But when we analyzed the data provided in the Wells report, we found that the Patriots balls declined by about the expected amount, while the Colts balls declined by less. In fact, the pressure of the Colts balls was statistically significantly higher than expected. Contrary to the report, the significant difference between the changes in pressure of the two teams’ balls was not because the pressure of the Patriots balls was too low, but because that of the Colts balls was too high.

How could this be? The report’s own findings suggest an explanation: At halftime, N.F.L. officials measured the pressure of “only a sample” of the Colts balls (four out of 12) before they ran out of time; the second half of the game was about to begin. This implies that the Colts balls sat in the warm room where they were to be measured — and thus increased in pressure — for almost the entirety of halftime before being measured.

All of the 11 available Patriots balls, by contrast, were measured at halftime, which suggests that they were measured earlier, when they were colder — and thus lower in pressure. Although this explanation contradicts the Wells report’s conclusions, it fits all the evidence.

There are other factors discussed in our study that undermine support for the Wells report’s conclusions. For example, there is considerable uncertainty concerning the actual pressure of the footballs. The N.F.L. official who checked the pressure before the game used some combination of two pressure gauges to measure the Patriots and Colts balls, but it is not known which particular combination.

One of the gauges, as the report notes, records pressures that are higher than the other. If the official used that gauge to measure the Patriots balls (but not the Colts balls) pregame, then those balls may well have started out with too little air, which could explain a later appearance of intentional deflation. The report, however, does not consider that possibility.

Our recommendation? When the N.F.L. hears Mr. Brady’s appeal of his suspension later this month, it should proceed with the knowledge that the Wells report is unreliable.