Beatpaths picks were 9-5 this week. One of the variants that absorbs more graph data correctly picked Atlanta over Green Bay this week. I was 0-1 for my personal picks this week, which puts me at 4-4 overall.
A couple of interesting beatloops this week. The NY Jets earlier victory over Miami is looking more and more valuable each week as Miami continues to bump off high quality teams. As a result, the NY Jets have no beatlosses this week, shedding the beatloss to Miami-conquered San Diego.
Also, Atlanta’s win over Green Bay beatloops away CAR->ATL and GB->MIN, while Minnesota’s win over New Orleans beatloops away NO->TB->GB
And here’s something new that I may or may not continue in future weeks. The graph of all the beatloops so far this season:
And finally, this week’s beatpaths graph:
I like the beatloops stand alone graph. Please keep it as a regular feature if it is not too much trouble.
Quick interesting thought for a different way to do the graphing.
Instead of trying to separate the teams into tiers generate a graph that is more concerned with radially spacing beat paths coming in and out of each team then draw iso-lines of your tie-breaking numbers.
Implementation is a bit more complicated then the current implementation but I think that it would reveal some relationships that are currently lost.
The beatloops graph is great, keep it up
I know it’s just a meaningless consequence of your graphing program, but undefeated TEN under winless DET is sort of disorienting. I have to remind myself that your graph in no way is arguing that the NFC west (except Arizona) is better than the AFC south.
I really like the beatloop graph, although it may get too messy later in the year. It makes it a lot easier to figure out iterative resolution:
I already went over the MIA-NYJ loops; iterative resolution doesn’t change the graph appearance.
The big 8-team mess gets broken at GB->MIN and MIN->CAR, leaving CAR->CHI->IND->MIN->NO->TB->GB, with Atlanta off to the side on a CAR->ATL->GB path. However, the TB->CHI win then creates a 5-team beatloop which wipes out most of that. All you have left is CAR->ATL->GB, TB->GB, and TB->CHI, all at half strength. Green Bay looks worse, the NFC south looks better.
Oh, and we now have half of the divisions in clear pecking orders. The AFC North and South, and the NFC East and West, have a beatpath running through them. Denver joins TEN/PIT/NYG/ARI as the only teams with a beatpath to the rest of their division, but their loss to KC has prevented a clear pecking order from developing.
My graphs are up: http://www.twomuffin.com/BeatPaths.htm
There is a difference between the Iterative and Standard graphs this week. Both NYJ and MIA have all connections to the graph BeatLooped away and are floating by themselves. This is what happens when two teams play the same exact 4 teams with opposite results. Strange.
I like the graph of beatloops; it’s nice to see that information. In the future, I’d put it after the main graph, though. It might get unreadable as the season goes on. Refresh my memory: last season, did you just list the beatloops under the graph, in text?
As the season goes on, the number of beatloops makes graphing a bit ridiculous. I don’t believe beatloops were ever listed regularly, however if you are ever curious about the beatloops for any given week you can use the link I posted above and click on the “show paths” link right above the team rankings. For the curious, here are the Standard Method beatloops for the week.
NYJ → MIA → NE → NYJ
NYJ → MIA → SD → NYJ
KC → DEN → OAK → KC
ATL → GB → MIN → CAR → ATL
TB → GB → MIN → NO → TB
CAR → CHI → IND → MIN → CAR
Doktarr: Out of curiosity based on your statement “undefeated TEN under winless DET is sort of disorienting” I remade the standard graph for this week using a new rule that a team cannot be on a lower level than a team that it has a higher ranking than. It stretched out the graph to make sure TEN was over DET, as well as clearing up all other ambiguous placements.
I haven’t decided whether or not I like how this looks. It seems to make areas of the graph easier to see, but it stretches the whole thing out more than I like. Use the link below to see the resulting graph.
http://www.twomuffin.com/images/GraphByScore.png
Right, of course, the NYJ->ARI->MIA path is in both 4-team loops, so it goes away too. That is really weird, although it feels intuitively right to me.
That version does make it easier to quickly see which teams have done well. To be clear, I don’t really have a problem with the standard graph; it just takes me a bit longer to get my head around it.
I rather like MOOSE’s graph with the rule about vertical placement, the only features I wish it had is the arrows going all the way to the team symbols and the color coded divisional backgrounds like the graph above. I know they don’t add a whole lot, but it’s a nice feature.
