Friday, June 5, 2015

Logo vs. Non-Logo Matters. But It Doesn't.

So there I was, going on and on about Logo vs. Non-Logo, thinking myself so incredibly clever for proving that Anderson used the Logo Gauge for the pre-game measurements. I pretty much did everything but put a gold medal around my own neck and hum the Star-Spangled Banner. But guess what I realized as I was driving home today?

It doesn't matter.

Let me explain with an analogy.

You have two bathroom scales. After a week of dieting, you weigh yourself, and according to Scale #1, you lost three pounds; according to Scale #2, you lost four. Obviously, you didn't lose three pounds and four pounds--so what happened? How can the scales tell you that you lost two different amounts of weight?

The answer is pretty simple and boring: The scales read differently. That's it.

Of course, you've only lost one true amount of weight. Yes, the scales show different numbers, but there is just one actual amount.

Now, let's say you get your hands on a super-accurate scientific scale (We'll call it the "Master Scale"). After an hour or two in full geek mode, you discover that the readings from each of your two bathroom scales can be converted into Master Scale readings using mathematical formulas.

So you plug the before and after readings from each scale into your formulas, and you find that your true weight started at 151.4 and ended at 148.1, for an actual weight loss of 3.3 pounds. And guess what? After the formulas are applied, the actual weight loss is the same, no matter what scale you look at!

Now, just substitute Logo Gauge and Non-Logo Gauge for Scale #1 and Scale #2 respectively, and Master Gauge for Master Scale, and you've got it.

In my post, I say that "[T]he 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)." We still need to know which gauge Anderson used before the game, of course, because this tells us the starting point for our calculation, but once we know this, the gauge we use doesn't matter in the slightest.

How about a little Excel porn to illustrate?

Halftime PSI Losses, Adjusted to Master Gauge Values
(click for enlarged view)

Look at that! As long as we adjust the starting PSI to reflect the discrepancy between the two gauges before applying the formulas, our Logo / Non-Logo Master Gauge losses are almost identical! But as you can see, the two figures aren't exactly the same. Why not?

Take another look at the Non-Logo Gauge's Starting PSI column. We reduced the 12.50 by 0.38 to adjust for the gauge discrepancy between Logo and Non-Logo--the average gauge discrepancy. The actual discrepancies varied from 0.30 to 0.45 during Exponent's study; the average is just a way of approximating that. And like all averages, it's close, but not exactly right 100% of the time. Nonetheless, the Non-Logo gauge average only differs from the Logo average by 0.03, a minuscule amount.

The bottom line here is that, no matter which gauge you are looking at for the halftime measurements, we see an average PSI loss of between 0.97 and 1.00 PSI on the Pats' footballs. The range is so tiny, and I'm in such a generous mood, that I'll even err on the side of caution and call it an even 1.00. To put it another way: The Patriots' footballs lost an average of 1.00 PSI between pre-game and halftime, regardless of which gauge measured them. Period.

And now for the obvious question: Why didn't Exponent figure this out?

Exponent used a Master Gauge in their report. They developed the conversion formulas. And then, after all that Stephen Hawking-level work, they didn't use their own formulas to figure out exactly how much pressure the Patriots' footballs lost. Accident?

The Master Gauge formulas would have provided a solid starting point for any serious study of actual pressure losses. Instead, Exponent attempted to convince us that Anderson used the Non-Logo Gauge, so they could in turn sell us the scary-looking data that went along with it--data that, we now know, is incorrect. Exponent told us that, on the Non-Logo Gauge, the Patriots' balls lost 1.39 PSI, and that on the Logo Gauge, they lost 1.01. The 1.39 reading is misleading and just plain incorrect--but it looks more scandalous, so it was used in the report.

Another interesting finding: The Logo Gauge PSI loss of 1.01 PSI is almost identical to the Master Gauge figure of 1.00. Clearly, the Logo Gauge is a lot closer to a calibrated gauge, and therefore more accurate, than the Non-Logo gauge. Hence the wishy-washy Wells Report wording we find on page 43:

"It was shown by our experiments that the Non-Logo Gauge was relatively accurate in an absolute sense when compared after the fact against the known calibration of the Master Gauge."

Oh really, bro? Was it relatively accurate? I bet your wife is relatively pregnant, too! How many millions did the NFL pay you for this report, again?

