Beating the Season Over-Under Follow-Up

Before the 2007 season began, I proposed a system that appeared to be able to systematically beat Las Vegas over-under lines on team wins. For the 2007 season, the results are in. The system's record would have been 8 correct, 3 incorrect, with 1 push (73% correct).

The system itself consists of two rules:

1. For teams predicted to win 9.5 games or more, bet on the under.
2. For teams predicted to win 6.5 games or less, bet on the over.

In other words, bet on mediocrity.

Historically, the system would have been 70% correct over the previous two years, and slightly over 58% correct over a 10 year period between 1996 and 2005. By betting 'over' on teams predicted to win 6 or less, instead of 6.5 or less, the overall rate would have improved to 61%.

Here is how the system fared this year. Over-under lines were taken from bodog.com on 6/30/07.

Unders	Line	Actual	Result
SD	11	11	-
BAL	9.5	5	W
CHI	10.5	7	W
IND	11	12	L
NE	11.5	16	L
DEN	9.5	7	W
PHI	9.5	8	W
CIN	9.5	7	W
Overs	Line	Actual	Result
DET	6	7	W
CLE	6	10	W
HOU	6.5	8	W
BUF	6.5	7	W
OAK	5	4	L

One thing I learned watching the results develop over the season is that the system is more successful the earlier in the year that the over-under lines are taken. Early in the year, long before training camps open, there is the least amount of information and the more likely it is that over-under lines are set based on the previous season's results. This is when uncertainty would be greatest, and perhaps when overconfidence is accordingly great. When looking for records of the over-under lines, I noticed that the earlier the line, the more confident it was--i.e. the further from 8 wins teams were predicted to win.

As player movements, retirements, injuries, team schedules, and pre-season games come into focus, over-under lines move to reflect the new information. Uncertainty is reduced, and the overconfidence would be mitigated. It might therefore better to place bets earlier rather than later in the pre-season, capitalizing on maximum uncertainty.

Why the System Works

The system is based on three principles:

1. The NFL season is extremely difficult to predict.
2. Regression to the mean is very strong in the NFL.
3. People are overconfident in their ability to predict team wins.

Humans, including NFL fans and gamblers, are susceptible to cognitive biases, and I believe these biases affect prediction markets. Cognitive (or heuristic) biases are systematic errors in judgment made in certain situations. These biases exist probably because they benefited early humans in their efforts to adapt and survive. For example, the "overconfidence effect" may bias people toward action rather than passivity in the face of a challenge.

But in a prediction situation, overconfidence is counterproductive. People who believe their prediction abilities are better than they truly are would take excessive risks. In one survey 80% of respondents claimed they were in the top 30% in driving skills. Similarly, it's likely that most gamblers also believe that they have some special ability or intuition to predict outcomes--otherwise they wouldn't be gambling.

Hindsight bias, also known as the "I knew it all along" effect, may also be a factor in fooling people into forgetting how poor their predictions really are. Ask yourself how well you thought New England would do this year. Be honest. According to the betting lines, half of all people thought they'd win 11 games or fewer. Remember how Randy Moss was supposed to be a "cancer?" How about the Bears? Half of bettors believed Chicago would win at least 11 games this year. But as the Bears floundered this year, many people forgot just how good they were expected to be--just on their defense alone. Most fans, including tv commentators, forget how uncertain things were before the first snap of the season. They say "it was obvious the Patriots would be unbeatable. They have Randy Moss!" or "obviously the Bears fell flat, Rex Grossman is terrible." I know that's my first instinct.

People also tend to remember correct predictions and forget incorrect ones--both by themselves and others. Today I noticed the cover page of an obscure football "prospectus" book I bought in August. It trumpeted, "Last year, we correctly predicted player X would have a breakout year! We said team Y would return to the playoffs!" That a book of over 300 pages of NFL predictions made four or five correct guesses is not an accomplishment. But it's the correct ones that are remembered.

Many people are also unable to grasp the concepts of randomness or luck. They discount regression to the mean because they expect extreme performances to continue. In the NFL, a team that finishes with a 14-2 record was probably a "fundamentally" 12-4 team that got lucky in a couple games. Fans and bettors may expect much of that 14-2 performance to carry over into the next season, thinking that 11 or 12 wins is a safe bet. But in reality, the team was a "12-win" team the previous season, so the chance of repeating such a successful year would be lower than expected. This effect is compounded when the same phenomenon affects a team's opponents. For example, part of the reason the Ravens and Bengals did not reach their over-under expectations is because division rival Cleveland improved from extremely poor performance.

This field of heuristics and decision-making fascinates me. I'm sure there is a lot of money to be made in not just betting markets, but equity markets. The one thing about sports though, is that it's relatively easy to analyze statistically. And no. I'm sorry to report I did not put my money where my mouth is.

'Dome at Cold'

This week features two of the three "dome team at cold weather" games of the 2007 season. Earlier, CIN defeated STL in week 14. Today CHI hosts NO and GB hosts DET.

Dome teams are at a severe disadvantage when playing in cold weather. Over the past five regular seasons, they've won only about 14% of the time in those situations. Accounting for relative team strength, they would be expected to win only 12% of the time.

GB is already a heavy favorite over DET, and the weather factor would only enhance GB's expected chance of winning. But the game prediction model features closer odds for the NO at CHI game. NO is favored with a 0.57 probability of winning.

However, when the weather is factored in CHI is going to be favored. Replacing the standard home field advantage coefficient with the "dome at cold" coefficient we get a 0.62 win probability for CHI.

With the weather factor, GB becomes a heavier favorite at 0.92.

Some people are already looking ahead to the likely AFC championship match-up between IND and NE. Although IND played NE very well, and nearly won the game earlier in the year without five starters, their next game will be very different. It will be in Foxboro, Mass. in late January. It was no fluke that the one year IND was able to get past NE to get to the Super Bowl was the year they hosted the game.

AFC Wildcard, Resting Starters, and 16-0 Teams

A few weeks ago, I wrote that the 2nd AFC wildcard playoff spot come down to the last week of the season between TEN and CLE. Their relative strengths of schedule clearly favored CLE, but the difference in opponent strength was primarily to due their final opponents of the regular season. CLE faces a weak SF while TEN faces an elite IND.

But with IND locked into the second seed, IND may not be so elite in week 17. I can't begrudge a team for resting its best players prior to the playoffs. It's legal and in their self-interest. But it is a shame that who gets into the playoffs can be determined by such a quirk.

If TEN played IND in any other week, they wouldn't have much of a chance to win. But against Jim Sorgi, they would probably be favored. IF TEN loses to a full-strength IND, Cleveland wouldn't even need to beat SF. They would keep the tiebreaker due to having a better conference record.

On a similar note, I estimated that NE had about a 52% chance of finishing the regular season undefeated. And it's no surprise that here are the unbeaten Patriots facing the Giants tonight for a chance at NFL immortality. It's also a shame that the Pats may not be facing an opponent at full-strength, as the Giants have clinched the 5th seed.

These unfortunate circumstances are really just due scheduling quirks. Had NE's or TEN's schedule been arranged any differently, their prospects for victory this weekend would be very different.

How rare is a 16-0 team?

Here is a quick back-of-the-envelope analysis. Let's say that every year there are two legitimate 13-3 teams. In other words, there are two teams in the NFL that have a fundamental .813 winning percentage against an average strength of schedule without luck of any kind. In a 16-game season, a team with an underlying .813 win probability would have a 2.8% chance of winning all 16 games. (0.813 ^ 16 = 0.0281).

