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Tue, 27 Nov 2007

week 12 power rankings 

combined              	offense               	defense               
NWE	100.000        	NWE	100.000        	PIT	100.000        
GNB	91.348        	DAL	88.412        	TAM	91.899        
DAL	87.502        	CLE	81.795        	IND	88.280        
IND	84.628        	IND	81.040        	SEA	83.732        
PIT	73.969        	GNB	78.505        	NWE	83.169        
JAC	73.190        	CIN	75.524        	GNB	80.832        
TAM	63.483        	SDG	72.373        	JAC	77.369        
SEA	61.943        	PIT	72.216        	KAN	74.473        
NYG	61.109        	DET	71.292        	PHI	72.405        
CLE	59.826        	ARI	70.420        	DAL	69.258        
SDG	56.212        	NYG	70.343        	SDG	69.141        
DET	53.405        	NOR	69.105        	TEN	67.777        
TEN	51.866        	JAC	68.731        	MIN	66.864        
PHI	45.569        	HOU	68.715        	WAS	64.877        
MIN	44.916        	MIN	67.397        	NYG	62.132        
WAS	44.288        	SEA	67.305        	BAL	61.330        
CHI	42.684        	PHI	66.754        	BUF	61.091        
NOR	42.629        	DEN	65.643        	OAK	59.663        
BUF	42.103        	CHI	64.351        	CAR	58.424        
HOU	41.820        	WAS	62.505        	CHI	58.162        
DEN	41.362        	TAM	62.311        	ATL	57.281        
ARI	41.339        	TEN	60.242        	SFO	53.944        
CIN	35.116        	OAK	58.616        	NOR	53.142        
KAN	32.132        	NYJ	55.344        	MIA	51.429        
CAR	30.489        	MIA	55.247        	HOU	50.821        
BAL	29.212        	BAL	53.785        	DET	49.637        
ATL	20.853        	CAR	52.832        	NYJ	49.264        
OAK	19.455        	STL	51.484        	ARI	48.391        
SFO	18.359        	BUF	51.433        	STL	45.438        
NYJ	14.322        	KAN	50.767        	CIN	42.556        
STL	11.407        	ATL	48.921        	DEN	41.844        
MIA	0.000        	SFO	47.145        	CLE	36.398        

passing offense       	passing defense       	rushing offense       	rushing defense       
NWE	100.000        	PIT	100.000        	MIN	100.000        	MIN	100.000        
GNB	96.487        	IND	93.316        	JAC	85.481        	PIT	96.717        
CIN	91.415        	MIA	84.576        	PIT	85.406        	BAL	95.448        
NOR	90.787        	OAK	75.990        	TEN	81.914        	DAL	93.793        
DAL	90.072        	TAM	73.950        	OAK	80.568        	NWE	87.075        
HOU	88.177        	NWE	69.465        	DEN	78.990        	TEN	81.780        
DET	86.451        	TEN	66.651        	WAS	78.721        	PHI	80.144        
IND	86.087        	KAN	65.019        	IND	78.708        	NYG	78.202        
SEA	85.777        	DEN	63.093        	NYG	78.328        	NOR	75.435        
CLE	85.650        	ATL	62.469        	DAL	78.313        	WAS	74.430        
ARI	85.513        	NYG	62.175        	NWE	78.269        	GNB	73.229        
PHI	82.731        	WAS	60.301        	PHI	76.086        	JAC	72.006        
DEN	81.538        	CAR	58.975        	TAM	74.879        	IND	68.346        
CHI	76.256        	STL	58.883        	CAR	73.957        	SEA	68.256        
WAS	76.106        	SEA	57.932        	MIA	71.569        	KAN	62.558        
NYG	74.211        	BAL	57.409        	CLE	71.393        	TAM	61.679        
SDG	73.406        	NYJ	55.063        	ARI	69.885        	STL	59.905        
STL	72.539        	HOU	54.241        	SDG	68.897        	SDG	59.488        
TAM	72.128        	DAL	53.992        	BUF	67.623        	ARI	58.839        
KAN	71.935        	ARI	52.965        	NYJ	66.070        	DET	57.621        
ATL	71.133        	GNB	52.897        	BAL	65.125        	CAR	55.492        
JAC	71.051        	PHI	52.479        	ATL	64.762        	BUF	51.748        
PIT	70.923        	SDG	50.298        	SEA	64.094        	HOU	51.553        
BAL	70.810        	CHI	49.698        	STL	62.251        	CIN	48.104        
NYJ	68.722        	SFO	48.823        	CIN	62.240        	ATL	48.050        
MIA	67.803        	CIN	36.637        	SFO	61.845        	SFO	47.780        
CAR	67.090        	JAC	35.728        	HOU	61.282        	CHI	44.510        
TEN	66.896        	NOR	34.315        	DET	61.212        	CLE	38.427        
OAK	63.995        	BUF	31.657        	NOR	59.513        	MIA	23.702        
BUF	63.564        	CLE	24.313        	CHI	59.096        	DEN	23.594        
MIN	61.092        	DET	22.418        	KAN	57.651        	NYJ	20.708        
SFO	57.466        	MIN	16.898        	GNB	57.358        	OAK	16.649

...or you can have the updated data.


