The picks were absolutely horrible this week at 6-10 – I guess that’s what you get when half the teams in the league don’t activate half their starters. The big story in the graph this week is the re-emergence of the DEN->PIT beatwin – it impacts a lot in the standings.
| Rank | Team | Notes | Last Week | BeatPower |
1 |
 |
(Beat NYG) An amazing season. I wonder if there’s a record for how many records a team sets in a season (beyond the obvious first-year teams). |
1 |
100.0(31/31 – 0/31) |
2 |
 |
(Lost to WAS) Dallas loses to Washington but is still ranked 2nd in the league. From what I’ve read, it seems Dallas tried to play this game pretty much at full power. I wonder how much of a concern it is to them that they loast. |
2 |
95.8(23/24 – 1/24) |
3 |
 |
(Lost to TEN) The loss to Tennessee doesn’t matter. I didn’t realize how extensive their sitouts were until after the game, and even with then the score was very close. |
3 |
92.0(22/25 – 1/25) |
4 |
 |
(Beat OAK) San Diego has times where they look like they’re stumbling, but in terms of games, they’ve been on a real tear, winning six straight. I’m really looking forward to the AFC playoffs. |
4 |
88.9(22/27 – 1/27) |
5 |
 |
(Lost to NE) I was most struck by just how depressed the Giants seemed on their final drive. They wasted time, were slow in getting to the line and between plays. And yet they still got the touchdown. I think they might have had a chance to get the ball back had they been more motivated at the end of the game. All that said, it was impressive how up they were for this game before that point. |
6 |
87.0(19/23 – 2/23) |
6 |
 |
(Lost to HOU) The reasoning behind why the Giants and Jacksonville swapped places this week is pretty subtle, but there were a lot of game outcomes that resulted in this swap, so it’s almost like the system wanted it to happen. Jacksonville evidently rested many starters and lost to Houston this week. |
5 |
82.0(18/25 – 2/25) |
7 |
 |
(Beat DET) Green Bay defeats Detroit and has another double beatloop with Chicago. Their strongest beatwin, Denver, now appears better than Tennessee’s strongest beatwin, so they rise above Tennessee in the rankings. |
8 |
84.0(19/25 – 2/25) |
8 |
 |
(Lost to GB) Denver’s beatwin over Pittsburgh re-emerges this week, which makes Detroit look a lot better. This setup of wins and losses really screws up the NFC playoff picture from the beatpath perspective. The main reasons for Detroit’s high placement is the fact that Chicago beat Green Bay twice, and because Detroit beat Tampa Bay. |
11 |
76.0(17/25 – 4/25) |
9 |
 |
(Beat IND) Tennessee does manage to grab the final wildcard slot from the beatpaths perspective, so the AFC picture ends up accurate. |
7 |
80.0(14/20 – 2/20) |
10 |
 |
(Beat MIN) Denver’s beatwin over Pittsburgh is restored, which pushes Denver up in the rankings. It felt like an unsuccessful failure of a season, but in the grand scheme, Denver had some quality wins that are either reflected in their beatpaths or protected them from losses to other tough teams. They have a split with Oakland, and their other beatloops are TEN->HOU, MIN->CHI, and MIN->SD . All that said, I’m not sure this ranking will hold up when the season is finally over – there are a lot of beatloop possibilities in the playoffs that would effect the very iffy-seeming DET->DEN->PIT beatpath. |
19 |
64.8(16/27 – 8/27) |
11 |
 |
(Lost to BAL) Pittsburgh’s game was essentially meaningless, but they are pushed down by DET->DEN. |
9 |
60.9(14/23 – 9/23) |
12 |
 |
(Beat SF) That’s got to be really rough to be Cleveland right now. After Indianapolis phoning it in like that and still playing a close game, it seems like that should have been an Indianapolis victory, and Cleveland’s rightful playoff spot. I wonder what the press was like in Cleveland on Monday. Maybe Kenneth knows, he appears to be my “man on the ground”. |
10 |
56.2(13/24 – 10/24) |
13 |
 |
(Beat JAC) Since the beatloop elements created by this game already existed in other beatloops, this game was largely irrelevant. Still, “Denver Lite” has got to feel pretty good about their season… and having a better record than Denver. Yay Kubiak. |
13 |
62.5(9/20 – 4/20) |
14 |
 |
(Beat BUF) Philadelphia finally gains a beatwin that isn’t gobbled up by their other losses, and rises significantly in the standings. From the beatpaths perspective, still not a playoff team, but they are ranked higher than either of the top teams in the NFC South or NFC West. |
