Advanced NFL Stats

Team Efficiency Rankings - Week 12

2009-11-24T21:01:00.001-05:00

The team rankings below are in terms of generic win 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, and all ratings include adjustments for opponent strength.

Offensive rank (ORANK) is offensive generic win probability, which is based on each team's offensive efficiency stats only. In other words, it's the team's GWP assuming it had a league-average defense. DRANK is is a team's generic win probability rank assuming it had a league-average offense.

GWP is based on a logistic regression model applied to current team stats. The model includes offensive and defensive passing and running efficiency, offensive turnover rates, defensive interception rates, and team penalty rates. If you're scratching your head wondering why a team is ranked where it is, just scroll down to the second table to see the stats of all 32 teams.

Click on the table headers to sort:

RANK	TEAM	LAST WK	GWP	Opp GWP	O RANK	D RANK
1	IND	1	0.80	0.47	2	5
2	NO	2	0.79	0.42	1	14
3	NE	4	0.74	0.50	4	12
4	SD	8	0.74	0.51	5	17
5	PIT	3	0.74	0.47	9	4
6	PHI	6	0.71	0.49	10	1
7	NYG	10	0.70	0.50	7	9
8	DAL	5	0.67	0.49	3	21
9	MIN	11	0.67	0.41	6	22
10	DEN	7	0.66	0.57	16	3
11	CIN	9	0.62	0.52	15	6
12	GB	12	0.62	0.42	11	8
13	BAL	13	0.61	0.53	12	11
14	HOU	14	0.54	0.47	8	26
15	NYJ	15	0.53	0.50	24	2
16	ARI	16	0.50	0.47	17	18
17	WAS	19	0.49	0.45	19	10
18	ATL	18	0.45	0.55	13	27
19	TEN	20	0.44	0.55	18	20
20	JAC	17	0.44	0.45	14	30
21	SF	23	0.42	0.51	25	7
22	CAR	21	0.41	0.50	26	13
23	CHI	22	0.41	0.47	20	16
24	MIA	25	0.40	0.56	21	23
25	SEA	24	0.37	0.48	23	19
26	BUF	26	0.35	0.46	27	15
27	STL	27	0.26	0.53	22	28
28	KC	29	0.23	0.55	29	29
29	TB	28	0.22	0.59	30	25
30	OAK	30	0.20	0.57	31	24
31	DET	31	0.17	0.51	28	32
32	CLE	32	0.12	0.54	32	31

And here are the sortable raw team efficiency stats. Passing, running, and penalties are in yards per relevant play. Fumbles and interception stats are in turnovers per relevant play.

TEAM	OPASS	ORUN	OINT%	OFUM%	DPASS	DRUN	DINT%	PENRATE
ARI	6.5	4.1	3.0	1.4	6.1	4.3	2.9	0.45
ATL	6.2	4.4	3.5	0.8	6.9	4.5	2.3	0.34
BAL	6.6	4.2	2.4	0.6	6.4	3.5	3.4	0.53
BUF	5.5	4.0	4.5	0.9	5.7	4.9	5.1	0.45
CAR	5.4	5.0	4.9	1.9	5.8	4.7	3.6	0.35
CHI	6.0	4.0	4.7	1.3	5.8	4.3	3.1	0.46
CIN	6.3	4.0	2.6	1.3	5.8	3.8	3.3	0.39
CLE	4.2	3.7	5.0	1.1	7.3	4.6	1.9	0.36
DAL	7.1	5.0	2.1	1.0	6.0	4.1	1.9	0.48
DEN	6.0	4.4	1.8	1.3	5.6	4.0	2.4	0.36
DET	5.2	3.9	4.7	1.0	7.5	4.5	1.7	0.44
GB	6.6	4.5	1.5	0.6	5.8	3.7	4.5	0.54
HOU	7.4	3.3	2.5	1.3	6.2	4.8	2.4	0.44
IND	7.9	3.8	2.6	0.6	5.5	4.1	2.9	0.31
JAC	6.2	4.8	1.8	1.0	7.1	4.2	2.7	0.30
KC	4.9	3.6	1.9	1.7	7.1	4.5	2.1	0.33
MIA	5.0	4.7	2.0	0.9	6.7	4.1	2.8	0.33
MIN	7.2	4.2	0.9	0.9	5.9	3.9	2.0	0.34
NE	7.2	4.0	1.5	0.7	5.6	4.4	4.1	0.40
NO	8.0	4.8	2.8	0.9	5.5	4.6	5.4	0.39
NYG	7.1	4.3	2.7	0.9	5.6	4.3	2.7	0.45
NYJ	5.8	4.7	6.4	1.2	5.3	4.0	2.1	0.35
OAK	4.2	3.9	4.5	1.2	6.7	4.4	2.4	0.36
PHI	6.5	4.6	2.3	0.8	5.3	3.9	4.6	0.48
PIT	7.1	4.2	2.9	1.1	5.4	3.4	2.2	0.40
SD	7.3	3.5	1.9	0.0	5.8	4.2	3.1	0.32
SF	5.2	4.5	2.9	0.7	6.4	3.5	2.9	0.42
SEA	5.7	3.7	2.3	1.2	6.3	4.3	2.3	0.39
STL	5.2	4.6	2.7	1.1	7.2	4.7	2.5	0.43
TB	4.8	4.2	4.9	2.3	7.1	4.9	4.3	0.35
TEN	5.6	5.3	3.5	1.8	6.6	4.4	2.8	0.39
WAS	6.0	4.0	2.9	1.0	5.3	4.4	2.2	0.40
Avg	6.1	4.2	3.0	1.1	6.2	4.2	3.0	0.40

Offenses Run Too Often On 1st Down

2009-11-23T05:00:00.010-05:00

NFL offenses generally run too often on 1st down. Accounting for the relative gains of each play type, and accounting for the risks of turnovers, offenses should pass more. There is currently an imbalance, where teams are too often running directly into defenses that are expecting runs.

Game theory tells us that when there are two strategy options, like run and pass, the expected payoffs for both options should be equal. You really don't need game theory to intuitively understand this. If one option yields a better payoff, then it should be chosen until the opponent responds with a strategy change of his own. Eventually, as the opponent responds, the payoffs for the two options equalize. The point at which the strategy mix equalizes payoffs is known as the minimax, or sometimes called the Nash equilibrium. The resulting strategy mix, or run-pass balance in this case, produces the best overall, long-run payoff.

When there are two strategy options and one of them yields a much higher payoff, it tells us two things. In this case, passing is more lucrative than running on 1st down, and this tells us: 1) offenses should be passing more often, and 2) for now, defenses should continue to be more biased toward stopping the run.

Recent Studies

There have been two recent studies that looked at the same issue, but both of them suffer from the same flaw. Freakonomics author Steve Levitt teamed with Kenneth Kovash to publish 'Professionals Do Not Play Minimax.' Another paper called 'Risk and NFL Playcalling' was recently presented. Both papers fail to account for the context of the game by considering time remaining and score difference. For example, a team ahead will use the run to work time off the clock, sacrificing optimum scoring but increasing its chances of winning. The time-value of the run is not captured.

A Solution: 'Normal' Football

One simple, but partial, solution I recommended was to limit the data to what I call 'normal' football situations. Normal football is when score and time are not significant considerations. The score is close, so teams are playing with a conventional and balanced risk-reward mindset. And time is far from running out in either half, so neither team is adjusting its play-calling because of the clock. So I took my own advice and ran my own numbers. I looked at plays where the score was within 10 points and the game is either in the 1st or 3rd quarter. Ultimately, the goal is to look at situations where neither team is desperate or hurried, and both teams are still playing a game of maximizing their net point advantage.

I'll also improve on previous efforts by examining play values of runs and passes according to field position. We'll see that the relative value of the runs and passes change near the end zones.

Expected Points

To value plays, I used Expected Points (EP). Every down and distance has a potential point value at each yard-line on the field. The values are determined by averaging the point advantage offenses have historically gained given a particular combination of down, distance, and field position. The key to understanding EP is that it not only accounts for points scored on the current drive, but it accounts for points eventually scored by either team on subsequent drives. For example, a 1st and 10 at midfield is typically worth 2.0 EP. A 2nd and 5 at an opponent's 45 is worth 2.2 EP. So a 5-yard gain on 1st down at midfield would produce +0.2 EP. This method factors in risks such as sacks, fumbles, interceptions, incompletions, penalties, safeties and everything else. If the question is, 'Does it factor in _____?' the answer is yes.

Results

If we look at all runs and passes on 1st down and 10 (or goal), and average the EP gain for each type of play, we can measure the payoffs. The graph below plots the EP gain for 1st down runs and passes according to field position. For example, at an opponent's 31-40 yard lines, the average pass results in a gain of 0.10 EP, and the average run results in a gain of 0.01 EP.

For the vast majority of the field, the pass has a higher average payoff. Runs have a higher payoff only inside final 10 yards before the end zone, so it appears teams are passing too often there. The discrepancy is especially apparent when an offense is backed up near its own goal line. This difference even accounts for the likelihood of a sack, or interception in such a vulnerable position. There are relatively few pass attempts in that situation, but still enough for a reliable estimate (402 of them).

In fact, for most of the field, the average value of a run is essentially zero or negative. This makes sense because a 1st down play needs at least 4 yards to be at least break-even in term of value, and most runs go for 3 yards or less. Between the 20-yard lines, 55% of runs on 1st and 10 gain less than 4 yards. The majority of runs on 1st down are actually setbacks.

Here is how the league-wide run-pass looks in recent years. The next graph plots the percentage of run plays on 1st down and 10 (or goal). Teams increase their tendency to run near both end zones.

