Some crazy activity this week. All in all, the picks were pretty accurate this week – 10-4 for all methods – but there was more than one true upset. Oakland?? We also have some new loop activity. I was 9-5 this week, and the BeatPicks were 3-1, making them 11-2 for the season.
BUF->NYJ shortens last week’s loop, and restores NE->ATL->MIA to the graph, which gives New England a big boost. New England’s dominating win this week is coincidental, since there’s no huge reward for beating Tennessee. The other big game in terms of beatloops is HOU->CIN, which hurts Cincinnati badly. It also helped San Diego – for about twenty-four hours, San Diego had no beatlosses this weekend – and cost Green Bay the Chicago beatwin that was propping them up. Here are the beatloops that are operative this week:
BUF->NYJ->NE->BUF
HOU->CIN->GB->CHI->SEA->JAC->HOU
HOU->CIN->PIT->SD->MIA->NYJ->HOU
HOU->CIN->BAL->SD->MIA->NYJ->HOU
And now, the Week 6 Beatpath Graph.
I’m glad to hear that we have a difference in the Iterative graph this week. This one has a pretty clear example of a difference – since HOU->CIN appears in multiple beatloops, it’s removed.
I think this also illustrates the question I’ve had about it for the last couple of years. Why should HOU->CIN be considered the weak link just because it’s in multiple beatloops? If a team is in multiple beatloops like that, then it also means that the team it vanquished had multiple beatpaths to it. In other words, CIN had multiple beatpaths to HOU, which means CIN really should have beaten them. If they lose instead, it makes an intuitive sense to me that the loss should hurt more.
I think I must have actually decided against the idea behind iterative on the way to developing the beatflukes variant. The aim is to determine which games are flukey. The above loops don’t seem to be enough evidence to consider HOU->CIN flukey, but beatflukes would consider HOU->CIN flukey if (and only if) CIN also had an entirely different beatpath to HOU, in which case it would then throw out HOU->CIN and restore the rest of the beatloop.
Also, to restate the algorithm, is it sufficient to count all the segments in all beatloops, and then remove the segment (or segments) that occur most frequently, and then refigure the graph until all the segments occur equally, at which time you revert to normal beatloop processing? (I want to think of a way to do it that doesn’t involve that fractional weakening approach.)
TT: I don’t think it’ll work like that. You have to take into consideration the double wins from division matchups, and the need to carry weakened links to the next level of loop resolution.
I don’t understand your argument about the HOU->CIN game though. You say that CIN should have beaten HOU and since they didn’t that “the loss should hurt more”. How much more can it hurt than for CIN to lose their BeatWins over PIT, BAL, and GB? You also say that BeatFlukes would have considered HOU->CIN flukey if CIN had an “entirely different path to HOU”. How much different do these paths have to be?
CIN->BAL->SD->MIA->NYJ->HOU
CIN->GB->CHI->SEA->JAC->HOU
Oh, I meant that CIN *is* hurt by all three of those paths disappearing, more than if only one of them had been removed, and that makes sense to me. In Iterative, those Beatwins aren’t removed. My question is, why shouldn’t HOU->CIN hurt CIN?
For beatflukes, it’s just if CIN would have a beatpath to HOU outside of the loops that are being removed.
I think that long ago, we had managed to restate the algorithm in a way that didn’t involve the fractional weakening… I wish I could remember what it was!
At some point I’ll try and get Iterative implemented here so I can do some backtesting. I finished a few other enhancements I had been wanting to do, including the new edgepower column coming in this week’s rankings.
Ah I see. Well the difference for the Iterative is that since CIN has the multiple paths, HOU->CIN is considered a fluke so CIN gets to keep their wins. The way that CIN is punished is that each of their wins is reduced in strength. If in the future those wins are involved in other loops, they will likely be eliminated first. So while CIN’s position on the graph isn’t destroyed as it is on the Standard graph, CIN’s paths are weakened which is shown on the graph with the dashed lines. The weakened paths are also accounted for in the overall points in that CIN only gets 0.66 points for their win over GB instead of a full 1. The cumulative effect of the weakened paths may have cost CIN a spot over ATL, but ATL shares some of the weak wins further down the path so the difference might not have been enough.
