The Vikings' and Lions' Paths to the Playoffs

I recently noted that according to NFL Forecast's computation of playoff odds for each team, MIN at 5-6 appears to have a far better shot at a wildcard spot than 6-5 Detroit. In fact, there are five more teams at 5-6, but none with as a good a shot as MIN. But since DET plays at MIN this Sunday I'll focus on those two teams.

First, MIN is the better team according to their efficiency stats. Although their passing game is below average, they don't throw as many interceptions as DET. Their running game is spectacular, on both sides of the ball. Usually, the running game is not as important as passing, except when it is exceptionally good as it is with MIN.
The list of NFL teams sorted from luckiest (positive numbers) to unluckiest is posted below. We would expect most teams to be within +/- 1.0 wins. So teams outside that margin can be deemed significantly lucky or unlucky.

Team	O Pass	O Run	O Int Rate	O Fum Rate	D Pass	D Run	D Int Rate	Pen Rate
MIN	5.6	5.6	0.029	0.031	6.4	3.0	0.028	0.38
DET	6.1	4.0	0.035	0.047	6.4	3.7	0.034	0.50
NFL Avg	6.1	4.0	0.032	0.026	6.1	4.0	0.032	0.37

But the real difference between the two teams lies in some stats that usually go overlooked. One thing that really hurts DET is their fumble rate. They lead the NFL in fumbles per play. Almost 5% of all offensive snaps result in a fumble. Their penalty rate is also the worst in the league at half a yard per snap. Accordingly, DET's generic win probability (GWP-the chance they'll beat a league-average team at a neutral site) ranks 27th at 0.33. In contrast, MIN's GWP ranks 13th at 0.56.

This Sunday MIN hosts DET in a crucial game. The prediction model gives MIN a solid advantage with a 0.78 probability of winning at home. That would split the season series and even up their records at 6-6. Now let's look at their remaining schedule.

DET's remaining schedule is listed in the table below. Their opponent's efficiency rank and the probability DET will win the game are also listed. DET has a tough schedule ahead. Their opponents' average GWP is 0.64. Plus, only two of their five remaining games are at home. The GB odds are relatively uncertain because by week 17, the Packers might be resting their starters if they've locked up their playoff seed.

Opponent	Opp Rank	Win Prob.
at Min	13	0.22
DAL	3	0.11
at SD	10	0.81
KC	21	0.51
at GB	6	0.13

Here is MIN's remaining schedule. They have a much easier schedule with an average opponent GWP of only 0.37, with three home games.

Opponent	Opp Rank	Win Prob.
DET	27	0.78
at SF	32	0.80
CHI	31	0.86
WAS	12	0.57
at DEN	14	0.57

Anything can happen, but it looks like MIN has a much better shot at a wildcard than DET despite being a game behind in the standings. That's one reason why this weekend's game is so important. If DET can upset MIN, they'd own the tiebreaker and a two game lead, possibly eliminating MIN from contention.

But let's not forget about the other teams in contention. Here are the other 5-6 teams scrapping for a wildcard berth, their efficiency ranking, and their average future opponent GWP.

Team	Rank	Opp GWP
PHI	9	0.57
WAS	12	0.52
ARI	23	0.42
NO	25	0.48
CHI	31	0.55

I'm not saying MIN will definitely or even probably make the playoffs, but they do have the best shot of all the teams behind the Giants (7-4). Of the other teams, PHI appears strongest, but they also have the toughest schedule. WAS is about even with MIN in terms of team efficiency but it has a much tougher schedule. The loss of Sean Taylor may also affect the team in unpredictable ways. ARI has a relatively weak schedule, but has not been playing well themselves and their secondary is banged-up. NO has been playing well lately but their defense is practically non-existent. They're probably the hardest team to predict this year because of their slow start. CHI is simply bad, even on defense. It's surprising they have 5 wins at this point.

It's possible and perhaps likely we'll see an 8-8 team make the playoffs out of the NFC again this year. I think MIN has the best shot to be that team.

Winning on the Road

Teams with good running offenses do not win any more road games than other teams, all things being equal. That's right--being good at running the ball does not help teams win on the road. Contrary to what we've been told for years, having strong passing game is far more important to visiting teams than having a good running game.

Let me make a clarification up front. I'm not suggesting that having a great running performance in an individual road game doesn't help win that game. I'm saying that being a "running team" doesn't help win on the road. Teams that are "built" to win on the road are those that pass well and don't fumble.

I stumbled on this somewhat by accident when I was studying the effect of climate on home field advantage. My usual game model is a logistic regression that estimates the probability of winning based on team efficiency stats and home field. A simplified version looks like this:

Team A season efficiency stats
Team B season efficiency stats
Team A at home [1 if true, 0 if false]

This method resulted in balanced weights for the coefficients for Team A and Team B, and the importance of home field was captured in the coefficient for 'Team A at home.' But during my research into climate effects, I decided to try an alternate model without the home field variable. It looked like this:

Visiting team season efficiency stats
Home team season efficiency stats

With this method we would expect unbalanced coefficients. Because home teams win more often, the coefficients for the home team were generally stronger than for the visiting team. This means that if two theoretically equal teams played, the home team would have a higher probability of winning, which is exactly what we observe.

By examining the imbalance of each stat we can see what kind of teams tend to win on the road. Here are the regression coefficients for each efficiency stat for both home and visiting teams. (Logisitic regression is more difficult to interpret than linear regression. The coefficients indicate the change in the log of the odds ratio of the outcome. But we are comparing the relative strength of each coefficient, so don't worry about the "log odds ratio" for now. Just pay attention to the relative size of the coefficient between home and away team stats.)

Team Stat	Home Coeff	Visitor Coeff
O Pass	0.40	-0.49
O Run	0.48	-0.04*
D Pass	-0.60	0.48
D Run	-0.27	0.16
O Int Rate	-16.40	15.61
D Int Rate	19.30	-17.63
O Fum Rate	-11.57	30.77
Pen Rate	-1.65	1.30

The model has very solid goodness-of-fit stats, and it is 69.9% accurate (retrodictively) in predicting game winners. The regression is based on all regular season game outcomes in the past five years (n=1280).