If someone gets really ambitious, what would be really spiffy is a way to select a team and see all the beatpaths that relate to the team, and from that which paths are due to actual wins by the team and which are due to the selected team beating Team A who beat Team B. Ideally (in my head), this would be done by just selecting the team on the graph, all teams and paths not linked to the selected team would gray out, and the remaining paths would be highlighted.
Chalk me up as another fan of MOOSE’s graph with the vertical placement rule. I think a sprawling-yet-consistent-with-the-rankings graph is more desirable than a tight-yet-unintuitive graph.
The NYJ and MIA situation is really odd, and the place where the difference between a 3 team beatloop and a 4 team beatloop gets kinda iffy. Just drawing out the games these two teams have been involved prior to removing any loops gives 3 different loops:
NYJ->MIA->SD->NYJ
NYJ->MIA->NE->NYJ
NYJ->ARI->MIA->NE->NYJ
NYJ->ARI->MIA->SD->NYJ
Interestingly, within this limited set of games, if you were to remove the longer loops first then go to the remaining shorter paths, you’d end up with just NYJ->MIA remaining but with the current system, you end up with a remaining NYJ->ARI->MIA beatpath. I’m not sure which is more correct, but it seems to me that the head to head win should mean more than the path through ARI.
One of the methods of weighting beatpaths I remember hearing about was to reduce the weight of a path the further removed from the team in question, assigning each path in relation to a team with a weight of 1/n where n is the number of hops away from the team, and a direct win has a value of n=1. Under a system like this, with the above set of games NYJ would have a score of 2.5 – 3 = -0.5 while MIA would end up with exactly the opposite score. Granted, this doesn’t take all the other games into account, so I wonder where this would go if that sort of path scoring system were used.
I like the traditional beatloop graph over Moose’s new rule graph. To me, it fits more inline with the spirit of only looking at win/losses. The only teams that Ten has beaten are teams that everybody else has also beaten.
JT: Per your recommendation of colored nodes by division and arrows that reach the box, here is an updated graph of the new tiered system.
twomuffin.com/images/GraphByScoreColored.png
As for an interactive graph, while I agree that it would be a fantastic feature, I believe it would take more effort than it is worth at this time. The best I can offer is a table which shows a team’s remaining BeatWins and BeatLosses which would be shown in a similar fashion as the longest BeatPaths and removed BeatLoops are.
You also argue that the NYJ->MIA win should mean more because it is “head to head” however I think you’re saying that because it is a division game. NYJ defeated ARI in a head to head matchup and ARI defeated MIA in a head to head matchup and thus keeping NYJ->ARI->MIA preserves more head to head matchups. If it were the case that:
NYJ->ARI->NE->NYJ
NYJ->ARI->SD->NYJ
NYJ->MIA->ARI->NE->NYJ
NYJ->MIA->ARI->SD->NYJ
Would you argue that we should keep NYJ->ARI instead of NYJ->MIA->ARI? If so, what about that particular game makes it more important?
Finally, you suggest a new weighting system based on path length. I admit I don’t fully understand where you’re going with this, or how you get the numbers you show. If you’re trying to do this scoring before loops are removed, I don’t get the purpose since as a loop, when summed over each team each link will have the same weight. If instead you’re using it after loops have been removed, based on this weeks Standard graph, I get vastly different numbers. NYJ has 15 paths leading out weighted by your methods to a 5.7 score. NYJ has no paths leading in for a 0 penalty leaving them with a 5.7. MIA has 0 paths leading out and 4 paths leading in which weight to a penalty of 2.3 giving a final score of -2.3.
Can you explain your weighting method more clearly with a full example so I can understand what you’re going for?
Bleh, the link is incomplete above.
http://www.twomuffin.com/images/GraphByScoreColored.png
Don’t worry Moose, most of us who have made it this far on the interwebs can handle cutting and pasting a link.
I very much like that colored node graph. It gives a ton of information without a lot of re-interpretation needed.
Interesting discussion about the relative importance of NYJ->ARI->MIA versus NYJ->MIA. Of course, with the iterative approach, you can start with either the 4-team loops or the 5-team loops, and you get the same result. Everything gets wiped out either way. You can slice and dice it as much as you like, but you have two 2-2 teams with exact mirror image records.
