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03 Nov 2006

The Bears Trend

Guest column by Douglas Walters

Eight weeks of football have passed this year, and there is one big question that remains unanswered: are the Chicago Bears for real? There have been comparisons to the 1985 Bears team that went 15-1 and won the Super Bowl. There has been talk of an undefeated season. Statistically, Chicago is one of the most complete teams in the league. Sounds like they should be wearing rings come February, right?

Allow me to step forward as the Bears' harshest critic. Do I think they will reach the playoffs? Absolutely. Do I think they will reach the Super Bowl? They're one of my favorites. Do I think they have a good chance of winning? Absolutely not. Using a new way of looking at the NFL, I intend to once and for all silence those who seek to begin production of the Super Bowl Shuffle, Volume 2.

Readers on this site have become very well acquainted with statistical analysis. It is fascinating to see the work that Football Outsiders has done to shed some light on new ways of looking at numbers. I'd be hard pressed to find anything more detailed and comprehensive. I think we can call this Fundamental Analysis -- looking at all of the factors that cause wins and losses. I would propose that there is a second angle that we need to use when analyzing the NFL. I would call this Technical Analysis, or Trend Analysis -- looking at the effects alone.

The main principle behind this work is the proven fact that football teams move in trends. A secondary principle would be that history repeats itself in football, just as it does in the rest of the world.

Using the winning percentage of each team over the past forty years, I created graphs that depict the movement of each team. The movement was in all aspects predictable. Some research into the stock market affirmed my conclusion: there are numerous ways to measure, analyze and forecast the movement of each team. I don't need to know how efficient a team is in the red zone, or how many yards per attempt the quarterback has. All I need are the effects, the wins and losses, and I can accurately tell you how the team will perform over a given period of time.

Of course, the first argument against any of this would be, "How can 22 guys running around a field be anything other than random?" My answer is this: human beings follow patterns, both physically and psychologically. Without getting into some discussion about whether Freud or Jung was right, I think we can all agree that we have routines, habits, etc. Football players have them too. When you combine the patterns of all people involved in the team, you get the team pattern. Take 16 teams, put their patterns together, and you get a conference pattern. The proof is in the charts.

As you can see, each season's winning percentage is plotted on the graph. The trend line marks their overall pattern of movement. I don't think this requires much explaining, and it does support my conclusion that Chicago is definitely a contender to reach the Super Bowl. Their success last year provided them with some upward inertia.

I'd like to present the New York Jets as our case study in movement around a trend. Take a look at exhibit A, the Jets graph dated back to 1996.

Their sudden drop to 1-15 marked a significant deviation from their trend. What happened next surprised a lot of people.

A sudden jump back over .500 put New York back in the AFC picture.

Their phenomenal season in 1998 carried them all the way to the AFC Championship game. The only problem was that they weren't really that good -- they had deviated from their trend and were doomed to regress back towards their trend.

And so the Jets fell back into their steady trend over the next few years. Strangely enough, they fell apart last year due to injury, and are primed for a comeback season in 2006. Currently they are 4-4. To some, the roller-coaster ride they took in the late nineties was horribly random. To me, it was simply several years of corrective movements that got them back on their historical trend.

Now for the bad news, Bears. Like I said before, the combination of 16 team trends gives us a conference trend. Logically, there are two ways to measure conference supremacy: Super Bowl wins, and inter-conference play wins. Each team plays four inter-conference games per year for a total of 64 games over the course of the season. Look at the following charts and take note of the similarity in trends.

Look at the past two years in particular: in 2004 the AFC won 44 out of 64 inter-conference games, and then won the Super Bowl. That was a peak year in all regards. In 2005 the AFC won 34 out of 64 games and the Super Bowl. Given that any waves regress to the mean we can assume that the NFC will win more inter-conference games this year, but not the Super Bowl. After Monday night, the AFC leads the current season 17-16.

The Super Bowl chart really puts the nail in the Bears' coffin. It doesn't matter how many wins they have this year, or how many points per game their defense gives up -- it's still an AFC-dominant year. I think if I was going to put money on anything (don't take that to mean that I'm recommending this) I'd have to take the Colts over the Bears in Super Bowl XLI. Indianapolis has been playing so well, for so long, against the best conference in football, that this season may very well be their best ever. Their win over the Broncos is a testament to their ability to dominate both technically and fundamentally.

Is it destiny, fate, or some other mystic power that guides teams to wins and losses? No. It may seem sometimes that teams or players are "due," but in reality it is just a simple trend that rises and falls with the physical and psychological strength of the team. I do have to say, however, that just as the best stock market analysts use both fundamental and technical methods of analysis, the best football analysts should do the same. There will certainly be occasions when teams are able to "buck the trend," so to speak, and the technical analysis of Football Outsiders will provide the answers. Even as I write this article, I'm anxious to see where DVOA puts the Colts after their big win over Denver (in the last rankings, I had the Colts at the top while FO had them ninth).

A final note: just as Football Outsiders has developed DVOA as their rating and ranking system, I have developed PRS (Probability Rating System) as the rating and ranking system of Trend Analysis. I use historical values as well as current values to rate each team. You can find all of this, along with other in-depth articles, on my blog. I'd appreciate any feedback you have for me, as I am always looking for more ways to update my work.

Posted by: Guest on 03 Nov 2006

95 comments, Last at 29 Nov 2007, 8:55pm by footballprofessor


by Fiver (not verified) :: Fri, 11/03/2006 - 2:23pm

Maybe I didn't have enough coffee this morning, but...whiskey tango foxtrot? Was this a joke?

"The main principle behind this work is the proven fact that football teams move in trends."

