Beatpaths Automatic Power Ranking

All right, after two days of hacking, we finally have an objective, automatically generated power ranking system. If you’ve been reading, you’ll notice that this is actually the third rev of the objective system. The system is beta, and we had a couple of minor bugs. The first was easy to find because it insisted on ranking Miami #3 (because they had beaten Denver). The second was a bit harder, but I think I got it squashed.

The basic principle of these rankings is that a team doesn’t lose a spot in front of another team, unless that team (or another team further back) outright takes it from them. King of the hill. Each team starts at the top of the rankings and walks down the list to see if it should be ranked above or below the team it’s being compared to. Here are the rules:

1) Check the beatpaths. Does the active team have a Beatpath ahead of the compared team? If so, rank it ahead. Is the active team in a Beatpath behind a team further down the rankings? If so, keep walking.
2) If that’s not conclusive, did the active team play the compared team this week? Keep walking if they lost. This was the source of a recent bug – you don’t always want to rank them ahead if they won. You only want to do it if they would normally be ranked just behind them.
3) If that’s not conclusive, check the “subjective rankings” if they exist. More on this in a second.
4) If that’s not conclusive, check the previous week’s power rankings. Was the active team ranked ahead of the compared team? If so, rank it ahead. If not, keep walking.
5) If you run out of ranked teams, rank it last.

In steps #3 and #4, if it’s about to insert the team, it also checks the team just before it in the rankings to see if it beat it last week. If so, it ranks it ahead of them, too.

The power ranking history goes back to the 2003 Super Bowl – at that time, the power ranking was ordered by BeatPoints, my name for the system that DavidH suggested in the comments last week. Every ranking that wasn’t dictated by a beatpath was deemed a subjective choice. But each week, if a beatpath confirms or contradicts a subjective choice, the choice is no longer subjective. As a result, almost every subjective choice I made back in 2003 has been bled out of the system. The only exceptions are:

  • The Jets are better than Detroit
  • Green Bay is better than the Jets
  • Miami is better than New Orleans

So, on to this week’s automatic power rankings: the system that ignores the quality of the teams, and ONLY focuses on the teams’ winning and losing histories.