Right now, we can't say what the optimum 1st down run-pass ratio should be. But we can say with high confidence that offenses would be better off passing more often. Because 1st down is widely known as a running down, play-action fakes are very effective, and I would guess that's primarily where the pass gets its advantage. As teams pass more often on 1st down, the effectiveness of play-action will suffer. But meanwhile, as defenses are forced to defend more against the pass, runs will become more successful.

We can repeat this same analysis for other down and distance combinations. For example, are teams running or passing too often on 2nd and long? What about 3rd and short, etc.? I'll be rolling out articles in the near future with a similar analysis for other situations.

The usual caveats apply. This is a baseline for the league as a whole, but the EP curves could be tailored to individual teams and opponents. Play calling is never as simple as just run or pass, and there are many different types of passes, ranging from deep bombs to short screens. Additionally, there is some amount of bias in the data. Teams that are good in passing would be expected to pass more often, and teams good in running would be expected to run more often. In other words, we can't just tell the 2009 Browns to pass far more often on first down because their particular expected payoff for passing may not be any better than for running. Still, the league-wide difference between running and passing is so stark that we can still make a general conclusion.

End Notes: Data consist of runs and passes from all non-preseason NFL games 2000-2008, limited to the 1st and 3rd quarters when the score is within 10 points. There are 21,537 passes and 28,036 runs in the study.

Last Thoughts on the 4th and 2

2009-11-22T21:37:00.002-05:00

At the risk of being accused of milking this thing, here are some final few thoughts on the topic. I watched the Football Night in America segment and a few things struck me.

Let me say I have a lot of respect for Coach Dungy. I also think that convincing someone skeptical is difficult, and we shouldn't expect someone to immediately come around. In general though, coaches (and former players/analysts) benefit from a perception that football is some unknowable mystery, and that they are the only priests that can divine the true answers.

From Dungy's perspective, he's enjoyed long career by doing it the conventional way. But the reason his way worked was because everyone else played the same way. To change his mind now might mean admitting, "I did it wrong all these years." That's a tough hurdle to overcome.

It starts with something like this--planting a seed of doubt that the conventional wisdom might not be so wise. A smart young coach will one day figure it out, maybe in college, and everyone else will be forced to catch up. It's amazing that this particular 4th down was a failure, but it has done more to advance the subject than any other 4th down play, including all the successful ones.

I was particularly struck by Bob Costas' remarks. Costas said the crowd at Lucas Oil Stadium went from jubilation to stunned silence when they saw the Patriots offense lining up for the 4th down. Costas said from their perspective, they would have gladly accepted the ball 40 yds back than give the Patriots a good chance to end the game with a simple 2-yd gain.

Think about what that tells you about Belichick's decision. 'Do what your opponent fears most' might not be a bad way to make football decisions.

Now, to correct some bad info from Dungy and Dan Patrick: The 4th down conversion rates I used are based on data from 1st and 3rd quarters when the score is within 10 pts. That way 'desperation' and 'prevent' plays are excluded.

Also, as I made clear in the original post, my numbers are league baselines. But once you start increasing the Colts' chances of scoring from either field position, the go-for-it option just gets better and better relative to punting. The stronger you gauge the Colts offense, the better the decision becomes.

I talked with a very well-known reporter at length on Friday, and he's still very skeptical. And that's ok. He was very interested in all the mitigating circumstances surrounding the play--the personnel, the events earlier in the game, the timeout, the personal histories. And that's great. Those considerations matter to some extent, but they're all relative to some baseline. There needs to be something concrete underneath all those other extenuating factors, otherwise there is nothing off of which to make those adjustments.

You might not buy my numbers, but the battle has already been won. Even the skeptics are now just arguing over what the particular numbers should be. They've unwittingly accepted the framework that there are numbers, and there is a way to use them to help make the best decision.

Lastly, let me say I am not a rocket scientist despite being called that on two different networks today. That was just my major in college. I consider myself a tactician, not a statistician or mathematician. My day job is as a naval tactics consultant. To me, stats and math are tools for better decisions, not ends in themselves. That's one thing I'm trying to get across--you really don't need fancy calculus, just some percentages and an open mind.

Team Playoff Probabilities - Week 11

2009-11-21T05:47:00.001-05:00

Courtesy of Chris at NFL-Forecast.com, here are the latest playoff forecasts. The tables below do not include results from the Thursday night Dolphins-Panthers game.

It looks like the AFC teams are relatively firm. As of now, the Colts, Bengals, Steelers, Patriots, Broncos, and Chargers are on the inside track. Baltimore, Jacksonville, and Houston are on the outside looking in.

The top NFC teams have a tight hold on playoff spots, but the wildcards are up for grabs. The Saints, Vikings, and Cardinals each have a good grip on their divisions if they keep playing well. The Cowboys are the class of the East at the moment, and have a good shot at a wildcard if they don't take the division. The other contenders include the Eagles, Giants, Packers, Falcons, and even the 49ers.

These playoff probabilities are calculated using the NFL-Forecast software mini-app that runs thousands of simulated seasons. The outcomes are based on game-by-game probabilities with every crazy tie-breaking scenario factored in. Chris has (wisely?) used the probabilities from Advanced NFL Stats as his default game probabilities for the past two seasons.

But if you don't like my numbers you can easily change them. Or you can play what-if scenarios. What if the Ravens beat the Colts this weekend? How would that change their chances for the playoffs? In fact, to account for Thurday night's game, you can simply slide the slider to 100% for the Dolphins to give them the win. Pretty cool.

There are two tables below. The first lists the probability that each team will finish in each place in their division. The second table lists the overall playoff probabilities, broken down by seed. The probabilities are rounded as percentages to make the table easier to read.

AFC EAST
Team	1st	2nd	3rd	4th
NE	93	6	1	0
NYJ	5	59	28	8
MIA	1	27	52	20
BUF	0	8	20	72
AFC NORTH
Team	1st	2nd	3rd	4th
CIN	73	27	0	0
PIT	27	64	9	0
BAL	0	9	90	0
CLE	0	0	0	100
AFC SOUTH
Team	1st	2nd	3rd	4th
IND	100	0	0	0
JAC	0	50	45	5
HOU	0	48	43	9
TEN	0	2	12	86
AFC WEST
Team	1st	2nd	3rd	4th
DEN	58	42	0	0
SD	42	58	0	0
KC	0	0	56	44
OAK	0	0	44	56
NFC EAST
Team	1st	2nd	3rd	4th
DAL	54	29	16	1
PHI	25	40	34	1
NYG	21	31	47	2
WAS	0	0	3	97
NFC NORTH
Team	1st	2nd	3rd	4th
MIN	98	2	0	0
GB	2	87	12	0
CHI	1	11	88	0
DET	0	0	0	100
NFC SOUTH
Team	1st	2nd	3rd	4th
NO	100	0	0	0
ATL	0	76	23	0
CAR	0	24	76	1
TB	0	0	1	99
NFC WEST
Team	1st	2nd	3rd	4th
ARI	88	12	0	0
SF	12	71	16	1
SEA	0	16	73	11
STL	0	1	10	89

AFC Percent Probability Playoff Seeding
Team	1st	2nd	3rd	4th	5th	6th	Total
IND	89	8	2	1	0	0	100
CIN	5	41	19	8	16	8	97
PIT	3	21	3	0	57	10	94
DEN	2	11	31	15	4	19	82
NE	0	10	26	56	0	1	94
SD	0	9	18	14	7	22	70
BAL	0	0	0	0	6	11	18
JAC	0	0	0	0	4	14	18
NYJ	0	0	0	5	0	1	6
HOU	0	0	0	0	5	15	20
MIA	0	0	0	1	0	0	1
BUF	0	0	0	0	0	0	0
TEN	0	0	0	0	0	0	0
CLE	0	0	0	0	0	0	0
KC	0	0	0	0	0	0	0
OAK	0	0	0	0	0	0	0
NFC Percent Probability Playoff Seeding
Team	1st	2nd	3rd	4th	5th	6th	Total
NO	83	15	1	0	0	0	100
MIN	16	63	14	5	1	1	99
DAL	1	6	33	14	13	16	83
ARI	0	8	25	54	1	1	90
PHI	0	4	17	5	17	19	62
NYG	0	2	9	9	11	16	47
GB	0	1	1	0	44	22	68
SF	0	0	1	11	2	4	17
CHI	0	0	0	0	2	3	5
ATL	0	0	0	0	10	14	24
WAS	0	0	0	0	0	0	0
SEA	0	0	0	0	0	0	1
CAR	0	0	0	0	1	3	3
STL	0	0	0	0	0	0	0
DET	0	0	0	0	0	0	0
TB	0	0	0	0	0	0	0

ESPN Interview

2009-11-20T09:00:00.004-05:00

ESPN's Sunday NFL Countdown will be doing a piece on 4th down decisions this weekend. The focus will center around Bill Belichick and his thoughts on the topic in an interview they did with him a few years ago. At the time, they also interviewed Dr. David Romer, author of 'Do Firms Maximize.' Yesterday, ESPN re-interviewed Romer, and interviewed me too. I'm anxious to see how it turns out.

I'm told it will probably air a few minutes before noon EST on Sunday. Set your DVRs now!

ESPN also talked about my take on '4th-and-2-gate' on the Monday Night Football pre-game earlier this week. A lot of people were harsh on Matt Millen and Steve Young for their comments, but I think they asked exactly the right questions. Young said, 'Is that in context? I'd want to see that in context.' I presume he wants to know if the score and time remaining were considered. Millen asked, 'But does that take into account the Colts offense?' They were rightfully skeptical, but they zeroed in on the heart of the matter immediately. I have to give them a lot of credit.

'Patriots Lead Colts at Halftime' - The Onion

2009-11-19T10:36:00.001-05:00

The guys at the Onion have previously made their opinions known about 4th down decisions. This time they take on the Patriots' 4th down call from Sunday night. Too funny for words.