21 |
70.0(12/20 – 4/20) |
15 |
 |
(Lost to CAR) Tampa Bay sure isn’t doing much to distinguish themselves, despite being the best team in the NFC South. This division would be notable in how bad it is if not for the suckitude of the NFC West. Plus, it’s just easier to feel sorry for the NFC South. |
12 |
53.6(3/14 – 2/14) |
16 |
 |
(Beat NO) Chicago defeating New Orleans is the explanation for DEN->PIT reappearing in the graph – Chicago almost got to retain their beatwin to Denver, but Denver defeating Minnesota took it right back away. But Chicago does manage to shed its Seattle beatloss, which helps it rise a bit. |
18 |
50.0(2/15 – 2/15) |
17 |
 |
(Lost to PHI) Buffalo suffers a beatloss to Philadelphia, but also looks a bit worse due to DEN->PIT, and so they fall slightly in the rankings. |
15 |
47.8(11/23 – 12/23) |
18 |
 |
(Beat TB) Carolina rises significantly with the victory over Tampa Bay, but other graph dynamics keep them from rising further. I’m curious, has Vinny ever officially retired before, or was every other time just him fading away? I’d love to see him come back two or three more times, like a friendly ghost. |
23 |
47.2(7/18 – 8/18) |
19 |
 |
(Lost to CHI) New Orleans ends the season with a lot of play in their rankings. They played well at times but just kind of seemed to lose their identity again. I’m only aware of their running back’s injury impacting their season, were there any other big explanations? |
22 |
36.7(1/15 – 5/15) |
20 |
 |
(Beat DAL) Washington holds steady. They’ve got some momentum but right now their game against Seattle looks pretty pathetic for a playoff game. |
20 |
39.1(8/23 – 13/23) |
21 |
 |
(Lost to ATL) #20 at #21 in the playoffs? Are you kidding me? Then again, I’m looking at Seattle’s schedule, and it appears they didn’t ever even have the opportunity to be very highly ranked. Their two most highly ranked losses are against Pittsburgh and Cleveland, and they haven’t even played anyone in the top ten. This brings up a good point about my yammering about beatpaths playoff seedings. The NFL kind of has to use its own division-based playoff seedings, because of how they match up divisions ahead of times in the schedule. When you’ve got the NFC West matched up against the NFC South, there’s just not much opportunity to be ranked very highly. Dynamic scheduling in the final four weeks of the NFL season, though… that could be very interesting. |
14 |
34.0(6/25 – 14/25) |
22 |
 |
(Lost to DEN) New Orleans defeating Chicago led to Detroit and Denver being pushed up in the rankings, but Minnesota losing to Denver had the same effect due to BUF->WAS->MIN re-emerging. So Minnesota sinks significantly. That said, Minnesota could rise up a bit more in the playoffs if Washington performs well. |
16 |
31.8(6/22 – 14/22) |
23 |
 |
(Lost to NYJ) Despite losing, the Jets are subtly helped by dynamics higher in the graph – other teams look worse now. |
27 |
15.6(0/16 – 11/16) |
24 |
 |
(Beat MIA) No great reward for defeating Miami, and Cincinnati is hurt by DEN->PIT. This is another team that just lost their way again. Pretty wild that Carson Palmer went public with his dissatisfaction of the coaching staff. It’s a shame because they have a lot of talent. |
17 |
20.8(3/24 – 17/24) |
25 |
 |
(Beat KC) The Jets also get downwardly leapfrogged. |
28 |
13.2(1/19 – 15/19) |
26 |
 |
(Lost to SD) Oakland holds steady on the loss to San Diego. And since they lost, let’s see here… that means that even if Denver had defeated Houston and San Diego, they still would have missed the playoffs. If they had defeated Oakland the week before, they would have been tied with Cleveland and Tennessee at 10-6. I *think* Denver would have won that tiebreaker. So it was that weird unmotivated game at Oakland that did them in, when they were probably still deflated by the Chicago loss. At any rate, Oakland can feel good about eliminating Denver from the playoffs by defeating them at home. |
26 |
10.0(1/20 – 17/20) |
27 |
 |
(Lost to CLE) The longer beatpaths above San Francisco push them down in the rankings a few slots. I don’t know how to feel about this team – from this distant perspective, it kind of seems like Mike Nolan is the problem. He’s had a weird passive aggressive way of dealing with Alex Smith that probably hasn’t helped the locker room chemistry. |