Rank Team Notes Last Week BeatPoints
1 The basic principle of this power ranking system is that a team can’t lose its spot to another team unless someone takes it from them. No one has taken anything from the undefeated Colts. 1 2
(19 – 0 = 19)
2 In terms of clearly beating powerful foes, Denver has had the most impressive season so far. 2 1
(21 – 0 = 21)
3 The Jags have also played some very tough opponents and won a lot of games, Denver being one of their few losses. If they do well with their easy remaining schedule, they should stay up top for a while… 3 3
(18 – 2 = 16)
4 These guys just haven’t gone bad yet. This week’s game against the Giants will be key… 5 4
(13 – 1 = 12)
5 Over the last couple of years, the Seahawks have had a knack for playing poorly and stumbling their way to close losses. Now they have a knack for playing poorly and stumbling their way to close victories. 6 6
(10 – 3 = 7)
6 The Falcons rise one spot, really only because of Cincinnati’s loss. 7 9
(5 – 0 = 5)
7 I’ve really enjoyed reading everyone’s reminiscing about Drew Bledsoe’s heartbreaking ways. Then I saw Drew “taking accountability” for his poor throw in that video footage after the game, and I was left thinking, Does this guy even know that it’s been a pattern for him? 8 10
(9 – 5 = 4)
8 Eagle’s victory over the Chargers basically protected themselves from falling. Philly has been underperforming for a while now. 9 13
(2 – 0 = 2)
9 The Chiefs have been playing well, and are now threatening Denver for supremacy in the AFC West. 10 12
(2 – 0 = 2)
10 San Diego has been in the 11-13 range since week three, and it’s dictated by their win over the Giants. They just haven’t been able to break through in either direction beyond that. 11 17
(0 – 1 = -1)
11 Really interesting dynamic here. The reason that Chargers have held so steady is because the Giants have been anchoring them there. Since week 3, New York has been one slot behind them. The Giants really want to go higher, but they haven’t been able to get themselves ranked ahead of San Diego yet. This week might be the week that both teams can rise higher. 12 14
(7 – 6 = 1)
12 The Buccaneers don’t have any BeatLosses… they could shoot up if they continue to play well. 13 5
(7 – 0 = 7)
13 The Dolphins’ only BeatLoss is to the Bucs. No matter how poorly they’ve played, there isn’t a lot keeping this team down right now. This could change easily. This also starts a murderous stretch in the power rankings, dictated by some past victories that are looking flukey. In keeping with the principles, the teams that haven’t outright taken the ranking haven’t risen above the higher teams. But you get the sense it’s going to break apart any time now. 14 20
(0 – 1 = -1)
14 Carolina has already overcome their loss to New Orleans, but not their loss to Miami. They’re still something of an enigma. 15 11
(4 – 0 = 4)
15 Their loss to Carolina is still hurting them. 16 16
(0 – 1 = -1)
16 This team could really make this logjam bust apart. You know they’re better than this ranking, even though the win/loss picture doesn’t tell it. Pittsburgh suffered earlier this season when they lost to New England, who was still suffering at the time from Carolina’s loss to New Orleans. Some of those beatpaths have been broken apart and the Steelers have been clawing their way back up the rankings since then, although Tommy Maddox didn’t help. 17 7
(10 – 3 = 7)
17 If Cincinnati is better than this, it should also help Pittsburgh rise back up. 4 8
(9 – 4 = 5)
18 The Raiders have been playing well lately, although they’re a bit schizophrenic. They could cause problems in the West. 18 18
(0 – 1 = -1)
19 Cleveland has slowly risen from #29 up to #19 this season. Maybe if they try really hard they can make it to the top half of the league. 19 23
(1 – 5 = -4)
20 The Bears are a Top Twenty team for the second straight week! 20 19
(5 – 6 = -1)
21 Anyone catch Mike Tice’s delicate phrasing about keeping his team off the street? That cracked me up. Mickey told Rocky not to have sex before a fight, maybe he had something there… 21 24
(4 – 9 = -5)
22 A rare subjective choice – Back in 2003, the Jets were ranked ahead of Detroit, so they are now, too. 31 22
(0 – 4 = -4)
23 The NFC North teams are all clumped together in the BeatPath graph, too. 24 15
(1 – 1 = 0)
24 It’s such a frustrating team. Everyone wants them to be better. Then they bust out against New Orleans, and then they suck again. 25 28
(0 – 12 = -12)
25 Well, they got stomped by a tough opponent. But no one below them has outright taken their ranking from them yet. 26 26
(0 – 7 = -7)
26 No, I don’t think there’s any way that St. Louis should be ranked below San Francisco, either. But the 49ers did beat them earlier this season… and St. Louis hasn’t taken it back from them yet. 27 21
(5 – 7 = -2)
27 You know they’re better than this. You’d think their bad luck would have run out by now. Maybe the bad luck can be bottled and sent to Osama…? 22 29
(2 – 14 = -12)
28 The Bills, despite their awesome NFL Primetime music, just don’t have a lot going for them. They sink lower because New Orleans lost to St. Louis. 23 31
(1 – 15 = -14)
29 Weren’t these guys supposed to be really great back in the preseason? 32 25
(3 – 8 = -5)
30 The Titans have been ranked #28 to #30 since week 3. 28 27
(2 – 12 = -10)
31 Believe it or not, Houston has not yet hit the bottom slot this season – mostly because they weren’t pathetic last year, and the lower teams haven’t done a thing to outright take Houston’s slot. 29 32
(0 – 19 = -19)
32 The Ravens have been #30 to #32 since week 3. 30 30
(0 – 13 = -13)

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5 Responses to Beatpaths Automatic Power Ranking

  1. DavidH says:

    So, I can’t figure this out from the explanation… you say that you take teams one by one and walk them down the rankings. I assume you mean you start with a blank list, then take a team and put them number 1. Then take another team and either put them at 1 and move the first team down a slot, or put the new team at 2. Then add another, etc. My question is – does the order that you walk the teams down in change the final ranking?

