Just a quick first pass analysis. I looked at all 60 MLS re-matches* during the 2003 regular season and split them in half, depending on how many days apart they were played. I scored each pair of games depending on how different the outcomes were, e.g. a one-goal win and a one-goal loss would be a "2." Short time lag: 1.45 goals per game (45 goals/31 games) Long time lag: 1.97 goals per game (57 goals/29 games) This is very preliminary, but it suggests that teams do have stretches of hot and cold form, even though most of the game-to-game changes are probably due to luck or playing well in a particular match (which is the same thing, imo). But it bears repeating, this data is only enough to give a hint of the truth. *A re-match is a pair of games between the same teams at the same location.
Very interesting, numerista. I'm not sure this should be totally surprising, however. There's other ways to interpret the stats other than invoking 'form', aren't there? Injuries, player availability, emergence of players, coaching changes, etc. are going to make teams better certain times than at others. One would expect that, as time passes, a team's results become less and less similar to results at some previous point in time.
Not totally surprising, and yes, you're right that "form" is probably too narrow a word for describing the reasons that a team's strength might vary. But rating systems generally assume that all in-season games are equally informative. These data suggest that recent games may be substantially more valuable than older ones.
What kind of predictive value are you talking about? In predicting the result of the next game, I think that current 'form' (whatever that means) is obviously more informative. I wouldn't be so confident about recent games being more predictive for the entireity of the season. Unrelated: were the two groups balanced in terms of the number of same venue (home-home or away-away) vs. mixed venue (home-away) games? Home teams have a .42 goal margin, so mixed venues would have an expected difference .84 higher than same venues. I don't think this would account for everything, but even a 60-40 bias could have a pretty significant effect.
I definitely think of predictive value in terms of the next game to play ... also, I only looked at same-venue rematches, so there's no possible source of noise in this data (although there is noise due to the small sample).