Well, hell, we had a spare moment after we removed the spare tire from our waistline and slapped it on the four-legged tricycle that passes for our transportation these days...and so, we decided to cruise through the hamburger stand now (aka the Play Index at Forman et fils) and anatomize the post-season prospects for teams based on their records in the first twelve games of the year.
The data we cobbled together is captured in the chart below, which gives a yearly breakdown of the number of teams with zero to twelve wins in the opening dozen. (And yes, this is our variation of doin' the dozens, but sans the rhyme'n'rap--we ain't got time for that right now.)
As you'll see, no team in our sample (2000 to 2015) went 12-0 or 0-12 (those rare events occurred back in the twentieth century) but as you'll see if you glance down the TOT column, we have pretty much a bell curve distribution.
And what we also have is mostly linear gradation for "fast dozens" (9 or more wins) all the way down to the "slow dozens" (4 or fewer wins). It's odd that teams with 10-2 and 11-1 starts managed to fall out the post-season more than what we'd expect, and that 68% post-season success rate for the 9-3 mark is probably inflated, but mostly what we see here conforms to what we'd expect.
We didn't keep notes about all of the sub-.500 teams (the 1-5 rows) who made the post-season, but we can tell you that the lone playoff team to start the year 2-10 was none other than the 2001 Oakland A's.
The problem with going back too much further in time with this data is that there is a significant drop in the percentage of teams making the post-season...thus the results become non-comparable. We will have to wait for this data to accumulate over the years to see if the odd peak for teams that start the year 9-3 will hold up--or not.