Because we assumed there are 2 such teams each year, the chance of neither team going undefeated is (1-0.028)^2 = 0.944, or 94.4%. The chance of one or both teams being undefeated is therefore 1-0.944 = 5.6%. We should expect an undefeated team about every 1 out of 20 years with the current state of talent distribution and a 16 game schedule.

I'm not saying the 2007 Patriots are really a 13-3 team that's been really lucky. Assuming they beat the Giants, my hunch is (and their stats say) they are really a 15-1 team that dodged a bullet or two (namely the Ravens and Eagles).

Week 16 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 16. A full explanation of the methodology can be found here.

Click on the table headers to sort.

Rank	Team	Last Wk	GWP	Opp GWP	O Rank	D Rank
1	NE	1	0.87	0.51	1	4
2	IND	2	0.87	0.52	3	1
3	DAL	3	0.77	0.47	4	7
4	JAX	5	0.76	0.53	2	10
5	TB	4	0.74	0.46	5	5
6	SD	7	0.68	0.50	15	3
7	PIT	8	0.67	0.48	12	6
8	SEA	9	0.65	0.41	13	11
9	GB	6	0.63	0.45	6	14
10	PHI	10	0.63	0.55	7	13
11	WAS	14	0.57	0.53	17	8
12	TEN	11	0.56	0.51	24	2
13	MIN	13	0.51	0.44	14	19
14	DEN	12	0.51	0.49	8	29
15	NYG	15	0.50	0.48	21	9
16	CLE	17	0.48	0.47	11	21
17	HOU	16	0.47	0.53	16	30
18	CIN	21	0.47	0.48	10	28
19	BUF	18	0.44	0.55	18	16
20	NO	20	0.43	0.51	9	32
21	NYJ	19	0.43	0.54	22	18
22	BAL	23	0.39	0.52	25	17
23	ATL	22	0.36	0.51	19	25
24	CAR	24	0.36	0.53	27	12
25	ARI	27	0.34	0.46	20	23
26	KC	25	0.34	0.51	29	15
27	MIA	26	0.33	0.53	26	22
28	STL	29	0.30	0.51	30	20
29	CHI	31	0.30	0.53	28	26
30	DET	28	0.30	0.51	23	24
31	OAK	30	0.23	0.50	31	31
32	SF	32	0.17	0.49	32	27

Game Predictions Week 17

Game probabilities for week 17 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.

These probabilities may not reflect that several teams are locked into their playoff seeds and possibly resting many of their starters. However, I will post these without regard to this consideration and allow everyone to apply their own correction. Teams that are particularly likely to not play at full strength are noted (*). My own sense is that the only games in which the favorite would now be the underdog are the TEN at IND and DAL at WAS games.

Vprob	Visitor	Home	Hprob
0.83	NE	NYG*	0.17
0.26	BUF	PHI	0.74
0.12	CAR	TB*	0.88
0.53	CIN	MIA	0.47
0.64	DAL*	WAS	0.36
0.14	DET	GB*	0.86
0.71	JAX	HOU	0.29
0.57	NO	CHI	0.43
0.70	PIT	BAL	0.30
0.69	SEA*	ATL	0.31
0.12	SF	CLE	0.88
0.12	TEN	IND*	0.88
0.43	MIN	DEN	0.57
0.84	SD	OAK	0.16
0.36	STL	ARI	0.64
0.31	KC	NYJ	0.69

Week 15 QB Ratings Adjusted for Pass Defense

In this post I'll recap how my QB rating is determined, and I'll add a new dimension--adjustments for opposing pass defenses.

QB Rating Recap

The QB rating I post often is different from most, including the NFL passer rating. The stat I use to compare QB performance is +WP16 or wins added per 16 games. +WP16 estimates the number of wins above average a quarterback's performance would mean to his team over a full regular season.

The +WP16 stat estimates the wins added based on a regression that analyzes what makes teams win. The QB stats included are passing yards per attempt, rushing yards per attempt, sack yards per attempt, fumble rates, and interception rates. +WP16 isolates QB performance by assuming an average rushing game and an average defense.

First downs and touchdowns are not included despite their apparent importance because they are intermediate outcomes between actual QB performance and the outcome of interest--team wins.

Perhaps the most unique aspect of +WP16 is that it does not include passing yards gained by receivers after the catch (YAC). Instead it is based on air yards--the yards the ball travels through the air forward of the line of scrimmage. The percent of passing yards made up of YAC varies widely from QB to QB. Brodie Croyle gets 68% of "his" yards from YAC while Ben Roethlisberger gets only 34% of his yards from YAC.

There is some debate over whether or how much YAC should be credited to QBs. In my mind, the answer is much closer to none than to all.

There is statistical evidence that YAC belongs to the receiver. Year-to-year correlations of YAC are far stronger for receivers than for QBs. Accuracy rates and QBs' abilities to read the defense and "see the field" (measured by interception rates) do not contribute to YAC. It appears that YAC is determined by receiver ability far more than QB ability.

The types of passes thrown by a QB also help determine YAC. Screen passes and check downs to RBs, which are not difficult passes, tend to produce more YAC relative to air yards. Deep out passes, which are more difficult and require more QB skill, tend to generate more air yards and often no YAC at all. The other type of pass that can create a lot of YAC is when a WR beats the defense deep by simply out-running them. Although it certainly helps if a QB can get the ball to a receiver who has gotten behind his coverage, those types of plays are rare and are really made possible by the WR, at least in my mind.

For the reasons above, I believe the truer measure of a QB's performance is one that does not include YAC. Here is the ranking of QBs based on performance so far this season:

