OK, so we did the math. Entering Saturday, the Red Sox’ magic number to clinch a playoff spot was 17. The Red Sox had 22 games left and the Minnesota Twins had 21. Thus, any combination of Sox wins and Twins losses totaling 17 would guarantee Boston’s fifth playoff appearance in the last six years.

Division title or not, that is really all that matters.

Now the more relevant and important stuff, at least in the short term:

Assuming the Red Sox follow their customary practices and grant their pitchers an extra day of rest at every opportunity, Josh Beckett has three or four starts left: Sept. 10 vs. Tampa Bay, Sept. 16 at Tampa Bay, Sept. 22 vs. Cleveland and Sept. 27 vs. the Yankees. If and when the Sox clinch a playoff spot – and assuming Beckett’s continued health – the team certainly will tinker with its rotation to line up things for the playoffs.

This year, especially, the Sox will have great flexibility in managing their pitching staff. Unlike 2005, when make-up games and scheduling quirks forced the Sox to play 30 games in 30 days late in the year, this club has off days on Sept. 11 and Sept. 18. (Unsurprisingly, the 2005 club hit the wall and was swept by the Chicago White Sox in the first round of the playoffs.) Those open dates will allow manager Terry Francona and pitching coach John Farrell to juggle the rotation (if necessary) while giving much-needed rest to any positional players who need it.

Now to Beckett:

As Amalie Benjamin reported today, the Sox allowed Beckett to throw more than the anticipated 55-60 pitches, which is a very good sign. Beckett’s fastball frequently was clocked in the range of 93 mph, which certainly suggests just a hint of trepidation. (He usually hovers around 95-96 mph and can peak even higher.) Still, for a man who has not pitched since Aug. 17, his command was quite good and he spotted his fastball with encouraging precision.

With pitchers, remember, location is more important than velocity. (See: Byrd, Paul.) When Beckett is at his very best, as was the case in the 2007 postseason, he has both. And lest there be any doubt, a 93 mph gives him plenty of artillery. (Just the same, don’t be surprised if his velocity increases as he grows more assured.)

One final thing: According to one voice in the Boston organization, recent MRIs revealed Beckett’s elbow to be in pristine condition.

If that is indeed the case, their postseason hopes suddenly seem nearly as pure.