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Mon, 19 Nov 2007

week 11 power rankings

A couple changes this week: I included individual yards for/against data for each team, and for the off/def rankings (including yardages) I scaled to 100 but did not shift; this lets us say, e.g., "Dallas has been 88% as effective as New England on offense this year." 

combined              	offense               	defense               
NWE	100.000        	NWE	100.000        	PIT	100.000        
GNB	89.948        	DAL	88.125        	TAM	98.084        
DAL	87.434        	CLE	81.142        	NWE	96.117        
IND	84.182        	IND	79.909        	IND	94.656        
PIT	72.766        	GNB	76.340        	SEA	92.243        
JAC	70.157        	PIT	75.912        	GNB	91.090        
NYG	67.255        	CIN	73.013        	JAC	82.399        
TAM	59.928        	NYG	70.745        	PHI	81.381        
TEN	58.593        	SDG	70.119        	KAN	80.971        
DET	58.409        	DET	70.034        	TEN	79.308        
SEA	57.878        	HOU	69.357        	NYG	76.497        
CLE	55.563        	ARI	68.045        	BUF	73.135        
SDG	51.351        	NOR	66.693        	SDG	72.200        
PHI	48.928        	SEA	66.328        	BAL	71.062        
WAS	48.751        	JAC	65.021        	MIN	70.304        
ARI	46.286        	PHI	64.132        	WAS	70.139        
HOU	46.240        	WAS	63.292        	DAL	68.006        
BUF	46.227        	TEN	62.536        	CHI	67.927        
DEN	45.535        	MIN	62.337        	CAR	67.404        
MIN	38.415        	DEN	61.969        	ATL	64.935        
CHI	37.000        	TAM	61.747        	OAK	63.164        
KAN	35.755        	CHI	60.339        	SFO	62.156        
NOR	35.554        	MIA	58.782        	ARI	60.005        
CAR	35.457        	NYJ	57.953        	DET	57.693        
BAL	32.697        	OAK	57.090        	NYJ	56.483        
CIN	27.393        	CAR	54.860        	HOU	55.949        
ATL	22.319        	BAL	53.537        	NOR	51.081        
NYJ	15.555        	BUF	50.768        	DEN	50.339        
OAK	12.721        	STL	49.504        	STL	48.884        
STL	12.007        	KAN	49.457        	MIA	48.326        
SFO	11.159        	ATL	48.534        	CIN	39.694        
MIA	0.000        	SFO	40.331        	CLE	36.990        

passing offense       	passing defense       	rushing offense       	rushing defense       
NWE	100.000        	PIT	100.000        	MIN	100.000        	MIN	100.000        
GNB	96.241        	IND	94.924        	PIT	86.426        	BAL	96.494        
DAL	93.756        	MIA	83.989        	JAC	84.965        	PIT	93.830        
NOR	92.684        	TAM	83.613        	TEN	83.786        	DAL	92.796        
CIN	92.543        	NWE	80.982        	NWE	80.100        	TEN	90.362        
HOU	90.274        	OAK	74.020        	NYG	78.808        	NWE	84.442        
DET	89.256        	TEN	72.574        	OAK	77.840        	NYG	81.602        
SEA	88.335        	ATL	65.589        	IND	77.661        	GNB	79.707        
IND	87.520        	SFO	64.217        	PHI	77.610        	WAS	76.569        
CLE	87.004        	KAN	63.288        	WAS	77.385        	PHI	76.410        
ARI	81.640        	CAR	62.229        	DEN	77.383        	JAC	73.582        
DEN	81.265        	DEN	61.431        	CAR	76.143        	IND	71.732        
PHI	80.910        	BAL	60.435        	DAL	74.956        	NOR	71.138        
CHI	78.497        	PHI	60.345        	TAM	74.224        	SEA	70.164        
TAM	76.287        	STL	59.110        	MIA	73.060        	KAN	68.557        
STL	75.044        	NYG	58.184        	ARI	69.101        	TAM	64.435        
NYG	74.965        	ARI	56.332        	SDG	68.567        	ARI	64.271        
WAS	74.907        	HOU	56.049        	CLE	67.940        	STL	59.606        
KAN	74.813        	SEA	54.899        	BUF	66.412        	DET	59.124        
ATL	73.792        	CHI	54.203        	NYJ	66.374        	CAR	58.095        
PIT	73.721        	WAS	52.424        	BAL	65.870        	HOU	57.049        
BAL	73.254        	NYJ	51.089        	SEA	63.124        	SDG	55.997        
SDG	73.207        	GNB	50.571        	ATL	62.646        	BUF	54.536        
NYJ	71.848        	DAL	47.193        	HOU	60.938        	ATL	50.168        
MIA	70.683        	SDG	45.577        	STL	60.199        	SFO	47.750        
JAC	69.687        	CIN	36.339        	SFO	58.075        	CHI	47.443        
CAR	69.304        	BUF	33.569        	CIN	57.624        	CIN	44.197        
TEN	66.335        	JAC	32.741        	DET	57.485        	CLE	36.528        
OAK	65.296        	NOR	27.343        	NOR	56.993        	NYJ	25.887        
BUF	63.750        	DET	24.614        	CHI	56.371        	DEN	24.843        
MIN	63.215        	CLE	20.395        	GNB	55.273        	OAK	21.659        
SFO	55.519        	MIN	11.868        	KAN	52.643        	MIA	20.537

Updated code for those following along at home.