Rank	Name	QBRat	Att	Yds	Int	Rush	Yds	Sk Yds	Fum	AY/A	%YAC	+WP16
1	Brady	119.7	503	4235	6	29	91	107	4	4.9	42	2.48
2	Garrard	101.6	307	2310	2	45	166	91	3	4.8	37	2.21
3	Manning P	95.2	464	3634	14	19	-4	122	5	4.9	37	1.29
4	Anderson	85.8	459	3384	14	30	64	100	5	4.5	38	0.95
5	Romo	101.0	462	3868	17	25	116	166	9	4.9	41	0.89
6	Schaub	87.2	289	2241	9	17	52	126	7	5.0	36	0.87
7	Roethlisberger	104.1	404	3154	11	35	204	347	9	5.2	34	0.86
8	Cutler	90.8	398	3096	12	41	163	119	8	4.3	44	0.46
9	Garcia	93.6	307	2244	4	34	116	98	3	3.7	50	0.44
10	Palmer	86.2	522	3700	17	22	11	119	5	4.3	40	0.36
11	Hasselbeck	92.0	510	3620	10	35	68	183	8	4.0	44	0.17
12	Brees	92.1	550	3819	15	22	53	89	7	3.8	45	0.11
13	Favre	97.7	492	3905	13	25	-9	89	8	3.8	52	-0.16
14	Warner	87.6	360	2748	15	13	-4	140	11	4.7	38	-0.22
15	Kitna	84.6	497	3707	17	21	55	304	15	4.7	37	-0.26
16	McNabb	86.8	397	2716	6	43	199	192	7	3.4	50	-0.33
17	Campbell	77.6	417	2700	11	36	185	110	13	3.6	44	-0.44
18	Jackson	69.6	222	1516	10	42	180	47	3	3.6	47	-0.58
19	Pennington	85.8	228	1501	7	18	27	142	3	4.1	38	-0.61
20	Boller	75.2	275	1743	10	19	89	159	5	4.0	37	-0.74
21	Young	70.1	342	2223	16	82	375	132	7	3.5	46	-0.92
22	Edwards	75.6	213	1336	5	9	25	71	2	3.1	51	-0.94
23	Bulger	71.4	353	2216	13	9	13	248	6	4.1	35	-1.11
24	Manning E	72.6	482	2974	17	24	56	186	7	3.5	43	-1.11
25	Losman	76.9	175	1204	6	20	110	103	4	3.4	50	-1.21
26	Rivers	80.0	412	2828	15	26	31	153	10	3.7	46	-1.22
27	Culpepper	78.0	186	1331	5	20	40	130	8	4.0	44	-1.24
28	Harrington	77.2	348	2215	8	14	33	192	0	3.0	52	-1.26
29	Smith	57.2	193	914	4	13	89	121	6	3.1	35	-1.43
30	Lemon	69.9	247	1479	6	25	86	120	6	3.0	50	-1.52
31	Clemens	59.0	225	1414	10	19	93	125	4	3.4	46	-1.80
32	McNair	73.9	205	1113	4	10	32	85	8	2.8	49	-2.02
33	Huard	72.6	296	1952	13	9	-1	204	4	3.6	45	-2.03
34	Grossman	66.4	225	1411	7	14	27	198	6	3.5	44	-2.03
35	Griese	75.6	262	1803	12	13	28	114	6	3.3	52	-2.22
36	Testaverde	65.8	172	952	6	8	23	46	3	2.6	52	-2.24
37	Frerotte	62.0	162	1010	11	6	3	59	3	3.9	38	-2.34
38	McCown	68.6	182	1105	11	29	143	78	10	3.0	51	-3.14
39	Croyle	71.7	169	963	5	5	16	72	4	1.8	68	-3.57
40	Dilfer	55.1	219	1166	12	10	25	182	8	3.0	43	-3.87
Rank	Name	QBRat	Att	Yds	Int	Rush	Yds	Sk Yds	Fum	AY/A	%YAC	+WP16

The biggest surprise at the top of the list is David Garrard. He's ranked so high primarily because of his phenomenally low turnover rate, having thrown only three interceptions all year. His air yards per attempt (AY/A) is impressive too. He ranks among the elite QBs in the league with 4.8 yds/att. In total, Garrard ranks second behind Brady with +2.21 wins added.

Adjusting for Opponents' Pass Defense

When comparing team performance, opponent strength matters a great deal. Schedules in the NFL are not balanced. During the regular season a team only plays 13 of the 31 other teams in the league, 3 of them twice. If those 3 teams a team's own division are among the toughest, and the 18 teams it never plays comprise some of the weakest opponents, then the team would appear to be much worse than it would be if it had an average schedule.

Early in the season opponent adjustments are most important, because as the season goes on and each team faces more different types of opponents, each team's strength of schedule tends to even out. But not completely.

It stands to reason that QB performance ratings would also be affected by opponent strength, specifically opponent pass defense. To confirm this effect, each team's strength of pass defense was computed. That includes average pass yards per attempt allowed, sack yards per pass play, and interception rate. Each stat was weighted according to how important they are towards winning based on the same regression model that determine the weights of the QB rating. This produced a unit-less pass defense score.

Then each QB's average opponent pass defense strength was determined. QBs were counted as having played a team if they had more than 10 attempts in a game.

To see how opposing pass defenses affect QB performance, the correlation coefficient between each QB's rating and his opponents' average pass defense strength was calculated. The correlation was 0.098, which is weak but what we'd expect. About 9% of a QBs season-long performance can be attributed to his opponent's pass defense. Or strictly speaking, one standard deviation (SD) increase in opposition strength results in one SD reduction in QB performance.

The last step in the process was to adjust the QB rating (+WP16) accordingly. Each QB's rating was adjusted by 0.098 SDs for each SD of opponent strength. The stronger the average opponents' pass defense, the higher the adjustment for the QB.

The table below lists each QB's unadjusted rating, his average opponent's pass defense strength, and the adjusted rating. To make the numbers a little easier to understand, pass defense strength is converted into GWP (generic win probability), or the probability a pass defense would win a game against a league-average opponent given an average run defense and offense.

Rank	Name	+WP16	Opp Pass D Str	Adj +WP16
1	Garrard	2.21	0.56	2.53
2	Brady	2.48	0.50	2.48
3	Manning P	1.29	0.53	1.43
4	Schaub	0.87	0.54	1.06
5	Anderson	0.95	0.49	0.87
6	Romo	0.90	0.49	0.86
7	Roethlisberger	0.86	0.47	0.69
8	Cutler	0.46	0.53	0.60
9	Garcia	0.44	0.53	0.58
10	Palmer	0.36	0.51	0.40
11	Brees	0.11	0.54	0.34
12	Hasselbeck	0.18	0.47	0.04
13	Favre	-0.16	0.50	-0.14
14	Kitna	-0.26	0.52	-0.15
15	Warner	-0.22	0.49	-0.27
16	McNabb	-0.33	0.51	-0.27
17	Campbell	-0.44	0.50	-0.43
18	Jackson	-0.58	0.49	-0.64
19	Pennington	-0.60	0.49	-0.65
20	Boller	-0.74	0.51	-0.66
21	Young	-0.91	0.52	-0.80
22	Edwards	-0.94	0.48	-1.02
23	Culpepper	-1.24	0.54	-1.04
24	Bulger	-1.10	0.51	-1.07
25	Harrington	-1.26	0.53	-1.08
26	Rivers	-1.22	0.52	-1.10
27	Manning E	-1.11	0.50	-1.12
28	Losman	-1.21	0.47	-1.36
29	Smith	-1.43	0.51	-1.38
30	Lemon	-1.51	0.48	-1.62
31	Clemens	-1.80	0.50	-1.80
32	Grossman	-2.03	0.54	-1.82
33	Huard	-2.03	0.52	-1.91
34	Testaverde	-2.24	0.54	-2.04
35	Griese	-2.22	0.53	-2.08
36	McNair	-2.01	0.44	-2.34
37	Frerotte	-2.33	0.50	-2.34
38	McCown	-3.14	0.50	-3.16
39	Croyle	-3.57	0.51	-3.50
40	Dilfer	-3.87	0.51	-3.82

David Garrard

At this point in the season (going into week 16), we wouldn't expect there to be much change in the ratings by accounting for opponent strength. Most teams have faced some good pass defenses and some weak ones. And indeed there is relatively little change in the rankings.

There are some notable exceptions, however. The QB who faced the weakest pass defenses was Steve McNair who played against CIN, ARI, CLE, and SF, all of which had below average pass defenses. McNair still managed to turn in a miserable performance in 2007 due to age, injury, or probably both.

The other notable exception is David Garrard. Garrard faced the toughest pass defenses of any QB in 2007. If not for an injury that kept him out of three games against TB, NO, and TEN in weeks 8,9, and 10, he would have an even tougher year. Despite his uphill battle, Garrard is playing extremely well this season. Before adjusting for opponent strength he ranked second among all QBs (not even counting for his week 17 demolition of OAK.)