Belichick told reporters..."The only time they've been able to stop us is on on short-yardage passing plays, so if we're careful to execute and avoid any situation where we give Peyton Manning excellent field position, I'm extremely confident we'll leave here with a 'W.'

Thanks to Justin for the pointer.

Game Probabilities - Week 11

2009-11-19T07:00:00.002-05:00

Weekly game probabilities are available now at the nytimes.com Fifth Down. This week I also look at what's plaguing the Jets, and how it affects their match-up against the Patriots this week.

Belichick 4th Down Follow-Up

2009-11-18T08:00:00.004-05:00

Thanks to the commenters on the original post, all 200+ of you, for all the great criticisms and suggestions. The Internet is a big place, and although not every comment was helpful, I was pleased to see such a thoughtful and constructive debate. In this follow-up, I'll try to address some of the most common criticisms and questions. I suspect some skeptics will never be fully satisfied, but I feel many of the comments deserve a response.

1. You used 38 yds for the expected punt distance, the average punt distance for that region of the field. But Patriots punter Chris Hansen had averaged 4 punts for 44 yds. Why not use that distance instead?

Four punts is a tiny, tiny sample of Hansen's and the Patriots' true expected net punt distance. Punters in NFL are generally all the same. Differences among punters are almost completely due to two factors: 1) where on the field they tend to kick from, and 2) luck. We're far better off using the league average, based on hundreds of punts, rather than a tiny sample of 4.

However, indoor punts may indeed tend to be longer. Even if we use the 44 yd punt distance, it doesn't change the final analysis. The likelihood of an offense scoring from their own 28 instead of their own 34 is 0.27 instead of 0.30. This changes the ultimate comparison to: 0.79 for the conversion attempt vs. 0.73 for the punt. Those 6 yards would be gobbled up by Manning's offense in a heartbeat.

2. Your estimate of the Patriots' 60% chance of converting that 4th and 2 is too high, and it doesn't take into account the particular details of the situation.

It's true that this figure does not take into account the stress of the situation, the type of turf, the time of day, or the pull of the gravity of the moon. The 60% figure is a league-wide average for 4th and 2 situations outside the red zone, which is a reliably consistent stat across the recent decade.

Situational variables are usually grossly over-weighted. As far as I know, 2 yards are always 2 yards. The field is still level. The rules are the same. There are still 11 guys on offense and 11 on defense. Every single play in the NFL, including every 4th down in my data, is stressful and takes place in front of thousands, if not millions, of fans. The players are professionals accustomed to high-stakes risks, so let's not over-think this. The true answer might be 62% or 57%, but 60% is a reliable and fair baseline estimate.

Additionally, differences in strength and ability between any two NFL teams on any single play are usually very, very small. It's only when we tally the results of dozens upon dozens of plays in a game that the differences between teams accumulates to a point when we can tell the better teams from the mediocre ones. In any case, in terms of general efficiency, the Patriots offense is ranked 5th, and the Colts defense is ranked 4th.

3. Not punting was an insult to the Patriots' defense. Belichick offended his players by not showing confidence in them.

Agreed. If your goal is not not offend, then punting is the right call. But if your goal is to win the game, going for it is the thing to do.

4. The 30% chance of the Colts scoring a TD following a punt is too low. Same for the 53% chance for scoring from the Patriots' 28 following the failed conversion attempt. The Colts offense appeared unstoppable in the 4th quarter.

I agree. Their chances of scoring a TD from either field position was likely higher than the league average. Should we throw out the entire analysis? No, as I said in the original article, we should look at what happens to the numbers when we start increasing the Colts chances of scoring. And as we do, the go-for-it option becomes more and more preferable. Remember, as you increase the scoring chances from one field position, you have to increase the chances from the other. Manning isn't amazing from the 30 yds out, but average from 70 yds out, and he had plenty of time from either field position.

The better you assess the Colts' chances of scoring, the better the go-for-it option becomes relative to the punt option. Why? It's because more than half of the mathematical weight of the go-for-it option ignores how good the Colts offense is. If the conversion is successful, it doesn't matter how good the Colts are.

5. The 53% and 30% chances of the Colts getting a TD don't take into account the time and score.

Yes, they do.

6. There are so many unquantifiable considerations that affected the unique situation at hand that you cannot possibly put them into a mathematical equation to know the precise probabilities.

True. There are any number of variables that might have an effect. So the conclusion is therefore...punt? That makes no sense. Why?

What I've tried to do is lay out the major, dominant considerations--down, distance, field position, time, and score. Other factors certainly come into play, but at some point we need to make our best estimate based on reliable facts. As Tony Dungy said after the game, "you have to play the percentages." Well, we all agree on that, and further, that statement assumes there are percentages to be known. The question is, what are the percentages? It turns out they're not what Dungy and most other critics think they are.

We can never know with perfect certainty that the Patriots' chance of winning was truly 79% if they went for it or 70% if they punted. The best we can do is estimate the center-points of two bands of uncertainty. And although that leaves a lot of room for error, it's far better than simply assuming the punt is better because that's what Rockne and Lombardi did.

7. Stats and numbers are just cold, stubborn, heartless things that don't consider how people feel or how foolish we often are.

Yes...yes, they are.

Team Efficiency Rankings - Week 11

2009-11-17T22:54:00.000-05:00

RANK	TEAM	LAST WK	GWP	Opp GWP	O RANK	D RANK
1	IND	2	0.80	0.47	4	5
2	NO	1	0.79	0.44	1	16
3	PIT	3	0.76	0.50	9	3
4	NE	5	0.73	0.50	3	12
5	DAL	6	0.70	0.49	2	17
6	PHI	8	0.70	0.48	10	1
7	DEN	4	0.69	0.54	15	4
8	SD	7	0.69	0.48	5	21
9	CIN	9	0.66	0.57	11	6
10	NYG	10	0.65	0.49	8	10
11	MIN	12	0.64	0.42	6	23
12	GB	11	0.63	0.43	13	7
13	BAL	15	0.59	0.50	12	11
14	HOU	14	0.57	0.48	7	26
15	NYJ	13	0.55	0.47	24	2
16	ARI	17	0.49	0.51	17	14
17	JAC	19	0.49	0.47	14	30
18	ATL	16	0.46	0.53	16	25
19	WAS	25	0.46	0.42	21	13
20	TEN	20	0.45	0.57	18	20
21	CAR	24	0.44	0.51	25	9
22	CHI	18	0.43	0.45	19	18
23	SF	22	0.42	0.50	26	8
24	SEA	21	0.39	0.47	23	19
25	MIA	23	0.38	0.57	22	22
26	BUF	26	0.32	0.47	28	15
27	STL	27	0.29	0.53	20	27
28	TB	28	0.22	0.56	27	29
29	KC	30	0.20	0.51	29	32
30	OAK	29	0.17	0.55	31	24
31	DET	31	0.15	0.56	30	31
32	CLE	32	0.11	0.59	32	28

And here are the sortable raw team efficiency stats. Passing, running, and penalties are in yards per relevant play. Fumbles and interception stats are in turnovers per relevant play.

TEAM	OPASS	ORUN	OINT%	OFUM%	DPASS	DRUN	DINT%	PENRATE
ARI	6.4	3.8	3.3	1.3	6.2	4.2	2.9	0.46
ATL	6.3	4.5	4.0	0.9	6.6	4.6	2.3	0.37
BAL	6.4	4.4	2.3	0.7	6.1	3.5	3.1	0.57
BUF	5.1	4.1	4.2	0.5	5.6	5.1	5.3	0.45
CAR	5.6	4.8	5.3	2.2	5.8	4.6	4.0	0.36
CHI	6.2	3.8	5.0	1.4	5.8	4.2	3.1	0.45
CIN	6.3	4.0	2.4	0.9	5.9	3.9	3.4	0.39
CLE	3.6	3.7	5.7	1.3	6.9	4.7	1.4	0.35
DAL	7.2	5.1	2.0	0.9	5.9	4.1	1.9	0.50
DEN	6.2	4.2	1.7	1.1	5.5	3.8	2.6	0.34
DET	4.7	3.9	4.7	1.1	7.3	4.7	1.9	0.45
GB	6.5	4.4	1.7	0.4	5.8	3.5	4.7	0.54
HOU	7.5	3.3	2.8	1.4	6.3	4.7	2.6	0.43
IND	7.7	3.9	2.2	0.7	5.3	4.3	3.0	0.30
JAC	6.2	5.0	1.7	0.9	6.9	4.3	2.3	0.29
KC	4.7	3.6	2.1	1.8	6.9	4.6	1.7	0.34
MIA	4.9	4.6	2.2	0.6	7.1	3.7	2.9	0.34
MIN	7.1	4.2	1.0	1.0	5.8	4.2	1.8	0.35
NE	7.3	4.1	1.7	0.4	5.6	4.5	3.1	0.41
NO	8.1	4.7	3.1	1.0	5.7	4.5	5.0	0.39
NYG	6.8	4.4	2.7	1.0	5.6	4.5	3.2	0.45
NYJ	5.9	4.7	5.3	1.3	5.1	4.1	2.5	0.36
OAK	4.1	3.9	4.7	0.8	6.7	4.4	2.3	0.39
PHI	6.5	4.5	2.2	0.7	5.5	3.7	4.9	0.49
PIT	6.9	4.3	2.6	1.3	5.3	3.4	2.4	0.37
SD	7.3	3.2	2.0	0.0	6.0	4.1	3.1	0.34
SF	5.2	4.4	2.9	0.7	6.3	3.3	3.3	0.44
SEA	5.6	3.8	2.2	1.1	6.1	4.3	2.5	0.37
STL	5.3	4.6	2.7	0.9	7.2	4.5	2.8	0.44
TB	5.1	4.1	4.4	2.8	7.2	4.9	4.9	0.37
TEN	5.6	5.3	3.8	1.8	6.6	4.4	3.2	0.42
WAS	5.9	4.1	2.9	1.1	5.3	4.3	2.0	0.42
Avg	6.1	4.2	3.0	1.1	6.1	4.2	3.0	0.40

Should the Patriots Have Let the Colts Score?