This statement was never explained and never proven. What is meant by "move"?
Is it April Fool's Day or something? Did you guys lift this from The Onion's sports pages?

by dryheat (not verified) :: Fri, 11/03/2006 - 2:29pm

I'll remember the lesson here next time I'm playing roulette. Red is definitely due.

by Ryan (not verified) :: Fri, 11/03/2006 - 2:34pm

Actually, the "trend" this year would appear to be how all the pundits favor every AFC team because of their "brutal" schedule while one of the big three comes out and smokes their AFC counterpart in the Super Bowl. (that is if PHI can contact doctor Heimlich) I've got a feeling this year's SB will be pretty boring.

by admin :: Fri, 11/03/2006 - 2:36pm

At Football Outsiders, we welcome opposing viewpoints. This is one.

by mactbone (not verified) :: Fri, 11/03/2006 - 2:43pm

Re 3:
That didn't help Seattle last year, why would it help an NFC team this year?

by Xao (not verified) :: Fri, 11/03/2006 - 2:45pm

Using the winning percentage of each team over the past forty years, I created graphs that depict the movement of each team. The movement was in all aspects predictable. Some research into the stock market affirmed my conclusion

I'm thinking it's not all that serious.

by centrifuge (not verified) :: Fri, 11/03/2006 - 2:46pm

While this does make for some interesting historical analysis, I absolutely cannot accept any predictive power unless you can show that certain teams always run in waves of certain wavelengths. Otherwise, it smacks of faulty causation.

by Ryan (not verified) :: Fri, 11/03/2006 - 2:47pm

PIT had a higher DVOA than SEA last year dude, so them winning on a neutral field wasn't a surprise, and their weighted DVOA's were within .3 of a point. What I'm saying is, the popular opinion will likely be an AFC team just becuase the AFC is so much "better" than the NFC, even if said AFC hasn't proven to be any better than it's opponent.

by The Ninjalectual (not verified) :: Fri, 11/03/2006 - 2:50pm

Are you saying that the reason the Bears will not win the Super Bowl this year is because the moon is in the AFC phase?

by zlionsfan (not verified) :: Fri, 11/03/2006 - 2:52pm

I'm sure I'm missing something here, but I don't see what in these graphs made the Jets' performance predictable, unless the prediction was that they'd eventually fall back toward .500, and even at that, the only way it predicted that was if you said it every season, and if you keep saying that a team will fall back to .500, well, eventually you'll be right, but that's not prediction. That's like Home Team 20, Visiting Team 17.

I don't even agree with the basic premise. When the only thing that two groups have in common is the uniform that they wore (in general terms - these days, you can't even be sure they'd be wearing the same uniform), I don't see why you could assume that the same patterns of behavior would apply specifically to those groups, say the '70s Jets and the '90s Jets.

And how does the stock market demonstrate that this method works for the NFL?

None of these seem to be predictive charts anyway. I don't see anything that predicts how Chicago will do this season. For that matter, I don't think the last chart even suggests that the NFC will win more interconference games than the AFC.

I don't see any analysis here. The only conclusion I see seems to amount to "over time, teams will get better or worse."

I'd rather have seen more discussion about beatpaths and power rankings.

by Ryan (not verified) :: Fri, 11/03/2006 - 2:52pm

Just like the A.L was going to SMOKE the N.L this year. We see how that went.

by Ryan (not verified) :: Fri, 11/03/2006 - 3:00pm

To be honest....it's impossible to accurately predict anything even close to 100%, unless you're psychic. So it's really worthless to be predicting who's going to win the SB through eight weeks anyway. It's a pointless discussion, that amounts to mostly trash talk and opinion. So in my totally biased opinion, I think the popular opinion is going to be way off this year, unless the Bears do actually go 16-0; but knowing the pundits, they'd still favor IND over them by 10 points. (Wink wink, IND Vs. N.E.) ;)

by worm (not verified) :: Fri, 11/03/2006 - 3:07pm

There are exceptions to everything, and the Bears this year are no exception from being an exception.

Just because the AFC has been stronger than the NFC, that doesn't mean that the best AFC team automatically has the advantage over the strongest NFC team.

by Andy (not verified) :: Fri, 11/03/2006 - 3:12pm

This seems to suggest that regression to the mean happens on a much larger level than most of us are willing to accept. Personally, I find it hard to believe that the performance of the 1985 Bears is a useful data point in predicting the fortunes of the 2006 version or that the success or lack thereof for a conference in the Super Bowl 10 years ago can tell me who will win this year. That said, I'd be interested to hear some more reasoning behind the underlying assumptions in this article.

by Doug (not verified) :: Fri, 11/03/2006 - 3:15pm

Well it's nice to stir the pot a little bit.

Re: 11

While some people may have believed the AL was going to "SMOKE" the NL this year, I've got a trend chart that says differently. I haven't really pushed hard to find anything similar in baseball, but 5 minutes of number crunching in Excel would show you that the AL was severaly differing from the historical trends.

If anyone wants to check out the Elliott Wave Theory (relating to stock market fluctuations) you can google it, and there are a few great sites that explain it. That's just one application of stock market analysis that can carry over to NFL trend analysis.

by bravehoptoad (not verified) :: Fri, 11/03/2006 - 3:34pm

A secondary principle would be that history repeats itself in football, just as it does in the rest of the world.

Whenever you hear a football person talking about the lessons of "history," what they're invariably talking about are stastical coincidences, otherwise known as the "clustering illusion." Somehow, that a little line is going up on a chart makes them think there's something going on that's causitive, and therefore predictive.

Never thought I'd see "logic" of this kind at FO.

by Rich Conley (not verified) :: Fri, 11/03/2006 - 3:36pm

I'd think this would be pretty interesting to look at in consideration with Cap numbers. More specifically, teams that tend to boom and bust.

Makes sense though, most teams tend to build a core of players, get a few good years, and then the players start to get older/leave for more $$, and then the team goes to hell trying to hang onto them.

It would be interesting to see the lines for NE/Phi/Pitt/Denver, IE those teams that look like theyre going to be strong for a long time.

by Ryan (not verified) :: Fri, 11/03/2006 - 3:37pm

NE is way under the cap, btw.

by Arkaein (not verified) :: Fri, 11/03/2006 - 3:40pm

I'm not sure how seriously the writer actually takes this stuff, but he really ought to know that you don't take a statistical observation and use it to "assume" an exact outcome.

In the previous AFC dominance period an NFC team won just befor the peak of AFC dominance. There are already two NFC wins during the current era, the Bears are strong enough to be in good position to be a third even if the AFC hasn't quite peaked yet.

by Rich Conley (not verified) :: Fri, 11/03/2006 - 3:44pm

16. To ignore that there are trends is silly.

In most cases, a team that goes 1-15 is going to be better the next year, but not by a whole lot. They'll probably win 4-7 games the next year, and then if theyre managed correctly should be getting near 8-8 and then in a couple years have a shot at the playoffs. Its regression to the mean. Its what those high draft picks are supposed to do.

