Do Stats Need to be Adjusted for Conference?

In this post and this post, I've found that the proportion of games won by the home team and those won by the "better" team (according to DVOA) is smaller for interconference games with a larger variance in the former proportion than for intraconference games. Games between divisional opponents have the highest of both proportions and the smallest variance in the former proportion. This led me to hypothesize that coaches are able to better adapt to teams they see more frequently, which makes inuitive sense, but I was also curious whether or not stats such as DVOA (or my VOLA stats) needed to be adjusted based on conference averages rather than league averages. Are NFC teams rewarded unfairly by DVOA for playing three quarters of its season in a conference full of weak teams? Ideally, opponent adjustments will filter out those effects, even if it's by league average. But perhaps 4 games against a stronger conference is not enough to filter out the effect. NFC Team X has played Y% better than league average when adjusted for opponent, but they were more likely to because of an easy schedule. Against AFC opponents, they'd be less likely to play at that level, even when adjusted for opponent strength. This effect might pop up more in games between average to below average opponents rather than when the NFC team is legitimately good. If the effect is real, then we'd see a greater proportion of interconference games being lost by the team with the higher DVOA when that team is in the NFC rather than the AFC.


I went back and looked at games from the entire history of DVOA (1996-2006). The DVOA totals used reflect the entire season's performance, including postseason. We should see the balance of power shift in favor of the AFC in 2000-6, given that only 1 NFC team ('02 Bucs) won the Super Bowl in that time span, and that team had a large and rare tactical advantage.

Year	% Was Better Team		% Was Better Team and At Home		Better Team Win % Overall
	AFC	NFC	AFC	NFC	AFC	NFC
1996	0.56667	0.43333	0.28333	0.21667	0.67647	0.65385
1997	0.56667	0.43333	0.25	0.18333	0.55882	0.53846
1998	0.55	0.45	0.28333	0.23333	0.69697	0.7037
1999	0.65	0.35	0.31667	0.16667	0.74359	0.57143
2000	0.65	0.35	0.31667	0.16667	0.64103	0.7619
2001	0.5	0.5	0.25	0.25	0.8	0.8
2002	0.59375	0.40625	0.29688	0.20313	0.63158	0.57692
2003	0.60938	0.375	0.28125	0.15625	0.66667	0.66667
2004	0.75	0.25	0.40625	0.15625	0.77083	0.5625
2005	0.65625	0.34375	0.32813	0.17188	0.61905	0.63636
2006	0.59375	0.40625	0.29688	0.20313	0.71053	0.5

The first table shows that the AFC might have been the better conference overall since at least 1996. For both conferences, the number of games in which their team was the better team is split evenly between home and away in almost every year, so neither conference's numbers should be unduly affected by home field advantage. For 6 out of 11 years, the AFC had a better win percentage when they were the better team than the NFC did when they were. In 2 of those seasons, the difference amounted to less than one game ('96 and '97). Looking at 2002-6, after the realignment, the AFC has had the better win percentage in 3 out of the 5 seasons. In 2003 and 2005, they were essentially even. In 2004, the NFC would have had to have won 3.33 more games in which they had the better team to match the AFC's win percentage. In 2006, they would have needed 5.4737 games. The predictive power of DVOA (where prediction = team with better total DVOA wins) was only 55.56% in 2006, compared to 66.67% in 2005 and 65% in 2004. Based on the table above, I'm guessing a large amount of the dropoff was because of interconference games, valuing NFC teams too highly given the gap between the conferences. That the year-to-year differences in better team winning percentage favor the AFC more strongly on average also indicates NFC teams being rewarded by a weak conference.

Year	Better Team Win % Home Better		Better Team Win % Away Better
	AFC	NFC	AFC	NFC
1996	0.76471	0.76923	0.58824	0.53846
1997	0.6	0.81818	0.52632	0.33333
1998	0.82353	0.78571	0.5625	0.61538
1999	0.78947	0.7	0.7	0.45455
2000	0.84211	0.8	0.45	0.72727
2001	0.8	0.86667	0.8	0.73333
2002	0.78947	0.76923	0.47368	0.38462
2003	0.83333	0.9	0.52381	0.5
2004	0.80769	0.6	0.72727	0.5
2005	0.7619	0.81818	0.47619	0.45455
2006	0.73684	0.46154	0.68421	0.53846

The NFC teams see a bigger gap in better team win % for home and away games. The average difference is 18.517% for the AFC and 22.807% for the NFC. Small sample size has some effect for the games in which the NFC team is better, however. On average, the difference seems to be one or two games that could go either way.

So DVOA does seem to unfairly reward some NFC teams for playing in a weaker conference. Which teams are throwing off the system, though: the good teams being bumped up to very good or the mediocre teams being bumped up to good? In most years, the average gap in DVOA between teams in games in which the AFC was the better team and lost was larger than that for the NFC. And in most years, the average DVOA of the better teams that lost was higher for the AFC than the NFC. I would say, then, that the NFC teams that are mediocre to slightly above average (Rams, Falcons, Panthers) are unfairly rewarded more than good NFC teams (Eagles, Cowboys) for playing in a weaker conference.

Though DVOA is far more sophisticated than my methods, I believe I can apply the lessons learned here to my prediction model, specifically my VOLA stats. For intraconference games, I might start using Value Over Conference Average rather than VOLA. For interconference games, I could use Value Over Other Conference Average. So if Team A average 6.5 yards per play, it could be average in the AFC, but it might above average in the weaker NFC. Perhaps you could do a similar thing for DVOA, but the math of it is rather hazy to me right now.