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.
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?