First, compare the coefficients for offensive passing efficiency. The coefficient for home teams is 0.40, and for visiting teams is 0.49. We can interpret these numbers by saying "having a good passing game is slightly more important in winning for the visiting team than for the home team." But the difference is slight, and may not be significant.

Next, compare the coefficients for offensive running efficiency. The coefficient for home teams is 0.48, but for visiting teams it is only 0.04--practically zero! (The difference of 0.44 is strongly significant.) The near-zero coefficient for visiting teams' offensive running efficiency is what tells us that running well simply doesn't matter on the road.

Also, for some reason, teams that tend to fumble more often than others are at a greater disadvantage as visiting teams. And conversely, teams that don't fumble tend to have a greater advantage as road teams.

There are imbalances between nearly all of the team efficiency stats, but none as stark as that for offensive running. This was such an unexpected result and I had no prior theoretical basis for the observation, so I confirmed the results with a simpler analysis using correlation coefficients.

For each team over the past 5 seasons (n=160), I added up their road and home wins. The correlations of each efficiency stat with home and road wins were calculated. If different stats affect a team's ability to win at home and on the road differently, as we saw in the regression, then we should see different correlation coefficients. For example, the correlation between offensive running efficiency and home wins should be much stronger than running and road wins.

	O Pass	O Run	O Int Rate	O Fum Rate	D Pass	D Run	D Int Rate	Pen Rate
Away Wins	0.55	0.10	-0.40	-0.42	-0.34	0.00	0.31	-0.16
Home Wins	0.48	0.22	-0.36	-0.36	-0.45	-0.07	0.36	-0.17

The correlations confirm the results from the regression. Being a good running team is more important to winning when at home, and not nearly as important to the visiting team. (Also note that stopping the run is just not important whether on the road or at home, as we've seen in previous research.)

I also did an even simpler analysis by comparing the average season running efficiency stats of all road winners and for all home winners. Again, the data was from every regular season game over the past five years (n=1280). The average offensive running efficiency for road winners was 4.13 yds/rush and for road losers was 4.10 yds/rush--a difference of only 0.03 yds/rush.

We see the opposite with passing efficiency. Road winners average 6.18 yds/att and road losers average 5.90 yds/att--a difference of 0.28 yds/att which is about 9 times larger than the difference we found for running. Again we see indications that passing efficiency tends to be the more important stat for the road team.

The obvious question is "why?" Why doesn't being a capable running team help win road games? My only theory is that passing well helps come from behind far more than running well. If road teams tend to find themselves behind more often than home teams, then unless they can pass, they wouldn't be able to score quickly and come back from a deficit. But home teams need to come back from deficits too, so the reason why running teams don't win on the road remains puzzling.

Playoff Race Predictions Wk 12

Beginning this week, NFL Stats and NFL Forecast are teaming up to predict the playoff races for the 2007 NFL season. NFL Forecast offers a free a web/java-based program that calculates playoff probabilities for each team and for each possible playoff seeding based on individual game probabilities. Check out the java program here. For the rest of the season, NFL Forecast will be using the game outcome probabilities published here at NFL Stats as its official baseline. The resulting playoff chances will be published weekly at the NFL Forecast blog. (By the way, some of the java code is being updated, so be patient if some of the functions are temporarily disabled. But the blog site has all the final output based on the NFL Stats game probabilities.)

NFL Forecast's playoff prediction engine goes beyond wins and losses, and accounts for the complex NFL tiebreaker and seeding procedures that baffle many fans.

My personal observations of the current playoff predictions focus on the second NFL wildcard spot. (Scroll down past the division ranking probabilities to the AFC/NFC Playoff Seeding Probability tables). It appears totally up for grabs. DET is currently holding the spot at 6-5, but there are 7 teams right behind at 5-6. I was very surprised to see 5-6 MIN with a 46% chance to grab a playoff spot, while DET has only a 4% chance. More on the reasons for this later.

Season Win Projections Week 12

Season win totals and division standing projections are listed below. As before, projections are based on each team's opponent-adjusted generic win probability (GWP). The projections account for future opponent strength (Fut Opp), and projected wins (proj W) is a total of current and estimated future wins. The methodology is described more fully here.

Team	Rank	Proj GWP	Fut Opp	Proj W
AFC E
NE	1	0.91	0.48	15.6
BUF	19	0.39	0.53	6.9
NYJ	24	0.34	0.54	3.7
MIA	18	0.43	0.49	2.1
AFC N
PIT	5	0.70	0.51	11.5
CLE	17	0.61	0.35	10.1
CIN	20	0.50	0.40	6.5
BAL	26	0.18	0.70	4.9
AFC S
IND	2	0.88	0.45	13.4
JAX	7	0.65	0.52	11.3
TEN	15	0.45	0.54	8.2
HOU	16	0.31	0.67	6.6
AFC W
SD	10	0.69	0.40	9.5
DEN	14	0.58	0.46	7.9
KC	21	0.43	0.47	6.2
OAK	29	0.14	0.67	3.7
Team	Rank	Proj GWP	Fut Opp	Proj W
NFC E
DAL	3	0.85	0.50	14.2
NYG	11	0.53	0.54	9.7
WAS	12	0.55	0.52	7.7
PHI	9	0.54	0.57	7.7
NFC N
GB	6	0.79	0.38	13.9
MIN	13	0.68	0.37	8.4
DET	27	0.23	0.62	7.2
CHI	31	0.19	0.55	6.0
NFC S
TB	4	0.87	0.34	11.3
NO	25	0.39	0.48	6.9
ATL	22	0.41	0.48	5.1
CAR	28	0.21	0.62	5.0
NFC W
SEA	8	0.71	0.41	10.5
ARI	23	0.47	0.42	7.4
SF	32	0.18	0.50	3.9
STL	30	0.23	0.52	3.2

Week 12 Efficiency Rankings

NFL team efficiency rankings are listed below in terms of generic winning probability. The GWP is the probability a team would beat the league average team at a neutral site. Each team's opponent's average GWP is also listed, which can be considered to-date strength of schedule. GWP modifies the generic win probability to reflect the strength of past opponents. Offensive ranking (O Rank) is based on each team's offensive GWP, i.e. it's the team's GWP assuming it had a league-average defense. D Rank is vice-versa. Rankings are based on a logistic regression model applied to data through week 12. A full explanation of the methodology can be found here.