In the year of Tom Brady and the Patriots, it may be David Garrard who is the best QB this season. After factoring in opponent strength, his +WP16 rating jumps from +2.2 to +2.5, edging Brady for the top spot. That's remarkable considering Garrard wasn't even his team's starter in training camp. Jaguars coach, Jack Del Rio, looks like a genius for cutting Leftwhich and sticking with Garrard.

Playoff Race Predictions Wk 15

Don't forget to check out NFL-Forecast.com for an update on playoff race probabilities.

Luckiest Teams through Week 15

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	Wins	Exp W	Luck
GB	0.68	12	9.6	2.4
CLE	0.48	9	6.7	2.3
SF	0.14	4	2.0	2.0
NYG	0.50	9	7.0	2.0
DET	0.29	6	4.1	1.9
ARI	0.31	6	4.3	1.7
NE	0.88	14	12.3	1.7
CHI	0.25	5	3.5	1.5
CAR	0.33	6	4.6	1.4
NO	0.42	7	5.9	1.1
DAL	0.78	12	11.0	1.0
BUF	0.47	7	6.6	0.4
MIN	0.54	8	7.6	0.4
SEA	0.63	9	8.8	0.2
OAK	0.27	4	3.8	0.2
PIT	0.63	9	8.8	0.2
HOU	0.49	7	6.9	0.1
TEN	0.58	8	8.1	-0.1
IND	0.86	12	12.1	-0.1
JAX	0.73	10	10.3	-0.3
SD	0.67	9	9.4	-0.4
WAS	0.54	7	7.5	-0.5
KC	0.32	4	4.5	-0.5
CIN	0.41	5	5.8	-0.8
BAL	0.35	4	4.9	-0.9
STL	0.29	3	4.0	-1.0
TB	0.76	9	10.6	-1.6
DEN	0.55	6	7.7	-1.7
ATL	0.36	3	5.0	-2.0
PHI	0.61	6	8.6	-2.6
NYJ	0.44	3	6.1	-3.1
MIA	0.31	1	4.3	-3.3

Game Predictions Week 16

Game probabilities for week 16 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
0.75	PIT	STL	0.25
0.84	DAL	CAR	0.16
0.48	CLE	CIN	0.52
0.82	GB	CHI	0.18
0.10	HOU	IND	0.90
0.45	KC	DET	0.55
0.04	MIA	NE	0.96
0.44	NYG	BUF	0.56
0.09	OAK	JAX	0.91
0.60	PHI	NO	0.40
0.41	WAS	MIN	0.59
0.47	ATL	ARI	0.53
0.18	BAL	SEA	0.82
0.29	NYJ	TEN	0.71
0.93	TB	SF	0.07
0.29	DEN	SD	0.71

Week 15 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 15. A full explanation of the methodology can be found here.

Rank	Team	Last Wk	GWP	Opp GWP	O Rank	D Rank
1	NE	1	0.88	0.54	1	5
2	IND	2	0.87	0.54	3	1
3	DAL	3	0.79	0.50	4	7
4	TB	4	0.76	0.48	6	6
5	JAX	5	0.74	0.57	2	11
6	GB	6	0.69	0.47	5	12
7	SD	9	0.68	0.51	14	4
8	PIT	8	0.63	0.47	16	3
9	SEA	7	0.63	0.39	13	9
10	PHI	10	0.62	0.55	8	14
11	TEN	13	0.58	0.53	22	2
12	DEN	12	0.55	0.49	7	27
13	MIN	11	0.55	0.44	12	17
14	WAS	15	0.54	0.53	18	8
15	NYG	14	0.50	0.50	19	10
16	HOU	18	0.50	0.52	15	25
17	CLE	17	0.48	0.46	9	26
18	BUF	16	0.47	0.56	17	16
19	NYJ	19	0.44	0.55	21	19
20	NO	21	0.43	0.50	11	32
21	CIN	20	0.42	0.47	10	31
22	ATL	24	0.36	0.51	20	22
23	BAL	22	0.35	0.49	25	20
24	CAR	27	0.33	0.51	27	15
25	KC	25	0.33	0.54	31	13
26	MIA	28	0.31	0.53	26	28
27	ARI	23	0.31	0.43	23	23
28	DET	26	0.30	0.52	24	21
29	STL	29	0.29	0.46	29	18
30	OAK	30	0.27	0.50	28	24
31	CHI	31	0.25	0.52	30	30
32	SF	32	0.14	0.43	32	29

The Best Defensive Player in the NFL is...Neil Rackers?

My previous look at place kickers considered field goal kicking. Accounting for attempt distances and home field environment (dome, warm, etc.), I estimated that one standard deviation in FG kicking accuracy results in about 2.3 more successful FGs per season (worth 6.7 points). In this article, I'll look at kick offs and how they affect the ability of the opposing team to score.

Starting field position is obviously an important factor in scoring. The closer an offense is to scoring position, the fewer consecutive first downs are required to get there. A kicker who can kick deep can help his team by giving his defense more opportunities to force a punt or a turnover before his opponent is able to move into scoring position. Further, if the opposing offense is stopped, his offense will receive possession of the ball that much closer to scoring position on its own.

Kick off depth is easily measured, but the resulting field position is dependent on kick return and kick coverage performance. To isolate the performance of the kicker from the rest of the kick off squad, I ran a quick linear regression that estimates the expected resulting starting field position based on the depth of the kick. Average kick distances and return yards for each kicker (with >20 kick offs in a season) in the 2004-2006 seasons are plotted below. (Kicks that result in touchbacks are excluded at this point because there is no return. They will be factored back in later.)


We see that the deeper the kick, the longer the return. The longer a kick travels the more time and space the returner has to run before being met by the coverage team. Not every yard of extra kick distance translates into field position. About half of each marginal yard of kick distance is given back up in the return. If one kicker kicks 60 yd kicks, and another kicker kicks 70 yd kicks, the second kicker will only benefit by 5 yds of resulting field position after the average return.

Now we can calculate the expected resulting field position for each kicker in the NFL. Touchbacks are now factored back in. The expected starting field position of each kicker over the previous three seasons ranges from the 23.7 yd line to the 31.4 yd line. The average is the 27.4 yd line with a standard deviation of 1.49 yds.

Click on the table headers to sort.