2009-11-17T08:00:00.007-05:00

After the Patriots' failed 4th down conversion attempt in the now epic game against the Colts, they wound up facing a Colts offense with a 1st down on the Pats' own 14-yard line. With 1:20 on the clock, the Patriots could have allowed the Colts to score an easy touchdown, yielding a 1-point lead, but giving the Patriots a shot to take the lead back with a possible FG drive. Or, they could have played straight defense, hoping to keep the Colts out of the end zone.

I'll take a look at league-wide averages, and then we can make adjustments from there. Against a team needing a TD, playing straight defense yields a TD about 62% of the time. This means the Patriots would have a 0.38 Win Probability (WP).

Allowing the Colts to score gives the Patriots a 1-point deficit and a first down at around their own 30 (or so) following the kickoff. The league-average chance of scoring either a FG or TD in that situation is about 20%, for a 0.20 WP. Below is a graph of the "30-second drill," which shows the probability of scoring a FG or TD when a team has a first down and is down by 1, 2 or 3 points with 25 to 35 seconds left in the game.

Right now, the numbers appear to favor playing straight defense. It's 0.38 WP for the straight defense and 0.20 WP for the matador maneuver.

But now a few particulars--The New England offense was able to move the ball pretty well, so you'd have to think their chances of responding with a FG might be higher than 20%. But then again they had no timeouts, and time was already tight. Still, we've seen Brady do it before.

On the other side of the coin, you'd have to think that Manning was at the top of his game, and the Patriots defense was on its last legs. You could make the case the Colts offense was far more than 62% likely to score the TD from the 14.

The better you think the Colts offense was, the better it would have been to let them score from the 14. And the better you think the Patriots offense was, the better it would have been to let the Colts score. Both of the particular considerations of the situation weigh in favor of letting the Colts score. Whether those particular situations are enough to make the call to allow the TD depends on how strong you think each offense is. But if you're "playing the percentages," you try to stop the Colts.

Still, there is a lot of uncertainty. (There are a few 'about's and 'typically's in my analysis above.) Allowing a team to take the lead like that should require a good deal of certainty. The Colts were probably more than 62% likely to score, but by how much? I'm not sure there's enough confidence to make that call, but it certainly would have been defensible.

[Edit: I added the graph above and refined the numbers since the original posting.]

The Two-Minute Drill

2009-11-16T22:58:00.003-05:00

In my recent posts on the Maurice Jones-Drew kneel-down and the Belichick 4th down decision I cited a few stats about how likely an offense that needs a touchdown to tie or win is to score one with about 2 minutes remaining in the game. Normally I like to back up obscure stats like that with some firmer context, and I was finally able to get around to it for these numbers.

The chart below graphs the percentage of time a team that needs a TD, defined as being down by 4 through 8 points, gets a TD on its current drive given a 1st down at various field positions with 2:00 +/- 15 seconds left. (I know that's quite the run-on sentence, but I don't know how else to say it.)

It's remarkably linear. I'm somewhat surprised how unlikely offenses are to get the TD inside the 20. A lot of that is sample size. Teams are more and more likely to be stopped the closer you get to the end zone, so the number of cases gets progressively smaller. But two-minute drills are typically characterized by 70-yard drives, not 20-yard drives, so I'm more interested in the scoring rates at the other end of the graph.

The next graph looks at teams that need just a field goal with two minutes left, defined by teams trailing by 1, 2, or 3 points. The graph plots the percentage of drives that result in either a field goal made or touchdown. Field goal success rates are charted here.

Again, the plot looks linear, but probably less so toward FG range. The noise in the data increases toward the end zone here as well. For example, there are 6 cases in the 6-10 yard line bin, and two of them were interceptions resulting in a 67% success rate. Teams inside FG range with 2 minutes to go wouldn't necessarily be happy to settle for FG attempts. With that much time on the clock, the opponent would have plenty of time to respond with their own score. Here again, however, I'm mostly interested in the longer drives that typically eat a good deal of clock.

Edit: Here is a post from last year with graphs for all drives in all game situations. It's interesting to compare and see just how much more often teams can score when their back is against the wall. They can use all four downs and turnovers are no more costly than a stop. It makes we wonder whether teams should play that kind of abandon all game long.

Note: Data from all NFL games from the 2000 through 2008 seasons.

MJD Taking a Knee

2009-11-16T00:32:00.006-05:00

With just under two minutes remaining against the Jets, Jaguars RB Maurice Jones Drew broke free for a go-ahead TD. Instead of plunging into the end zone he took a knee at the one-yard line. This decision allowed the Jaguars to run out the clock before kicking a chip-shot FG for the win. A TD would have allowed the Jets almost two minutes to answer with a TD of their own. How important was MJD's decision?

The analysis was a little more complicated than I thought because had the Jaguars scored the TD, they would have gone for the 2-point conversion. With a single XP, a Jets TD wins. With a failed 2-pt conversion, a Jets TD also wins. But with a successful conversion, a Jets TD only ties, so there is nothing lost and a lot to gain for the Jags by going for the 2.

Two-point conversions are, on average, successful about 45% of the time.

For teams that need a single TD to win or tie (down by 4 through 8 points) with 1:50 +/-15 seconds and a 1st and 10 near their own 33 (the average kickoff result) teams have roughly a 30% chance of getting the TD they need. (See the first chart in this post.)

The Jets had no timeouts, so it must be a little lower but they still had enough time with 1:48 on the clock. Let's say they had a 25% chance of getting the TD. This may seem high, and in normal circumstances it would be, but the Jets could play with abandon. They've got 4 downs on every series and an interception is no more costly than a stop. Defenses also tend to play 'prevent' schemes.

So, given a successful 2-pt conversion and the prospect of overtime, the Jets' WP would be:

0.25 * 1/2 = 0.125 WP

An unsuccessful 2-pt conversion and the prospect of a win, would give the Jets simply:

0.25 * 1 = 0.25 WP

Because the 2-pt conversion is successful 45% of the time and unsuccessful 55% of the time, the Jets' total probability of winning would be:

(0.45 * 0.125) + (0.55 * 0.25) = 0.19 WP

Now, a FG attempt from inside the 5 is successful 98-99% of the time. Let's say 98% in case something went awry during the 2 kneel-downs the Jags would need to run out the clock, such as a fumbled snap. That would simply be the Jags' WP--0.98.

Comparing the two WPs, we can value Drew's decision to kneel at the 1 instead of scoring the TD:

0.98 - (1-0.19) = 0.17 WP

That's a really big play. It improved the Jaguars' chances of winning by 17 percentage points. To put it in perspective, the decision to kneel (not including the rest of the run) was comparable in importance to the Jaguars' 37-yard interception return to the Jets' 4-yd line in the 3rd quarter. Smart, selfless player and smart coaching.

I especially liked it because my fantasy opponent this week had MJD!

Belichick's 4th Down Decision vs the Colts

2009-11-16T00:18:00.005-05:00

New England coach Bill Belichick is taking a lot of heat for his decision to attempt a 4th down conversion late in the game against the Colts. Indianapolis came back to win in dramatic fashion. Was the decision a good one?

With 2:00 left and the Colts with only one timeout, a successful conversion wins the game for all practical purposes. A 4th and 2 conversion would be successful 60% of the time. Historically, in a situation with 2:00 left and needing a TD to either win or tie, teams get the TD 53% of the time from that field position. The total WP for the 4th down conversion attempt would be:

(0.60 * 1) + (0.40 * (1-0.53)) = 0.79 WP

A punt from the 28 typically nets 38 yards, starting the Colts at their own 34. Teams historically get the TD 30% of the time in that situation. So the punt gives the Pats about a 0.70 WP.

Statistically, the better decision would be to go for it, and by a good amount. However, these numbers are baselines for the league as a whole. You'd have to expect the Colts had a better than a 30% chance of scoring from their 34, and an accordingly higher chance to score from the Pats' 28. But any adjustment in their likelihood of scoring from either field position increases the advantage of going for it. You can play with the numbers any way you like, but it's pretty hard to come up with a realistic combination of numbers that make punting the better option. At best, you could make it a wash.

Game Probabilities - Week 10

2009-11-12T09:25:00.000-05:00

Weekly game probabilities are available now at the nytimes.com Fifth Down.

Efficiency Rankings - Week 10

2009-11-10T16:49:00.001-05:00

RANK	TEAM	LAST WK	GWP	Opp GWP	O RANK	D RANK
1	NO	2	0.82	0.46	1	13
2	IND	1	0.81	0.42	3	4
3	DEN	3	0.80	0.56	10	1
4	PIT	4	0.78	0.49	4	5
5	NE	7	0.73	0.48	5	16
6	DAL	6	0.72	0.48	2	24
7	SD	5	0.70	0.47	7	14
8	PHI	9	0.67	0.44	15	3
9	CIN	13	0.65	0.56	13	6
10	NYG	11	0.64	0.48	9	9
11	GB	8	0.61	0.38	11	11
12	MIN	10	0.59	0.44	8	22
13	NYJ	14	0.59	0.49	21	2
14	HOU	15	0.57	0.48	6	27
15	BAL	12	0.57	0.55	12	17
16	ATL	16	0.49	0.54	14	23
17	ARI	19	0.47	0.52	17	15
18	CHI	17	0.46	0.46	18	19
19	JAC	20	0.44	0.44	16	31
20	TEN	23	0.44	0.60	19	18
21	SEA	21	0.43	0.46	22	10
22	SF	18	0.41	0.50	24	8
23	MIA	22	0.41	0.63	20	21
24	CAR	24	0.39	0.51	27	7
25	WAS	25	0.37	0.37	25	20
26	BUF	26	0.35	0.48	28	12
27	STL	27	0.23	0.48	23	29
28	TB	31	0.21	0.56	26	30
29	OAK	28	0.20	0.60	31	25
30	KC	30	0.17	0.54	30	32
31	DET	29	0.16	0.54	29	26
32	CLE	32	0.13	0.60	32	28

And here are the sortable raw team efficiency stats. Passing, running, and penalties are in yards per relevant play. Fumbles and interception stats are in turnovers per relevant play.