Rank	TEAM	Last Wk	GWP	Opp GWP	O Rank	D Rank
1	NE	1	0.91	0.54	1	3
2	IND	3	0.86	0.54	6	1
3	DAL	2	0.85	0.50	2	5
4	TB	4	0.77	0.48	4	7
5	PIT	5	0.71	0.42	15	2
6	GB	7	0.69	0.48	5	11
7	JAX	8	0.67	0.53	3	19
8	SEA	6	0.63	0.38	11	12
9	PHI	12	0.60	0.55	7	20
10	SD	10	0.60	0.54	13	9
11	NYG	9	0.57	0.53	17	8
12	WAS	11	0.57	0.59	20	6
13	MIN	15	0.56	0.51	12	13
14	DEN	13	0.54	0.51	8	27
15	TEN	14	0.49	0.52	27	4
16	HOU	16	0.48	0.47	16	24
17	CLE	17	0.46	0.49	9	29
18	MIA	23	0.42	0.56	19	21
19	BUF	19	0.41	0.59	18	18
20	CIN	20	0.40	0.50	10	31
21	KC	21	0.40	0.50	26	10
22	ATL	22	0.39	0.50	22	17
23	ARI	18	0.39	0.42	21	15
24	NYJ	27	0.37	0.56	23	30
25	NO	28	0.37	0.48	14	32
26	BAL	24	0.35	0.42	28	14
27	DET	26	0.33	0.49	24	16
28	CAR	25	0.30	0.50	25	23
29	OAK	31	0.25	0.45	29	25
30	STL	29	0.25	0.46	31	22
31	CHI	30	0.23	0.52	30	28
32	SF	32	0.18	0.45	32	26

Game Predictions Week 13

Game probabilities for week 13 NFL games are listed below. The probabilities are based on an efficiency win model explained here and here. The model considers offensive and defensive efficiency stats including running, passing, sacks, turnover rates, and penalty rates. Team stats are adjusted for previous opponent strength.

Vprob	Visitor	Home	Hprob
0.23	GB	DAL	0.77
0.59	ATL	STL	0.41
0.27	BUF	WAS*	0.73
0.22	DET	MIN	0.78
0.40	HOU	TEN	0.60
0.19	JAX	IND	0.81
0.37	NYJ	MIA	0.63
0.61	SD	KC	0.39
0.44	SEA	PHI	0.56
0.27	SF	CAR	0.73
0.81	TB	NO	0.19
0.49	CLE	ARI	0.51
0.72	DEN	OAK	0.28
0.77	NYG	CHI	0.23
0.16	CIN	PIT	0.84
0.93	NE	BAL	0.07

NFL Home Field Advantage by Climate 2

In a previous post, I looked at how home field advantage is affected by weather. Each NFL city was categorized by its December climate--dome, warm, moderate, and cold. By comparing the winning percentage of home teams in games in the early season (weeks 1-12) and the late season (13-17) the effect of cold weather was estimated.

In this post, the effect of cold weather on home field advantage will be measured more precisely. By using logistic regression, relative team strength is accounted for. In addition, the statistical significance of the observed weather effect indicates if the effect is real and systematic, or just a result of luck and small sample size.

The last post left off with this table. The left most column describes the visiting team's climate, and the top row describes the home team's climate. For each combination of visiting and home climate, the change in home team winning percentage from early to late in the season is listed. Positive numbers indicate that cold weather may favor the home team. For example, when dome teams play at warm cities, the home team winning percentage was 20% higher late in the season than early in the season. But when dome teams play at moderate cities, the home team winning percentage appeared to be 9% lower late in the season.

Difference	Dome	Warm	Mod	Cold
Dome	0%	+20	-9	+35
Warm	-5	+14	-7	-3
Mod	-8	-24	-6	-13
Cold	-8	+2	-15	+8

Several match-ups indicate that the cold and wind of late-season outdoor football has an effect on HFA. Consistent with other research, it appears that dome teams suffer when playing in cold climates.

Another remarkable combination is moderate weather teams playing in warm cities (-24%). But it's not clear why moderate teams would have an easier time playing in the balmy breezes of Florida or San Diego in December. Other notable match-ups are dome teams playing at warm cities (+20%), and cold teams playing at moderate cities (-15%).

To determine if the observed differences in HFA between early and late season games is really due to the change of weather, and not due to relative team strength or luck, several logistic regression models were run. The models were based on every regular season game from the 2002 through 2006 seasons (n=1280). For each game, each team was designated either Team A or Team B. The general model specification was the following:

Dependent variable:
Team A won

Independent variables:
Team A season efficiency stats
Team B season efficiency stats
AHome
[Weather dummy variable]

The team efficiency stats include offensive and defensive passing and running efficiency, turnover rates, and penalty rates. AHome is a dummy variable that is 0 when Team A is away and 1 when Team A is home. The [Weather dummy variable] is 1 when the particular climate match-up of interest is present for the game, and 0 when otherwise.

A general HFA variable (AHome) was included to isolate the effect of weather from the general home field advantage due to travel, psychology, officiating, or other effects.

Several models were run for each climate match-up of interest. The table below lists the statistical significance of the 'weather variable' and the resulting home field advantage calculated from the regression results. Note that the overall HFA rate is 57.5%.