Kicker	Seasons	KOs	Avg Dist	TB Pct	Exp Fld Pos
Neil Rackers	3	206	67.9	30.6	23.7
Michael Koenen	2	147	64.2	18.4	24.8
Paul Ernster	1	75	67.9	25.3	25.0
Olindo Mare	3	184	65.7	27.6	25.0
Josh Scobee	3	225	65.4	22.7	25.6
Kris Brown	3	201	64.4	14.9	25.8
Stephen Gostkowski	1	81	65.5	14.8	25.9
Todd Sauerbrun	2	100	60.0	11.3	26.2
Joe Nedney	2	132	60.2	8.6	26.3
Sebastian Janikowski	3	193	63.6	15.4	26.3
Jason Hanson	3	204	64.1	15.2	26.4
Micah Knorr	1	61	64.4	24.6	26.4
Jeff Wilkins	3	233	63.4	8.4	26.5
Wade Richey	1	53	63.1	13.2	26.5
Rob Bironas	2	141	63.2	14.9	26.5
Jay Feely	3	249	63.9	15.1	26.5
Mitch Berger	2	89	65.1	5.2	26.8
Phil Dawson	3	191	61.4	10.0	26.9
Aaron Elling	2	70	63.5	2.9	26.9
John Carney	2	95	61.6	4.7	27.0
Shaun Suisham	1	26	64.1	0.0	27.1
Billy Cundiff	3	122	63.1	6.2	27.1
Jose Cortez	1	38	63.9	10.5	27.3
Paul Edinger	2	128	59.1	0.0	27.4
Jason Baker	1	24	63.0	4.2	27.4
Adam Vinatieri	3	247	63.5	10.9	27.4
David Akers	3	204	64.3	12.0	27.5
Rian Lindell	3	221	59.7	4.6	27.5
Matt Bryant	2	119	62.5	7.6	27.6
Craig Hentrich	1	73	57.6	4.1	27.6
Josh Brown	3	246	63.1	8.9	27.6
John Kasay	3	194	62.1	5.4	28.1
Jeff Reed	3	244	61.6	6.5	28.2
Dave Rayner	2	154	63.3	8.3	28.2
Nate Kaeding	3	270	62.6	5.6	28.3
Lawrence Tynes	3	260	61.2	5.4	28.4
Robbie Gould	2	149	63.3	6.8	28.5
Matt Stover	3	128	61.3	6.7	28.6
Shayne Graham	3	257	61.5	6.7	28.6
Ryan Longwell	3	218	59.6	3.7	28.7
Toby Gowin	1	76	63.0	9.2	28.8
Todd Peterson	1	61	56.4	1.6	29.0
Mike Nugent	2	137	60.0	2.2	29.1
John Hall	2	81	60.7	2.7	29.3
Martin Gramatica	2	46	60.9	4.4	29.3
Jay Taylor	1	21	57.0	0.0	29.4
Steve Christie	1	71	57.7	2.8	29.7
Mike Vanderjagt	2	78	59.0	3.3	30.0
Nick Novak	2	44	58.8	2.1	31.4
Average	2.2	144	62.3	9.7	27.4

The Importance of Field Position

I think the best way to examine the football-significance of kickoff field position is to look at two contrasting cases. Let's compare the league's best kicker, Neil Rackers, with one of its recent "worst," Mike Vanderjagt, who was cut by the Cowboys last year. Racker's average expected field position was the 23.7 yd line and Vanderjagt's was the 30.0 yd line, a difference of 6.3 yds.

How important are those 6 yards? The field is 100 yds long, so are they 6% important? It's difficult to quantify, but here is one way to think of field position: In almost all cases, to move into scoring position, either for a TD or FG, an offense needs a consecutive number of first downs. The closer an offense is to scoring position, the fewer first downs it needs. In other words, lets think of a typical drive as a sequence of 1st downs instead of a sequence of plays.

In baseball, the game rests on the outcomes of at bats, not necessarily every ball and strike. Think of a series of downs as the equivalent of an at bat, and individual plays as pitches. We're not as interested in each pitch as we are with the outcome of the at bat. The analogy continues because to score in baseball, several consecutive successes (hits or walks) are usually required. In football, several first downs are usually needed to score. (And in both sports there is always the slim possibility of a home run/long pass or breakaway run.)

In the NFL, a successful first down yields 15 yards on average. So those 6 yards of field position mean that in 6 out of 15 cases, an opposing offense needs one additional first down more than they otherwise would need to score. That additional first down gives a defense one more opportunity to force a kick or a turnover. That additional first down could turn what would be a TD drive into a FG drive, or turn a FG drive into a scoreless one.

In any given series of 4 downs in the NFL, an offense succeeds in gaining another first down (or touchdown) 65% of the time. So defenses are able to interrupt the consecutive series of first downs 35% of the time. So 6 yds of deeper field position per kickoff reduces the probability the the offense will score.

(6 / 15) * 0.35 = 0.14 --> 6 yds of field position adds a 0.14 probability of interrupting a scoring drive.

(It was pointed out to me that series in the red zone are often more difficult because of the compression of the field, so not every series has an equal probability of success. That's true, however the red zone series happen on a TD drive whether or not the drive started on the 20 or the 40 yd line. The "extra series" that is sometimes required by a deep kickoff does not cause an additional red zone series. It would be on the front end of a drive and not in the red zone.)

Over the previous five years, NFL teams scored an average of 23.4 FGs and 34.6 offensive TDs per season, resulting in 312 pts per season. A 14% reduction equates to 43.7 point difference between Neil Rackers and Mike Vanderjagt.

312 * 0.14 = 43.7 pts per season

I know my favorite team sure could use an extra 43.7 points this season. Depending on how they are distributed, that would usually mean an extra win or two. However, only 37% of drives begin immediately following a kickoff. That would mean that the difference isn't really 43.7 pts per season, but:

0.37 * 43.7 = 16.1 pts per season

But, in a way, all drives originate from a kickoff. All drives' starting field position subsequent to a kickoff are biased by the kickoff result. For example, a poor kick that results in a starting field position at the 40 yd line will result in all subsequent drives being closer to the kicking team's end zone than otherwise, until another kickoff. For that reason, I think the real answer is a lot closer to 43.7 points per season than 16.1 points per season.

Additionally, an extra series on a drive means there are more plays that could result in a turnover. About 10% of all series result in either a fumble or interception. That further strengthens the effect of field position and the importance of deep kickoffs.

We began the analysis by comparing Rackers and Vanderjagt, who were extreme examples--about 4 standard deviations apart. If we repeat the above analysis by looking just a single standard deviation in kickoff distance (1.49 yds), the effect is 10.9 pts per season per SD.

My previous look at FG kicking estimated that every additional SD in accuracy resulted in 6.7 more pts per season. When compared to 10.9 pts per kickoff SD, it appears that kickoff performance is the more important aspect of place kicking. Interestingly, when Vanderjagt was cut in 2006 by the Cowboys, the news articles didn't bother to mention his short kickoffs, only that he didn't like to do it.

An Alternate Analysis of Field Position

Previous studies have examined the point value of various field positions. Perhaps the best has been David Romer's study regarding 4th down situations. To evaluate when coaches should "go for it" on 4th down, he evaluated the point value of a 1st and 10 from each position on the field. The figure below is from his study.


Between the 15 yard lines, the value change is linear--0.04 points per yard. A 6 yard difference, therefore, equates to 0.24 pts per drive. With an average of 182.6 drives per season, that's a difference of 43.8 pts per season--almost exactly the same result yielded by the "one additional first down" analysis.

Season Win Projections Week 14

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. Precise playoff predictions based on individual game probabilities can be found at NFL Forecast.