TEAM	OPASS	ORUN	OINT%	OFUM%	DPASS	DRUN	DINT%	PENRATE
ARI	6.2	3.8	3.7	1.5	6.4	3.9	2.8	0.40
ATL	6.4	4.3	3.9	1.0	6.5	4.5	2.5	0.39
BAL	6.4	4.5	2.5	0.7	6.6	3.5	2.7	0.59
BUF	5.0	4.0	4.0	0.3	5.4	5.1	5.4	0.44
CAR	5.4	4.7	5.9	2.2	5.8	4.4	3.9	0.36
CHI	6.3	4.0	4.2	1.6	5.9	4.2	3.0	0.44
CIN	6.4	4.2	2.7	1.0	6.3	3.8	3.5	0.35
CLE	3.9	3.8	5.6	1.5	7.0	4.9	1.6	0.34
DAL	7.6	5.1	1.9	0.8	6.1	4.2	2.1	0.49
DEN	6.4	4.2	0.4	1.1	5.2	3.4	2.8	0.35
DET	4.8	3.9	5.6	1.0	7.0	4.7	2.1	0.48
GB	6.8	4.5	1.9	0.5	5.9	3.5	5.0	0.51
HOU	7.5	3.3	2.8	1.4	6.3	4.7	2.6	0.43
IND	7.8	3.7	1.9	0.7	4.9	4.3	3.0	0.32
JAC	6.1	5.1	1.9	0.7	6.9	4.3	1.8	0.29
KC	4.6	3.5	2.0	1.5	7.5	4.4	1.2	0.35
MIA	4.8	4.5	2.1	0.5	7.2	3.7	2.8	0.36
MIN	6.7	4.1	1.1	0.7	6.2	4.1	2.2	0.31
NE	7.1	4.1	1.6	0.2	5.4	4.5	2.8	0.39
NO	8.2	4.5	2.6	1.1	5.6	4.4	5.4	0.39
NYG	6.8	4.4	2.7	1.0	5.6	4.5	3.2	0.45
NYJ	5.7	4.8	5.1	1.4	4.8	4.0	2.7	0.38
OAK	4.3	3.6	4.4	0.9	6.8	4.5	2.2	0.35
PHI	6.3	4.7	2.3	0.8	5.3	3.6	5.3	0.48
PIT	7.6	4.0	2.6	1.6	5.4	3.8	1.9	0.38
SD	7.3	3.1	2.2	0.0	5.6	4.2	3.4	0.36
SF	5.2	4.4	2.7	0.6	6.4	3.4	2.1	0.42
SEA	5.6	3.5	1.9	1.2	5.8	4.4	2.8	0.32
STL	5.0	4.6	2.7	1.1	7.1	4.2	2.3	0.48
TB	5.0	4.1	4.5	2.1	7.5	4.8	5.1	0.35
TEN	5.4	5.4	3.8	1.6	6.7	4.4	2.9	0.39
WAS	5.8	4.0	3.2	1.3	5.3	4.2	1.8	0.46
Avg	6.1	4.2	3.0	1.0	6.1	4.2	3.0	0.40

The Value of 1st Down and 5 Situations

2009-11-10T08:00:00.002-05:00

In a recent post I illustrated how to decide whether to accept or decline a penalty based on expected point (EP) values. I compared 1st down and 5 situations, often resulting from a defensive offside, 2nd down situations.

I had to assume a roughly linear point advantage for the 1st and 5 situations because there weren't nearly as many in the data as other situations. But when I actually plotted out the empirical average EP values for 1st and 5s and each yard line, I noticed something strange. Compared to the curve of 1st and 10 values (for which there is an abundance of data), the curve of 1st and 5 EP values was oddly shaped. As we'd expect, there is a fair advantage for 1st and 5s from a team's own 20 through the opponent's 45 or so. But from there all the way to the opponent's 5, the value of a 1st and 5 is apparently lower than that for a 1st and 10.

Here is a graph of what I'm talking about. The raw 1st and 5 average values are red, and the smoothed curve is blue (the chart legend has them swapped by mistake). The 1st and 10 values are green. Normally, you'd expect the blue line to be slightly above the green line throughout the field.

My first instinct is that it's just due to noise, but the graph above shows some pretty clear trends in the raw average EPs. I grouped the values into 10-yard increments and replotted the 1st and 5 values along with their standard errors. The red and green lines represent +/-2 standard error bands.

It looks unlikely that the shape of the curve is due to sample error. There would have to be a number of 2-standard error deviations for it to fit. So maybe there is some systematic reason why 1st and 5s are less valuable after an offense gets past midfield. Is there a bias where certain types of teams draw offside penalties in different parts of the field? Unlikely. Do coaches suddenly make dumb play calls on 1st and 5 inside midfield? I wouldn't put it past them, but it's hard to imagine any scenario that would make a 1st and 5 less valuable than a 1st and 10 at the same yard line.

The only viable theory I have is that there is a systematic bias based on offensive strength. Say there are bad offenses and good offenses. Good offenses get bigger gains on first down and would tend to decline the penalty. So we are left with bad teams accepting more than their share of 5-yd penalties. But, bad offenses would also tend to have the ball more often on their own side of the field than good offenses do. So I'd expect the values on 1st and 5 to be lower in an offense's own side of the field, not the other way around.

Ideas?

Second-Guessing Coughlin and Reid

2009-11-09T11:51:00.004-05:00

Toni Mokovic at Fifth Down questions the late-game decision-making of Tom Coughlin and Andy Reid in their respective losses Sunday. Let's see what WP says.

The Giants had an opportunity to put away the Chargers with a touchdown to put the game out of reach. They went conservative, opting for the FG and a 6 point lead. The lead didn't hold up as the Chargers were able to drive for a game-winning TD.

After suffering a penalty on 1st down, the Giants had a 1st and goal from the Chargers' 14 yard line. After a run and a pass for no gain, the Giants faced a 3rd and goal from the 9. Run plays on 3rd and goal from from the 9 are TDs 13% of the time, while pass plays are TDs 20% of the time. Passes from there are intercepted about 4% of the time.

Being up by 10 points (a TD) would have won the game. Being up by 3 (an interception) would have given the Giants a 0.79 WP. Being up by 6 (a FG) would have given the Giants a 0.82 WP. In this situation, a FG does not help very much.

Going through the math (and assuming fumbles are equally likely), a pass attempt roughly gives the Giants:

1.00 WP * 0.20 + 0.82 WP * 0.76 + 0.79 WP * 0.04 = 0.85 WP

A run gives the Giants:

1.00 WP * 0.13 + 0.82 WP * (1-0.13) = 0.84 WP

Surprisingly, the play call on 3rd down doesn't cost very much. In retrospect, what he should have done was go for the TD on 4th and goal from the 4. Whether it's a run or pass, a team has a 40% chance of scoring from the 4. That would give the Giants:

1.00 WP * 0.40 + 0.79 WP * (1-.0.40) = 0.87 WP

This compares favorably to the 0.82 WP for kicking the FG, but not by much. Putting this in perspective, Coughlin's decision to run instead of pass on 3rd down cost 0.01 WP. His decision to kick the FG cost 0.05 WP. But his defense's inability to stop the Chargers' TD drive cost 0.84 WP. This one really is on the players.

In Philadelphia, the Eagles were down by 7 with 4 minutes remaining and faced a 4th and 11 on the Cowboys' 34-yard line. Reid opted for the long FG attempt, which was successful, making it a 4-point game. The Eagles still needed a TD to win. Going for the conversion isn't as unlikely as many would think, about 28% of the time. Still, kicking the FG wasn't a terrible decision. I'll spare everyone the math, but it's about a break-even decision.

The Eagles had no timeouts remaining, so a single 1st down conversion by the Cowboys seals the game. Sure enough, that's exactly what happened, and the Eagles never saw the ball again.

What Reid should have done is followed the FG with an onside kick. Chances were very good they wouldn't get the ball back, particularly because the Cowboys are one of the league's top running teams this year. You don't even need to do the math. To win the game Reid had to assume his defense would force a 3-and-out, so an unsuccessful onside kick wouldn't really hurt that much. A successful onside kick would give the Eagles all kinds of time and decent field position too.

Following their FG, the Eagles had a 0.18 WP assuming a conventional deep kick. An unsuccessful onside kick gives them a 0.15 WP, and a successful onside kick gives them a 0.29 WP. The break-even recovery rate (r) needed for the onside attempt to be worthwhile would be:

0.18 = r * 0.29 + (1-r) * 0.15
r = 21%

That's the recovery rate when the receiving team fully expects the onside kick, and that's not necessarily the case with 4 minutes left in the game. If I were Reid (in hindsight), I would have considered an onside kick from a conventional formation.

Accept or Decline: 1st & 5 vs 2nd & Short

2009-11-09T08:00:00.020-05:00

Your team has just run the ball for a hard-fought 8-yard gain on 1st down bringing up a 2nd and 2. The defense was flagged for offsides giving you the option of making it 1st and 5. Should your team accept or decline the penalty or take the gain?

