At this point; the answers all of you are seeking are in the report. Not a single question I've answered hasn't been thoroughly broken down, explained, and proven in either the report itself or the appendix. If you don't want to believe the report because it doesn't jive with your feelings or what you want to already believe; nothing I can say or do will change that.
The thing it doesn't cover is that the pre-game readings were not recorded and only 4 Colts balls were tested at halftime. Or I should say, it does cover it, but only to admit they assumed 13 for all the Colts balls. The entire thing is based on extremely vague statements like the Colts were probably going for 13... not recording of individual measurements, not recording of which gauge was used. The assumptions it makes are not justified.
Let's say the Patriots were hovering around 12.5 pre-game, and the Colts 4 balls were around 13.1. If they switched gauges (with a .38 difference), the true difference between Patriots and Colts is about .98, or 1 pre-game.
At halftime, Prioleau's average for the Patriots is 11.49, while his average for the Colts is 12.27 (eliminating ball 3). A difference of .78... so the Colts balls actually deflated more than the Patriots did from pre-game to halftime! Or maybe the officials are doing weird things again?
Let's assume they switched gauges again at halftime, so the difference becomes about 1.15. So the Patriots balls would have deflated more... if our original assumptions were correct. If the Colts 4 balls (the only ones tested) were at 13.25 pre-game, then they deflated the exact same amount as the Patriots.
You should be able to see the issue here. It's not the statistics or the science, it's using vague statements as though they are exact.
If Priloleau did NOT switch his gauge between Patriots and Colts at halftime, he actually shows the Colts deflated their balls and the Patriots didn't. But even if he did switch gauges, that only gives a difference of .15. So maybe the Patriots deflated their balls by .15... or maybe the Colts 4 balls were .15 higher than the vague assumption. Or maybe the difference is because the Patriots balls were measured first, and the Colts 4 balls (all they had time for) were measured only after rising in the higher temperatures.
At this point you may be thinking "the officials didn't do that weird stuff", but the evidence strongly suggests they did. They themselves indicated they used the high gauge for the Patriots pre-game. The investigators themselves claim that the low gauge never measured higher than the high gauge in all their tests, which means Priloleau probably switched gauges between measuring the Patriots and Colts. The odd behavior of the officials, combined with no recordings and only vague memories, is not enough evidence to say anything substantial.