<sigh>
Page 165. Read from there. They explain scientifically how a) the gauge switching wouldn't have mattered and b) show that it was incredibly unlikely it was done so. They even take your exact scenario and show how it wouldn't make a difference. Page 215 and 227 is the nail in the coffin on that front. Seriously? You aren't even trying to read the explanations. You're just looking for something to validate your own conspiracy theory.
There is no conspiracy theory. In fact, it isn't even up for debate: the officials literally did not know which gauges they used and when. Nobody disputes that.
The officials don't know how measurement was done pre-game. Pre-game measurements were not recorded. They don't know how measurement was done at half-time. The Colts half-time measurements make no sense.
Based on that alone I would throw out the case. For the officials to not care which gauges they were using, when the measurements are so different, proves all the data suspect and shows they did not care about the issue until later.
I'm not saying I think they didn't deflate the balls, just that the NFL's procedure was so faulty the case should be thrown out.
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As for the pages you just mentioned, they don't preclude either of the two scenarios I bring up.
1. The possibility that they used different gauges pre-game. Every scenario in the report uses the same gauge pre-game. Indeed, their method was to use the Colts balls as a control: they assumed the same gauge was used for the Colts and Patriots, and then they set up the experiment so that the Colts balls would end up at the measurements they eventually reached.
As a result, they omit the possibility that the Patriots balls were initially tested with the high gauge and the Colts with the low gauge. And they set the pre-game temperature lower explicitly to make sure the Colts balls would end up in the proper range. To be clear: they assume that the Colts balls were 13, using the same gauge as the Patriots balls, and based on that they lower the temperature.
If the Patriots balls were measured with the high gauge (which the official thought they were), then their halftime measurements are not surprising:
Had the Logo Gauge been used pre-game, there is a small window in which the Game Day results from both teams are theoretically explainable. However, this would require the testing of the Patriots footballs to have begun immediately upon entering the Officials Locker Room, before the balls had time to warm up.
The results for both teams can be explained if the Logo gauge (high gauge) was used for both and the Patriots balls were tested immediately before warming up.
However, if a different gauge was used then the results are easily explained. If a different gauge was used, the temperature could have been higher in pre-game conditions, and the Patriots balls would fit perfectly.
2. It is unknown which gauges were used for the Colts halftime measurements. I think you will admit there is something very strange about those measurements.
The investigators never found the low gauge higher than the high gauge. The Patriots balls were all higher with the high gauge. But the same tester tested 3 of the 4 Colts balls lower, and one very high (12.95!). This result is completely out of the realm of anything the investigators found.
The report suggests that he likely switched gauges, but the anomaly ball casts doubt on the whole thing. Never in all their testing did they get results like that.
Since we don't know what gauges are used, the Colts halftime measurements may be overinflated. There could be more instances of the high gauge, or some other mistake leading to higher measurements; before denying that, recall again that the measurements are out of bounds with anything else the investigators found.
Yet the Colts 4 balls, with all the uncertainty of how they were measured, and the bizarre results, are used as the control. They are used to determine pre-game conditions, including lowering the temperature pre-game so that the Colts balls could reach the heights of their dubious halftime measurements.
I should also point out again the obvious problem of the numbers used. They could only test 4 Colts balls at halftime before running out of time. All we have to go on is a general statement that the Colts balls were around 13 to start the game. Yet we know the officials cared little about the results (they didn't know which gauge they used, and they didn't write down the results). Therefore it is not really supportable to assume a measurement of 13 for the 4 Colts balls. Especially when you consider the anomaly ball.