Team	Rank	Proj GWP	Fut. Opp	Current	Proj W
AFC E
NE	1	0.92	0.42	13	15.7
BUF	16	0.48	0.52	7	8.4
NYJ	19	0.36	0.59	3	4.1
MIA	28	0.24	0.56	0	0.7
AFC N
PIT	8	0.71	0.45	9	11.1
CLE	17	0.61	0.36	8	9.8
CIN	20	0.64	0.30	5	6.9
BAL	22	0.32	0.55	4	5.0
AFC S
IND	2	0.90	0.42	11	13.7
JAX	5	0.75	0.46	9	11.2
TEN	13	0.51	0.55	7	8.5
HOU	18	0.25	0.72	6	6.7
AFC W
SD	9	0.75	0.38	8	10.2
DEN	12	0.51	0.56	6	7.5
KC	25	0.38	0.44	4	5.1
OAK	30	0.11	0.74	4	4.3
Team	Rank	Proj GWP	Fut. Opp	Current	Proj W
NFC E
DAL	3	0.84	0.47	12	14.5
NYG	14	0.39	0.64	9	10.2
WAS	15	0.37	0.64	6	7.1
PHI	10	0.50	0.58	5	6.5
NFC N
GB	6	0.86	0.28	11	13.6
MIN	11	0.63	0.44	7	8.9
DET	26	0.27	0.55	6	6.8
CHI	31	0.20	0.56	5	5.6
NFC S
TB	4	0.90	0.26	8	10.7
NO	21	0.52	0.40	6	7.6
CAR	27	0.13	0.76	5	5.4
ATL	24	0.25	0.60	3	3.8
NFC W
SEA	7	0.81	0.34	9	11.4
ARI	23	0.52	0.35	6	7.6
STL	29	0.22	0.58	3	3.7
SF	32	0.12	0.56	3	3.4

The Bills, Redskins, and Unsportsmanlike Conduct

On December 2^nd, Joe Gibbs may have cost his team a playoff spot. His 15 yd unsportsmanlike conduct penalty for consecutive time outs to ice Buffalo kicker Ryan Lindell backfired. It gave Lindell a 36 yd FG attempt instead of a 51 yd attempt to win the game as time expired. The cost of Gibbs’ mistake is only now becoming clear as the playoffs picture comes into focus.

Lindell is a decent kicker and has kicked 5 out of 7 lifetime FGs from beyond 50 yds. But 7 attempts is not terribly significant statistically. Chances are he’s not too different than most starting NFL kickers. Below is a graph of NFL-wide FG probability of success vs. attempt distance. A best-fit equation yields how that 15 yd penalty changed Lindell’s chance to win the game with only seconds remaining.


Those 15 yards changed the FG probability from 0.58 to 0.88, a difference of 0.30. And although Lindell proved (as Gibbs called the first timeout) that he had the leg to make the longer kick, that is not an indication that Lindell is immune from the laws of probability.

Today the Redskins find themselves at 6-7, one game back in the race for the last wildcard spot in the NFC. Had Lindell missed from 51 yds, the Redskins would have won and they’d be tied with Minnesota at 7-6, who they will face in week 16.

The Bills, on the other hand, are now at 7-6 partially thanks to their win over Washington. They are now one game behind Cleveland for the 2nd wildcard spot in the AFC with about a 20% chance of sneaking into the playoffs.

What a difference 15 yards and one kick can make /could have made.

Playoff Probabilities

Updated playoff probabilities based on updated Week 14 data are now available at NFL-Forecast.com.

Game Predictions Week 15

Game probabilities for week 15 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	Vistor	Home	Hprob
0.52	DEN	HOU	0.48
0.76	CIN	SF	0.24
0.36	ARI	NO	0.64
0.10	ATL	TB	0.90
0.50	BAL	MIA	0.50
0.45	BUF	CLE	0.55
0.80	GB	STL	0.20
0.47	JAX	PIT	0.53
0.07	NYJ	NE	0.93
0.77	SEA	CAR	0.23
0.65	TEN	KC	0.35
0.93	IND	OAK	0.07
0.15	DET	SD	0.85
0.17	PHI	DAL	0.83
0.40	WAS	NYG	0.60
0.15	CHI	MIN	0.85

Week 14 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 14. A full explanation of the methodology can be found here.

Rank	Team	Last Wk	GWP	Opp GWP	O Rank	D Rank
1	NE	1	0.89	0.55	1	5
2	IND	3	0.87	0.54	4	1
3	DAL	2	0.82	0.49	2	6
4	TB	4	0.76	0.48	6	7
5	JAX	6	0.72	0.55	3	13
6	GB	7	0.70	0.48	5	12
7	SEA	8	0.68	0.40	11	8
8	PIT	5	0.67	0.46	14	3
9	SD	9	0.64	0.52	15	4
10	PHI	10	0.58	0.54	8	21
11	MIN	11	0.57	0.45	10	15
12	DEN	15	0.56	0.49	7	23
13	TEN	14	0.55	0.53	24	2
14	NYG	12	0.52	0.49	19	10
15	WAS	13	0.51	0.54	20	9
16	BUF	17	0.50	0.56	16	14
17	CLE	16	0.47	0.47	9	29
18	HOU	18	0.46	0.50	17	26
19	NYJ	19	0.44	0.53	21	22
20	CIN	20	0.43	0.51	12	30
21	NO	24	0.41	0.50	13	32
22	BAL	21	0.36	0.51	25	16
23	ARI	22	0.36	0.44	22	19
24	ATL	25	0.34	0.49	18	28
25	KC	23	0.32	0.53	31	11
26	DET	30	0.31	0.52	23	18
27	CAR	27	0.31	0.49	30	17
28	MIA	26	0.29	0.54	27	25
29	STL	28	0.28	0.46	29	20
30	OAK	29	0.26	0.46	26	27
31	CHI	31	0.25	0.52	28	31
32	SF	32	0.14	0.45	32	24

Team Efficiency Stats

I've received a few requests to see the data used by the efficiency model, so here it is a table of all 32 teams. The NFL average is listed at the bottom. O Pass, D Run, etc. are in "yards per attempt." Turnover rates are also per attempt--interceptions per pass attempt and fumbles per play. Pen rate is penalty yards per play for both offense and defense.

The weights of each variable can be found in the post here.

Team	O Pass	O Run	O Int	O Fum	D Pass	D Run	D Int	Pen Rate
ARI	6.54	3.61	0.038	0.037	5.77	3.95	0.032	0.46
ATL	5.19	3.88	0.026	0.022	6.48	4.25	0.038	0.47
BAL	5.10	4.02	0.023	0.030	6.56	2.83	0.035	0.32
BUF	5.86	3.81	0.033	0.018	6.68	4.22	0.029	0.45
CAR	5.10	4.07	0.036	0.029	6.14	3.62	0.031	0.41
CHI	5.49	3.23	0.039	0.033	6.46	4.42	0.023	0.37
CIN	6.59	3.52	0.032	0.021	6.94	4.23	0.036	0.47
CLE	6.88	4.07	0.034	0.027	6.46	4.63	0.028	0.43
DAL	8.13	4.35	0.037	0.015	5.48	3.79	0.040	0.32
DEN	6.84	4.41	0.034	0.034	6.65	4.61	0.035	0.36
DET	6.10	3.96	0.034	0.049	6.49	3.93	0.035	0.55
GB	7.27	3.79	0.021	0.027	6.07	3.97	0.032	0.34
HOU	7.00	3.66	0.039	0.037	6.33	4.50	0.028	0.21
IND	7.04	3.97	0.032	0.014	5.12	4.00	0.043	0.30
JAX	6.54	4.33	0.018	0.018	6.64	3.96	0.035	0.33
KC	5.30	3.32	0.040	0.025	5.96	4.16	0.035	0.38
MIA	5.14	4.24	0.036	0.026	6.85	4.29	0.034	0.37
MIN	5.84	5.63	0.029	0.027	6.36	2.99	0.028	0.37
NE	8.04	4.09	0.014	0.012	5.73	4.13	0.045	0.38
NO	6.32	3.53	0.031	0.027	7.25	3.89	0.026	0.27
NYG	5.64	4.40	0.041	0.021	5.70	3.81	0.030	0.35
NYJ	5.48	3.71	0.038	0.014	6.80	4.25	0.034	0.24
OAK	5.62	4.24	0.042	0.038	6.47	4.81	0.046	0.41
PHI	6.11	4.53	0.033	0.015	6.15	3.75	0.018	0.33
PIT	6.44	4.10	0.037	0.020	4.39	3.62	0.021	0.34
SD	6.39	4.08	0.037	0.021	5.92	4.15	0.048	0.40
SF	3.99	4.21	0.038	0.043	6.16	3.78	0.025	0.36
SS	6.29	3.69	0.023	0.016	5.45	4.01	0.034	0.19
STL	5.27	3.55	0.046	0.023	6.17	4.14	0.030	0.38
TB	6.68	4.30	0.014	0.017	5.35	3.73	0.031	0.32
TEN	5.69	4.06	0.039	0.031	5.47	3.97	0.036	0.42
WAS	5.93	3.91	0.027	0.038	5.71	3.94	0.021	0.37
Avg	6.12	4.01	0.032	0.026	6.13	4.01	0.033	0.37

