Last month, Apple failed to make its own self-imposed deadline to release iTunes 11 by the end of October.

iTunes 11 is a radical overhaul of Apple’s media management, shopping and syncing software for the Mac and PC that seemingly addresses the numerous complaints of bloat and convolutedness that have been leveled at the app over the years. It also has a much more attractive and modern design.

Consequently, numerous Apple fans — including ourselves — were disappointed when Cupertino quietly announced they were pushing back iTunes 11’s release by a month, into November. But when in November?

We have no inside information on when, exactly, iTunes 11 will be released, but we think there’s an excellent chance that it will be released by no later than the end of next week, and most likely next Wednesday. Here’s why.

The best way to tell what Apple is going to do in the future is usually to look at what they’ve done in the past. Luckily, we’ve got a lot of data on when Apple has released new iTunes versions in the past. Over the last 11 years, in fact, Apple has released eighty-four different versions of iTunes.

Statistically there’s a 73% chance Apple will release iTunes 11 mid-week.

Here’s what you need to know about those eighty-four versions of iTunes. Of them, two were released on Sunday, fourteen on Monday, twenty on Tuesday, twenty five on Wednesday, sixteen on Thursday, and seven on Friday. That means that Wednesday is the first most likely day for a new iTunes version to be released, followed by Tuesday, then Thursday.

We can reasonably say, then, that there’s a roughly 73% chance that Apple will release iTunes 11 during a mid-week. But which week this month?

We have a lot of good data here, too. Of all eighty-four versions of iTunes that have been released to date, only five of them have been released in November. Of these five versions, none have ever been released later than the 20th of the month.

It’s important to recognize why this is: Apple’s an American company, and Thanksgiving is the fourth Thursday of every November. Apple is actually a more generous company than most when it comes to giving workers time off for Thanksgiving, giving Apple corporate staff the entire Thanksgiving week off to spend with their families. That means that any major products that Apple has in the pipeline need to be released before Thanksgiving week begins, or else it will most likely be delayed until December, because of how long it takes teams to build back momentum when they come back from the holidays.

This year, Thanksgiving falls on the 22nd of the month, which is the earliest in the month Thanksgiving can actually be. Apple has given corporate employees the week off starting on Monday the 19th. Since we have never seen a version of iTunes be released after the 20th of November, and since the last workday most Apple employees will be working is the previous Friday, Apple is historically extremely unlikely to release iTunes 11 past November 16, 2012, if it’s going to come in November at all.

Apple could always surprise us, come back from Thanksgiving, and push iTunes 11 out the door. Historically, though, the data says they won’t. Instead, iTunes 11 will either ship next week, probably on Wednesday, or be delayed again to December. That would look bad for Apple. Nothing’s certain, but our best guess says iTunes 11 next week.