Very good. # 1 in the NFL in fact. No this is not a homer rant. Caveat: this thread is not for those who don’t take much stock in, or are against “non-sense” computer power rating calculation, BCS and stuffs... I am not an X-and-O football fan, but use probabilistic algorithms (Bayesian) to rate the win capability of a team and predict the outcome of a game. Just for fun and betting. I know most fans don’t care much about computer ratings, but some betting people take this seriously (I do only small bet, <$500 a week, but some of my colleagues use our system for high rolling..) The reason I start this thread is that this is for the 1st time this season our computer model shows that the Pats have a good chance to win it all. (Las Vegas line is 9/1). The Pats have jumped from #4 to #1 in our system thanks to their victory over the Jets. (which was much more impressive that it appears) AFC playoff team ratings: Bal: 10.5 (overall) 11.2 (home) 9.6 (away) NE: 10.5 (overall) 9.2 (home) 10.8 (away) SD: 10.2 (overall) 11.9 (home) 8.7 (away) Indy: 9.0 (overall) 12.1 (home) 7.4 (away) There are many computerized power rating system out there, e. g. Sagarin (http://www.usatoday.com/sports/sagarin/nfl06.htm, DVOA, Troy Aikman,... they range from simplistic with a lot of fudge factors to highly complex, arcane algorithms. Examples of some lesser known rating calculations, but which are just as solid can be found, e. g. http://www.nutshellsports.com/wilson/nfl.html. Our result is that the 4 top AFC teams are so close with each other now that any can beat any. If fact, on neutral ground, the Pats are slightly better than the Chargers. Right now, our game model predicts SD-NE 26-24, mainly because of SD HFA. (The Pats’ away power is an advantage also, but not enough to overcome SD’s home). [Note: Our model is non-linear and non-commutative, and differs from many other models that use power rating linear subtraction to obtain point spread, which would not be able to generate paper-scissor-rock (Colts/Bronc/Pats) scenario. Our model actually produces a probabilistic outcome for a given game]. For this small 2-pt difference (1.7 to be exact), between SD-NE, it is practically statistically insignificant. So, all those accolades on the talented Chargers are just BS in our model. In terms of team play, the Pats are just as good mathematically. I don’t have an explanation, but a conjecture: Individual standouts, (e. g. probowlers) are for human-interest stories, but like BB said “the power of the wolves is in the pack”. The style of the Pats play is to do a great job as a pack, which reduces the need of individual heroics that are good for high-light films. Our model unfortunately cannot take into account of “post-season” effect, because there aren’t enough statistical data for “post-season”. (Not enough games). So any post-season considerations, e. g. Belichick-Brady experience vs. Rivers’ inexperience cannot be quantified without some arbitrary fudge factors, (which are no-no’s in our model). But if indeed, the Pats can raise their performance a notch in playoff, I would be very nervous and would not be that confident if I were a Chargers’ fan. Same time last year before the Denver game, our model projected a loss. It really showed that the ‘05 Pats were just not good. (It projected the Colts as the front runner, with Steelers and Broncs distant 2nd). This year is really different. The Pats have risen to #1 now (on paper) and I am more optimistic (on paper).

First of all, welcome to the board, and I hope you keep posting out here. I think you will find that there are several of us who enjoy thinking along these lines. Sounds like most of us, myself certainly included, have a lot to learn from you. Your prediction is especially interesting to me since I had already decided that my "prediction" for the game's score in the board's "prediction" thread this week would be one or two points in favor of the Pats, though I haven't yet chosen the respective numbers. Question: You say that your model gives a probabilistic outcome for the game, presumably yielding most likely mean scores for each team. What does the distribution around the 26 and 24 look like for each team? What is the Standard Deviation around the 1.7 point spread?

Question: You say that your model gives a probabilistic outcome for the game, presumably yielding most likely mean scores for each team. What does the distribution around the 26 and 24 look like for each team? What is the Standard Deviation around the 1.7 point spread?[/QUOTE] Thanks. The distribution is not Gaussian and therefore does not have finite SD. We use confidence region instead. So the 90%-confidence region is roughly an ellipse (not true ellipse) with one end says SD 32-NE 20 ( ) and the other extreme is NE 28- SD 18 ) )

I guess we'll find out on Sunday. I do know that I don't need stats to tell me that the Patriots are playing the best ball in the NFL right now and have been ever since the Miami "wake up call" game that saw the OC make some major play calling changes. SD and Baltimore might have the highest seeds but that has more to do with how they were playing in September and October than it does in January. Pittsburgh illustrated perfectly that a team needs to peak at the right time to win the SB - and even though SD is 14-2, that means nothing as of Sunday. It's 0-0 at game time. Potentially One and done for the Chargers.