Another Plug for NFL Forecast

One cool feature of the web-based playoff prediction engine found at NFL-Forecast.com is the "predicted wins" tab. Each teams' final win total is plotted as a probability distribution according to the game probabilities calculated here at NFL Stats. The neat part to me is the "probability of making the playoffs with x wins." It gives the probability of making the playoffs for each win total.

For example, Cleveland's playoff probabilities for each win total look like this:

8 wins--5%
9 wins--30%
10 wins--80%
11 wins--100%

It takes a minute or two to play with the app to realize how neat it really is. You can move the slider bars for any game, setting your own game probabilities--you're not stuck with mine. (To account for today's results, I moved the sliders to 100% for each winner.) Then click on Forecast/Forecast Remainder of Season. You can then click on the tabs at the bottom of the app to see playoff probabilities, expected win totals, division standings, and (for the MIA, SF, STL, and ATL fans out there) the 2008 draft order probabilities.

If you're a fan of a team on the bubble, you can move the sliders to see your team's playoff odds for "what if" scenarios. Let's say the Redskins win out--they'd have a 97% chance for a playoff spot. (Three straight wins would include a victory over MIN in week 16, and determine the tie-breaker. )

And if Detroit wins out, they'd have a 53% chance of making the playoffs.

Pretty cool.

Browns vs. Titans for the AFC Wildcard

CLE and TEN are both 7-5 with 4 games remaining. With JAX currently playing well and sitting at 8-4, it looks like the final wildcard spot will go to either the Browns or Titans. BUF, at 6-6, still has an outside chance, but the clear favorite for the wildcard right now is CLE. NFL Forecast gives CLE about a 50/50 shot at the wildcard and TEN about a 33% chance.

CLE and TEN are mirror images of one another. CLE has one of the top ranked offenses but one of the worst defenses, while TEN has a very strong defense but weak offense. All things considered, and accounting for opponent strength, TEN ranks 14th in the league and CLE ranks 16th. Here is how each team's stats break down:

Team	O Pass	O Run	O Int Rate	O Fum	D Pass	D Run	D Int Rate	Pen Rate
CLE	6.88	4.07	0.034	0.027	6.46	4.63	0.028	0.43
TEN	5.69	4.06	0.039	0.031	5.47	3.97	0.036	0.42
NFL Avg	6.12	4.01	0.032	0.026	6.13	4.01	0.033	0.37

But the symmetry stops there. CLE has a far easier schedule than TEN for the final four weeks, and that is why they are the favorites for the wildcard spot despite being a very average team. Here is how the rest of CLE's schedule shapes up:

Opponent	Win Prob.
at NYJ	0.43
BUF	0.59
at Cin	0.44
SF	0.87

TEN's schedule is far tougher.

Opponent	Win Prob.
SD	0.45
at KC	0.54
NYJ	0.63
at IND	0.12

The difference in the two teams' schedules is mostly due to their final opponents. CLE gets SF at home while TEN visits IND. The biggest uncertainty is how the Colts will play in week 17. If they have locked up the #2 seed they may rest their starters allowing TEN to have a much better chance of winning.

BUF still has a shot, especially if they can beat CLE (at CLE) next week. The Bills almost certainly need to go at least 3-1 in the last four weeks with this schedule:

Opponent	Win Prob.
MIA	0.69
at CLE	0.41
NYG	0.53
at PHI	0.30

It will likely go down to the final week of the season. Unfortunately, the winner earns the right to a road game at (probably) SD or PIT for the right to visit NE.

Luckiest NFL Teams Week 13

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.

Rank	Team	GWP	Wins	Exp Wins	Luck
1	DET	0.27	6	3.3	2.7
2	CHI	0.25	5	3.0	2.0
3	GB	0.67	10	8.0	2.0
4	NYG	0.52	8	6.3	1.7
5	CLE	0.47	7	5.6	1.4
6	NE	0.89	12	10.6	1.4
7	ARI	0.40	6	4.8	1.2
8	CAR	0.33	5	3.9	1.1
9	SF	0.16	3	1.9	1.1
10	TEN	0.51	7	6.1	0.9
11	PIT	0.69	9	8.3	0.7
12	DAL	0.86	11	10.3	0.7
13	OAK	0.28	4	3.3	0.7
14	NO	0.37	5	4.4	0.6
15	BUF	0.46	6	5.6	0.4
16	SEA	0.66	8	7.9	0.1
17	IND	0.84	10	10.1	-0.1
18	JAX	0.68	8	8.1	-0.1
19	STL	0.29	3	3.5	-0.5
20	HOU	0.46	5	5.5	-0.5
21	KC	0.38	4	4.6	-0.6
22	DEN	0.47	5	5.7	-0.7
23	SD	0.64	7	7.7	-0.7
24	MIN	0.57	6	6.8	-0.8
25	WAS	0.51	5	6.1	-1.1
26	BAL	0.43	4	5.1	-1.1
27	TB	0.77	8	9.2	-1.2
28	ATL	0.36	3	4.3	-1.3
29	CIN	0.45	4	5.3	-1.3
30	PHI	0.59	5	7.1	-2.1
31	NYJ	0.45	3	5.5	-2.5
32	MIA	0.35	0	4.2	-4.2

Season Win Projections Week 13

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. Precise playoff predictions based on individual game probabilities can be found at NFL Forecast.

Team	Rank	Proj GWP	Fut Opp	Proj W
AFC E
NE	1	0.89	0.50	15.5
BUF	17	0.48	0.48	7.9
NYJ	19	0.40	0.56	4.6
MIA	26	0.30	0.56	1.2
AFC N
PIT	5	0.63	0.57	11.5
CLE	16	0.59	0.38	9.4
CIN	20	0.63	0.32	6.5
BAL	21	0.30	0.64	5.2
AFC S
IND	3	0.88	0.42	13.5
JAX	6	0.73	0.44	10.9
TEN	14	0.43	0.58	8.7
HOU	18	0.28	0.69	6.1
AFC W
SD	9	0.74	0.38	10.0
DEN	15	0.46	0.51	6.8
KC	23	0.45	0.43	5.8
OAK	29	0.14	0.71	4.5
Team	Rank	Proj GWP	Fut Opp	Proj W
NFC E
DAL	2	0.89	0.42	14.6
NYG	12	0.41	0.61	9.6
PHI	10	0.54	0.55	7.2
WAS	13	0.46	0.55	6.8
NFC N
GB	7	0.84	0.27	13.4
MIN	11	0.71	0.35	8.8
DET	30	0.18	0.64	6.7
CHI	31	0.23	0.53	5.9
NFC S
TB	4	0.87	0.33	11.5
NO	24	0.47	0.40	6.9
CAR	27	0.15	0.74	5.6
ATL	25	0.31	0.55	4.3
NFC W
SEA	8	0.76	0.38	11.0
ARI	22	0.48	0.42	7.9
STL	28	0.25	0.55	4.0
SF	32	0.13	0.56	3.5

Playoff Race Predictions Wk 13

For the rest of the 2007 season, NFL Stats and NFL Forecast are teaming up to predict the playoff races. 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. NFL Forecast is using the game outcome probabilities published here at NFL Stats as its default baseline.