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Wed, 14 Nov 2007

moooooooore powerrrrrrrrrr

...rankings.

I was bored and decided to write some code to produce NFL power rankings. Perhaps one of my perenially disappointed faithful readers might care to peruse. (Gautham actually suggested splitting the offensive and defensive power rankings; previously I'd only looked at overall power rankings, which I present below.)

First, a little explanation: these are split offensive and defensive power rankings; in other words, normalized rankings by points for and points against considering the record of the opposition as given by the same ranking. My assumption here is that my rankings should be zero-sum when offense and defense are combined. That is, every (adjusted) point counted towards an offense is counted precisely the same against the opposing defense. The rankings are determined as follows:

  1. Rank offenses and defenses by adding up points for and points against. Normalize to a 0-100 scale, with 100 being most points for and least points against.
  2. Given the above rankings, normalize the points scored: pnorm = pscore * (1 - (offensive_rating - opposing_defensive_rating)). Note that this is zero-sum, since the defensive rating for the team on defense is used against the offensive rating of the team on offense.
  3. Repeat the above, but this time use the rankings returned in the last step. Continue iterating until the algorithm converges on a set of rankings. These are now both perfectly self-consistent (that is, using the rankings to normalize the scores yields exactly the same rankings) and zero-sum (all points counted for a defense are also counted against an offense).

Note that this is very much a discrete feedback system, and as such is subject to instability. To ameliorate this problem, we add a "gain" term as such: pnorm = pscore * (1 - gain*(offensive_rating - opposing_defensive_rating)), where gain < 1. While monitoring the state variables, we experiment with gain until we get close to the largest value that yields a stable system, in this case 1/4. Yes, this is hacky. Bite me, Hippo.

Finally, using approximately the same algorithm (details if you insist), I do the same thing for total performance, taking into account win/loss, point differential, defensive performance, and home field advantage.

So now we have a mess of numbers. What are they? Well, in one sentence, they are normalized offensive and defensive ratings adjusted for relative strength of schedule. How, relative? Well, we look at the difference between the opposing defense and our offense (or vice-versa), not our defense versus the league average or some such. Think of it this way: if the worst team in the league had to play a bunch of mediocre teams, those would be hard-fought wins; conversely, the best team in the league should have little trouble with those same teams. Relative strength of schedule takes this into account.

Here are the numbers: 

combined                offense                 defense
NWE	100.000        	NWE	100.000		PIT	100.000
GNB	88.877        	DAL	83.321		SEA	89.290
DAL	85.341        	IND	72.842		TAM	85.638
IND	83.189        	CLE	67.917		NWE	84.650
PIT	80.843        	PIT	64.065		GNB	83.451
JAC	66.579        	GNB	58.556		IND	81.508
TEN	66.043        	DET	54.766		TEN	76.748
DET	64.926        	CIN	54.511		BUF	70.769
NYG	63.272        	NYG	53.387		JAC	66.878
SDG	56.904        	SDG	51.525		KAN	59.164
TAM	53.994        	HOU	49.478		BAL	56.930
SEA	53.481        	NOR	48.993		PHI	56.024
WAS	52.787        	ARI	41.471		SDG	53.106
CLE	51.385        	PHI	40.369		CAR	51.544
BUF	50.391        	JAC	38.916		CHI	51.263
PHI	43.508        	SEA	37.553		MIN	49.928
CHI	41.806        	TEN	36.275		NYG	49.785
HOU	40.583        	WAS	34.992		ATL	49.339
ARI	40.051        	MIA	34.039		WAS	49.119
DEN	39.732        	MIN	32.003		DAL	45.858
NOR	39.701        	CHI	29.441		OAK	43.484
KAN	38.975        	TAM	29.306		ARI	36.620
CAR	38.408        	DEN	28.936		SFO	30.923
BAL	36.894        	NYJ	26.355		DET	23.899
MIN	32.504        	OAK	23.123		NYJ	21.136
CIN	31.475        	CAR	21.660		NOR	19.135
ATL	26.070        	BUF	17.196		HOU	18.749
OAK	15.436        	KAN	15.675		DEN	15.649
SFO	13.263        	ATL	15.238		MIA	7.479
NYJ	6.447        	BAL	14.313		STL	6.008
STL	3.783        	STL	14.185		CIN	5.766
MIA	0.000        	SFO	0.000		CLE	0.000

Sucks for Cleveland that they have a terrible defense, since their offense pretty much rocks...

I'll keep these updated weekly until the end of the season.

Edit: here's the code if you want to play with it yourself.


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