Unfortunately for devoted fans of the New England Patriots, their top-performing team is entering its sixth Super Bowl of the Brady-Belichick era with doubts hanging over its unprecedented success.

When the allegations first trickled out that the Patriots had under-inflated game balls during the AFC Championship faceoff against the Indianapolis Colts, they were easy to dismiss — especially among those of us who want to see New England teams triumph.

Even if the footballs were deflated and a lower air pressure offered a competitive advantage, the Patriots clearly didn’t need it, went one strain of thinking. The Patriots dominated the Colts 45-7 during a downpour at Gillette Stadium.

“They could have played with soap for balls and beat us,” tweeted Indianapolis tight end Dwayne Allen.

Science could explain the lower air pressure of the Patriots’ footballs, went another line of thought.

“If they had inflated the balls inside the building and put it to the minimum amount, and then brought it outside to temperatures that were about 30 degrees lower, that would drop the PSI by between 1 and 2,” Boston University physics professor Martin Schmaltz told Boston.com.

Then, there’s the line of thinking that dismisses the “Deflategate” (or “Ballghazi?”) allegations because it’s common practice among NFL quarterbacks to tamper with their footballs and tailor them to their liking.

As if it wasn’t already strange for the world to obsess over the PSI of footballs — especially when the NFL itself has seemingly consequential issues to tackle — things got stranger Monday when Fox Sports reported the NFL was focusing on a locker room attendant as “a person of interest.” If this seemed familiar, it is what Saturday Night Live presciently offered in its opening skit last weekend.

But the Patriots might have to answer to more than a locker room attendant’s bathroom break as part of the NFL’s full investigation.

In 2006, the NFL’s competition committee approved a rule change — for which Patriots QB Tom Brady led the charge — that allowed visiting teams to use their own sets of footballs when on offense rather than allowing the home team to supply them. Quarterbacks, whether at home or on the road, could have control over the balls they used in play.

“The thing is, every quarterback likes it a little bit different,” Brady said in support of the rule change. “Some like them blown up a little bit more, some like them a little more thin, some like them a little more new, some like them really broken in.”

The Patriots were already a top-performing team before that rule change. But some of their statistics, particularly their fumble rate, became — some argue — impossibly good after that 2006 rule change.

“The bottom line is, something happened in New England,” football statistician and engineer Warren Sharp wrote this week on his website, Sharp Football Analysis. “It happened just before the 2007 season, and it completely changed this team.”

Turnovers are key to determining the winner of football games.

“Since 2000, teams who won the turnover battle won 79 percent of their games, regardless of ANY other statistic,” Sharp wrote. “And as far as turnovers are concerned, the number one concern for a team with a quarterback as skilled and proficient as Tom Brady is not interceptions (because there won’t be many), it’s fumbles.”

And, the Patriots don’t fumble much. They fumble so little, it is “improbable,” Sharp says.

Especially because their fumble numbers plummeted beginning with the 2007 season after the rule change.

From 2002 to 2006, a period that saw the Patriots win two Super Bowls, the team averaged 91 plays per lost fumble. From 2010 to 2014, the average more than doubled to 187 plays per lost fumble. Not only is this a remarkable increase, it dwarfs other teams in Sharp’s analysis. During that same time period, those teams averaged 80 to 140 plays per lost fumble. On a chart, there’s the bell curve of distribution you’d expect to see. And then there’s the Patriots, standing completely alone far removed from the bell curve.

Sharp’s analysis has drawn strong criticism, including from physicist — and Patriots fan — Drew Fustin, who writes that Sharp errs in eliminating from the analysis teams that play in domes. His various analyses show the Patriots near the top for most measures, but not an outlier when it comes to fumbles. In his assessment, the Atlanta Falcons have the lowest fumble rates. But Fustin’s analysis does show dramatic improvement in the Patriots’ fumble rate after 2006 — when they shot from 19th in the 32-team league after years of middle-of-the-pack performance to second. Since the 2007 season, the Patriots have remained near the top save for 2013, when two disastrous games dramatically raised the fumble count.

There could be a number of explanations for the improvement.

“Could the Patriots be so good that they just defy the numbers?” Sharp asked in a Jan. 22 posting. “As my friend theorized: Perhaps they’ve invented a revolutionary in-house way to protect the ball, or perhaps they’ve intentionally stocked their skill positions with players who don’t have a propensity to fumble. Or perhaps still, they call plays which intentionally result in a lower percentage of fumbles. Or maybe it’s just that they play with deflated footballs on offense. It could be any combination of the above.”

Given Coach Bill Belichick’s relentless attention to detail and performance — he benched a top running back, Stevan Ridley, several times after fumbles — the combination explanation seems feasible.

Super Bowl XLIX on Sunday, when game officials can be counted on to be super-vigilant about the condition of game balls, will be a first test.

Susan Young is the BDN’s editorial page editor. Matthew Stone is opinion page editor.