The resulting playoff chances are published weekly here.

Game Predictions Week 14

Game probabilities for week 14 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
0.18	CHI	WAS	0.82
0.14	CAR	JAX	0.86
0.92	DAL	DET	0.08
0.31	MIA	BUF	0.69
0.35	NYG	PHI	0.65
0.12	OAK	GB	0.88
0.17	PIT	NE	0.83
0.55	SD	TEN	0.45
0.27	STL	CIN	0.73
0.73	TB	HOU	0.27
0.20	ARI	SEA	0.80
0.83	MIN	SF	0.17
0.43	CLE	NYJ	0.57
0.33	KC	DEN	0.67
0.84	IND	BAL	0.16
0.43	NO	ATL	0.57

Week 13 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	0.89	0.54	1	5
2	DAL	3	0.86	0.51	2	4
3	IND	2	0.84	0.54	5	1
4	TB	4	0.77	0.47	4	7
5	PIT	5	0.69	0.43	15	2
6	JAX	7	0.68	0.55	3	20
7	GB	6	0.67	0.50	6	13
8	SEA	8	0.66	0.41	12	11
9	SD	10	0.64	0.52	13	6
10	PHI	9	0.59	0.54	8	19
11	MIN	13	0.57	0.48	10	14
12	NYG	11	0.52	0.49	21	9
13	WAS	12	0.51	0.57	22	8
14	TEN	15	0.51	0.51	25	3
15	DEN	14	0.47	0.50	11	31
16	CLE	17	0.47	0.50	7	30
17	BUF	19	0.46	0.59	17	17
18	HOU	16	0.46	0.48	16	28
19	NYJ	24	0.45	0.55	19	24
20	CIN	20	0.45	0.54	9	29
21	BAL	26	0.43	0.48	24	12
22	ARI	23	0.40	0.43	18	16
23	KC	21	0.38	0.52	31	10
24	NO	25	0.37	0.51	14	32
25	ATL	22	0.36	0.49	20	22
26	MIA	18	0.35	0.55	23	23
27	CAR	28	0.33	0.46	27	15
28	STL	30	0.29	0.47	28	21
29	OAK	29	0.28	0.43	29	25
30	DET	27	0.27	0.49	26	18
31	CHI	31	0.25	0.51	30	27
32	SF	32	0.16	0.45	32	26

How the Ravens Can Beat the Patriots

Simple--Never punt.

I might go a step further and say, "Never kick a FG" (unless it provides a lead in the final 3 minutes of the game).

What do they have to lose?

QB Rating Week 12

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 12. Air Yards is the yards passed forward of the line of scrimmage not including WR yards after catch (YAC). TO% is total turnovers (fumbles and interceptions) per pass attempt, sack, or rush.

Rank	Name	QBR	Att	Pct	Yds	Y/A	Rush	Yds	Sk Yds	Air Yds	TO %	+WP16
1	Brady	127.9	392	72.4	3439	8.8	22	64	80	1978	1.4	3.30
2	Garrard	103.1	209	65.1	1626	7.8	36	145	77	987	0.4	2.92
3	Romo	107.1	382	66.0	3352	8.8	22	86	118	2002	4.0	2.11
4	Anderson	89.5	365	58.1	2758	7.6	24	51	84	1714	3.3	1.76
5	Schaub	87.3	284	66.5	2207	7.8	17	52	119	1423	4.0	1.53
6	Warner	90.8	254	62.2	2009	7.9	11	-4	89	1304	4.3	1.45
7	Garcia	96.0	282	64.5	2135	7.6	34	116	84	1094	1.4	1.45
8	Manning P	89.4	379	63.3	2821	7.4	14	-9	101	1783	3.5	1.42
9	Roethlisberger	106.0	288	67.0	2380	8.3	21	141	254	1487	3.8	1.15
10	Palmer	90.8	418	67.5	3076	7.4	15	15	100	1860	3.8	1.10
11	Cutler	89.6	300	64.7	2384	7.9	28	121	93	1303	3.9	0.89
12	Hasselbeck	89.6	402	62.4	2887	7.2	27	55	133	1575	2.4	0.76
13	Delhomme	111.8	86	64.0	624	7.3	6	26	46	311	1.5	0.72
14	Favre	97.9	439	67.4	3412	7.8	22	-6	89	1685	2.9	0.56
15	McNabb	87.3	326	59.8	2329	7.1	30	135	151	1179	2.3	0.35
16	Campbell	79.1	364	60.2	2384	6.5	31	169	96	1341	3.8	0.28
17	Brees	85.0	456	67.3	2997	6.6	15	52	64	1634	3.7	0.26
18	Kitna	87.4	381	65.4	2897	7.6	21	55	264	1751	3.9	0.24
19	Pennington	87.5	190	67.4	1317	6.9	17	23	102	819	3.6	0.21
20	Boller	74.6	208	59.6	1242	6.0	9	41	113	764	3.0	-0.06
21	Jackson	62.8	144	54.2	900	6.3	21	122	30	474	4.0	-0.18
22	Testaverde	69.8	118	54.2	699	5.9	5	28	28	389	3.5	-0.23
23	Young	65.3	264	61.4	1663	6.3	68	297	96	926	4.6	-0.44
24	Harrington	79.7	314	63.1	2031	6.5	14	33	169	980	2.0	-0.48
25	Manning E	75.0	371	58.5	2376	6.4	20	46	144	1338	4.3	-0.61
26	Losman	76.9	175	63.4	1204	6.9	20	110	103	596	3.8	-0.61
27	Bulger	73.3	279	60.9	1789	6.4	7	14	211	1087	3.7	-0.61
28	Culpepper	78.0	186	58.1	1331	7.2	20	40	130	750	4.0	-0.64
29	Rivers	81.1	330	61.2	2301	7.0	23	31	107	1216	4.6	-0.66
30	Lemon	69.4	166	57.8	923	5.6	18	70	86	482	2.6	-0.73
31	Green	72.6	141	60.3	987	7.0	7	32	53	515	5.2	-0.81
32	Smith	57.2	193	48.7	914	4.7	13	89	121	595	3.1	-0.83
33	Huard	74.7	262	62.2	1766	6.7	9	-1	166	951	4.2	-1.18
34	Clemens	56.9	159	49.1	892	5.6	13	71	80	469	3.8	-1.22
35	McNair	73.9	205	64.9	1113	5.4	10	32	85	568	3.5	-1.41
36	Griese	77.1	217	61.8	1508	6.9	9	16	101	730	5.4	-1.71
37	Grossman	63.3	173	54.9	1101	6.4	14	27	146	633	4.9	-1.74
38	Carr	58.3	136	53.7	635	4.7	17	59	74	315	3.3	-2.04
39	Dilfer	62.8	171	53.8	950	5.6	5	25	138	517	5.1	-2.54
40	McCown J	59.5	122	58.2	760	6.2	19	99	78	348	8.5	-3.71