I didn't mysteriously get better mileage this week. It all averages out in the end I guess.

Why do you think the formula is off? Are you looking at miles-driven versus dispensed-fuel, or are you comparing with a trip computer showing MPG, or what?

What did you do for your very first fill up? For example, if my car came filled from the dealer, I'd add my very first fuel-up at whatever mileage it had when I got the car, check "I missed a fuel-up" and if it didn't come with a full tank, "this is a partial fuel-up". That should correct things if you're always one fuel up from being perfectly accurate.

The formula isn't off... The first fuel up doesn't mean anything except to mark when you first gave the vehicle a full tank and the odometer reading if you use that (the amount of gas you added there won't affect your mpg). When you fuel up the second time to a full tank, the amount that you fill up is how much gas you used to go the distance that's on your odometer or trip.

The only source of error could come if a "full tank" is different each time you fill up.