Visitor	Home	p-value	HFA (%)
Dome	Cold	0.03*	88
Dome	Warm	0.28	75
Warm	Warm	0.58	71
Warm	Cold	0.74	76
Mod	Warm	0.11	40
Mod	Cold	0.95	62
Cold	Mod	0.13	49

Accounting for relative team strength, the only truly significant result is for dome teams in cold weather (p=0.03), with an expected home team winning percentage of 88%. This result is confirmed by the actual 86% home team winning percentage when dome teams play at cold cities late in the year. The regression's estimate of 88% suggests that the cold city home teams may have been slightly weaker compared to their dome opponents over the past 5 years.

Two other types match-ups might be considered marginally significant--moderate teams at warm cities (p=0.11), and cold teams at moderate cities (p=0.13). Both results indicate a reduced HFA later in the season for those match-up types. But since there were 16 combinations of climate match-ups, chances were that we could see one or two type-II errors, i.e. see significance when none is truly there. Because there is no a priori theoretical reason why to expect those results, we shouldn't deem them significant.

Finally, one last model specification was run to make sure no other climate match-up types were significant. The final model included all late-season match-ups types together. No additional types were significant.

It's clear that situation of a dome team playing playing in a cold city late in the season creates a much stronger HFA than normal. But a larger data set is needed to conclusively analyze other weather match-ups. Dividing 1280 games into 16 types of match-ups and 2 weather periods creates small sub-samples.

A prediction model's accuracy may benefit from enhancing the weight of HFA in certain situations. Looking ahead, there are only three 'dome at cold' match-ups in 2007. STL travels to CIN in week 14, and NO visits CHI and DET visits GB in week 17.

Season Win Projections Week 11

Season win totals and division standing projections are listed below. As before, projections are based on each team's opponent-adjusted generic win probability (GWP). The projections account for future opponent strength, and total wins account for current and projected wins. Methodology is described here.

Team	Rank	Proj GWP	Fut Opp	Proj W
AFC E
NE	1	0.90	0.55	15.4
BUF	19	0.44	0.51	7.7
NYJ	27	0.28	0.57	3.7
MIA	23	0.34	0.54	2.0
AFC N
PIT	5	0.74	0.47	11.4
CLE	17	0.60	0.42	9.6
CIN	20	0.51	0.43	6.1
BAL	24	0.22	0.63	5.3
AFC S
IND	3	0.87	0.52	13.2
JAX	8	0.59	0.52	10.5
TEN	14	0.50	0.52	9.0
HOU	16	0.38	0.55	7.3
AFC W
SD	10	0.65	0.53	8.9
DEN	13	0.62	0.44	8.7
KC	21	0.50	0.52	7.0
OAK	31	0.15	0.52	2.9
Team	Rank	Proj GWP	Fut Opp	Proj W
NFC E
DAL	2	0.87	0.54	14.2
NYG	9	0.60	0.51	10.6
WAS	11	0.51	0.58	8.0
PHI	12	0.43	0.57	7.6
NFC N
GB	7	0.73	0.43	13.4
DET	26	0.26	0.51	7.6
MIN	15	0.59	0.47	7.5
CHI	30	0.24	0.50	5.4
NFC S
TB	4	0.87	0.40	11.2
NO	28	0.35	0.42	6.1
CAR	25	0.30	0.55	5.8
ATL	22	0.32	0.51	4.9
NFC W
SEA	6	0.71	0.38	10.3
ARI	18	0.56	0.41	8.4
STL	29	0.22	0.44	3.3
SF	32	0.21	0.44	3.3

Luckiest NFL Teams After Week 11

Based on opponent-adjusted generic win probability (GWP), the number of expected wins can be estimated for each team. Teams that have won more games than expected can be considered lucky, while teams with fewer wins than expected can be considered unlucky.

The list of NFL teams sorted from luckiest (positive numbers) to unluckiest is posted below. We would expect most teams to be within +/- 1.0 wins. So teams outside that margin can be deemed significantly lucky or unlucky.

Team	GWP	Actual Wins	Expected	Luck
GB	0.64	9	6.4	2.6
DET	0.35	6	3.5	2.5
CHI	0.24	4	2.4	1.6
CLE	0.48	6	4.8	1.2
TEN	0.50	6	5.0	1.0
NYG	0.61	7	6.1	0.9
NE	0.91	10	9.1	0.9
JAX	0.61	7	6.1	0.9
NO	0.33	4	3.3	0.7
DAL	0.85	9	8.5	0.5
BUF	0.45	5	4.5	0.5
ARI	0.45	5	4.5	0.5
CAR	0.37	4	3.7	0.3
BAL	0.38	4	3.8	0.2
HOU	0.48	5	4.8	0.2
SF	0.20	2	2.0	0.0
OAK	0.20	2	2.0	0.0
KC	0.41	4	4.1	-0.1
DEN	0.52	5	5.2	-0.2
PIT	0.74	7	7.4	-0.4
SS	0.65	6	6.5	-0.5
IND	0.85	8	8.5	-0.5
PHI	0.56	5	5.6	-0.6
WAS	0.56	5	5.6	-0.6
SD	0.57	5	5.7	-0.7
STL	0.27	2	2.7	-0.7
ATL	0.38	3	3.8	-0.8
MIN	0.49	4	4.9	-0.9
CIN	0.43	3	4.3	-1.3
NYJ	0.35	2	3.5	-1.5
TB	0.80	6	8.0	-2.0
MIA	0.38	0	3.8	-3.8

Poor Miami. They've played well enough to win about 4 games, but are still waiting for their first victory.

NFL Home Field Advantage by Climate

In this post I'll begin an analysis of home field advantage in the NFL and its relationship to climate. Others have examined the connection between weather and HFA previously, but here I'll attempt to present the data with a clear and novel approach. This post represents the 'clear' part. In following posts, the novel part will use logistic regression to account for team strength and determine the significance of each particular type of climate match-up.

I began by dividing each home city into four categories: dome, cold, moderate, and warm based on a combination of each city's average December high temperature and wind speed. The dome cities include STL, NO, MIN, DET, IND, and ATL. The cold cities are GB, BUF, CLE, CHI, KC, DEN, NYG, NYJ, NE, PHI, PIT, and CIN. Moderate cities include BAL, WAS, CAR, SEA, OAK, SF, TEN, and DAL. The warm cities are MIA, TB, JAX, HOU, SD, and ARI.