24 |
17.3(2/26 – 19/26) |
28 |
 |
(Beat PIT) Defeating Pittsburgh didn’t have any material impact on the graph or rankings. I honestly didn’t get the impression that Billick was really a downward dragging force on this team. Was firing him a good move? |
25 |
13.0(1/23 – 18/23) |
29 |
 |
(Beat SEA) Atlanta rises three slots by beatlooping away some losses after defeating Seattle. Despite all their troubles it seems there are some encouraging aspects to this team. |
32 |
12.5(0/24 – 18/24) |
30 |
 |
(Beat STL) Arizona did have a couple of good wins against the AFC North this season, but they didn’t end up as impressive as they first looked, and got beatlooped away by their loss to Baltimore. Other losses such as to Washington and Carolina are still reflected in the graph. Defeating the worst team in the league doesn’t help much. They looked talented in their losses, though, so maybe they’ll be a real story next season. |
30 |
13.5(1/26 – 20/26) |
31 |
 |
(Lost to CIN) Man, Bill Parcells just looks mean, doesn’t he. I think he’s the scariest coach/manager/whatever creature in the NFL. He looked like a vulture in this game, ready to pick through a dolphin’s carcass. |
31 |
2.1(0/24 – 23/24) |
32 |
 |
(Lost to ARI) Anyone up for a post-mortem of St. Louis in the comments? It can’t all be because of injuries, can it? I’ve always liked this team – very fun to watch when they’re on. |
29 |
3.8(0/26 – 24/26) |
Sorry, I live in St. Louis, so I don’t know what they feel like in Cleveland.
Though they have no one to blame but themselves…
Losing Deuce was a big loss for NO, and they didn’t respond correctly at first–they tried to make Reggie Bush take over Deuce’s responsibilities, and they’re not the same player. Other than that, the defense (which was bad last year) added a cover-2 corner to a man scheme, which resulted in one of the worst years by a corner, ever. And Brees wasn’t really himself at the start. So, the team kind of regressed on both sides of the ball, and ended up losing ground because they weren’t that good to begin with. They should bounce back next year.
I don’t know if Billick was a problem in Baltimore, but I think the impression was that he wasn’t adding much. He’s supposed to be an offensive guy, remember, and that team made its living on defense–so whatever made them successful, might be traced to someone else’s efforts. At least, that’s what the thinking appears to be.
As for the Rams…they were a team in decline anyway, and the injuries just overwhelmed that. The loss of Pace basically decimated the line, which took away a lot of Bulger’s effectiveness, which made the passing game suffer, and Jackson’s injury pretty much left their offense in tatters. Plus, their defense wasn’t that good last year, and didn’t improve much this year. None of that means they should have been as bad as they were earlier, though…I’m not exactly sure what happened. But with the injuries, 5 wins would have been an accomplishment.
My graphs are up:
http://www.twomuffin.com/start.php?page=BeatPaths.htm
http://www.twomuffin.com/start.php?page=BeatPathsWeighted.htm
http://www.twomuffin.com/start.php?page=BeatPathsDoktarr.htm
A couple weeks ago I mentioned how rare it should be for a team to reach a 9.00 rating on my scale and that the Patriots passing it was just another mark of how dominant this team has been. I supposed that it was the best rating ever and probably by a bit. Out of curiosity, I ran all three algorithms on every year from the AFL/NFL merger in 1970 and listed the top 12 teams for each year.
STANDARD
——————
’07 Patriots (9.02) – ???
’86 Giants (9.00) – Won Super Bowl
’79 Steelers (8.90) – Won Super Bowl
’81 49ers (8.51) – Won Super Bowl
’91 Redskins (8.45) – Won Super Bowl
’04 Steelers (8.41) – Lost AFC Championship to #2 Patriots
’83 Redskins (8.03) – Lost Super Bowl to #8 Raiders
’75 Rams (8.03) – Lost NFC Championship to #8 Cowboys
’89 49ers (7.97) – Won Super Bowl
’87 Saints (7.93) – Lost in Wild Card round
’85 Bears (7.89) – Won Super Bowl
’03 Patriots (7.84) – Won Super Bowl
WEIGHTED
—————–
’70 Vikings (9.49) – Lost in Divisional Round
’83 Redskins (9.45) – Lost Super Bowl to #2 Raiders
’84 Dolphins (9.25) – Lost Super Bowl to #2 49ers
’80 Falcons (9.11) – Lost in Divisional Round
’07 Patriots (8.83) – ???
