Throughout the course of revising my model this last year, I stumbled upon a few interesting statistics and relationships. I figure that anybody who is visiting a site like this would find them nearly equally interesting.
Returning Starters vs. Home Field Advantage
As I wrote about in the Ratings Explanation page, home-field advantage is traditionally worth 3 points for the home team. To account for this in my score estimates, the home offense receives 1.5 additional points, and the away offense is subtracted 1.5 points. This isn't anything atypical from what other sites have done for home-field advantage in football.
Another metric that I derived was the average added value of returning starters for a team. Oddly enough, one additional returning starter for an offense or defense is worth the same amount of points per game as home-field advantage.
My favorite way to interpret this is that two extra average returning starters (1.5 points per game, multiplied by two) is worth as much to a team throughout the course of a season as playing every game at home would be (switching an away game to a home game is a 6 point swing, and teams play half of their games at home already).
My preseason ratings are calculated based on a team's number of returning starters and their end-of-season AdjO & AdjD for the previous four seasons. The most recent season is predicably the best predictor of future success - explaining about 75% of a team's rating for the upcoming season. My initial assumption was that each subsequent season would account for less and less of the preseason rating, but that wasn't the case. What I found instead was that the season from four years previous is one of the better predictors.
I initially thought this was just statistical noise, so I dug deeper. I found that the relationship held true for the last six consecutive seasons, far too coincidental to be explained away by chance. My theory to explain this has to do with rectuiting in the Division III landscape. Compared to Division I programs, D3 teams (obviously) have much less media exposure, meaning that recruits are less likely to be aware of a team's long-term record, and their view of a program is impacted greatly by their most recent season's success. This means that many of a team's starters were recruited following their season from four years previous.
Change in National Average Score
If you've viewed my Historical Ratings Interactive, you may have noticed the upward trend in scoring over the last 11 seasons. If you've been following football at all over the last 11 seasons, this was absolutely not a surprise to you. If you've spent as much time studying this as I have (trust me, you haven't), you may have also noticed something interesting about the weekly fluctiation of the National Average score.
If you ignore the 2006 season for being the outlier that it is, the national scoring average seems to follow a repeating pattern every year, where the average decreases in the first few weeks of the season and seems to peak in the playoffs. If the trend was simply a steady increase throughout the season, I would assume this was part of the larger trend of scoring increases, but the slight dip in scoring at the beginning of the year makes me unsure.
If this phenomenon isn't just statistical noise or my brain seeing a pattern where one doesn't exist, then I would assume that it means that offenses tend to improve more, either because of adjustments to new personnel or the expansion of the playbook as the season progresses, than defenses do throughout the season.
If you made it all the way through my musings on the minutiae of D3 football stats, I feel like you deserve a reward.