Based on all NFL regular season games from the 2002 through 2006 seasons, the winning percentage of the home team was calculated for each type of climate match-up. I divided the season into "early" and "late." The early season is defined as weeks 1 through 12 and the late season is defined as weeks 13 through 17. For example, the winning percentage of the home team in match-ups of cold teams at moderate cities in the early season is 57%, with n=77 examples of such cases.

The home winning percentage of all types of weather match-ups are presented below in a series of pairs of tables. Each table is presented the same way, with the visiting team climate on the left and the home climate on the top. The first table in each pair is for the early season (pre-December), and the second table is for the late season (December games).

Sample size is usually an issue when populations are divided up among several classes. For that reason, the first pair of tables lists the number of cases of each type. For example, the top right cell of the first table lists the number of games featuring dome teams playing at cold cities in the early season. The same cell in the second table lists the same type of match-up in the late season.

Wk 1-12	Dome	Warm	Mod	Cold
Dome	31	29	44	62
Warm	34	20	50	62
Mod	40	49	51	78
Cold	59	66	77	128

Wk 13-17	Dome	Warm	Mod	Cold
Dome	15	17	21	21
Warm	16	11	17	30
Mod	25	20	17	40
Cold	20	28	43	59

The second pair of tables simply lists the straight-up winning percentage of the home team in each type of match-up. For example, the bottom left cell of the first table lists the home team winning percentage when cold teams play at domes in the early season. The same cell in the second table lists home winning percentage of cold teams at domes in the late season.

Wk 1-12	Dome	Warm	Mod	Cold
Dome	61%	45	61	51
Warm	68	50	66	66
Mod	60	59	59	76
Cold	53	52	57	50

Wk 13-17	Dome	Warm	Mod	Cold
Dome	61%	65	52	86
Warm	63	64	59	63
Mod	52	35	53	63
Cold	45	54	42	58

What immediately stands out is the very high winning percentage of cold teams hosting dome teams late in the season. The most remarkable result, however, may be the 35% home winning percentage of moderate teams hosting warm teams. Note that there are only about 20 cases of each type of match-up in the past 5 years, so these results could be due to luck or due to general team strengths of the according type of teams. Perhaps a couple warm teams have been relatively dominant over moderate weather division rivals between '02 and '06.

The final table lists the difference in home winning percentage between late season and early season match-ups. Simply put, it is late season winning percentage minus early season winning percentage. A high positive number indicates cold weather may give an advantage to the home team. A negative number or near-zero number suggests otherwise. We'd expect to see a zero for dome teams at dome teams, because outdoor weather is obviously not a factor. This method begins to account for relative team strengths over the period studied.

Difference	Dome	Warm	Mod	Cold
Dome	0%	20	-9	35
Warm	-5	14	-7	-3
Mod	-8	-24	-6	-13
Cold	-8	2	-15	8

Take dome teams for example. By reading across, we see that dome teams seem to have no greater HFA in late season than the early season against other dome teams--as we'd expect. We also see that they are at a 20% disadvantage playing at warm cities but, for some reason, have a 9% better advantage playing at moderate cities late rather than early. Lastly, we see that dome teams appear to be at a severe disadvantage playing in cold cities late in the season, apparently giving up 35% advantage to the cold.

As mentioned above, some of the observed differences in HFA due to weather may be due to luck and relative team strengths among the weather-classes. The final table is a simple way of accounting for team strength, but it does not address the possibility that the differences are primarily due to luck. The final part of this article will use logistic regression to more powerfully account for team strength and test for statistical significance.

Game Predictions Week 12

Game probabilities for week 11 NFL games are listed below. The probabilities are based on an efficiency win model explained here and here. The model considers offensive and defensive efficiency stats including running, passing, sacks, turnover rates, and penalty rates. Team stats are adjusted for previous opponent strength. Games in which the model disagrees with consensus favorites are highlighted in red.

Vprob	Visitor	Home	Hprob
0.70	GB	DET	0.30
0.06	NYJ	DAL	0.94
0.86	IND	ATL	0.14
0.27	BUF	JAX	0.73
0.71	DEN	CHI	0.29
0.42	HOU	CLE	0.58
0.31	MIN	NYG	0.69
0.37	NO	CAR	0.63
0.21	OAK	KC	0.79
0.78	SEA	STL	0.22
0.48	TEN	CIN	0.52
0.19	WAS	TB	0.81
0.18	SF	ARI	0.82
0.25	BAL	SD	0.75
0.09	PHI	NE	0.91
0.14	MIA	PIT	0.86

I wouldn't put too much stock in the NO-CAR probability. The QB/WR injury situation in CAR needs to be watched, and NO has been so inconsistent.

Week 11 Efficiency Rankings

NFL team efficiency rankings are listed below in terms of generic winning probability. The GWP is the probability a team would beat the league average team at a neutral site. Each team's opponent's average GWP is also listed, which can be considered to-date strength of schedule. GWP modifies the generic win probability to reflect the strength of past opponents. Offensive ranking (O Rank) is based on each team's offensive GWP, i.e. it's the team's GWP assuming it had a league-average defense. D Rank is vice-versa. Rankings are based on a logistic regression model applied to data through week 11. A full explanation of the methodology can be found here.