“tiers” in the iterative rankings, assuming I understand Moose’s new graphing standard correctly:
NYG
WAS DEN
CAR TB
DAL CHI TEN ARI
NE PHI BUF
PIT NO ATL MIN SF KC GB OAK (and MIA NYJ)
BAL JAC SEA
IND CLE DET STL
CIN HOU
This is actually the same height (9 tiers) as the standard graph.
oops. Forgot SD, which drops Oakland down.
NYG
WAS DEN
CAR TB
DAL CHI TEN ARI
NE PHI BUF
PIT NO ATL SD MIN SF KC GB (and MIA NYJ)
OAK BAL JAC SEA
IND CLE DET STL
CIN HOU
OK, last time, honest, I actually drew it out this time:
NYG
WAS DEN
CAR TB
DAL CHI TEN ARI
NE PHI BUF
PIT NO ATL SD MIN (and MIA NYJ)
SF KC GB OAK BAL JAC
SEA IND CLE DET
STL CIN HOU
You have NO and SF on the same level and ATL, GB and KC on the same level which can’t happen since NO->SF and ATL->KC and ATL->GB. SD should be on the level with NO/ATL but I don’t see them anywhere in your list. Having them there would also force OAK down a level.
It looks like you were building this graph from the top down, while I prefer to keep every team graphed as low as possible so I start from the bottom up.
The first 3 teams have no wins so are all placed on the bottom rung of the ladder.
Tier 1: #32 HOU, #31 CIN, #30 STL
While DET is the next team, they are tied with CLE and must be on the same level. Since CLE->CIN, CLE must be graphed higher so start the next tier.
Tier 2: #28 (tie) CLE/DET, #27 IND, #26 SEA
JAC->IND forces the beginning of the next group.
Tier 3: #25 JAC, #24 BAL, #23 OAK, #22 GB, #21 KC, #20 SF
Again due to a tie, MIN gets to be graphed with SD. Since SD->OAK, we start a new level.
Tier 4: #18 (tie) MIN/SD, #16 (tie) NYJ/MIA, #14 (tie) NO/ATL, #13 PIT
This 3-way tie is bumped up because of PHI->PIT
Tier 5: #10 (tie) BUF/NE/PHI
ARI->BUF moves us up another tier.
Tier 6: #8 (tie) ARI/TEN, #7 CHI, #6 DAL
TB->CHI starts the next group.
Tier 7: #5 TB, #4 CAR
DEN->TB forces a step up.
Tier 8: #3 DEN, #2 WAS
And then NYG->WAS tops off the graph.
Tier 9: #1 NYG
Hah, looks like you corrected yourself before I could finish.
Your last one is consistent with mine. Here’s a graph of it.
http://www.twomuffin.com/images/IterativeByScore.png
Re: 14 (Boga):
I like the traditional beatloop graph over Moose’s new rule graph. To me, it fits more inline with the spirit of only looking at win/losses. The only teams that Ten has beaten are teams that everybody else has also beaten.
I agree that you can’t necessarily put Tennessee at the top level, but to have a 5-0 team below an 0-4 team is still wrong. The only reason the original graph is that way (in my understanding) is to have the shortest lines possible. The only reason for that is aesthetics.
but to have a 5-0 team below an 0-4 team is still wrong.
Not necessarily – it highlights that the 5-0 team has only beaten unimpressive teams, while the 0-4 team has only lost to much more impressive teams.
By the way, I think we ran into this with Baltimore last year. Baltimore was what, 4-0? And the media was writing about them a lot, when here the low placement in the graph showed them as only beating unimpressive teams. They eventually came down to earth. The low placement doesn’t mean they’ll be favored to lose against other teams higher up in the graph, it just means we don’t have the win/loss data to assume they would.
While I agree 100% with what TT is saying, there was a case last year that bothered me. If you look at Week 7 of last year, CHI had BeatLooped away all of their wins and all but one of their losses. The only loss remaining was to DAL who was near the top of the graph at the time so despite having 0 wins and 1 loss on record, they were graphed 4th highest. Their rating (by my reckoning) placed them 15th with a negative score (-0.34).
Compare this to PHI in Week 10 of last year. PHI was in the same situation, a single loss to NYG (4th on the graph), however they also kept a single win over NYJ (31st on the graph). How do you decide which level to put them on? By my previous rule, they were graphed on the level above NYJ which put PHI (-0.33) in the company of BAL (-4.46).
