Insofar as the U.S. Supreme Court grants merits review to approximately 80 or so cases per Term, attention to those cases selected for review (as well as those not selected) warrant attention. And the good folks at Empirical Scotus are beginning to do just that. Indeed, a recent post "looks at whether and how the timing of certiorari (cert) petition filings affects the likelihood of a grant. It does so looking at data based on petitions the Justices granted from the 2015 and 2016 Terms."
What they find is that the sweet-spot for most petition grants is found between 78 and 131 days with a sizable number of grants also taking place between 131 and 184 days.
As the data in this quick-and-dirty cross-section of SCOTUS petition grants relate to the Court's 2015 and 1016 Terms, those with some time and the inclination might consider building a slightly larger dataset so to exploit something of a natural experiment and compare cert granting trends for the standard nine-member Court and trends for the current eight-member Court. While presumably the traditional "Rule of Four" remains constant, the game theoretics likely change slightly for the Justices when Court membership temporarily moves from nine to eight.