To simplify things, let’s only consider situations between the 20-yard lines. Looking at each option in terms of the probability of converting for a 1st down, you should be indifferent. Both situations convert equally as often at an 85% rate. But 1st down probability isn’t the whole story.

We can also look at each option in terms of Expected Points, the average point advantage an offense can expect given a particular combination of down, distance and field position. In this case, the 1st and 5 is the better option. Between the 20s, where the EP curve is nearly linear, the average value of 2nd and 2 situations is 0.2 EP less than the average value of 1st and 5 situations (accounting for being 3 yards further back).

The advantage for the 1st and 5 holds throughout the range of field positions between the 20s. As an example, a 1st and 5 at midfield is worth 2.5 EP. A 2nd and 2 at an opponent’s 47, is worth 2.3.

The 1st and 5 is so valuable simply because it gives you an extra down. It’s essentially an opportunity for a free shot downfield, which is likely why the conversion probabilities are equal but the EP values are not. The defense is really in a bind because it has to guard equally against any play type. That’s true of 2nd and short as well, but the 1st and 5 gives the offense an additional down of unpredictable abandon.

Coaches should accept the penalty on gains anything short of 8 yards, simply on the basis of the probability of conversion. And on an 8-yard gain, coaches should accept the penalty on the basis of expected points. A 9-yard gain is essentially a wash, and a 2nd and 1 can be very lucrative if taken advantage of.

One caveat: This analysis is based on the assumption that between the 20s, 1st and 5s are roughly equally advantageous over a 1st and 10 at the same field position. (There just aren't that many 1st and 5s to be certain.) But as I'll show in a future post, it's possible this hasn't been the case. In fact, the data might suggest that 1st and 5s have actually been less valuable than a 1st and 10 at the same field position.

Note: Data are from the 1st and 3rd quarters of all 2,400 non-preseason games from 2000 through 2008.

Another Run-Pass Balance Study

2009-11-08T12:00:00.009-05:00

Benjamin Alamar, author of the Passing Premium paper (critiqued here), takes a second stab at comparing the values of running and passing with new research. A brief presenting his methodology and findings was presented at a recent symposium on sports statistics. This time Alamar uses expected points as a measure of value, and compares the EP values gained by passes with those of runs. He defines risk as the probability each play type will result in a negative EP change, and finds that running is both less productive and "riskier" than passing. There are three fairly big problems in the methodology. Fortunately, all three can be rectified.

First, Alamar creates his EP values using a simple linear regression (see slide 10). Using down, distance, and yardline (plus other variables controlling for quarter and other effects), he produces an EP equation. This is a really bad way to estimate EP values. They're not linear, and there are any number of interacting effects within. The Levitt-Kovash paper, in contrast, uses a regression with quintic terms and full interactions to create their EP values. (I prefer a more direct method--looking at the data empirically and smoothing it using a method called LOESS.)

Slide 11 shows the results for 1st and 10 situations. It looks like an exponential function and doesn't resemble the real EP curve for 1st and 10s. Romer, Levitt-Kovash, myself, FO all pretty much agree on the shape of the curve, but Alamar's is way off. It doesn't even make sense given the regression results from slide 10. There's no way to get a curve like that with the regression table he presents, so there's something missing in there somewhere. (I haven't seen the full paper, if there is one, so maybe there is some explanation.) To fix this, he needs to redo how he gets his EP values. There are any number of ways; he could even borrow them from FO, me, or even Levitt and Kovash.

The second problem is the same flaw that plagues the Levitt-Kovash paper. Time and score are very important considerations in the value of any play. The value of a run to a team ahead can be far more than just the EP advantage gained. Running time off the clock can be just as valuable, if not more valuable. Additionally, the advantage of a low-variance outcomes needs to be considered. The regression used to create Alamar's EP values does not does not account for the time-value of plays.

There are two possible solutions to the time/score problem. One possibility is to use win probability instead of EP. WP is a measure of utility that properly accounts for time and score in addition to down, distance, and field position. But a WP model is extremely difficult to produce, and any model is going to have thin spots where a lot of assumptions need to be made. This is true particularly on 2nd and 3rd downs when to-go distances are variable.

The second possibility is to restrict the analysis to "normal" football situations. By normal I mean early in the game when neither team has a big lead. This is when teams are (or at least should be) playing at their optimum risk-reward balance for net point maximization. With enough data, there should be no problem restricting things to the first quarter when the lead is 10 points or less.

The third problem has to do with his definition of risk--the probability a play will result in a negative change in EP. Suppose I want to cross a busy street, and I have two strategies: I could wait patiently until traffic clears, or I could run wildly across as fast as I can. Waiting patiently has a very high probability of resulting in a negative utility for me. My time is precious, and waiting can be costly. On the other hand, running wildly across the street results in no wait, plus there is a still relatively low probability of a negative outcome--which in this case would be being hit by a car that doesn't stop for me. Given this definition of risk, running wildly would be the safer strategy.

The problem is that the size of the negative outcome for each strategy is vastly different. The majority of runs are actually negative in terms of EP. Runs that result negative EP changes include up to 4-yard gains. Incomplete passes would also be negative, but so would pass plays with the added risk of interceptions and sacks. The costs of negative passing plays are disproportionately higher than for runs. The full weighted distribution of consequences needs to be considered.

Defining risk this way leads to some conclusions that don't make sense. Consider an offense with a small lead facing a 3rd and long deep in its own territory. A draw play is considered the epitome of a low risk play. Passing for the first down is the risky thing to do because of size of the cost of an interception or sack. But the probability of a negative for a run is much higher than for a pass because any gain shy of a 1st down would be deemed negative. In terms of the probability of winning the game, the run is the less risky choice.

My recommendation is to do three things. First, get a different table of EP values. Second, limit the data to "normal" time and score situations. And third, redefine risk that takes into account the sizes of the costs of negative outcomes.

Roundup 11/8

2009-11-07T13:36:00.003-05:00

A new site from the Harvard Sports Analysis Collective looks promising. (But what's with the term "Collective?" What happened to "Club?") Here they look at 2-point conversion decisions. They also look at what effect the new wedge rule might be having on kickoff distances (not much, especially if you consider the weather is about to get a lot worse). Do teams with RB committees run better than teams with a feature back? How much more accurate are FG attempts when kicked indoors? Overall, the site asks some neat questions and is definitely headed in the right direction.

Greg Easterbrook on coaching: "One factor here is the Illusion of Coaching. We want to believe that coaches are super-ultra-masterminds in control of events, and coaches do not mind encouraging that belief. But coaching is a secondary force in sports; the athletes themselves are always more important. TMQ's immutable Law of 10 Percent holds that good coaching can improve a team by 10 percent, bad coaching can subtract from performance by 10 percent -- but the rest will always be on the players themselves, their athletic ability and level of devotion, plus luck."

I'd mostly agree with Easterbrook, however I'd say that a good coach can make a good team 10% better, but a bad coach can absolutely ruin a good team. In most cases though, the NFL rarely features coaches bad enough to do that kind of damage simply because the league is considered the top of its profession. I think the bigger point is that modern coaching, beyond the leadership aspect, is mostly about the illusion of control.

Another chalk talk from Smart Football, this time about the smash route vs man coverage. Here's another post on zone run blocking. I can't get enough of these Xs & Os posts. I'm really hungry for this kind of analysis, and we rarely get it on TV or elsewhere. Last Sunday I saw Mariucci (who's usually a buffoon) on NFL Network explain how, on one type of screen play, the TE needs to block against the zone but can just drag off his coverage against man-to-man by running a short crossing route. I thought, gosh, that makes so much sense. Why can't we get more analysis like that?

Jason Lisk finds that non-divisional opponents are 96-182 (0.345 win %, which indicates a very strong home field advantage) when visiting a new stadium for the first time. This supports the environmental familiarity theory of home field advantage, but Jason says the small sample size doesn't let us make any definitive conclusions. I'm more optimistic. If we say that the "true" HFA win % in the NFL should be .570, then the .655 Jason found with n=278 is solidly significant (p=.002). This isn't to say we can be certain that new stadiums cause exactly a .655 win %, but it does mean some systematic effect is at work. There may be some bias in the data due to one effect or another (average/middling teams tend to show higher home win % for example), but it's not sample size that's holding us back from drawing an inference.

Neil Paine uses Doug Drinen's SRS ratings to find the best 2-game stretches. The Ravens' 2000 Playoff/Super Bowl run takes the #1,#2, and #4 spots.

Neil also points out just how bad the Browns and Derek Anderson in particular have been. Anderson had that one promising year, so he's kind of a head-scratcher. I realize the team around him was better in 2007, but this year he's just a disaster. Two years ago he threw for 29 TDs and 6.8 Net Yards per Attempt. So far this year he has 2 TDs and 3.7 netYPA. Looking back at his career year, there may have been some indications that he wasn't all he was cracked up to be. His Int rate was 3.6%, well worse than average, and his completion % was 56.5%, which is very low for someone you'd think was breaking out.

Here's another article on Kevin Kelly, the high school coach who never punts. It's interesting is to read the comments of some notable college coaches. Texas Tech's Mike Leach says “It’s an interesting idea. Statistically, there’s definitely some validity to it." Michigan State's Mark Dantonio says "Often, it’s simply a gut decision. Is the timing right and do you have the confidence in your offense to execute the play against the defense that’s called?” LSU's Les Miles says, "To me, it’s a statistic, a position, a feel that gives a coach the, ‘This is the right time to do this.’"

Lastly, from the baseball world, here's a great post on game theory in pitching from Fangraphs.

Game Probabilities - Week 9

2009-11-05T09:41:00.000-05:00

Weekly game probabilities are available now at the nytimes.com Fifth Down. This week I also lead-in with break down of the Chargers-Giants matchup.