So going back to the fact that our default graph “highlights that the 5-0 team has only beaten unimpressive teams, while the 0-4 team has only lost to much more impressive teams”, the new graph basically states that the teams DET has lost to aren’t really that impressive. It also shows an obviously open space below TEN which we can learn to interpret as the fact that their placement on the graph is being propped up and could crash without supporting evidence. This may be preferable to simply punishing TEN for the schedule they were given.
This is a good debate. Let’s keep it up. I’ll base my graphs next week on the results.
MOOSE: Sorry, I got a bit off and rambled a bit in my hurry to finish my post before I had to leave the computer. The colored graph looks nice, and I agree that the wishlist idea I proposed is probably too much effort to make it more than a wish at the moment. I’d try to code it up myself if I could find the time. I wasn’t suggesting that NYJ->MIA was more important because it was a division game, but because it was the outcome of two teams meeting on the field and one coming out the victor. That seemed more of a determination of which of these two teams was the better than an indirect relationship through ARI. But I do see your point about this method leaving more game results intact in the graph. I think I was just rambling because it seemed like a bit of an anomaly to me that MIA has beaten two teams that have beaten NYJ but there is still a beatpath from the Jets to the Dolphins. But I suppose that’s how it works out.
As for my scoring system, I agree, it really doesn’t make sense to apply it to loops. Rather, it would be similar to the scoring method you use on your pages, with one difference, that the further removed from direct wins by a team is, the less it is worth.
For example, from this weeks Standard graph after the loops are resolved, ATL is involved in the following paths:
OUT
ATL->DET
ATL->KC
IN:
DEN->TB->ATL
Under the current system this resolves to an Out value of 2, an In value of 2, and a Raw score of 0.0. What I am suggesting (and I’m not sure it’s a good idea or not) is that the links get weighted less the further removed they are from the team the score is for. The suggestion is that the score be weighted based on the number of steps (N) away from the team in question, with a value of 1/(1+N) where a direct win has a value of N=0.
In this suggestion both of the Out paths are from direct wins by ATL, so they’d both be weighted at 1, giving ATL an Out score of 2. On the IN path, the TB->ATL involves ATL, so that would have a score of 1, but the DEN->TB path is 1 step away from ATL, and thus have a score of 0.5. That would give ATL a total IN score of 1.5 and a Raw score of 0.5.
I see that this would give more weight to on the field wins that do not get beatlooped away, while giving less weight to long beatpaths (while not removing all credit for a long path). I did the Raw scores of GB (it was another easy one) and got -0.0833.
I really don’t know right now how this would affect the ratings, but it I’m somewhat curious to see how it would turn out.
Boy, I wish I could participate in the debate more this week.
I’ve got two massive deadlines with clients, J2EE and php… maybe next week. I even still have one of Kenneth’s comments flagged from two seasons ago about another possible way to look at beatloops!
I agree entirely with TT that the point of this site is to look at the wins, and that graph placement is a secondary concern. But making the graph placement consistent with the power rankings (i.e. no team is in a lower tier than a team it is ranked above) retains that consistency. We are simply replacing a fairly arbitrary standard with one that gives the graph a bit more information. Since the rankings are, by definition, consistent with the graph, there’s never a conflict.
Moose, thanks for putting that graph together.
JT: Ok, from a rating perspective that makes more sense. I thought it was a good idea so I ran some scenarios with it. Unfortunately, it failed one of my essential rules in that it can rate a team higher than a team that it lost to. Consider the 6 games:
A->D
D->E
E->F
B->D
C->D
E->G
E->H
This makes a graph that essentially looks like this:
A B C
\|/
D
|
E
/|\
F G H
Run the scores, and you’ll see that D gets a score of -0.5 and E gets a score of +0.5 despite the fact that D->E. This cannot be allowed.
doktarr, that’s an interesting way of looking at it. The beatpath graph being based on the power rankings. I’ve just never looked at it that way before because I always generate the graphs first, and then the rankings. But the rankings only really depend on the beatpath “model”, which can be drawn in kabillions of different ways. It might be possible to draw the graph in a way that is more related to the rankings in the future.