Saying a 30 year old trend affects a team is kind of silly, but looking at the fact that teams tend to be cyclical isnt.

by JJcruiser (not verified) :: Fri, 11/03/2006 - 3:46pm

Well I thought this was fascinating. I don't think it dooms any given team, including the Bears, to losing the Superbowl, but it certainly makes sense in the context of the league, for the critical reason that:

As soon as a team gets very good, it is penalized by having a tougher schedule the following year and lower draft picks. Although the efficacy of lower versus higher draft picks, considering the exponential increase in salaries when you get into those very top draft picks, is debatable, I don't think it is debatble that the league makes it hard for teams to sustain greatness. Thus, it would make sense that teams would fluctuate in a wave.

What doesn't make sense, however, is the apparent ability of a few teams to stay great and a few to not be terrible. The Bears and Jets were interesting teams, but graph the Cardinals. Or the Lions. Or the Patriots. Or the Steelers. I'm not sure the relatively constant wavefunction works for all the teams, but it seems to have worked for the Bears so far.

Still, very interesting article. Thanks.

by Pat (not verified) :: Fri, 11/03/2006 - 3:49pm

the Bears are strong enough to be in good position to be a third even if the AFC hasn’t quite peaked yet.

Then again, it's worth noting that the reason the Bears are undefeated is because they're playing a creampuff schedule unlike anything else in the NFL. DVOA says even taking that into account, they're fantastic, but it's definitely worth noting that historically, the "king of the midgets" doesn't win the Super Bowl.

by Doug (not verified) :: Fri, 11/03/2006 - 3:59pm

re: 21

Fortunately, I have indeed graphed each team. While the fluctuations of some teams is a little wild, I'd say 90% of teams have a solid wave structure over the past 40 years. I'm not saying that I expect their wave lengths and/or amplitudes to remain steady forever. The main point is that humans have patterns, and those patterns are reflected in team performance.

by ABW (not verified) :: Fri, 11/03/2006 - 4:02pm

While I can see how looking at 40 year long trends can be interesting, I remain completely unconvinced that they can be predicitive on a single year. You can say something like "over the next 5 years, the Lions are probably going to get better", but saying something like "the Lions are going to get better next year" doesn't seem to me to be justified by my admittedly cursory glance at this.

Also, I am suspicious of doing things like poly fits to data sets of completely discrete data like wins and losses. Seems like a technique that is more appropriately applied to continuous data like a rating system(which appears to be what you are doing on your blog).

by Gerry (not verified) :: Fri, 11/03/2006 - 4:05pm

I think people are rejecting the concept prematurely.

I am very intrigued by the success this method has had in predicting games when teams are 'overrated' or 'underrated' by sufficient quantities.

Have you gone back and looked at how the 'predictions' would have fared in past years?

by Crushinator (not verified) :: Fri, 11/03/2006 - 4:06pm


Which is sort of funny since the same DVOA metrics say that Pittsburgh won despite being outplayed by Seattle.

by Independent George (not verified) :: Fri, 11/03/2006 - 4:09pm

I've seen this type of analysis before - this is exactly the type of reasoning people use when they try to time the stock market. It starts with a misunderstanding of efficient markets (all results are random!), followed by the gambler's fallacy (NASDAQ has been trending downward - it's bound to shoot upwards soon!), and generally ends with heartbreak (WTF happened to my money?).

Not that I disagree with the conclusion (after all, the chances of any given team winning the Super Bowl is 1/32, so it's always a good bet to say that a team won't win it). But the analysis is shaky, at best.

by Doug (not verified) :: Fri, 11/03/2006 - 4:13pm

re: 25

I ran into a little snag with that...one of the factors in the rating system is a value assigned to the strength or weakness of their historic trend. I have run the numbers all the way back through 1998 but I recently noticed that the values I assigned to their trends were based on how the line was place as of 2006, not as of the current year that I was working with. If you look at the Jets chart from 1996 you see their trend line ended at around the .180 mark, but if you look at 1996 from the 2006 chart their line is at about the .450 mark. It'll make a big difference in how the ratings come out, and I hope to make the changes in the near future.

re: 24

My brother is an absolute genius on the Einstein level, and he's working on a better equation for the trend lines that will make their fit better not only historically, but for forecasting purposes as well. That's a "near future" project as well.

by J.D. (not verified) :: Fri, 11/03/2006 - 4:24pm

The first thing I immediately thought when reading this article was that while the wave trends may have held some validity prior to the 1990s, in this age of free agency, constant coaching change, and even more frequent ownership change, I can't imagine how a team's performance even 8-10 years ago could be any harbringer of current performance.

The second thing I thought was that while regular-season wins by conference may follow general trends based on overall talent, coaching aptitude, and the like, Super Bowl wins are more or less random. When one team that wins 70% of its games plays another team that wins 70% of his games, it's lunacy to say that the outcome can be predicted with any accuracy without knowing the teams and individual matchups. The ultimate statistical no-no is attempting to draw conclusions from a small sample size, and one game per year is about as small as you can get.

by navin (not verified) :: Fri, 11/03/2006 - 4:27pm

I'd like to see San Fran's wavelength. They were above ten wins from 1983 though 1998. I guess it predicts a long downturn right now.

by Gerry (not verified) :: Fri, 11/03/2006 - 4:30pm

Re: 25
Good to hear. I am interested in seeing what comes of that, as well as the predictions going forward this year.
I share most of the skepticism expressed on this thread with regard to the whole Super Bowl question, but am very open to what you are doing with regard to the overrated and underrated teams by the trendlines.

by Gerry (not verified) :: Fri, 11/03/2006 - 4:31pm

Er, that should have said "Re: 28", since 25 was my own bloody comment. :/

by B (not verified) :: Fri, 11/03/2006 - 4:32pm

So, the Colts will go 16-0, then?

by Yuri33 (not verified) :: Fri, 11/03/2006 - 4:35pm

(Full Disclosure: I am a die-hard Bears fan, but none of what I say below has anything to do with football)

I've been lurking on FO for a while, and while there have been quite a few contraversial articles, none have prompted me to speak out. But this one takes the cake. This is by far the weakest statistical analysis I have ever seen in my life. I'm currently a science grad student right now, and if I presented any of my data with this kind of analysis in a paper, I'd be laughed out of the room. Fitting polynomial models to 40 year old win percentages on Excel?

