of a legal term to imply that there's criminal activity going on here. The upshot of this is that Pete Carroll is now "defrauding" the NFL by being "generally aware" of his team's PED issues. Oh, and then they've actually admitted in interviews that they set out to commit defensive penalties on every play from scrimmage in order to get around the rules. I guess Carroll should be gone for the season for "defrauding" the NFL?

      Don't worry, when he looks to see if you responded he'll give you a long response as to why this is completely unique and no other rule violations can be considered "defrauding the NFL". He'll also skirt the issue of why the NFL is entitled to non-work related texts and emails to third parties contrary to labor law and the NFL's shop law.

  25. Oh and lastly, when Robert Mueller was investigating whether anyone at the NFL had seen the Rice tape, many NFL employees turned over their cell phones to be examined. Their WORK cell phones. Because, you know, if you were conspiring to obtain evidence illegally from law enforcement agencies, of course you'd use your office phone to do that. Guess how many PERSONAL cell phones Mueller examined during his investigation. No really, I want you to guess.

    Hint: It's less than one. And it's not a negative number.

    In fairness Mueller's job was the same as Wells', to exonerate the NFL. So there was zero reason for Mueller to produce anything incriminating. Wells' job was to tar Brady and Gostkowski, which was how poor Ghost ended up in the Wells Report despite his entire involvement in the day's events being the question "Hey, what happened to kicking ball #1?" Oh yeah, it was stolen by an NFL employee.

  26. Brady and the Pats were punished because the evidence suggested they tried to break the rules. Whether or not they actually broke the rules just doesn't much matter.

    1. Nope. No evidence suggests this that I know of. Can you point me to this evidence? I'm looking for a piece by piece list of any evidence that hasn't been completely discredited.

    2. How does the evidence suggest "they tried to break the rules"? The evidence in the Wells Report actually exonerates Brady and the Pats. And, the text messages the NFL has are based on nothing more than speculation, assumption, conjecture, and they're taken completely out of context.

      Wrap your head around this for some context. The text message from Jim McNally to John Jastremski that says "deflate and give somebody that jkt" was from November 30, 2014, when the Pats were @ Green Bay. McNally does not travel with the team and Jastremski does not have access to the balls at away games, as the home team brings the balls to and from the field. Look what Jastremski is doing on TV, just before halftime (see link); he's on the sideline looking inflated in his jacket and he's also holding a jacket. It's highly plausible that "deflate" does in fact refer to losing weight / muscle mass.


    3. "It doesn't matter that they didn't break the rules because there was a nefarious conspiracy!!!!!!!"

      Good luck with that.

      The real problem is your fallacious reasoning, you're starting with the conclusion and trying to make everything fit it. When it absolutely doesn't fit you're getting sniffy. The NFL's arguments here are so transparently terrible that the only people fooled by them are those determined to fool themselves. The NFL has Brady's work related texts, which is more than they ever got from Favre. And Favre was fined $50k, despite having committed actual breaches established workplace law (sexual harassment is a civil violation and legally actionable, unlike this case).

      When will we see your angry diatribe about the Seahawks "defrauding" the NFL? How about Aaron Rodgers? Unlike Brady Rodgers actually admits tht he tries to circumvent the rule. So that's "defrauding" the NFL, no?

  27. This tour d'force clearly explodes the Wells Report's inaccuracy but the public would rather listen to text messages taken out of context. Furthermore, they would have difficulty with the math. If the Wells report did not accept the Ideal Gas Law, I am sure they would still be trying to discredit that. That's why Brady will have to take this to Civil Court after the Goodell "fair" hearing of his appeal.
    If the NFL was so interested in investigating the psi of the balls, they should have gauged them again after the game.
    If Goodell is so interested in the integrity of the game, why did he ignore the violation that the Colts' intern gauged the balls? Why didn't the Wells Investigation grill that intern for four days and then ask for more time the way they did McNally? Why can Aaron Rodgers admit he tries to violate the rule and the NFL says nothing? How can they hold it against Brady for not giving up his phone when Favre didn't. So many questions and such a long time before they will be asked at a fair hearing.

  28. I couldn't have said it better myself. This report proves nothing and it will be a sin if Brady is punished at all. What a farce!!

  29. As pointed out by sharp eyed commentators, there is probable than not fraud in the Wells report. This issue should be looked at. Specifically, Wells reports reproducible psi accuracies that are unbelievable and also presents the assumption that the original psi’s were either consistently 12.5 or 13 ignoring almost certain measurement spread due to human and gauge variability. Please consider the range of the intercepted ball which was measured three times : 0.4 psi range, values of 11.45, 11.35 and 11.75 psi, mean of 11.52, SE= +/- .12 psi. This was the only ball measured multiple times with the same gauge by the officials. This much more realistic spread of measured values in is stark contrast to Wells’ assertions of relatively tight consistent reproducibilities of within .05 psi. It should also be noted again that not only were the initial pressure values not recorded, but the gauges used on game day had most probably not been calibrated immediately prior to use, therefore rendering the data useless.

    1) The Wells report does not accurately address issues affecting pressure such as temperature, time and effects of game realistic ball handling, evaporative cooling due to cold wet saturated balls, preparation of footballs with attendant effects upon multiple variables, etc. Also e.g., the times of recorded measurements during game day are not reported, nor is the sequence of measuring and filling footballs reported, thus obscuring the likely reinflation of the Colts’ balls due to warming. The data is useless. Garbage in garbage out, the statistical analyses of imaginary numbers is just that: imaginary.

    The data in the Wells report is slanted crap, the analysis is crap and the conclusions are crap. Not only that, but the whole treatment of data in the Wells report would probably form a basis to make an accusation of malice in any defamation court case, along with Wells outright lie that he had direct evidence of Brady’s guilt.

    All of the pressure experiments reported in the Wells report need to be reproduced by an independent body. Also, the graphs need to be conventionally depicted showing error bars and expanded y axes of pressure. Showing graphs with scrunched y axes of pressure and without showing error bars of the logo, non-logo and master gauge pressures is deceitful. In fact, I believe that if the error bars were shown in a conventional graph it would be immediately further apparent that Wells analysis is incorrect and duplicitous.

    Also, the Wells report claims “thousands” of measurements were taken with these gauges probably leading to drift observed in measurements. Really? Thousands of measurements each with the logo and non-logo gauges? Yeah, sure. Wells probably means measurements made by all of the gauges tested including all of the irrelevant gauges used. More duplicity. What else is new?

  30. I was wondering why nobody had mentioned colts ball #3.I thought initially it was due to misread,misreport or misprint.never considered they swapped columns,assumed 12.95psi was 11.95psi.