RANK	TEAM	Last Wk	GWP	Opp GWP	O Rank	D Rank
1	NE	1	0.91	0.49	1	2
2	DAL	3	0.85	0.49	2	5
3	IND	2	0.85	0.54	4	1
4	TB	5	0.80	0.48	3	6
5	PIT	4	0.74	0.43	12	3
6	SEA	6	0.65	0.41	9	16
7	GB	7	0.64	0.47	8	14
8	JAX	9	0.61	0.53	5	22
9	NYG	8	0.61	0.51	14	8
10	SD	13	0.57	0.54	16	10
11	WAS	12	0.56	0.57	19	7
12	PHI	10	0.56	0.49	7	20
13	DEN	15	0.52	0.53	6	29
14	TEN	11	0.50	0.52	28	4
15	MIN	14	0.49	0.50	13	21
16	HOU	18	0.48	0.45	17	25
17	CLE	20	0.48	0.54	10	27
18	ARI	21	0.45	0.49	22	11
19	BUF	17	0.45	0.58	18	15
20	CIN	16	0.43	0.53	11	30
21	KC	26	0.41	0.50	27	9
22	ATL	19	0.38	0.47	23	18
23	MIA	27	0.38	0.53	20	23
24	BAL	22	0.38	0.41	29	13
25	CAR	24	0.37	0.52	24	19
26	DET	25	0.35	0.46	25	12
27	NYJ	28	0.35	0.53	21	31
28	NO	23	0.33	0.52	15	32
29	STL	29	0.27	0.48	26	24
30	CHI	30	0.24	0.53	30	26
31	OAK	31	0.20	0.43	31	28
32	SF	32	0.20	0.51	32	17

Updated NE Undefeated Watch

Pittsburgh and the Giants are obviously the biggest obstacles remaining for the Patriots. Here is the updated probability NE will finish the regular season undefeated.

Vprob	Visitor	Home	Hprob
0.88	NE	BUF	0.12
0.09	PHI	NE	0.91
0.90	NE	BAL	0.10
0.21	PIT	NE	0.79
0.03	NYJ	NE	0.97
0.03	MIA	NE	0.97
0.81	NE	NYG	0.19

0.88*0.91*.90*0.79*0.97*0.97*0.19 = 0.45

Season Win Projections Week 10

Season win totals and division standing projections are listed below. As before, projections are based on each team's opponent-adjusted generic win probability (GWP). The projections account for future opponent strength, and total wins account for current and projected wins. Methodology is described here.

Team	Rank	Proj GWP	Fut Opp	Proj W
AFC E
NE	1	0.91	0.50	15.4
BUF	17	0.40	0.57	7.8
NYJ	28	0.22	0.60	2.6
MIA	27	0.26	0.56	1.9
AFC N
PIT	4	0.81	0.46	12.7
CLE	20	0.55	0.38	8.8
CIN	16	0.56	0.41	6.9
BAL	22	0.26	0.64	5.8
AFC S
IND	2	0.92	0.42	13.4
JAX	9	0.58	0.53	10.0
TEN	11	0.57	0.49	10.0
HOU	18	0.36	0.59	6.5
AFC W
SD	13	0.61	0.42	9.3
DEN	15	0.58	0.40	8.1
KC	26	0.36	0.48	6.5
OAK	31	0.16	0.56	3.1
Team	Rank	Proj GWP	Fut Opp	Proj W
NFC E
DAL	3	0.88	0.48	14.1
NYG	8	0.61	0.51	10.3
WAS	12	0.42	0.62	7.9
PHI	10	0.49	0.60	7.5
NFC N
GB	7	0.74	0.37	13.2
DET	25	0.29	0.58	8.0
MIN	14	0.61	0.37	7.3
CHI	30	0.20	0.54	5.4
NFC S
TB	5	0.85	0.39	10.9
NO	23	0.41	0.47	6.9
CAR	24	0.30	0.58	6.1
ATL	19	0.34	0.59	5.4
NFC W
SEA	6	0.76	0.38	10.3
ARI	21	0.51	0.39	7.6
SF	32	0.19	0.45	3.4
STL	29	0.22	0.51	2.6

QB Rating Week 10

The QB Wins Added Per 16 Games stat (+WP16) estimates how many wins a quarterback adds to his team's record over the course of a 16-game season. +WP16 is explained here and here. Last year's ratings can be found in the second link. Here is the list of 2007 QBs and their vital stats through week 10.

Rank	Player	QBRat	Att	Yds	Air Yds	YAC	Int	Rush	Yds	Sk Yds	Fum	+WP16
1	Brady	131.8	299	2686	1559	1127	4	17	39	62	4	3.30
2	Garrard	102.9	148	1141	680	461	0	30	134	73	2	2.57
3	Roethlisberger	110.2	242	2020	1281	739	7	18	135	177	5	2.01
4	Manning P	90.8	315	2386	1541	845	10	10	-6	63	3	2.00
5	Romo	103.3	292	2555	1473	1082	11	15	81	89	4	1.97
6	Anderson	90.7	292	2231	1393	838	9	20	55	75	3	1.91
7	Palmer	91.1	328	2464	1509	955	10	13	16	90	3	1.56
8	Garcia	95.5	258	1967	981	986	3	30	111	71	3	1.40
9	Schaub	85.0	215	1658	1084	574	7	14	38	94	7	1.33
10	Hasselbeck	89.3	320	2301	1289	1012	8	22	47	84	2	1.05
11	Warner	86.2	178	1314	852	462	6	9	-2	45	6	1.03
12	Delhomme	111.8	86	624	311	313	1	6	26	46	1	0.76
13	Cutler	84.8	248	1882	1041	841	9	22	102	76	6	0.61
14	McNabb	91.7	315	2295	1152	1143	4	28	107	151	6	0.55
15	Losman	80.8	109	820	449	371	3	13	73	73	3	0.48
16	Boller	74.6	134	772	459	313	3	7	22	37	1	0.37
17	Favre	96.2	354	2757	1293	1464	8	17	-2	85	6	0.32
18	Brees	84.8	371	2447	1336	1111	12	14	38	45	5	0.30
19	Pennington	87.5	190	1317	819	498	7	17	23	102	2	0.25
20	Leinart	61.9	112	647	374	273	4	11	42	23	0	0.10
21	Kitna	92.9	298	2294	1335	959	8	19	46	211	11	0.10
22	Campbell	79.9	261	1735	906	829	7	27	147	81	9	-0.04
23	Harrington	81.0	264	1737	856	881	5	12	30	145	0	-0.15
24	Bulger	73.1	242	1602	971	631	8	6	15	152	4	-0.19
25	Manning E	78.6	283	1820	1007	813	11	15	41	91	5	-0.53
26	Holcomb	73.1	83	515	288	227	1	0	0	87	1	-0.64
27	Lemon	69.4	166	923	482	441	4	18	70	86	2	-0.69
28	Green	72.6	141	987	515	472	7	7	32	53	2	-0.77
29	Smith	57.2	193	914	595	319	4	13	89	121	6	-0.79
30	Young	62.2	192	1112	636	476	10	55	217	79	5	-0.93
31	Huard	74.7	262	1766	951	815	11	9	-1	166	3	-1.14
32	Rivers	77.9	255	1743	917	826	10	19	12	107	10	-1.31
33	McNair	73.9	205	1113	568	545	4	10	32	85	8	-1.37
34	Edwards	69.9	121	790	385	405	5	4	7	71	1	-1.48
35	Carr	65.7	114	540	260	280	3	15	54	65	1	-1.64
36	Griese	77.1	217	1508	730	778	10	9	16	101	6	-1.67
37	Culpepper	73.3	125	817	399	418	4	15	36	82	6	-1.86
38	Grossman	53.9	103	642	376	266	6	5	9	96	3	-2.53
39	McCown J	59.5	122	760	348	412	9	18	105	84	8	-3.67