Here's a simple little experiment you can do on Excel. When you fit your so-called trendline, check the R-squared value. Anything less than .8 or so would be considered by most statisticians as an error in the model equation you are using to fit with. You want another test? Try taking the first half of your data, fitting your poly equations to it, and then have Excel forcast to the present. See how well your equations predict the second half of your data. These are incredibly simple ways to check if what you are saying about trends have at least a modicum of validity.

The second to last chart is the one that solidified how worthless this article was. You took your poly equations, and proceeded to apply it to binary data. Any college freshmen in science could tell you that is a joke. If you really want to apply econimic theories to NFL stats, here's a couple of vocabulary terms to look up on Google: Auto-Regressive, Moving Average (ARMA) analysis, Prediction Cones, Binomial statistics. Then come back and talk to us about trends. Until then, leave statistical trend analysis to those of us who know how to use them, and know to use better tools than Excel.

by bfos7215 (not verified) :: Fri, 11/03/2006 - 4:37pm

I don't mind the conclusion that he thinks the AFC will win the Super Bowl, but this comment is out of line, "Do I think they have a good chance of winning? Absolutely not."

Especially, since he points out that the AFC's current dominance peaked 2 years ago, regressed last year, and at current is only a game ahead. I think that would lend to the argument that it's a toss up year.


by Doug (not verified) :: Fri, 11/03/2006 - 4:45pm

re: 34

Woo! Let me brush off the seat of my pants!

Your enthusiasm is impressive. From one who is attempting to learn a little more about statistical analysis than Excel can teach me, I think it would be fantastic if you stopped by my blog and dropped a few pointers. Like I said above, I've got some helpers who are working on better methods, so I'm definitely up for some extra tips. That said, I'll be the first to admit that this current method is weaker than I'd like it to be.

re: 33

In your dreams.

re: 30

Indeed, San Francisco was dominant for a very long time, and their trend line shows it. That said, they've turned back upwards. I like Alex Smith a lot, ever since I watched him beat up my BYU friends in his final year. I think he's very promising.

by doktarr (not verified) :: Fri, 11/03/2006 - 4:45pm



by zip (not verified) :: Fri, 11/03/2006 - 5:14pm

If this article had only given a shout-out to psychohistory, I would have totally bought it.

by DrewTS (not verified) :: Fri, 11/03/2006 - 5:19pm

Post 34 beat me to it. As soon as I saw the trendline on the Jets' full history graph, my first thought was "the R-squared on that thing has got to be damn near 0."

That said, I'm not against the whole "teams move in cycles" idea. That seems to fit with what I see in general. The conference wave, I'm more skeptical of.

by bravehoptoad (not verified) :: Fri, 11/03/2006 - 5:21pm

re: 20

Who says I'm ignoring that there are trends? What I'm disputing is that there's anything predictive about them. Check out the 2001 Bears--supposedly at the bottom of their "trend," but posting the third-highest win total in their history.

by Doug (not verified) :: Fri, 11/03/2006 - 5:32pm

re: 40

You're kind of helping me out here - if a team wins 4, 4, 6, and then 5 games, it doesn't take a trend line to tell you that they aren't for real. When the Bears went 13-3 that year their trend line went through the roof, which was a clear indicator that they would fall back down to where they belonged at the time. Lo and behold, they won 4 games the next year. That's regression to the mean.

I don't think I stated anywhere in the column that I could predict with Swami-like accuracy the exact win totals each year. That, echoing a few other comments above, is ridiculous. I believe that this method, however, can do a little bit better than "the Lions are going to get better next year".

by Pat (not verified) :: Fri, 11/03/2006 - 5:40pm

When you fit your so-called trendline, check the R-squared value.

Gasp! A science student, not realizing that an R-squared without errors is meaningless? For shame! :) It's equivalent to looking at a chi-squared without errors on the graph - if there's a known error, and it's not included, you won't get the right value.

And there is a known error. Quantization.

Each point on that graph has, at a minimum, a quantization error of 1/(number of games in season). That's half the distance between any of the grid ticks. For the first three graphs, the relative deviation is never much outside of that. That's really quite good agreement.

The last graph is crap because too many cycles were included, and it wasn't a high-order enough polynomial. Shouldn't be fitting polynomials anyway - you want a periodic function.

by chris clark (not verified) :: Fri, 11/03/2006 - 5:51pm

re 25, 20, 27, 17:

I agree that people are rejecting this prematurely. I think that expecting the team to have reliable cycles (e.g. biorhythms) would be foolish. I think expecting teams to improve in graphable (and to some extent predictable) patterns isn't.

Sure, one doesn't expect a roulette wheel to turn up red, just because it has given a lot of blacks recently--a roulette wheel is approximating a fair random device. However, team performance (and to some extent stock market prices) are not truly fair and random--they move due to cause (causes that are complex enough we can't accurately predict, but causes none the less).

In any case, if I read the article correctly, teams regress not to the mean of 8-8 performance, but a mean which represents their general performance over time, which can be trending up or down. The cause of that trend up-or-down is related to whether the team is succesfully growing young players or is falling due to players passing their prime or other similar effects.

Moreover, I would think certain conference effects on a team would be relevant also, and the site suggests the same thing. A team which is good in a weak conference, might overestimate how well it is actually doing, and as a result not make the changes needed to correctly improve (because the team is doing so well on its local measures), while a team in a tougher conference might work harder and thus improve more. As an annecdotal example, take IND who has handily won its conference for a few years, but has fared poorly in the post season. These results can affect a team over long periods of time and cause the 30-year analysis to be "accurate".

When one combines the two effects together, one might not be surprised to find that the trend line (and thus the mean to regress too) for DET was not substantially different from the trend line for CAR. That is when DET regresses to its mean, it regresses to a different mean than CAR does. Does CHI, NE, or INDs records this year surprise anyone? How about AZ, SF, or HOU? Which teams would you be more willing to predict a 10-6 record for next year? How about in 2 years or 3?

by chris clark (not verified) :: Fri, 11/03/2006 - 6:04pm

re 43 (correcting myself):

for conference I meant division. IND has one its division not its conference....

by chris clark (not verified) :: Fri, 11/03/2006 - 6:12pm

re 42: Pat's right! I'm not well enough versed in stats (only a few "introductory" college courses in the topic). However, unless you know the underlying distribution, you can't talk about errors. Now, for many purposes, one can make assumptions about the underlying distribution and see if the sample agrees with that, but that requires an assumption. The same arguments allow one to talk about when all the molecules rush to one side of the room, our our throwing a fair coin and getting 100 heads in a row. If a coin gave me 100 heads in a row, I would tend to doubt that it was actually fair. But not knowing the underlying distribution, I could be wrong.

by elhondo (not verified) :: Fri, 11/03/2006 - 6:15pm

I'm not sure these graphs are proof of the Bears losing a game or even indicative of that.

