I think we’re ready to transition from a “beta” power ranking to a “release candidate” power ranking.
In the beta series, the power ranking stuck to a “King Of The Hill” approach, where it was difficult for a team to sink in the rankings unless another team developed a beatpath over them. All in all, it was a pretty good method, but it wasn’t very responsive, and it made it very difficult for good teams to rise. Plus, there were some flaws, as a couple of commenters pointed out – if a team developed a beatpath over a team early on and then lost it, it was still more difficult for the other team to rise above it.
But really the biggest issue is that it just left a lot of beatpath data on the table. It was paying attention to beatwins, but it wasn’t really paying attention to beatlosses or beatloops.
It also helped to hone in on exactly how any beatpaths-related power ranking system should work, though. This is really the simple explanation of how the power rankings are figured:
- Find all teams with no beatlosses
- Choose the best of these teams with a tiebreaker, and append to the rankings
- Remove the team and all its direct beatwin arrows from the graph
That very simple routine will guarantee a power ranking consistent with all the beatpaths.
So the question is what tiebreaker to apply to step #2. (Ed note: I’m now using “BeatPower”, which is better explained here. But read on for a more wordy explanation.) Originally I chose the team with the longest beatpath segment, frequently using the previous week’s rankings to break ties. Other options were to take the team with the highest ranking the previous week, or looking at the team’s beatloops, or anything else.
But the principles of the method are to rely as much as possible on the entire beatpath graph. And so after pondering that for a while, I figured out a way to factor in a team’s beatlosses, beatloops, and beatwins. In some ways it is similar to the beatpoints concept I wrote about a few entries back, and that has been reported in the power rankings, although it doesn’t really have a mathematical relationship.
The tiebreaker is similar to a win/loss record. You add up the number of beatwins, beatlosses, and unique beatloop teams (including the team itself) for each team. That’s the total number of relationships that team has. Then the formula becomes (wins/total – losses/total). The number can range from 1 to -1.
Here are the first few teams in the power rankings for Week 8 of the 2005 NFL season:
IND: 17/17 – 0/17 = 1
DEN: 22/27 – 0/27 = 0.815
SEA: 12/19 – 0/19 = 0.632
NYG: 8/13 – 0/13 = 0.615
PHI: 15/23 – 1/23 = 0.609
HOU: 2/21 – 19/21 = -0.809
CLE: 1/25 – 20/25 = -0.759
GB: 0/30 – 27/30 = -0.899
The end result is that a team with a lot of beatloops will usually be in the middle of the rankings. A team that obliterates its beatloops without developing new beatpaths will still rise in the rankings. A team that wins, but finds its downstream beatpaths broken apart could find itself falling in the rankings.
Overall, the power rankings should be a lot more responsive, and almost entirely related to the beatpath graph of each week. The only time the previous week’s rankings would be looked at is if multiple teams end up with the same point score, but that’s rare in the case of this method. Also, any initial subjectivity in the first “seed” rankings get bled out quickly.
Here’s the short list of of the Beatpaths 2005 NFL Week 8 Power Rankings using this method:
IND, DEN, SEA, NYG, PHI, JAC, DAL, WAS, ATL, NE, PIT, SD, CAR, CIN, STL, KC, ARI, OAK, SF, TB, CHI, BUF, NYJ, NO, MIA, DET, TEN, MIN, BAL, HOU, CLE, GB