But intuitively, I’m looking at the graph as-is and it still just seems to make sense to me. An arrow from one team to another, in my mind, has just always been an indication that that team is better than the other. It never says how much better. Just better. When I imagine pulling Tennessee away from the teams it has beaten, it feels like a value judgment to say that the team is “more better” than those teams. Because, who’s to say that Baltimore or Minnesota shouldn’t be pulled up with them? But… at this point, I’m also very used to looking at the graphs just in terms of relationships, rather than vertical tiers implying quality.
Also, for those who are wondering, the vertical placement in the graph doesn’t have any affect on the power rankings. The rankings this week are equally considering all the teams that have no beatlosses for first place, including Tennessee.
Eyeballing the Miami beatloop, it sure seems that NYJ->MIA is the flukey one.
Comparing the number of different discrete paths from each team to each team.
MIA:NYJ – 2:1 (Miami has two paths to NYJ, NYJ has one to MIA)
MIA:NE – 1:1
MIA:SD – 1:1
NYJ:NE – 1:1
NYJ:SD – 1:1
SD:NE – 1:1
Is that logically equivalent to the Iterative approach? I see how fluking out NYJ->MIA would create the ARI beatloop and make MIA and NYJ float alone, like how Moose found.
I’ve felt the same way up until now. What’s making me change my mind isn’t so much that TEN gets pulled up, but that in cases similar to the Week 10 PHI of last year that I referenced above, I wont have to put PHI at the top or bottom, I’ll be able to find out exactly who they should be graphed beside. All of the vertical placement will still follow the base rules but in addition will never contradict the rankings. I think this is a good thing, if only for clarity’s sake.
I’m in the process of modifying my code to go based off the the rankings. Luckily I already calculate those first so basing the tiers off of them shouldn’t be too much. I’ll post next week’s graphs using the new style and if I like it, I’ll retroactively make the graphs for previous weeks.
Please keep the ideas coming, I want to have the best overall ideas before I spend the time to post historic seasons. It’ll be a lot of work I’d rather not have to redo later.
SD:NE hasn’t happened yet, stay tuned Sunday.
Yes it looks like that’s another way of explaining the iterative method. I tried another more complicated loop and the logic worked out the same from both angles, even to the weakening of existent links.
Moose: Agreed, that is a scenario that should not be allowed to happen. Thanks for running it.
As for the graph, I liked how Moose’s graph only elevated a team to be at the same level as teams rated below it in the rankings. I think to actually push them higher in the graph would have been too much. But in the case of TEN and KC, we don’t have a direct connection. Just from looking at the graph, KC might be just slightly worse than the teams that have beatpaths to it, and TEN might be slightly better than the teams it has beathpaths to. Of course, either team may be much worse/better than those teams they’re connected to as well. So just putting them at an equal footing, seems to make sense.
ThunderThumbs: Does not NYJ have 2 paths to MIA?
MIA to NJY paths:
MIA->SD->NYJ
MIA->NE->NYJ
NYJ to MIA paths:
NYJ->MIA
NYJ->ARI->MIA
Or am I not understanding something about what you’re saying?
Anyway, this will likely resolve itself with a few more games, I’m guessing.
JT, I was looking at it specifically within the context of the beatloops that were taken out. But it turns out it’s the same difference – if I take that out, then the ARI beatloop emerges anyway.
Yeah, I guess another way of stating the thing about TEN’s vertical placement is that there’s no objective reason – based only off of wins, losses, and who beat who – to believe that Tennessee is better than Detroit. Aside from the fact that TEN had a beatpath to DET through MIN and ATL that got beatlooped away. Of course, there’s no reason to believe DET is better than TEN either, so it’s basically up to the tiebreaker approach to decide. In mine, TEN would be favored just because TEN has been higher ranked than DET in the past.
Well, the more I look at it, the more I think that the situation with MIA and NYJ is just a matter of limited information, and either the standard or iterative method gets these teams right. I lean toward the standard method in this case, since I like to think that actually beating a team on the field matters, so if you have to try to determine where these teams fit, that should mean something. It would be really convenient if they would just play each other again, the results either way would do a lot to help sort this out, but that’s not going to happen until the last week of the season. It seems like a scheduling fluke that to this point that each team has played 4 games, one between the two of them, and the other 3 against the same 3 opponents. I guess it’s not that odd, since outside of MIA and NYJ, there are only 2 teams that MIA plays that NYJ does not (and the other way around), but to draw the same three teams at the beginning of the season just seems odd. Add on that both of these teams can’t seem to decide if they’re Jeckel or Hyde, and this is the mess you get.