But I bet they're indicative of this guy not having a shot with Catholic Match Girl.

by will (not verified) :: Fri, 11/03/2006 - 6:21pm

While there are statistical problems with what you are trying to do here (as has been pointed out), my real trouble with your article is analytical. You are, at a basic level, trying to take a general trend (AFC better than NFC) and apply it to a specific situation (the Bears). Unfortunately, even assuming your trends to be correct, there is plenty to indicate the Bears as an outlier within the NFC-such as their record (nearest teams have 2 more losses), or the DVOA difference between them and the next team down. Even if a general trend is correct, apply it to outliers at your own risk.

by Pat (not verified) :: Fri, 11/03/2006 - 6:27pm

However, unless you know the underlying distribution, you can’t talk about errors.

We know one error. Quantization. It's got to be there. This is just because we're fitting a function with a smooth variate on an unsmooth measurement. It's independent of the underlying distribution because it's a measurement error, not an intrinsic fluctuation.

As for any other errors, you're right, of course.

by Doug (not verified) :: Fri, 11/03/2006 - 6:35pm

Let's hope my wife doesn't read comment 46, for a number of reasons.

As for 47, my writing of this column did cause me great fear, because I do understand that applying a generalized trend to a specific team is rather risky to say the least. I just can't help but ask myself, if I flipped the coin 40 times, would I go 11-2 heads, then 15-1 tails, then 7-2 heads? Obviously that's not a very scientific test, but I'm not a very smart guy and it's things like this that make me think.

To all you happy Outsiders, I'm interested to know what you think about the issue of slope (I address this in several posts on the blog). If Blogger would let me, I'd post an interesting table that details the slope vs. winning percentage of each team. Oddly enough, there are four major groups of teams that are divided both by slope and winning percentage. I'm trying to get that up today, but if not, I'll get it on over the weekend.

by emcee fleshy (ATL) (not verified) :: Fri, 11/03/2006 - 6:38pm

Try this in your excel spreadsheet:

Set A1 as 1964
Then fill down until A44=2006.

Set B1 as "=1+ROUND(RAND()*14,0)"
Then paste that formula all the way down to B44.

Then set C1 as "=B1"
Then Set C2 as "=ROUND(AVERAGE(B1,B2),0)"
Then paste that formula all the way down to C44.

Now, make a line chart with the Y axis as column A and the data as Column C.

Now, Set a trend line with a polynomial of 6.

Look familiar? Hit return a couple of times, it'll recalculate as much as you want. It will continue to look familiar.

Brought to you by your friends at =RAND()

by chris clark (not verified) :: Fri, 11/03/2006 - 6:50pm

re 48: Pat's right! Yes, quantization is the reason one can't compute a 5 digit value from samples accurate only to 2 digits.

On that same point, I would be suspicious of 3 digit power rankings based solely on w/l records, simply too much quantization. If those rankings were done the same way DVOA does, looking at the much more plentiful play-by-play data, and measured year-over-year one might get some useful (or at least interesting) results. I think one could get the same thing simply by using the long-term fitting over the DVOA value, since it is a less quantitized value than the w/l number (or even the pf/pa number). Unfortunately, we don't have 30 years worth of DVOA measurements, while we do have that data for w/l and pf/pa records. So, perhaps if Doug redid his analysis with pf/pa values over time, he would have a slightly less quantitized measurement.

However, I would not abandon the results just because they were showing long-term trends that may be cyclic. I would just be supsicious if they suggested that the Jets won on the SB 28 year intervals.

by Wanker79 (not verified) :: Fri, 11/03/2006 - 6:58pm

Doug, I think the main reason you've gotten so many negative responses in this thread is actually pretty simple. I think you're stretching the predictive ability of your work beyond what it is capable of (specifically the Bear's having no chance at winning the SB). I think that if you backed off the SB trand and focused more on the individual team trends and maybe the conference trends, your ideas would be more accepted (or atleast given more of a chance).

I like what you've done (except for the SB stuff), and I've always been curious if the "the NFL moves in cycles" thing was more myth of fact. And this seems to support the notion that it is more fact.

Pointing out Chicago's 2001 season was probably a fluke (it's obvious in hind-sight, but your data would have said in 2001) and stuff like trying to predict that a particular team is due for a downswing in the next year or two seems to be the more reasonable (and realistic) use.

I'm not telling you what you should and shouldn't do with your work. I'm just letting you know what I would do with it.

by tom (not verified) :: Fri, 11/03/2006 - 7:07pm

I'm probably going to make some huge mistakes in this post, and let me first just admit that my Statistics A-level was ten years ago. Ah well, here goes...
Surely the trend lines would only really be useful predictive indexes if the factors that produced them remained constant, ie salary cap strategy, emphasis on o-line, continuity of coaching staff, etc? I can see how with enough data one could evaluate the likely boom-bust cycle of a particular way of doing business in the NFL, but seeing as each different team is adopting a slightly different methodology, how is an overall graph of performance going to tell you anything useful? If you tried to tie this to something like the attitude a franchise to cap-management, then maybe you could come up with something a little more concrete. This just seems a bit abstract to me, like a set of numbers tied to nothing useful.

by Rob (not verified) :: Fri, 11/03/2006 - 7:08pm

I think it is, at the least, very, very interesting. For all the bashing that's going on, can we agree that there is some merit at least? I agree with Wanker79, that this data has uses, maybe just not this one thing (predicting the super bowl winner). Moreover, I think looking at it, and looking for underlying causation, has a lot of potential for determining what predicts a football team's success. So, let me just say, it's really interesting work, and good luck developing it more, Doug.

by Travis (not verified) :: Fri, 11/03/2006 - 7:08pm

I’d like to present the New York Jets as our case study in movement around a trend. Take a look at exhibit A, the Jets graph dated back to 1996.

Their sudden drop to 1-15 marked a significant deviation from their trend. What happened next surprised a lot of people.

A sudden jump back over .500 put New York back in the AFC picture.