Thanks. The distribution is not Gaussian and therefore does not have finite SD. We use confidence region instead. So the 90%-confidence region is roughly an ellipse (not true ellipse) with one end says SD 32-NE 20 ( ) and the other extreme is NE 28- SD 18 ) )[/QUOTE] OK. While I am conceptually aware of elliptical distributions vs the stuff that most people think of when you say "distribution" you're definitely sending me back to my stat texts this weekend (it's gonna rain anyway), but I do note that the mid point of the scores in the 90% (why only 90%) confidence region are 25 for SD and 24 for NE, so there's something in the "rough" ellipse that I would need to understand better that yields the 26-24 score.

[/QUOTE] OK. While I am conceptually aware of elliptical distributions vs the stuff that most people think of when you say "distribution" you're definitely sending me back to my stat texts this weekend (it's gonna rain anyway), but I do note that the mid point of the scores in the 90% (why only 90%) confidence region are 25 for SD and 24 for NE, so there's something in the "rough" ellipse that I would need to understand better that yields the 26-24 score.[/QUOTE] Think of it as a bivariate dist P(x,y), with x=NE score, y=SD score. It's not symmetric. The area around the mean that you integrate P(x,y) such that it is =90% is the confi region, which has a rough ellipse shape. It stretches one side more than the other. One can choose any level of confi (0-90%) and generate a family of contours. The smallest confi is near the mean (26,24), and grow larger till 90% or 95% (Just a number people usually pick for calc). A line x=y divides the P(x,y) into 2. Integrate over the entire upper half gives SD prob of winning. Likewise, the lower half gives NE. In this case, 53.9% for SD and 46.1% for NE. If I assume TB and the offense has a little more power (a fudge number) it can easily tips to say, NE 60% and SD 40%. If I assume Rivers befuddled because of whatever and lower his unit performance a little, it can be very comfortably 75%-25% and a 7-10 points victory. Personally, I worry about the team fitness, body clock, and their blood serotonin levels at 8 PM... The at-home Chargers may find that extra adrenalin rush late to pull out in the last minutes. Best regards.

awesome thread--do stick around--I'm going to be interested in this type of analysis for draft probabilities!

Haha, so let's put that into English.... the Pats might lose by 12 or win by 10? Whew, really going out on a limb here, aren't you?

Totally agree with you. Their power rose dramatically after the Jaguars game, Titans, and impressively with the Jets. These teams are good and not rah-rahs like Chargers' fans make them to be. We can make a case that the Pats actually improved after each game, and NOT just proved themselves with challenges. The analogy is like this. A person, say Joe goes through weight lifting test. He starts at 200 lbs, but you notice how hard he has to strain himself to get it. Next he does 240 lbs, but you notice he does with less effort. The conclusion is that he actually increases his capability after the 200-lb test. Otherwise, you would expect he had to work even harder to do the 240 lbs. What does not bode well for the Chargers is their last 3 games did not show any evidence of such improvements. But absence of evidence is not evidence of absence, so they may pull out some thing in them for playoff and crush the Pats. I doubt it. But any claims of their "superior talents" (which may be true individually) are just bull**** at the team-play granularity.

No, the extra game is not used to add anything, it is scaled to the number of plays (not games). SD and Balt are not penalized for not playing. But of course, SD could have played a game with a tough opponent, and if their performance were better than the previous rating, SD rating would also increase. SD is still the top team no doubt, but the differences between the top three, per evidence, are not as big as hype would make it. If NE and SD play a 7-game series, I'll take NE 4-3.

Hope you post on a regular basis! Sounds like you have a lot of interesting things to say about football.

Hmmm...this is terrific and I look forward to learning more. it also looks like there are one or two soft variables that could drive the model's outputs in different directions...reminds me of what my stats professor once said to me...in the final analysis it comes down to whether you'd bet your next paycheck on the outcome...

OK, your model's projection came close enough (26--24 vs 24--21) that I'm curious what it says about Sunday's game under similar assumptions.

I didn't read this thread, so just ignore this if it's totally off the point. But I'm answering the subject line only here: How good is this current Pats team? Well, they're 14-4 and playing away in the AFC Championship team. That's -exactly- how good they are.