’90 49ers (8.75) – Lost NFC Championship to #3 Giants
’95 49ers (8.53) – Lost in Divisional Round
’93 Bills (8.33) – Lost Super Bowl to #2 Cowboys
’72 Steelers (8.22) – Lost AFC Championship to #5 Dolphins
’81 49ers (8.19) – Won Super Bowl
’89 49ers (8.14) – Won Super Bowl
’91 Redskins (8.03) – Won Super Bowl
DOKTARR
—————
’70 Vikings (9.46) – Lost in Divisional Round
’89 49ers (9.43) – Won Super Bowl
’91 Redskins (8.98) – Won Super Bowl
’86 Giants (8.74) – Won Super Bowl
’83 Redskins (8.73) – Lost Super Bowl to #3 Raiders
’92 Bills (8.66) – Lost Super Bowl to #10 Cowboys
’93 Chiefs (8.59) – Lost AFC Championship to #3 Bills
’88 Bills (8.54) – Lost AFC Championship to #2 Bengals
’95 49ers (8.39) – Lost in Divisional Round
’82 Dolphins (8.35) – Lost Super Bowl to #8 Redskins
’07 Patriots (8.30) – ???
’76 Patriots (8.21) – Lost Divisional Round to #2 Raiders
As you can see, the Patriots are only considered the best team ever by the standard method, and only barely. I noticed some interesting things while doing this exercise. The ’85 Bears and ’72 Dolphins were not even the best team in their respective years in each algorithm. Only eleven teams were unanymously chosen as the best of the season out of these 38 years, and only 4 of them make all 3 top 12 lists. The ’89 49ers, the ’83 and ’91 Redskins, and the ’07 Patriots.
I didn’t look specifically at any individual year, but the 1970 Vikings are far and away the top team in two of the three algorithms. The standard algorithm agrees that they were the best team of the season, but only rated them at 6.93.
I also found it interesting that the previous best team by the standard measure was the ’86 Giants, whose defense was of course run by Bill Belichick. They appear 4th all-time by Doktarr’s measure, but were not the top team of ’86 by the weighted measure (’86 Chicago Bears: 7.76).
For fun, here are the worst teams of all time:
Standard: ’76 Buccaneers (-8.82) – The 0-14 team.
Weighted: ’91 Colts (-9.36)
Doktarr: ’04 49ers (-9.63)
Interesting… the most striking thing about those ratings is that the “standard” system seems to be a much better predictor of success than the “weighted” one. What does that say? Teams that win close games in the regular season are better prepared for the playoffs than ones who win in blowouts and lose a few close ones, maybe?
I’m gonna do another comparison of our two approaches, where I look at teams that are rated drastically differently. I’ll use Moose’s rating system and look at gaps of five or greater. For comparison, I’ll look at the end of season DVOA ratings.
TB 15->5
WAS 20->6
MIN 22->7
Three huge jumps that lie on a single beatpath. The big culprit is that Minnesota retains credit for the win over San Diego in my version of the algorithm. The CHI->GB games have less of an impact. What actually happened was that CHI->GB was in five different beatloops, so the other 10 beatwins involved were each reduced to 60% strength, but retained. (Actually GB->MIN->CHI and GB->DET->CHI were reduced to 80% because they went from a weight of 2 to a weight of 1.6, but you get the idea.)
I think this shows the strength of the incremental system, as one (or even two) games that are inconsistent with other results can’t screw up the system too much, no matter how many beatloops they are involved in. (KC->MIN gets wiped out by simultaneously reducing the weights of eight different 4-team beatloops!) At the same time, the incremental system gives the double beatloop some real significance, as oppose to being roughly equivalent to a single beatloop.
Personally, I think these three teams are a little overrated in the incremental version, and underrated in the standard version. DVOA puts these teams at 7, 12, and 14, which sounds about right to me.
NYG 5->11
Not really a drastic drop – mostly fueled by the rise of the three teams above, and Minnesota retaining its beatpath. DVOA has this team at #16, lower still.
ARI 30->14
DET 8->15
Another two teams that our algorithms have consistently disagreed about. Both have mixed together extremely inconsistent seasons. Your algorithm has been kind to Detroit but refuses to let Arizona off the hook for the San Fran losses. My algorithm has basically decided that they’re both mediocre. DVOA has them right together just like I do, but lower down – #23 and #24. That 8->24 gap is the biggest between DVOA and your rankings, while my biggest is Carolina’s 13->27.