Their phenomenal season in 1998 carried them all the way to the AFC Championship game. The only problem was that they weren’t really that good — they had deviated from their trend and were doomed to regress back towards their trend.

by Travis (not verified) :: Fri, 11/03/2006 - 7:11pm

I’d like to present the New York Jets as our case study in movement around a trend. Take a look at exhibit A, the Jets graph dated back to 1996.

Their sudden drop to 1-15 marked a significant deviation from their trend. What happened next surprised a lot of people. A sudden jump back over .500 put New York back in the AFC picture.

Their phenomenal season in 1998 carried them all the way to the AFC Championship game. The only problem was that they weren’t really that good — they had deviated from their trend and were doomed to regress back towards their trend.

It's good to see that the fates predicted the hiring of Rich Kotite and Bill Parcells, Vinny Testaverde's Achilles injury, and Bill Belichick's leaving.

by RobinFiveWords (not verified) :: Fri, 11/03/2006 - 7:12pm


What would be most helpful is a test of the predictive ability of your models using historical data. As a comparison, I think that whenever Aaron considers significant changes to DVOA, Weighted DVOA, DAVE, he re-runs the data from past years to see whether the predictive ability of the model increased or decreased with the changes. So if you want to test the ability to predict five years into the future, put data for the past 40 years into your model and then see how well the 1975 predictions panned out in 1980; 1976 in 1981; 1977 in 1982; etc.

by BB (not verified) :: Fri, 11/03/2006 - 7:41pm

Should this be titled "DA Bears trend" ?

by nate (not verified) :: Fri, 11/03/2006 - 7:43pm

This is a complete joke.

a) history does not repeat itself. the variables are never exactly the same. cute and inane phrase, though. limit yourself to sports, where a system is designed in a framwork for certain constant, longitudinal data and you could argue similar situations reoccur. that would be a start.

b) of course sports are cyclical- gms/owners/executives/coaches change over time, and have varying competency- eventually you are going to get a good one(s) (or a bad one(s)). however, if the frequency of these cycles is not shown to be either constant or somehow predictable, there is absolutely no predictive value here. and there's not. this isn't even mentioned or touched upon.

by Gerry (not verified) :: Fri, 11/03/2006 - 8:43pm

Christ almighty. I agree with Wanker almost 100%.

That should never happen when the topic isn't "the Redskins and Cowboys suck."

by Kevo (not verified) :: Fri, 11/03/2006 - 8:45pm

This theory is to football as intelligent design is to science.

by fyo (not verified) :: Fri, 11/03/2006 - 9:25pm

Fit some random-looking data to a polynomial and get something that looks cyclical (away from the boundaries). Wow. That's surprising. Might as well just have used a sinusoidal function.

(And before anyone gets their panties in a bunch, "random-looking" is probably more like a bounded, center-attracted random-walk - but the argument still applies).

by jason (not verified) :: Sat, 11/04/2006 - 2:39am

#50: Very well done. Absolutely correct.

#62: Correct.

#54: No.

by Travis (not verified) :: Sat, 11/04/2006 - 3:04am

For those too lazy to create the spreadsheet in #50 themselves, but not too lazy to download it: here's a version.

by manning,e (not verified) :: Sat, 11/04/2006 - 12:26pm

As a social science researcher (appeal to authority) I find this a very interesting way of looking at the nfl. Human beings are predictable by probabilites, and when examining any system or set comprised of variables totally created by humans, (except whether though the domed and climate controlled stadium of the future makes football a totally closed human system) if you have past activities you can assume present realities, however you can never assume future functions.

clustering illusion does not apply to social science, there is a whole field of cluster analysis-ever watched an episode of that silly cbs show Numbers? Pattern recognition and cluster analysis applied to human predictability is all they ever talk about.

I would be interested to know if these numbers were generated by pattern recognition software like partec or something like that or in something like wolfram's mathematica or in something i dont even know about.

interesting work. I might work on a similar idea using cellular automata or chaos math.

by manning,e (not verified) :: Sat, 11/04/2006 - 12:39pm


Dont you think that your being a little harsh? It' an article in Football Outsiders not the Journal of Applied Statistics. Give the article credit for where credit is do, thinking of applying cultural variables to what is normally thought of as subject not worthy of such examination...look up articles on Jstor or Ebsco and try to find anyone doing any interesting research utilizing trying find a link between the nfl and cultural significance..they dont exist,believe me I've tried to find them. I accept the article as an interesting attempt at something that more social science researchers should be applying. The numbers are secondary because it isnt like a program like Mathematica couldnt find significane if there was significance to find in ten seconds and any monkey who can enter numbers into a machine could figure out how to use it. It doesnt take a phd (yours or mine) to figure out that the chore of researchers is no longer to understand in total the math they are using but rather to understand what would be interesting to study mathematically and how they could use present technology to find the answer to their problem. This article at least to me presents an interesting problem and should be congratulated for that.

by Doug (not verified) :: Sat, 11/04/2006 - 12:56pm

Thanks manning,e. The social science aspect of this is probably more interesting to me than the NFL aspect, just because I'm a psych major.

by doktarr (not verified) :: Sat, 11/04/2006 - 1:40pm


No, he's not being overly harsh at all. Doug hs not even begun to establish any sort of predictive link between this so-called "trend", and what will happen to the Bears this year. Even the correlation isn't very good here, and we all know that correlation does not imply causation.

A line like "Given that any waves regress to the mean we can assume that the NFC will win more inter-conference games this year, but not the Super Bowl", is wrong in so many ways that it is laughable. The people who are trashing this article are absolutely correct. Sorry.

by Kevin Quinn (not verified) :: Sat, 11/04/2006 - 1:56pm

I just spent some time attempting to repeat your work. What you are trying to do is ineteresting and worthy of investigation. However, it seems to me to be a classic example of the evils of data mining at best, and spurrious nonsense at worst.

First of all, are your results (especially for the conferences) significantly different than random noise? Did you do any regression diagnostics, and if so, were you careful to make sure that your regressions were legit?

In my repetition of your work, in order to get R-sqr values above 10%, I had to use polynomial model of degree 5 or 6. I forced the intercept to be 0.5 for what I would hope are obvious reasons. What possible theoretical explanation could there be for team-unique 6th order polynomials?

I also did some time series analysis, but got nothing that was statistically different than zilch on average, although I gave up after a while.