In case you want more of an explanation as to why Exponent is so Non-Logo Gauge crazy, check this out, from page 113 of the Wells Report:

"...the Ideal Gas Law predicts that the Patriots balls should have measured between 11.52 and 11.32 psi at the end of the first half, just before they were brought back into the Officials Locker Room. Most of the individual Patriots measurements recorded at halftime, however, were lower than the range predicted by the Ideal Gas Law."

Twenty-two individual measurements of the Patriots' balls were taken at halftime (11 balls were measured once each by the Logo and Non-Logo Gauges). Now, technically, it's true that half of the 22 measurements were below 11.32 PSI, and I guess you could interpret 50% as "most". But eight out of those 11 were from the Non-Logo Gauge, which, as we've already established at length, was not used for the pre-game measurements and is not relevant. Only three of the low measurements came from the Logo Gauge, and they are only off by an average of 0.29 PSI--including one football that was short by just 0.12, which is roughly the amount of air released when a bumble bee farts.

Halftime Readings Compared to Minimum Expected Range Per Ideal Gas Law
Green = within / above expected range, Red = below expected range

Summary of Halftime Readings Compared to 
Expected Range Per Ideal Gas Law

Get it? they had to add the ominous-looking Non-Logo numbers to make tampering seem plausible. If they only looked at the real (Logo Gauge) numbers, eight of 11 footballs would be within the expected range. These numbers strongly suggest that no tampering occurred, and we aren't even taking moisture into account yet!

The Ideal Gas Law only deals with pressure and temperature--not moisture. But moisture causes footballs to lose pressure, too--significant pressure. Even if a football has not been tampered with, and would otherwise be in the acceptable range per the Ideal Gas Law, the moisture would force it lower. Exponent merely points to readings that are "too low" and never acknowledges moisture as a possible cause.

Figure 26 (Appendix I, page 53) of the Wells Report shows that wet footballs would have lost about 0.40 PSI on the Logo Gauge due to the moisture that day (this comes out to 0.38 on the Master Gauge). Let's see what happens if we simply add this amount to the halftime readings:

Halftime Pressure Readings, Adjusted for Pressure Lost Due to Moisture 
Green = within expected limits, Red = Below expected limits

Whoa! I haven't seen this much green since The Sound of Music! All we had to do was add back in the pressure that was lost due to the heavy rains that day, and every single ball falls easily at or above the expected pressure range. Every single one. Are you still wondering why Exponent neglected to mention this?

How did Wells handle this little problem? He employed some L. Ron Hubbard-style logic to convince us that Anderson used the Non-Logo Gauge before the game, and then simply avoided adding the "moisture factor" to anything.

The Wells Report pushed the Non-Logo Gauge scenario because the numbers from that gauge help Wells' case. But we've now proven that the Patriots' footballs lost an average of 1.00 PSI, regardless of gauge. The fact that Wells is pushing one gauge over the other tells us that they either don't know what they're talking about, or they do know, and are hoping we don't figure it out.

Exponent spends a great deal of time building their Non-Logo case, and I'm way too cynical to believe that they were mistaken and that it was just a coincidence that they were so wedded to an angle that made the Patriots look guilty. If a scientific research firm gives in to ulterior motives like this, they have forever lost their credibility as far as I'm concerned, and I wouldn't trust them enough to read a digital clock for me.

And in the unlikely event that these were all honest mistakes, they should fare no better. If Exponent cannot be trusted to reach logical conclusions in a critical case such as this one, how can anyone have the confidence to act on their findings?


  1. Or, it simply just doesn't matter. We don't need to determine which gauge was used, or convert to a master gauge or anything nearly that eye-glazing to the average person. Because, even if we assume the worst case scenario as presented in the report at face value, it's still only a loss of 2.8% pressure, 0.32 psi, compared to what is predicted, if we only account for temperature change.

    A loss that small would have no effect on the performance of the football, none; it would be pointless. So, even taking the most extreme case possible at face value, there's no reason to think the Patriots footballs are anything other than what you would expect them to be: normal footballs used normally in a normal game.

  2. The only text I have trouble with is 10/17, where "Tom sucks" from McNally is responded to 1 min 23 sec later with "Talked to him last night. He actually brought you up and said you must have a lot of stress trying to get them done..." and they
    deny the response refers to Tom and get into a story about selling tickets. Really??? How about just stress getting the refs not to overinflate them? Seems a little odd to introduce a new party immediately in response to a reference to TB.