Hi, just found your site. I got interested in this topic after stumbling across a paper (A network-based ranking system for American college football) on Sunday. It uses a method similar to the one that you use, so I was wondering if you’ve seen or discussed it before.
Maybe to explain it just a bit: It only takes into account wins and losses, just like your system. And it uses the idea of “beatpaths”, although it doesn’t use that term. The logic is that if A beats B and B beats C, then A would probably beat C if they played. So it counts that game towards A’s wins (and C’s losses) but makes it worth only a fraction (say one-half) of a real game. And it works for longer paths too: if also C beat D then it will count A beating D (but worth maybe only one-quarter of a real game). When you encounter “beatloops”, they automatically cancel each other out since everyone will get the same number of wins and losses from the loop (a team’s rating is just their wins minus their losses).
It seems like this might be a more natural way of resolving beatloops. In any event, the math turns out to be very simple and it takes only a couple of minutes to set it up in a spreadsheet, which I did on Sunday. I ended up going 10-4 in the games on Sunday and Monday, picking the Saints over the Giants, but getting the upsets wrong like everyone else (meaning according to the ESPN, FOX and CBS power ratings, which also happen to agree with your picks). This week the only game I have different is the Cardinals over the Giants. If you’re interested I can post the full rankings.
And just a side note: I know of the power rankings at ESPN, FOX and CBS, but do you know of other sites that have rankings? A couple of sites were mentioned in another thread: footballoutsiders.com, which have the Eagles in second place, and advancednflstats.com, which last week had the Titans at #12 and Minnesota at #17. Are we supposed to take them seriously?
Dogooder,
Thanks so much for posting a link to that paper. You’re right, they do a lot of the same things we’ve been doing here. TT started this site right around the time that paper was published. Must have been something in the water at that time… We’ve also been looking into retrodictive pick records, and discussing Monte Carlo simulations in some emails back and forth.
Last year I dug around Google Scholar looking for other papers on football ranking systems. If you have access to journal archives, there’s some interesting stuff on neural networks, using google’s pagerank, and other criteria for ranking nodes in directed cyclic graphs.
Regarding FootballOutsiders, there’s something about their measurements of ‘team efficiency’ that *always* makes the Eagles look good. Every year there is constant indignation in the comments section about the high ranking of the Eagles. The one caveat that they do admit in their DVOA rankings: they also include a measurement of variance, and the Eagles despite having a high efficiency also have a really high variance, meaning that they’re going to have flukey play where they play down to worse teams.
So, their system doesn’t necessarily punish teams for inconsistency, whereas something like Beatpaths would be more likely to punish a team for inconsistent play. You might think of it as: according to FootballOutsiders, the Eagles are *potentially* the second best team; according to Beatpaths, the *actual* results of Eagles play mean that they’re not great even if they have a lot of potential.
I don’t know anything about the AdvancedNFLStats methods, so I can’t say why they rank the Titans and Vikings the way they do.
dogooder, I would take any stats-based system far more seriously than any purely subjective system. In any case, if you’re looking for a good site for football information, I recommend ColdHardFootballFacts.
Regarding the “network-based ranking system”, it’s an interesting idea. If I understand it right, your comment isn’t entirely correct – if three good teams loop, each of them would gain more wins from their win in the loop than they would lose from their loss in the loop; and a loop between poor teams would have the opposite effect. However, if I apply it with a percentage ranking (instead of taking the difference), that approach could help give teams with many loops a more definite position. I may put together something like that for comparison/contrast with the normal beatpath rankings. Thank you.
Tom, thanks for those pointers.
Thurhame, you’re right about the loops, that they don’t actually cancel each other out if the teams in the loop have played teams outside the loop. If the only games played are A beats B, B beats C, and C beats A, then they’ll all have the same ranking. However, if there is a game between A and D, then C will be ranked higher than B regardless of the result of the game. This is because C’s “virtual” wins over D (if A beats D) are more immediate than B’s (that is, C>A>D is worth more than B>C>A>D), while B’s virtual losses to D (if A loses to D) are more immediate than C’s. Not sure if there’s a “correct” answer in this situation, but I thought it was interesting, anyway.
I checked this method over the previous seasons and it predicts correctly about 60% of the time, apparently not quite as good as the simple Isaacson-Tarbell method (although that takes into account home and away teams). I’ll probably mess around with this a bit more in the coming days and let you guys know if I find anything interesting.