Believing the numbers: when do goals for and against stabilise?

At this point of the year it's important that we try and establish what numbers can be believed. In other words: how small is too small for a sample size? Consider, for example, that through six gameweeks last season: Aston Villa ranked 10th in goals scored at home and 3rd on the road. They wound up being the 2nd worst attacking side in the league, managing to notch just one goal more than Stoke. Tottenham placed 19th in home defense, shipping an average of 2.5 goals per game. They finished the year as one of the league's best defenses, ranking 4th at home and 5th on the road. QPR conceded just one goal in their first three away games. They went on to concede 40 more in the next 16, at an alarming rate of 2.5 a game, enough to rank behind everyone outside of lowly Blackburn. We could go on and on. The point being, six games is not enough to write teams off or buy into short lived success. When then, is long enough? Using data from the past two seasons (ideally we'...