DEN 10->16
PIT 11->17
CLE 12->18
Pretty self-explanatory. Both algorithms string these three out under Detroit, so Detroit’s fall leads directly to this. DVOA has these three as #18, #8, and #13 respectively. So DVOA is basically saying that the DET->DEN->PIT path is bogus. I can’t really argue with that, but there’s not a whole lot of data to get rid of it. Both algorithms leave it in, and it screws both graphs up in different ways.
PHI 14->20
Just when your algorithm finally gives Philly some credit, my algorithm finally strips them of the Detroit win and knocks them down. The biggest culprit is that Seattle’s loss to Atlanta knocks Seattle down, and they still have credit for their win over the Eagles. I think it’s pretty fascinating that they moved in opposite directions in our two versions in the same week, and it’s an interesting and subtle case for comparing the algorithms.
CHI 16->21
BUF 17->22
Victims of Philadelphia’s slide.
I forgot to mention – PHI, CHI, and BUF are ranked #11, #20, and #19 respectively by DVOA. So my algorithm seems to under-rank the Eagles but does pretty well with the other two. This makes sense given Philly’s several close losses.
It’s interesting that the top stayed pretty vertical on my graph despite week 17′s wacky results, but the bottom turns into a bit of a muddle, as four different teams are reduced to zero beatwins.
“Conflict picks” ended the regular season 6-3, I believe. I’ll save playoff prediction comments for the next thread.
I think that a very important piece of evaluating these results is not taking rankings at face value. Above you note DEN->PIT->CLE as a string. They happen to be evenly spaced out with ratings of 0.21, -0.29, and -0.71 respectively. However, take a look at #18-20 on your list and you’ll see CLE at -0.71, SEA at -1.40, and PHI at -1.47. This says that rank 19 and 20 are a lot closer to each other than 18 and 19 are. This applies to DVOA ratings as well. I know it’s difficult to compare different rating systems in another way, but just keep in mind that the rankings are not the real data.
Yeah, absolutely Moose. I’m more interested in looking at the places where the two beatpath algorithms drastically disagree, and I’m using DVOA simply as a guide to see which one is closer to conventional (stathead) wisdom.
I love the Redskins, but putting them at #2 pretty much closes the door on any serious consideration of the point differential algorithm.
I love the Redskins, but putting them at #2 pretty much closes the door on any serious consideration of the point differential algorithm.
That and Denver being 30th. The Skins benefit from outscoring the Cowboys in their season split, while the Broncos suffer from being outscored by Oakland in their split. The only reason I keep running this method is to show the people who keep coming here saying that we need to use points, can see how badly that method performs.
I’m still trying to figure out what significance there may be, if any, between the results of the historical runs I did. While the standard method appears better at predicting Super Bowl success based on the numbers above, that isn’t the full story. Considering all 37 previous seasons (’70-’06), the standard method picked 11 winners correctly, the iterative (doktarr) method picked 9, and the weighted only picked 6.
However, the eventual Super Bowl winner averaged a ranking of 3.35 on the weighted system, a 3.51 in the standard system, and a 4.48 on the iterative system. While the weighted system didn’t predict many #1s to win correctly, 10 Super Bowl winners were ranked #2 instead. Furthermore, the weighted system only ranked two Super Bowl winners out of the playoffs, the ’70 Colts and ’71 Cowboys. It has been right for the last 35 years. The standard system only missed twice also, but was wrong about the ’99 Rams and ’00 Ravens instead. The iterative system however, missed 5 times in total, the four mentioned above plus the ’88 49ers.
So while the weighted method obviously gets some teams way wrong, it seems to have some merit… somewhere… that I can’t quite determine.
Do you guys know how to read the three-team tiebreaker rule? The first tiebreaker is head to head among the group, and if DEN, TEN, and CLE had been tied, I would have seen that as DEN 1-0, TEN 0-1, and CLE 0-0 (since Cleveland didn’t play any team). That would mean Denver wins the tiebreaker, but that doesn’t seem right since Cleveland didn’t get a chance to play either team.
I’m a bit leery about drawing too many conclusions from the super bowl champs’ spot. I’d be more interested in which algorithm correctly picks more games. There are two ways you can look at this:
- Given the games that had happened to that point, which approach picks more games for the next week correctly? This would be the a priori approach. My “conflict picks” were 6-3 in the second half of the season, but this is obviously a pitifully small sample.
- Given the final ranking for the season, how many games would be “picked correctly”; i.e. not considered upsets? The would be the a posteriori approach.
