A couple of things (not an expert, but what I think I've picked up from reading the forums over the years).
First, FICO is completely based on what the credit report says "now", i.e. no part of the score is based on changes from last year / month / week, just what the current state is today. So, if a card has a balance of $1,000 and a limit of $5,000, it doesn't matter whether last month it was $0, $1,000 or $5,000, your score *now* is based entirely on the state of the credit report *now*. So, whether you pay a balance off over time or in one payment, if you pull your score when the balance is X dollars, X dollars drives your score no matter what your payment pattern was (assuming not late).
Second, the state of your credit report is based on the last reports from each item. So, in my experience, all credit cards report on the date of the statement (in my case, Citibank, AmEx, BofA, USAA, Barclays). Only thing that gets reported is the balance as of that date and whether you were late on the payment. The credit report will show the last reported balance and the "late or not" status for N months back, but not the balance for N months back, so FICO has no way to really know what your balance pattern was, only what it is now. My revolving bank line, on the other hand, reports on the last day of the month, even though the statement closes on the 6th or 7th. So, again, balance on the report date matters, nothing else. Since I can push the bank line back and forth at will with no penalty, I've occasionally paid it down on the 30th and borrowed it back on the 2nd when it made sense to do so, which bumps my FICO score. Depends on available liquid assets, of course.
This can lead to some interesting hacks. If you have a CC with a balance on the 10th than closes on the 15th, you can pay it off using the bank revolving line, let it close with a zero balance, watch your FICO score go up, increase your chance of a BT offer, and then use a BT to pay off the revolving line (assuming you kind of wanted the BT anyway, since it might cost 3% or $75 or whatever). On the 31st, the bank line will report (again) as zero, so from FICO it never went up, and from the 15th through the 15th of the next month, your FICO score is up a bit because both items were "paid off per FICO", making other BTs or loans a bit easier. i.e. good time to do a car loan, or whatever.
Anything that improves (lowers) either your total balances or total credit utilization ratio will make your score better, by an amount that will be the same amount whether you did it in one payment or 100. And, as noted up above, as the accounts age your score will improve, but this effect happens whether you pay them down, fast or slow, anyway, it's a separate FICO factor.
