"I would think with interest rates going up the annuity factor would be larger, not smaller. "
The annuity factor is larger. Despite what the lotteries advertise, the real jackpot is the cash jackpot and in the unlikely event that a winner decides to take the annuity the cash jackpot will be invested to buy the annuity. The higher interest rates mean the annuity that can be bought with a given amount of cash is bigger.
If you were paying attention on Thursday or Friday you might have seen a great example of that. The advertised jackpot was bumped up $30 million from 550 to 580, but the cash jackpot only went up by 800k. On Wednesday the $277.4 cash jackpot bought an annuity with a total payout of $550 million and a day or two later another 800k bought a $580 annuity.
"we can expect to see higher rollovers when a jackpot isn't won. "
You'd think so, wouldn't you? Monday's advertised PB jackpot is bigger relative to the cash value because of the higher interest rates, but after 34 rolls it's only at $610 million. 3 months ago, when interest rates and the annuity factor were lower MM reached 1.34 billion after 29 rolls. For the current PB run that's 117% as many rolls, and 46% as much annuity.