Empirical analysis without any theory guiding it is pretty much crapola. In my opinion, this exercise should be filed with sunspot theory and tinfoil hats.

by Kevin Quinn (not verified) :: Sat, 11/04/2006 - 2:10pm

I neglected to mention another issue in my above post: When you use the 6th order poly team-specific models to forecast, they blow up (or down), and generally do a sad job of predicting out-of-sample data.

by manning,e (not verified) :: Sat, 11/04/2006 - 3:59pm

im not saying the math is good, im saying for this to be an applaudible arguement all you have to appreciate is the idea. and the idea is instead of doing what dvoa attempts to do which is also applaudable, it is an interesting idea to think up other variables that might effect the outcome of a football game. How cool would it be to code some varaibles and then do a manova on some cultural main affects that contribute to wins or loses? I think very cool.

Given that there are always 2 teams and only four outcomes of every game

(Team A wins)
(Team B wins)
(Game Cancelled)

there are a number of ways in which various cultural theories can be mathematially applied for one of those four outcomes. Since you know the total outcome of the entire sample and every one of its units (games) (until the next game is played) you also begin by knowing what the probality of any of those four outcomes happening on a given day.

Since you also know how many players are within the game that lead towards a certain goal you could also come up with an analysis of how much each players motivation for said goal is worth. With dvoa of each player you could factor in how much say a fully motivated peyton manning is worth. But what if one of the 11 players on team A is actually motivated for his group to fail? Then team B has 12 motivated players and team A has 10. Further given that football is based on a hiearchy of power bases you can factor in coach or owner, or governmental, motivation for given outcome and that is where football gets really interesting.

One interesting study so far is spousal abuse rates when home team loses. Think of the social control variables attached to specific sports outcomes. While to me trend studies arent specifically interesting they can be interesting when combined with dvoa and to me thats why thought any thought should be appreciated, because its better than the show the nfl is actually putting on--see pink introduction to monday night football.

by Steve Sandvik (not verified) :: Sat, 11/04/2006 - 5:02pm

What is this frequentist doing here? I want my Bayesian statistics back! I can get past trends masquerading as prediction in the newspaper on any subject I choose.

There may, in fact, be something to this idea. But it needs to *start* with prediction of past events. That's the minimum standard for something with genuine predictive power. That's not something you do next, it's what you do first, before you go claiming you have a line on what's going to happen in the Super Bowl.

If I recall correctly, Estimated wins is a strong predictor of playoff success. One might conclude from that that it's better to come out of the *weaker* conference, since that would result in a weaker schedule. (Though it might be best to come out of the weakest division in the stronger conference, depending on relative conference and division strength).

In the end, I don't think you have enough samples to make a reliable Super Bowl prediction, since it hasn't been all that long since they changed the conference alignment and scheduling system, which one might reasonably expect to impact the correlation between conference strength and Super Bowl winner. In fact, those changes correspond with the rightmost region of all your graphs, so I'd be extremely leery of using anything to the left of that as a strong predictor.

by D (not verified) :: Sat, 11/04/2006 - 6:01pm

Interesting article with some aspects worth further study, but I'm not really comfortable with the idea that historical trends fated Scott Norwood to shank the final kick in SB XXV.

by Lincoln (not verified) :: Sat, 11/04/2006 - 6:19pm

I wonder what the Arizona Cardinals, or Detroit Lions curves would look like.

by Lance S. (not verified) :: Sat, 11/04/2006 - 6:20pm

Cultural main effects ... wha?

by Gerry (not verified) :: Sat, 11/04/2006 - 7:50pm

"One interesting study so far is spousal abuse rates when home team loses."

Having fun trolling?

by Bilbo (not verified) :: Sat, 11/04/2006 - 8:06pm

A (very) little knowledge is a dangerous thing. This is like watching a seven year old with a circular saw and a router - they certainly can cut some wood, I just wouldn't want them making my furniture. And no, you do not get credit for trying - grades for effort ended in elementary school.

by QuantyCurmudgeon (not verified) :: Sat, 11/04/2006 - 10:19pm

This is the article FO should never have published. It's just embarrassingly bad and devalues the good work that FO has done with their own stats. How did it ever get through FO's quality filter? Do they really want to be associated with this nonsense? What's next, predictions based on biorhythms of the coaches and the phase of the moon?

Please try again once you have an out-of-sample backtest that shows predictive success with a decent t-stat.

by TBW (not verified) :: Sun, 11/05/2006 - 2:07pm

Couldn't you do the same thing(in terms of graphing), but flipping a coin instead of using NFL records, and get the same basic chart ? It sure as hell wouldn't mean you could make a meaningful prediction about the NEXT coin flip.

Regression to the mean is a powerful thing, except that you never know when it is going to occur, so it is useless for making exact predictions about a single event.

by Doug (not verified) :: Sun, 11/05/2006 - 6:29pm

Chicago just made my point for me today. Thanks Bears.

by ZH (not verified) :: Mon, 11/06/2006 - 10:48am

RE# 65
Cellular automata are probably not going to be much useful for analyzing football. Cellular automata, Stephen Wolfram's book aside, are probably not capable of handling something as complex as football in an acccurate manner. Complexity social science using agent-based modeling programmed into something like RepastSimphony are probably better for analyzing football.

by ZH (not verified) :: Mon, 11/06/2006 - 11:09am

As to the article itself, as an economics major currently involved in research (as a research assistant) regarding the structure of financial securities markets, I can state that few serious economists believe any longer in this type of pattern charting and most any other analysis that relies on pattern searching as having any accuracy with regard to predicting the future price of securities.
John Authors in The Financial Times a couple of weeks ago had an article about how the use of Fibonacci numbers (a pattern searching method) has now been totally discredited. Additionally experimental economics researchers have found that when people use such pattern chart analysis they are only right about half the time and are easily fooled by randomly generated computer models of a securities price series.
Given all this and this method's inaccuracies with regard to securities prediction, there is no reason to believe that it is any better with regard to football.

by manning,e (not verified) :: Mon, 11/06/2006 - 1:32pm


thanks for the heads up on repast,def gonna look into that extensively (this is why I find a thread like this much more interesting then the rest of the website, because its experimental and can generate new knowledge as you have for me--those criticizing the math of the bears sucking model should note that if you arent making mistakes it probably means you arent taking chances)

I think a level 4 automata rule could def generate some intersting results. I am a believer that the NFL is utterly rigged, a cultural device utilized to replay national storylines, such as the patriots (america) win!(during times of war-anyone remember the bills giants superbowl?looks a lot like the ram-patriots superbowl and both during the first year of both wars in iraq!)or the patriots lose(sad) three days before a midterm election on national t.v.

