I want to expand and emphasize a statement I made in my earlier post on how APR works. I wrote:
a simple sort of teams from largest to smallest power index is used to generate a power rankings
This is important. Each team's position in the power ranking is based only on the relative values of their respective power index values generated by APR. In particular:
No consideration is given to the ranking a team had in the previous week. It is possible (and in fact, not unusual) for teams to fall even though they won, or rise even though they lost.
No consideration is given to win-loss records, and it's very possible for, say, a 4-2 team to be ranked below a 1-5 team.
An example
I know it's possible for a 4-2 team to be ranked below a 1-5 team, because it happened during the 2007 season.
After the week 6 games of the 2007 season, the Baltimore Ravens were 4-2. The ESPN power rankings had them in the #7 spot. But APR ranked them #25. Below the 1-5 Falcons, the 1-4 Bengals, and the 1-4 Saints. In all, APR had 12 teams with .500 or worse records ranked above the Ravens that week.
Why should a team with a winning record be ranked so low? As usual with APR, the Ravens had played a some weak teams, including losses to the Browns and Bengals, and a 2-point victory over a very weak 49ers squad.
APR is meant to be a predictive measure of power (e.g. how well teams perform the following week). In this case, the low ranking was clearly justified, as the Ravens lost their next 9 games (including giving the Dolphins their one win of the season). The only game the Ravens won after week 6 was in week 17, against a Steelers team playing Charlie Batch at QB.
Conclusion:
This is exactly the kind of thing APR is meant to show: the power of each team as it continues to play games in the season. If you read this description of the SRS ranking algorithm, the discussion makes a distinction between predictive systems (which team is more likely to win their next game) and retrodictive systems (which team accomplished more in the past). APR (like SRS) is a predictive system, and should be approached as such.