Australia's coach Justin Langer read a spreadsheet incorrectly in coming up with a "total hundreds" statistic that counted international centuries twice.

Hundreds have been a common theme of Langer's recent public discussions on team selection, either side of Tuesday's announcement of the 15-man squad to play two Tests against Pakistan in the UAE in October.

The unselected Glenn Maxwell, Langer said, had only made 17 centuries "above A-Grade cricket" while the suspended Steven Smith and David Warner had 79 and 88 respectively. Aaron Finch, meanwhile, was credited with 41 hundreds across all forms. This was cited as a reason why Maxwell, in particular, needed to be more productive to regain a place in the Test team.

However, these figures could only be reached by tallying all the common statistical categories for centuries - Test, ODI, T20I, first-class, List A and T20 - as though they are entirely separate. This overlooks the fact that the latter three categories already include their international equivalents.

Smith, then, does not have 79 hundreds but 48; Warner not 88 but 53. Finch's tally slips from 41 to 28, and Maxwell's from 17 to 13. So the overall, basic point about hundreds scored still stands in terms of Maxwell not making as many as the rest, but the nuance is a matter for questions. Over the past 48 hours, many in Australian cricket have been asking them.

Langer, it must be said, did not deliberately inflate these tallies to enhance his point. ESPNcricinfo understands that he made a tabulation mistake and has, after being informed, returned to quoting the correct figures. He also stands by his comments about needing Maxwell to pass three figures more often in all formats.

But queries remain nonetheless. Langer was talking in these terms as far back as August 18, when an interview with him was published in The Australian. "He's [almost] 30 years old, for example," Langer said of Maxwell at the time. "Steve Smith's 29 and got 79 hundreds, Glenn Maxwell's got 17 hundreds."

This week, after the squad was officially announced, Langer was still referring to Maxwell's tally as 17 as opposed to 13, and Travis Head's as 15, versus his actual tally of 14. Many are now wondering how many discussions these figures were mentioned in, and whether they included the selection meeting itself.

"At the end of the day, in Test cricket and there's a method to our madness, Glenn Maxwell is 30 years old and everything above A-grade cricket he's scored 17 hundreds," Langer told SEN Radio. "I'll put that in perspective for you, Steve Smith has scored 79 hundreds and David Warner's scored 88 so we all know Maxwell's a terrific bloke, he's a brilliant fieldsman, he's got talent to burn, but he's also a very frustrating cricketer because he needs to score more hundreds.

"Travis Head, for example, is six years younger than Maxwell and he's got 15 hundreds and white or red ball, he's a developing cricketer, he's a terrific young bloke, he's a captain of South Australia, has been for three years and incredibly impressive."

Among the many problems confronting Australian cricket in the year of Newlands, ball tampering, and a loss of public trust is the continuing role of the selectors. There are those within Cricket Australia who no longer believe in the concept of a selection panel, and there was a subtle downsizing that took place earlier this year when Mark Waugh resigned and was not replaced, meaning more selection power - specifically over the T20I team - now resides with Langer as coach.

But of even more importance is the fact that the players and the public are struggling more than ever to make sense of decisions made by the selectors, and respect the office bestowed upon Langer, Trevor Hohns and Greg Chappell by the Cricket Australia board. When the justifications put out through media avenues were based on incorrect information quoted repeatedly, that loss of public trust was only exacerbated further. It has only been a matter of days since CA launched a public relations campaign with the tagline "it's your game".

Of course, Langer is no-one's idea of lazy or unconscientious, and his image of tireless hard work and commitment to the cause was undoubtedly a factor in CA's decision to appoint him as Darren Lehmann's replacement on a four-year contract. But the oft-quoted line about great power being accompanied by great responsibility is accurate in this case, and the spotlight on Australia's head coach is far greater than anything Langer experienced in Western Australia from late 2012 to earlier this year, or as an assistant to Tim Nielsen and Mickey Arthur from 2009 to 2012.

Among the first things Langer said publicly as coach was about acknowledging the contrition of the suspended Smith, Warner and Cameron Bancroft in the context of making mistakes. He expanded to state that "every single person in Australian cricket" had areas in which to get better. Selection, though a tricky business, must be underpinned by sound and correct reasoning.

When contacted, Cricket Australia declined to comment.

Daniel Brettig is an assistant editor at ESPNcricinfo. @danbrettig