    And my other question is – how much do the original 2003 rankings influence this list? I know you said there are only 3 subjective rankings left, but if you had started with an entirely different ranking, would there be completely different subjective rankings left, and a completely different power ranking listed here?

    I can’t figure this stuff out myself. At least not right now. Maybe if I took a couple hours to play with stuff, but I probably ought to be workinginstead. 🙂

  2. ThunderThumbs says:

    That’s very much the right question to ask. I’ve got to say that at this point, I “mostly understand” the system although there are still some questions I have.

    First, about the 2003 rankings. I ranked them by BeatPoints, and then generated a data structure of every better/worse relationship that wasn’t explicitly defined by a beatpath. That means that since the 2003 superbowl, pretty much every better/worse relationship that is even possible has been covered by a beatpath, aside from the three subjective ones that are left. I think, but am not sure, that that basically means that just about any seed ordering would be basically canceled out at this point. You’d have some different orderings earlier on, but I think it should all have settled out by now. I don’t have this logically proven, but I should at least be able to test it by running the system a few times with some randomly seeded orderings back in 2003. I’d think that with enough computer science chops, it might even be able to figure out just how many possible power rankings there are each week (given different seeds).

    As for the order you walk the path. Here also, I haven’t been sure how much the walking order would change the final order. It seems like it might. So to protect against that I’ve been very careful about the order in which I evaluate the teams, again erring towards the teams that appear better. The evaluation order is by the length of the beatpath below that team. The tiebreaker (if multiple teams have the same beatpath length below them) is the order of the previous week’s power rankings.

    One kind of funny possibility is if I’m able to prove that a power ranking is “stable” (meaning any other order from a different seed is impossible), then I might even be able to go “back in time” week by week and recalculate the earlier power rankings.

  3. ThunderThumbs says:

    DavidH – I just reran the scenario with the 2003 seed reversed. Meaning, I ordered them by beatpoints as I have all along, and then I put that 2003 super bowl power ranking in reverse order and used it as the seed. That seemed about as destructive as possible to have the super bowl winner ranked last.

    By week 10 of 2004, the power rankings were in the exact order that they were when the seed wasn’t reversed. So it pretty much heals itself.

    That means that at this point, the ordering of the initial seed has no effect on the order of the current power rankings.

  4. ThunderThumbs says:

    Whoops, I was wrong in the last comment. I tested by reversing the initial power rankings, but not by reversing the initial set of subjective rankings. When I corrected for that, we are still in the self-healing process, but very very close. It looks like in Week 8, two adjacent teams will have their order swapped, but that’s about all.

    I could probably fix all this by having my seed be the 2002 super bowl rather than the 2003 super bowl.

  5. ThunderThumbs says:

    It looks like the order in which you evaluate the teams has a significant difference on the power rankings. I’m still trying to understand the exact nature of how the order affects it. Right now I’m evaluating the teams in order of maximum beatpath length, from the top down. Another option is in order of beatpoints, which has some subtle differences. Doing it in order of the previous week’s power rankings does not work very well – you find the top teams slowly get pushed down the rankings (IND not even close to the top).

    Other possibilities I’m considering: in descending order of absolute value of beatpoints (outside in), or ascending order (inside out). Or if the goal is to evaluate in order of team quality, then actually evaluate it multiple times each week, feeding the power rankings back into itself until there’s no further adjustment. But all of this is brute force – I probably need to sit down with a pen and paper and come to a more theoretical understanding.

    I like the general feel of the current method – it’s very much “King Of The Hill” – the high teams tend not to fall when losing unless they suffer a beatloss.

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