    1. What the Wells Report in Context says is that when texting, Jastremski has a habit of referring back to earlier conversations. They even offered to show proof of this and Wells wasn't interested.

      I think this may have to do with selling tickets on eBay or StubHub. You can get a lot more than face value if you sell tickets there, but #1, it's against Patriots' policy to do this, and if they catch you, you can have your season tickets revoked, and #2, if you don't sell them before kickoff, you're pretty much stuck with them and can't sell them at all. If you wait too long, then it might be too late to sell them on the Patriots ticket exchange, so I could see where it would be a bit stressful if you were trying to get rid of them before a game.

      I can't believe he was talking about a plot to let air out of footballs. If there was such a plot, he would have brought it up after the Jet game, when Jastremski said the balls were 16 PSI. McNally was at that game and brought the balls to the field. Why didn't he deflate them down to Brady's preferred level after the refs were done with them? And why didn't Jastremski ask him that same question?

    2. Thanks or the reply.You are the man! That's great that Kessler has your work. AEI is getting credit, but you were 20 days ahead of them.
      Between you, I think Kessler should have a field day.

  3. You've written a lot of good on this issue, but your table on the Master Gauge conversion has an error. The starting PSI for the Non-Logo gauge says 12.12, but it needs to be 12.50 -- which is how you will end up with ~1.38 PSI loss on that same table.

    1. Of course it's 12.12! Anderson used the Logo Gauge for the pre-game measurements,and the balls were 12.50 on that Gauge. Remember, the Logo Gauge reads higher than Non-Logo by an average of 0.38, meaning that a 12.50 on Logo is only 12.12 on Non-Logo.

  4. This one probably belongs in the "too little, too late" box, but I hope you will take the time to read it any way. While there was a lack of recordkeeping prior to the AFCCG, well-documented data is available to determine which gauge was used for pre-game measurements.

    We know the Patriots footballs were inflated to 13 psi by game officials after psi measurements had been recorded at halftime. Based on Exponent's game day simulation, we know that inflation occurred between 8 minutes and 12 minutes into the halftime. Finally, we know the post-game psi measurements for four Patriots' footballs and four Colts' footballs.

    Since there is a linear relationship between temperature and pressure, it is possible to calculate the temperature of the Patriots' footballs when they were inflated. Let's assume inflation took place at the midpoint, 10 minutes into halftime. Using Exponent's transient curve for wet footballs (see Figure 22 in Exponent's report), we can calculate that the Patriots' footballs had reached 62 degrees at the time they were inflated. Using Gay-Lussac's Law and the Non-Logo Gauge readings, we can then calculate the post-game temperature of the footballs when they were measured, which was 63.4 degrees.

    Walt Anderson and Exponent agree that the Colts' footballs were inflated to 13 psi in a 69 degree shower area prior to the AFCCG. Having determined that the footballs were at 63.4 degrees when measured after the game, we can use the post-game measurements of the Colts' footballs and Gay-Lussac's Law to calculate what their psi would be once they reached the pre-game shower area temperature of 69 degrees. The average post-game pressure of the Colts' footballs was 12.35 psi with the Non-Logo Gauge. This means at 69 degrees they would measure 12.64 psi. If we use the average post-game Logo-Gauge pressure of 12.71 psi, the footballs fully recover to 13 psi once they reach the pre-game shower area temperature of 69 degrees.

    So, the Colt's footballs fail to return to their pre-game pressure level at their pre-game temperature if we use the Non-Logo Gauge measurements. With the Logo Gauge measurements, the Colts' footballs fully return to their pre-game pressure level. This means Walt Anderson remembered correctly. Contrary to what Exponent says in its report, the data show that Anderson used the Logo Gauge when checking the footballs prior to the AFCCG.

    What if we assume the Patriots' footballs were inflated to 13 psi using the Logo Gauge at halftime? Then the post-game temperature of the footballs would have been a fraction over 70 degrees. In that case, the Colts' footballs fail to recover to 13 psi with the Non-Logo Gauge by a much wider margin.

    Exponent says they didn't use post-game data because (among other reasons) it was "significantly less certain" compared to information from the pre-game period." The hell it was less certain!