# Schedule Adjustment for Counting Stats

Edit:There is another version of this article available in pdf which includes more explicit mathematical formulas and an example worked in gruesome detail.

# Rationale

We all know that some games are easier to play than others, and we all make adjustments in our head and in our arguments that make reference to these ideas. Three points out of a possible six on that Californian road-trip are good, considering how good those teams are; putting up 51% possession numbers against Buffalo or Toronto or Ottawa or Colorado just isn’t that impressive considering how those teams normally drive play, or, err, don’t.

These conversations only intensify as the playoffs roll around — really, how good are the Penguins, who put up big numbers in the “obviously” weaker East, compared to Chicago, who are routinely near the top of the “much harder” western conference? How can we compare Pacific teams, of which all save Calgary have respectable possession numbers, with Atlantic teams, who play lots of games against the two weak Ontario teams and the extremely weak Sabres? Continue reading

# Adjusted Possession Measures

A little while ago I wrote an article at SensStats discussing score effects and suggesting a new formula which we might use to compute score-adjusted Fenwick. This article addresses several interesting questions and new avenues that were suggested to me by various commenters.

1. The method in the above-linked article simultaneously adjusts for score and for venue (that is, home vs away). It’s interesting to estimate the relative importance of these two factors. As we’ll see, it turns out that adjusting for score effects is dramatically more important than adjusting for venue effects.
2. We might consider adjusted corsi instead of adjusted fenwick; it turns out that adjusted corsi is a better predictor of future success than adjusted fenwick at all sample sizes.
3. Most interestingly, we might consider how score effects vary over time, and see if we can create a score-adjusted possession measure that takes this variation into account. We find here that performing such adjustments is indistinguishable in predictivity from the naive score-adjustments already considered.

Several people have pointed out that score effects have a strong time-dependence. At least as far back as 2011, Gabriel Desjardins (@behindthenet) noted the effect and readers with keener memories than me will no doubt remember still earlier examples. Just last week, Fangda Li (@fangdali1) wrote an article arguing that score effects play virtually no role outside of the third period. This article will show that, while score effects are magnified as the game wears on, time-adjustment for possession calculations is not justified. Continue reading