Advance Game Predictions Weeks 12-17

Here is a list of the win probabilities of all remaining games in the 2007 NFL schedule. These will be continue to be updated as the season progresses.

Game Predictions Week 11

Game probabilities for week 11 NFL games are listed below. The probabilities are based on an efficiency win model explained here and here. The model considers offensive and defensive efficiency stats including running, passing, sacks, turnover rates, and penalty rates. Team stats are adjusted for previous opponent strength. Games in which the model disagrees with consensus favorites are highlighted in red.

Vprob	Visitor	Home	Hprob
0.35	ARI	CIN	0.65
0.20	CAR	GB	0.80
0.45	CLE	BAL	0.55
0.04	KC	IND	0.96
0.18	MIA	PHI	0.82
0.89	NE	BUF	0.11
0.35	NO	HOU	0.65
0.16	OAK	MIN	0.84
0.86	PIT	NYJ	0.14
0.35	SD	JAX	0.65
0.78	TB	ATL	0.22
0.11	WAS	DAL	0.89
0.67	NYG	DET	0.33
0.51	STL	SF	0.49
0.10	CHI	SEA	0.90
0.50	TEN	DEN	0.50

It seems as if the consensus favorites and the mathematical models have converged. Only one game difference between them the past two weeks. I would not be confident in the Baltimore prediction without knowing the injury status of their secondary. Without a healthy McAlister, Rolle, and Reed, I don't see how they could be the favorite.

Week 10 Efficiency Rankings

NFL team efficiency rankings are listed below in terms of generic winning probability. The GWP is the probability a team would beat the league average team at a neutral site. Each team's opponent's average GWP is also listed, which can be considered to-date strength of schedule. GWP modifies the generic win probability to reflect the strength of past opponents. Offensive ranking (O Rank) is based on each team's offensive GWP, i.e. it's the team's GWP assuming it had a league-average defense. D Rank is vice-versa. Rankings are based on a logistic regression model applied to data through week 10. A full explanation of the methodology can be found here.

RANK	TEAM	Last Wk	GWP	Opp GWP	O Rank	D Rank
1	NE	2	0.91	0.53	1	3
2	IND	1	0.89	0.56	4	1
3	DAL	3	0.86	0.50	2	4
4	PIT	5	0.79	0.43	7	5
5	TB	4	0.78	0.50	3	8
6	SEA	6	0.66	0.42	12	16
7	GB	12	0.63	0.48	9	14
8	NYG	7	0.62	0.52	16	6
9	JAX	9	0.60	0.54	6	21
10	PHI	10	0.60	0.51	5	22
11	TEN	8	0.56	0.52	27	2
12	WAS	11	0.53	0.53	22	7
13	SD	19	0.53	0.51	18	9
14	MIN	15	0.48	0.51	13	17
15	DEN	24	0.48	0.53	10	25
16	CIN	14	0.48	0.52	8	26
17	BUF	13	0.47	0.54	20	11
18	HOU	16	0.45	0.47	15	28
19	ATL	25	0.43	0.45	19	19
20	CLE	17	0.43	0.53	11	27
21	ARI	22	0.41	0.48	24	15
22	BAL	21	0.39	0.42	29	10
23	NO	18	0.38	0.52	14	32
24	CAR	20	0.37	0.51	23	18
25	DET	23	0.37	0.44	25	12
26	KC	26	0.33	0.45	28	13
27	MIA	28	0.32	0.53	17	30
28	NYJ	27	0.30	0.53	21	31
29	STL	30	0.23	0.49	26	29
30	CHI	31	0.22	0.49	30	24
31	OAK	29	0.20	0.41	31	23
32	SF	32	0.17	0.51	32	20

Weather and Home Field Advantage

Someone recently pointed out a study that indicated home field advantage (HFA) is not the same for every stadium. While that's certainly true, it's very hard to quantify. By definition, the same team is always the home team when measuring a particular location's HFA, so in any given year there would be a lot of team strength captured in a variable accounting for the field's HFA.

The efficiency model I've used includes a factor for HFA, but it is the same regardless of climate. This is the beginning of an effort to quantify the effect of climate on HFA and to see how much of HFA is due to climate differences and how much is due to other factors such as crowd noise, referee psychology, or travel.