So far my football as a business model has predicted 3 out of the last five superbowl winners correctly. This year my model has it narrowed down to 5 teams and luckily for me being a giants fan the giants are the nfc representative but the nfc is more cloudy with the broncos,ravens, and patriots all possible representing the afc.. my model has the giants going 14-2 just like the dolphins of 83 before losing to the nfc team.

since I am presuming the social system of football to be a world with order, without chance the possibilty of automata being predictive is possible because the boundries of the grid are known. I will def take a look at how a model of business protocol can be mixed with individual modeling.thanx

by Steve Sandvik (not verified) :: Mon, 11/06/2006 - 6:01pm

Chicago didn't make any point for you. The odds are Indy's going to lose a game too. It's hardly clever to predict that a team won't go 16-0, regardless of what people who should know better might be claiming, and you didn't need an spurious graphs to show that. They nearly lost to the Cardinals, for heaven's sake.

by Ian (not verified) :: Mon, 11/06/2006 - 9:08pm

I surfed over here from Baseball Prospectus and I have to say I am disappointed. This "analysis" has no predictive power whatsoever. I encourage the original poster to run the excel file found in comment 64, and stop being so smug when GASP the Bears lose a game.

by Doug (not verified) :: Tue, 11/07/2006 - 12:43pm

Hey, I can't help but be a little happy when
GASP the Bears lose
GASP the Falcons lose
GASP the Cowboys lose
GASP the Patriots lose
GASP the Vikings lose.

The AFC vs. NFC games are leaning in favor of the AFC 20-17. The amazing thing is that the top AFC teams in winning percentage are 11-2 against NFC opponents. The top NFC teams in winning percentage are 6-6 against the AFC. Look at who their opponents were. I've got a point.

PRS has picked winners with 70% accuracy this year. If that's not predictive power, I don't know what is. I can't help but wonder how things will be in a year from now. Newer and more accurate mathematics, along with a better understanding of the psychological factors involved, should produce even more accurate results. There's no doubt in my mind.

by Kayser (not verified) :: Tue, 11/07/2006 - 8:21pm

My first thought was that this is garbage.

My second thought was that Bill Parcells already does this analysis and picks his jobs based on it. Doug - Can you let us know if the curves of Parcell's teams were at or near the relative minimum when he took over?

by doktarr (not verified) :: Thu, 11/09/2006 - 3:38pm

PRS has picked winners with 70% accuracy this year. If that’s not predictive power, I don’t know what is.

That's right.

by Doug (not verified) :: Fri, 11/10/2006 - 12:15pm


Actually yes, when Parcells has taken over each team starting with the 1983 New York Giants, the team has been in a trough. In each case the team has improved drastically.

by Alex (not verified) :: Sat, 11/11/2006 - 5:35am

"PRS has picked winners with 70% accuracy this year. If that’s not predictive power, I don’t know what is."

This is the kind of thing people have been asking about. You didn't say how your predictions had fared in the past, so people were reluctant to agree with you. Now all you have to do is show us what your method would have predicted for the Super Bowl winner in previous years, and tell us how accurate you would have been. Think back to 2002, for instance. If you had been doing this back then, you would have written a similar article saying that the NFC champion won't win the Super Bowl. But Tampa Bay won, 48-21, over the Raiders. So we know that there have been exceptions to this "trend", and you haven't given us any proof that the Bears aren't going to be another exception.

by Ted (not verified) :: Wed, 12/06/2006 - 5:09pm

I just stumbled on this article. Wow, no wonder it's rare for any stock fund manager to consistently beat an index, with analysis like that! Come on, a CURVE FIT on the 0-or-1 data for Superbowl wins is completely nonsensical. In each of the charts presented, the residual errors (differences between the fitted curve or model and the actual data) were huge. Anyone who's taken very basic statistics would conclude that the models were all insignificant compared to the otherwise randomness of the data. Did you notice that his curve fit of the Jets data changed dramatically with more data added in (clearly not predictive)? The trend analysis certainly doesn't explain the rapid improvement in the Bears record in the 80's (all well above the trend), nor their 13-3 season when the "should" have been bottoming out, nor why they wouldn't win the Superbowl. In the current period, it looks like the NFC has been winning every third year. Thinking that this was a hoax, I skimmed over this crank's blog, inaccurately titled "The Science of Football." He actually proposed that he should be able to predict game performance based on the players' BIRTHDAYS and some formula to predict their biorythms. This doesn't even approach the level of junk science, and is out of place at Football Outsiders.

by Doug (not verified) :: Tue, 06/05/2007 - 1:54pm

How sweet it is! BOOYAH!

by Cyrus (not verified) :: Thu, 11/29/2007 - 5:39pm

You just linked to this from another thread. I read through it, and was impressed at first that you predicted the Colts and Bears in the Super Bowl, with the Colts winning.

Turns out that is exactly what happened.

But then I remembered that both the Colts and the Bears had the best division in their conference at this point, so regardless of whatever math you used, you could have just picked the best team in each conference and given weight to the AFC.

Right now, Week 12 of 2007, I pick the Patriots and whoever wins the DAL/GB game tonight, with the edge going to the Patriots in the Super Bowl.

No math required.

(Although I am interested to see whether you had made any predictions concerning this year, or whether you would be willing to make some predictions for next year. Will SF keep sucking? Will Arizona improve finally? Can the Colts and Patriots remain on top in the AFC?)

by Cyrus (not verified) :: Thu, 11/29/2007 - 5:39pm

Best "record", not division. That was a typo.

by footballprofessor (not verified) :: Thu, 11/29/2007 - 8:55pm


I linked back to this for a couple reasons.

1. nobody should be surprised that the Jets were good last year and are bad again this year. Simple trend charts are actually really nice tools for forecasting, because they show very clearly when regression to the mean will happen.

2. i did make some predictions regarding this year - namely that New Orleans and San Diego would collapse, and that the Colts and Steelers would be favored to win the Super Bowl. The one team that I feel I missed completely was the Patriots...I said 10 wins and no Super Bowl. I'll say it right now though - I still don't think they'll make the Super Bowl, and I think they'll collapse due to free agency and injury over the off-season.

I run a site, click my name for the link. Plenty of good research and content.