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What it means is that if Walt Anderson used a gauge that closely resembled the calibration of the gauge the Patriots used, he should have measured the Patriots balls at 12.0. The fact that he measured them at 12.5 means the gauge he was using (which he recalls as the logo gauge) would have been reading around 0.5 higher. Not coincidentally, the Logo gauge consistently measures ~.5 higher than the other gauges. This means Walt had to have used the Logo gauge, and the simulation using the Logo gauge shows that the half-time measurements of Patriots footballs are entirely explained by the effect of weather on air pressure.
Oh, ok. I see what you're saying, now. So JJ measures the balls after gloving at 12.6psig. When the ball equilibriates to room temp in 15-20 minutes the pressure has dropped to 12.0psig. Now the balls come to Anderson, whose gauge measures them at 12.5psig but since we're assuming JJ's gauge read true we thus assume Anderson was using the logo gauge. Makes sense as far as it goes.
However, what grounds do we have to assume that JJ's gauge reads true?