The table below lists each home team along with their average December weather. Click on the table headers to sort

Team	Avg Dec T	Avg Dec Wind	Wind Chill
GB	29	10.5	19.7
BUF	36	13.3	27.3
CLE	37	12.1	29.0
CHI	37	11.0	29.5
NE	42	12.2	35.3
KC	42	11.2	35.7
PIT	42	10.4	36.0
NYG	44	10.8	38.3
NYJ	44	10.8	38.3
CIN	44	10.2	38.5
PHI	44	10.1	38.6
DEN	44	8.4	39.3
SEA	46	9.5	41.3
WAS	46	7.8	42.0
BAL	49	9.3	45.0
TEN	49	8.9	45.2
CAR	54	7.4	51.9
SF	56	7.1	54.4
DAL	57	10.8	54.5
OAK	58	7.1	56.8
HOU	65	8.0	65.0
ARI	65	5.1	65.8
JAX	66	7.8	66.3
SD	66	5.6	66.8
TB	72	8.4	73.5
MIA	75	9.2	77.1
ATL	70	0.0	79.2
DET	70	0.0	79.2
IND	70	0.0	79.2
MIN	70	0.0	79.2
NO	70	0.0	79.2
STL	70	0.0	79.2

It's not a surprise that Green Bay is coldest by far, followed by places such as Buffalo, Cleveland, and Chicago. Green Bay would even qualify as a cold climate through November with an average 36 deg wind chill. But I was surprised by how much colder (and windier) a place like Kansas City is than Baltimore or Washington. I'm still considering how to classify each city. Domes are easy, but where is the line drawn between cold and moderate? Should there be cold, moderate, and "warm" classes? For now I'd put the line between cold and moderate at 40 deg wind chill, between DEN and SEA. I'd also define warm weather teams starting at 60 deg between OAK and HOU.

Continue reading this article here.

Season Win Projections Week 9

Season win totals and division standing projections are listed below. As before, projections are based on each team's opponent-adjusted generic win probability (GWP). The projections account for future opponent strength, and total wins account for current and projected wins. Methodology is described here.

Team	Rank	Proj GWP	Fut Opp	Proj W
AFC E
NE	2	0.91	0.50	15.4
BUF	13	0.45	0.53	7.6
NYJ	27	0.22	0.61	2.5
MIA	28	0.25	0.56	2.0
AFC N
PIT	5	0.81	0.46	12.5
CLE	17	0.51	0.44	9.1
BAL	21	0.32	0.62	7.5
CIN	14	0.56	0.42	6.4
AFC S
IND	1	0.93	0.44	14.5
TEN	8	0.61	0.49	10.9
JAX	9	0.53	0.55	9.2
HOU	16	0.36	0.60	7.5
AFC W
SD	19	0.46	0.49	7.7
DEN	24	0.52	0.39	7.1
KC	26	0.38	0.46	7.0
OAK	29	0.26	0.48	4.0
Team	Rank	Proj GWP	Fut Opp	Proj W
NFC E
DAL	3	0.85	0.50	13.8
NYG	7	0.57	0.55	10.6
WAS	11	0.46	0.60	8.7
PHI	10	0.46	0.61	6.7
NFC N
GB	12	0.64	0.40	11.1
DET	23	0.38	0.53	8.1
MIN	15	0.57	0.39	7.6
CHI	31	0.19	0.50	4.5
NFC S
TB	4	0.85	0.41	11.0
NO	18	0.51	0.43	8.1
CAR	20	0.38	0.56	7.0
ATL	25	0.32	0.59	4.5
NFC W
SEA	6	0.80	0.35	10.4
ARI	22	0.52	0.40	7.1
SF	32	0.17	0.49	3.3
STL	30	0.21	0.49	1.7

The Most Accurate NFL Prediction System

Last week I posted a link to ThePredictionTracker.com, a site that tracks predictions of many NFL prediction systems. I love this site because so many people are out there making predictions, but rarely do we ever get an honest look at how accurate they've been. It even includes accuracies from previous years.

I'm especially pleased because based on the records of the other systems, the one used here at NFL Stats has been the most accurate NFL prediction system since its inception. (Please forgive the self-congratulations.) The NFL Stats logistic regression efficiency model has been estimating game outcome probabilities over the past two seasons with the highest total accuracy rate of any system.

Admittedly, there is some amount of luck involved in predicting sports outcomes, which is why various systems should be compared over more than a single season. You might notice that the system that is doing the best so far this year (Greenfield's Team Rankings system) was among the very worst in 2006. This would suggest the system is prone to a very high degree of luck. Systems with true predictive value are still susceptible to luck, but should still rank above average fairly consistently.

In 2006 the NFL Stats model accurately predicted the winning team in 122 out of 195 games for a rate of 62.6%. So far in 2007, the model has been correct in 58 out of 82 games for a rate of 70.7%. The two-year total is 180 correct out of 277 games for an accuracy rate of 65.0%. (Although 65% doesn't sound very impressive, 2006 was an unusually difficult year to predict.)

I added the two-year totals for all the other systems listed at ThePredictionTracker.com. I included systems that made predictions in both 2006 and 2007 with at least 100 total games predicted. Only 3 of the systems were excluded. In total, there were 61 systems compared. The table below lists each system and its 2-year record.

System	Correct	Total Games	Accuracy %
BBNFLStats	180	277	65.0
Deslock Rankings	160	249	64.3
Pigskin Herald	170	269	63.2
ARGH Power Ratings	212	337	62.9
Hank Trexler	249	397	62.7
Least Squares	249	397	62.7
Logistic Regression	190	303	62.7
Mike Greenfield	172	275	62.5
Eric Hollobaugh	163	261	62.5
Roger Johnson	189	303	62.4
Brian Gabrielle	247	397	62.2
Sonny Moore	247	397	62.2
Beck Elo	246	397	62.0
Line (updated)	246	397	62.0
Pythagorean Ratings	246	397	62.0
Sagarin	246	397	62.0
Sagarin Elo	245	397	61.7
Stephen Kerns	245	397	61.7
System Median	245	397	61.7
Computer Adjusted Line	245	397	61.7
CPA Rankings	244	397	61.5
Least Abs. Val Reg	244	397	61.5
Steven Jens	244	397	61.5
System Average	244	397	61.5
John Coffey	169	275	61.5
CPA Retro Rankings	243	397	61.2
Lee Burdorf	243	397	61.2
Sagarin Predictive	243	397	61.2
Sports Report Elo	233	381	61.2
Viacheslav	233	381	61.2
NutShell Retro	223	365	61.1
Kambour Rating