One thing that I hear frequently from fans and read (somewhat less frequently) in those two-line game previews you see in free newspapers available to commuters is the use of recent team performance as a harbinger of things to come (e.g. "the Oilers are slumping offensively having scored just three goals in their last three games"). The information is always (well, almost always) correct, but the implication may well be false. There seems to be an implication that the slump (or hot streak) is somewhat predictive, that a team's recent offensive output might be indicative of how many goals they'll score in their next game.
That seems pretty questionable to me, and so I decided to go out and get some data. In the chart below, I've plotted the number of goals the Oilers have scored in each three game segment this season against the number of goals they scored in their next game:
That looks pretty random to me, and in fact, there is no correlation between the two variables (Pearson's r = -0.00). But the Oilers are just one team. What if we look at the other teams in the Northwest division? The correlation between these two variables is somewhat negative for the Canucks (r = -0.20), Flames (-0.30) and Avalanche (r = -0.31), and somewhat positive for the Wild (r = 0.22). That still seems pretty random, but there are three teams in a similar range.
What about the rest of the Western Conference? Let's look at the numbers:
Interesting. None of these correlations are very strong, but five of the Western Conference teams have a positive correlation, two are pretty much even, and eight have a negative correlation. If we looked at an even larger sample, I'd expect a similar result, with more teams on the mild negative side than the mild positive side. Why? It's not because previous scoring patterns are predictive; goals still look like they're distributed somewhat randomly to me.
It's because of regression. If a team has a scoring binge, they're probably doing so with a high shooting percentage, which means they're scoring more than their fair share of goals. Similarly, during a slump, the team probably has a low shooting percentage, which means they're scoring less than their fair share of goals. The result is that we'd expect teams to regress back to their true shooting talent, which means most teams end up with a mildly negative correlation. In other words, the Oilers were never going to keep scoring like they were during their five-game winning streak and they're not going to continue to suffer a lack of goals like they have been in their current six-game losing streak.