The second approach is one I’m less curious about – because it’s mathematically possible to always find a ranking that would have the best season picks record up to that week. I know that the standard method doesn’t quite rise to that level, but I also remember once last season when I was curious about that approach, but found a game that, while leading to a better record, wouldn’t have made sense to contradict. But it still would be interesting to find a system that would a) find that best ordering (combined with some tiebreaker), and then b) see that *that* method’s future-picking record would be.
TT: The head-to-head in a three way only applies if all three teams played each other, and only if one team swept the other two. Since CLE didn’t play the other two, it doesn’t apply. Going to the second step leaves the conference records, CLE and TEN are 7-5 to DEN’s 6-6 which eliminates them. Since a team is now eliminated, it starts over again on the 2-team tiebreaker schedule. CLE-TEN didn’t play, so no head-to-head. They have the same conference record, so that doesn’t help. Next is common opponents. CLE and TEN each played: HOU, CIN, OAK, and NYJ. CLE went 3-2 while TEN went 4-1. Game over, TEN gets the final spot. This is why if CLE had won last week instead of this week (against CIN, a common opponent) it would have gone to the next step, strength of victory, where CLE had the advantage.
Ah, got it. So, if Denver had won its last four games, it would have been 8-4 in conference, eliminating Cleveland, and Denver had the head to head over Tennessee. So it looks like it was Denver’s loss to Oakland that knocked them out of the playoffs.
One of the things I’m working towards evaluating is the playoff results. Based on regular season results only, between matchups of the Super Bowl contestants the methods scored as follows.
Standard: 18-19
Weighted: 18-19
Iterative: 16-21
I’ll have to revisit the first round of the playoffs though to see how things went there. This will all be good research to do during the offseason. By then, we’ll be able to add this year’s results to the data set.
That’s taking end of regular season results and using them to predict super bowl winner? I wonder how that changes if the playoff games are figured in.
One thing that’s worth noting as we throw these comparisons around is that we’re really talking about a pair of distinct algorithms:
1) The algorithm that eliminates beatloops and leaves an acyclic directed graph.
2) The “tie-breaker” algorithm that produces a linear ranking using the remaining beatwins.
As it throws out far fewer beatwins, the iterative approach is much less reliant on the tie-breaker. While I’ll admit that I find this aesthetically nice, it’s ultimately not worth much if the other approach is more accurate. So far we see evidence for slightly better results for the standard approach (plus tiebreaker) in predicting SB wins, but slightly better results for the iterative approach (plus tiebreaker) in predicting regular season wins.
Note that there is no “tie-breaker” in my standard method rankings like in TT’s. Each team has a specific amount of paths in and out which determine it’s rating and that’s that. If two teams have the same difference, they will have the same rating and one will arbitrarily be ranked higher based on which team entered the system first, which is why looking at the ratings is more appropriate than the rankings.
Another thing we need to keep in mind is that we don’t consider these methods perfect, but we have do decide what we want to get out of them and objectively evaluate the results, and only make adjustments to make the programs behave properly.
Currently, I believe our “mission statement” is to create a completely objective ranking system that places the teams in order considering only a teams wins and losses relative to each other. Basically, we’re looking for an automated Dr. Z. We make no claims about being able to predict future results, but in retrospect matchups should follow the graph.
Therefore, to fully look at the value of these algorithms, the playoff and Super Bowl results should be put in before seeing if the Super Bowl pick is “right”. I will do this at some point in the future, but I think this again can be part of offseason coverage since we’ll need some topics for the long dark winter.
Moose, that’s what I mean by a tie-breaker. Tie-breaker was admittedly a really bad choice of words on my part. Forget I said it. What I mean is, you have
1) an method to come up with the graph, and
2) another method that uses the remaining beatwin data to decide which team is better between two teams, with the constraint that you choose a method that will always be consistent with the graph.
All I’m trying to say is that these are two separate things.
If #2 produces a result that is a tie, then you can choose to have or not have an actual tie-breaker.
Yeah, I’ve been using “tiebreaker” loosely too. For a while, beatpower was the tiebreaker, and rather than that being paths in and out, it was just number of teams above and below. I do like paths, although I’m curious if there’s still a way to capture the *shape* of beatpaths below a team… because a beatpath graph below a team that goes down as a stalk and then splays out at the bottom (call it a stork) might have the same number of paths as one that splays out just below a team, then with single paths below (call it stilts)… yet the latter would be much more stable and less rickety, indicating a stronger team.
TT: The formula I use gives many more ponits for “stilts” than “storks” for the exact reason. Multiple wins higher in the graph count for more than splits down below.