"Teams improve the most from Week 1 to Week 2."
I've read this a bunch over the last week, and I wanted to know if it's true. The theory appears to be that the first game experience serves as a wake-up call to teams and as a means to get accustomed to game speed, which jump-starts the team's development over the rest of the season. It makes sense. I've been there, but for me it always seemed to be the scrimmage that helped more than the first game.
How can you analyze this though? If everybody plays on the first week, and both teams improve immensely over the first week, it would stand to reason that any discernable improvement would be a wash.
But not every team plays on the first week. Since 2013 there have been 52 games between teams with a Week 1 bye and teams who played on Week 1. By analyzing the difference between predicted and actual game outcomes, I should be able to tell if the team who played Week 1 had any improvement beyond a team's natural progression (and conversely, I should be able to tell if a Week 1 bye hurts a team's chances of victory).
In the chart below, each box represents one game outcome. A box with a positive value indicates that the team with a Week 1 bye outperformed their expectation, and a negative value means that the team who played Week 1 outperformed their expectation. I am only including games since 2013 in this sample because 2013 was the first season for which I have returning starter information for every DIII team, and these adjustments have made my Week 1 & 2 game score predictions about 10% more accurate.
The average outcome from these 52 games is that the team who didn't play Week 1 tends to outperform their estimated outcome by about 2 points. Factored with the fact that defenses tend to be more prepared than offenses at the beginning of the season, I feel that this fairly thoroughly debunks the theory that teams improve the most between Weeks 1 and 2 (this means that the national average for games in the first few weeks should be around -0.25 for this same sort of analysis). So if your team had a bye last week and their opponent didn't, relax. Odds are both teams are on relatively equal footing.