Efficiency Rankings - Week 9

2009-11-04T08:00:00.003-05:00

The efficiency rankings are beginning to settle down approaching the midpoint of the season. Big movers include San Diego climbing from 8 to 5 and Arizona dropping like a rock from 11 to 19.

The Cards played poorly against a bad team, and most teams are tightly bunched around the league average. So it doesn't take much movement in GWP to drop a number of spots from the top to the bottom of the "pack."

There continues to be a correlation between opponent-adjusted team strength and strength-schedule. This indicates that the death of parity is greatly exaggerated. It seems that so far this year there have been a disproportionate number of games between the very best and very worst teams. Ironically, this may indicate parity is stronger than ever. The scheduling system is supposed to give the top teams two extra games against other division leaders, and the bottom teams two extra games against the other dwellers. If a dweller or two turns into an elite team, or if an elite team suddenly becomes a doormat, the current disparity is what we'd get. Besides, parity isn't just about keeping teams from having very good or very bad records in any one year. It's also about making sure they aren't the same teams year after year.

The team rankings below are in terms of generic win 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, and all ratings include adjustments for opponent strength.

Offensive rank (ORANK) is offensive generic win probability, which is based on each team's offensive efficiency stats only. In other words, it's the team's GWP assuming it had a league-average defense. DRANK is is a team's generic win probability rank assuming it had a league-average offense.

GWP is based on a logistic regression model applied to current team stats. The model includes offensive and defensive passing and running efficiency, offensive turnover rates, defensive interception rates, and team penalty rates. If you're scratching your head wondering why a team is ranked where it is, just scroll down to the second table to see the stats of all 32 teams.

Click on the table headers to sort:

RANK	TEAM	LAST WK	GWP	Opp GWP	O RANK	D RANK
1	IND	1	0.83	0.40	3	8
2	NO	2	0.82	0.47	1	9
3	DEN	3	0.77	0.53	13	1
4	PIT	4	0.75	0.45	6	6
5	SD	8	0.71	0.45	4	22
6	DAL	5	0.71	0.44	2	25
7	NE	9	0.71	0.48	5	14
8	GB	6	0.68	0.42	9	7
9	PHI	14	0.67	0.39	14	3
10	MIN	12	0.63	0.47	10	20
11	NYG	7	0.62	0.44	8	19
12	BAL	13	0.62	0.54	11	15
13	CIN	10	0.62	0.57	15	11
14	NYJ	19	0.56	0.48	21	2
15	HOU	15	0.53	0.43	7	31
16	ATL	18	0.53	0.57	12	24
17	CHI	17	0.49	0.48	19	12
18	SF	22	0.47	0.52	22	4
19	ARI	11	0.42	0.52	18	10
20	JAC	16	0.42	0.46	16	30
21	SEA	21	0.42	0.51	23	13
22	MIA	20	0.42	0.62	17	17
23	TEN	23	0.39	0.60	20	16
24	CAR	26	0.36	0.45	28	5
25	WAS	24	0.36	0.35	24	21
26	BUF	25	0.33	0.46	29	18
27	STL	27	0.25	0.50	25	28
28	OAK	29	0.20	0.59	31	23
29	DET	28	0.20	0.57	27	26
30	KC	30	0.17	0.56	30	29
31	TB	31	0.16	0.54	26	32
32	CLE	32	0.14	0.61	32	27

And here are the sortable raw team efficiency stats. Passing, running, and penalties are in yards per relevant play. Fumbles and interception stats are in turnovers per relevant play.

TEAM	OPASS	ORUN	OINT%	OFUM%	DPASS	DRUN	DINT%	PENRATE
ARI	6.0	3.3	3.8	1.7	6.3	3.8	2.9	0.44
ATL	6.6	4.0	3.9	1.2	6.6	4.5	2.3	0.38
BAL	6.7	4.6	2.0	0.8	6.6	3.5	3.1	0.59
BUF	5.0	4.0	4.0	0.3	5.3	5.1	5.4	0.44
CAR	5.3	4.7	6.7	1.7	5.3	4.5	4.1	0.38
CHI	6.2	3.9	4.6	1.8	5.7	4.0	3.0	0.40
CIN	6.4	4.3	3.1	1.1	6.5	3.9	3.1	0.35
CLE	3.9	3.8	5.6	1.5	7.0	4.9	1.6	0.34
DAL	7.6	5.4	1.7	0.9	6.1	4.2	1.6	0.48
DEN	6.4	4.2	0.4	1.1	5.2	3.4	2.8	0.35
DET	4.9	3.8	4.5	1.1	7.1	4.8	2.1	0.46
GB	7.0	4.3	0.9	0.5	5.9	3.5	5.3	0.55
HOU	7.6	3.3	2.5	1.6	6.4	4.7	2.3	0.38
IND	8.2	3.7	1.5	0.8	4.6	4.5	2.8	0.33
JAC	5.8	5.4	2.1	0.9	7.1	4.3	2.1	0.29
KC	4.4	3.5	2.4	1.4	7.3	4.4	1.3	0.39
MIA	4.8	4.6	2.5	0.5	7.1	3.6	2.8	0.37
MIN	6.7	4.1	1.1	0.7	6.2	4.1	2.2	0.31
NE	7.0	4.1	1.4	0.3	5.4	4.5	3.3	0.39
NO	8.0	4.5	2.6	1.2	5.5	4.4	6.0	0.39
NYG	7.1	4.4	3.0	0.9	5.7	4.6	2.8	0.40
NYJ	5.7	4.8	5.1	1.4	4.8	4.0	2.7	0.38
OAK	4.3	3.6	4.4	0.9	6.9	4.5	2.2	0.35
PHI	6.4	4.8	1.7	0.9	5.0	3.7	5.7	0.45
PIT	7.6	4.0	2.6	1.6	5.4	3.8	1.9	0.38
SD	7.6	3.1	1.7	0.0	5.7	4.2	4.0	0.38
SF	5.3	4.3	1.9	0.7	6.3	3.2	2.3	0.45
SEA	5.5	3.5	1.9	1.4	6.0	4.2	1.2	0.31
STL	5.0	4.6	2.7	1.1	7.1	4.2	2.3	0.48
TB	4.8	4.2	4.6	2.0	7.8	4.7	4.4	0.38
TEN	5.1	5.5	4.1	1.8	7.0	4.3	2.2	0.38
WAS	5.8	3.9	3.2	1.5	5.4	3.9	1.5	0.41
Avg	6.1	4.2	2.9	1.1	6.1	4.2	2.9	0.40

Team Offense Win Probability Added 2000-2008

2009-11-03T08:00:00.007-05:00

Recently I looked at team defense through the lens of Win Probability Added (WPA). Every play changes a team's chances of winning, and we can sum all the ups and downs into a total WPA for any player, team, offense, or defense. In this post, I'll look at team offense.

As with defenses, one offense might be the best in yards and another might be the best in yards per play. Yet another offense might be the best in terms of points. WPA can cut through all that, and tell us which squads made the biggest impacts on winning.

WPA captures the things that other stats cannot. For example, consider an offense leading by one point with 3 minutes left in the game. A series of modestly successful runs to convert a first down and kill the clock won't make fantasy fans happy, but it effectively clinches the win. A stop and a punt would typically give the opponent over a 30% chance of winning, so that grinding first down conversion may mean more in terms of winning than almost any other series all season.

The WPA listed for each year are raw totals including playoff games. They effectively say 'this is the number of games a team would win given a completely average offense and special teams.' For example, the 2000 Colts offense posted a +4.5 WPA. This suggests the Colts offense would have won 12.5 games had their defense and special teams simply held serve, making absolutely no contribution toward winning.

I've also added a column for WPA per game to account for teams with playoff appearances. You could think of this number as how much a defense added to their team's chance of winning any given game. For example, the Indianapolis offense (+0.23 per game) would turn a 50% chance of winning a game into a 73% chance.

Click on the table headers to sort:

Offense	2000	2001	2002	2003	2004	2005	2006	2007	2008	Total	Per G
IND	4.5	1.1	0.0	3.1	7.0	5.2	7.7	4.3	3.7	36.2	0.23
DEN	3.3	-1.7	1.3	3.8	0.7	3.2	-0.6	2.7	3.3	15.8	0.10
NE	-2.8	1.1	0.2	0.2	4.0	2.8	0.0	6.5	1.7	13.5	0.08
KC	-0.1	0.6	4.5	5.1	3.8	4.4	0.4	-3.3	-2.4	12.8	0.09
PIT	1.0	3.5	1.1	-1.9	2.7	2.0	1.7	1.5	0.1	11.6	0.07
SD	-3.4	0.7	-0.1	0.2	3.9	1.8	3.3	0.8	2.9	9.8	0.07
SEA	-0.3	1.2	2.2	3.0	0.8	3.8	0.0	0.8	-1.4	9.8	0.06
NO	1.8	0.9	-0.1	0.6	1.5	0.0	1.2	0.6	2.9	9.4	0.06
MIN	4.8	0.0	2.6	3.9	4.5	1.3	-5.2	-2.2	-0.4	9.0	0.06
NYG	1.0	-0.5	-0.3	-0.2	0.7	1.0	0.9	0.9	3.7	7.0	0.05
SL	4.7	4.4	-0.1	0.4	2.6	-0.8	1.7	-2.9	-3.8	6.0	0.04
GB	0.6	1.3	0.4	2.9	1.9	-2.9	-1.6	1.7	1.8	6.0	0.04
TEN	0.7	0.8	2.9	0.8	0.2	-2.8	0.9	1.1	-0.8	3.3	0.02
CIN	0.0	-0.6	-3.3	2.6	-0.7	4.4	2.6	0.8	-3.2	2.3	0.02
ATL	-4.9	1.4	1.6	-1.0	0.0	2.3	1.7	-2.2	3.6	2.2	0.01
PHI	-0.7	-0.7	0.5	1.9	2.8	-4.0	3.1	0.7	-3.1	0.3	0.00
JAX	0.8	-0.6	-2.1	-1.0	-0.7	1.5	-0.2	1.6	-0.6	-1.6	-0.01
DAL	-1.7	-2.0	-3.7	-0.7	-1.4	-0.3	2.1	4.8	1.0	-2.0	-0.01
NYJ	-1.6	-0.3	2.6	-0.7	1.7	-3.1	1.4	-3.1	-0.1	-3.4	-0.02
BUF	1.5	-0.2	2.3	-3.0	-0.8	0.8	-2.0	-1.8	-0.1	-3.5	-0.02
SF	3.1	5.9	2.9	0.4	-4.7	-4.9	-0.2	-4.9	-1.8	-4.3	-0.03
HST			-5.1	-1.1	-1.4	-2.4	-0.8	1.3	0.7	-5.1	-0.05
OAK	2.3	1.3	4.3	-3.6	-0.6	0.5	-3.9	-2.6	-2.5	-5.3	-0.03
CAR	-2.5	-4.9	-3.7	1.4	2.1	1.9	-1.0	-0.9	2.5	-5.3	-0.04
WAS	-1.2	-0.9	-0.5	-0.9	-3.9	-0.6	0.4	-0.9	0.2	-8.4	-0.06
MIA	1.5	-0.7	1.4	-2.0	-7.1	-0.1	-2.4	-2.1	2.6	-9.0	-0.06
TB	0.0	-1.7	0.0	-1.1	-3.1	-0.3	-2.8	-0.5	-1.6	-11.4	-0.08
ARZ	-1.7	-0.6	-1.9	-2.6	-4.0	-2.5	0.1	-1.2	2.4	-12.1	-0.08
CLV	-1.7	-2.6	0.2	-2.3	-3.3	-2.1	-3.3	2.1	-4.3	-17.6	-0.12
BLT	-2.5	-1.4	-0.6	-5.1	-1.8	-4.2	1.0	-1.3	-1.7	-17.8	-0.11
DET	-2.4	-1.5	-5.4	-2.4	-1.4	-3.1	-3.7	1.0	-4.5	-23.6	-0.16
CHI	-2.3	-1.4	-4.2	-0.8	-5.9	-2.9	-2.7	-3.4	-0.8	-24.8	-0.17

If anyone needed any more confirmation of Peyton Manning's greatness, here it is. No other offense comes close to the Colts. In a distant second place is Denver, with less than half of the WPA of the Colts.

I was surprised to see that the Colts' 2006 season (7.7 WPA) eclipses the Patriots' undefeated 2007 season (+6.5). New England broke many offensive records that year, but running up the score doesn't add much to WPA. A late touchdown on top of a 0.98 WP doesn't make much of a difference.

The most inept team of the decade belongs to Chicago so far, but Detroit might overtake them this year. The worst single-year offense belongs to the 2004 Dolphins.

Team Defense Win Probability Added 2000-2008

2009-11-02T08:00:00.012-05:00

We've seen how a win probability model can help coaches make better decisions, but it can also help settle some water cooler debates around the office. One of the cool things we can do with a win probability model is compare teams and players based based on how much they contribute to their chances of winning. If we sum up all the defense's contribution toward winning the game, we can truly rank defenses.

One team might have the best defense in terms of total yards, and another might have the best defense in terms of yards per play. Yet another might be the best in terms of points allowed. All of these ways of comparing defenses is flawed in one way or another. For example, a defense with a poor offense will be facing short fields frequently.

Win Probability Added (WPA) can account for these various considerations and provide a very good estimate of how good a squad actually was. WPA should be considered a 'narrative' stat. It measures what actually happened and doesn't attempt to any more than that. I'll start by looking at defenses since 2000, as far back as my data goes.

The WPA listed for each year are raw totals including playoff games. In a way, you can think of them as saying 'this is the number of games a team would win given a completely average offense and special teams.' For example, the 2000 Ravens defense had a -6.0 WPA and would have won 14 games (8+6) had their offense and special teams simply held serve, making absolutely no contribution toward winning. (Edit: Tom Tango pointed out my original thinking was in error. I had previously said 12. Thanks!)

I've also added a column for WPA per game to account for teams with playoff appearances. You could think of this number as how much a defense added to their team's chance of winning any given game. For example, the Baltimore defense (-0.17 per game) would turn a 50% chance of winning a game into a 67% chance.

Negative numbers are good, and positive numbers are bad for defenses. Click on the table headers to sort:

Defense	2000	2001	2002	2003	2004	2005	2006	2007	2008	Total	Per G
BLT	-6.0	-2.7	-1.6	-6.0	-1.6	-0.5	-1.8	0.4	-5.8	-25.7	-0.17
TB	-2.7	-2.7	-6.5	-1.4	-1.2	-3.1	0.5	-2.1	-1.6	-21.0	-0.14
PHI	-2.8	-1.5	-3.9	-1.3	-0.8	-1.2	-0.2	1.0	-4.5	-15.4	-0.09
CHI	-0.6	-3.5	0.8	1.6	-1.6	-5.6	-4.9	-0.4	0.2	-14.0	-0.09
PIT	-1.4	-1.9	-1.1	0.3	-2.1	-2.5	1.0	0.0	-5.8	-13.6	-0.09
MIA	-2.2	-1.2	-1.4	-2.7	-2.6	0.3	-1.5	3.9	-1.5	-9.2	-0.06
NE	2.5	-1.9	2.5	-5.9	-3.2	1.5	-1.9	-1.5	0.1	-8.0	-0.05
CAR	-0.4	2.9	-4.8	-0.8	2.2	-2.7	-0.9	-0.5	-0.7	-6.0	-0.04
TEN	-2.4	2.5	0.1	-2.9	0.9	1.2	1.3	-0.7	-5.1	-5.3	-0.04
WAS	0.1	-1.3	-1.4	1.9	-3.2	-2.0	2.2	-1.1	0.0	-5.1	-0.03
NYG	-2.2	-2.2	0.1	2.2	1.1	-1.1	0.5	-2.8	0.9	-3.9	-0.03
NYJ	-1.4	-1.4	0.8	1.3	-1.8	0.2	0.7	1.2	-2.2	-2.7	-0.02
BUF	-1.5	2.3	-0.1	-1.3	-3.2	2.8	-1.0	0.1	0.5	-1.6	-0.01
GB	0.7	-1.6	-0.8	1.3	1.4	0.4	-2.7	-1.8	1.9	-1.5	-0.01
DAL	0.4	-0.2	-0.7	-1.3	1.5	-1.6	1.9	1.1	-0.9	-0.2	0.00
DEN	0.8	-1.0	0.9	-0.1	-1.9	-0.8	-2.2	1.2	3.8	0.4	0.00
SF	4.1	1.9	-0.6	0.3	1.2	-0.7	0.1	-0.8	-1.4	3.9	0.03
JAX	1.5	0.4	0.4	0.2	0.6	-2.2	-0.1	0.9	2.5	4.0	0.03
IND	2.7	2.1	-0.4	-0.2	2.2	-0.8	-0.6	-0.1	0.1	4.7	0.03
SL	2.1	-2.8	-0.9	-2.1	1.2	2.4	2.5	0.3	2.3	4.7	0.03
SEA	3.0	0.7	3.1	0.4	0.0	-1.2	-0.2	-2.1	1.3	4.8	0.03
SD	0.4	3.0	0.4	1.7	0.6	1.3	-1.6	-2.0	1.4	4.9	0.03
ARZ	2.4	1.1	1.7	3.0	-2.5	0.2	1.0	-0.8	-0.3	5.5	0.04
CLV	2.0	-2.3	2.5	0.9	-0.9	0.8	1.2	1.2	1.2	6.3	0.04
OAK	-1.3	-1.3	-0.1	1.2	3.8	3.1	0.1	1.1	1.6	8.1	0.05
ATL	0.1	4.1	-1.5	1.3	-1.2	1.3	1.9	0.6	2.6	9.0	0.06
DET	-2.5	3.3	0.0	0.7	0.4	-0.6	2.3	1.5	5.2	10.1	0.07
MIN	2.9	2.6	5.2	0.9	4.3	0.5	-2.3	-1.9	-1.8	10.2	0.07
CIN	3.3	0.7	1.3	2.8	-0.3	0.9	2.1	1.0	0.0	11.6	0.08
NO	0.1	2.3	2.0	0.9	1.6	3.4	0.9	0.8	1.7	13.5	0.09
HST			-1.1	1.8	0.1	4.3	1.5	2.3	1.7	14.4	0.13
KC	0.0	1.5	4.8	1.4	5.1	1.9	0.0	-0.2	2.6	17.0	0.12

No surprises here. Baltimore's defense is undeniably the defense of the decade on the strength of their 2000, 2003, and 2008 squads. Tampa Bay is several games behind, both in terms of total WPA and per game WPA. Tampa also owns the best single season at -6.5 WPA. Baltimore owns the next two best seasons at -5.0 WPA. Other notable seasons belong to the 2008 Titans and Steelers, and the 2003 Patriots.

Minnesota's 2002 defense and Detroit's 2008 defense tie as the worst with +5.2 WPA. The Kansas City defense of 2004 is close behind at +5.1 WPA. Also note that Houston's defense would be the overall worst on a per game basis.

An Open Letter to Dan Dierdorf

2009-11-01T21:06:00.003-05:00

And to Brian Billick. And to all the other football analysts who use the word prideful. The Baltimore defense is not prideful. The Panthers offense is not prideful. I know you mean "full of pride," but there's already a word for that. It's called proud.

I realize that prideful has wormed its way into our lexicon, and now dictionaries even consider it a word, thanks primarily to your efforts. But please, what's wrong with just using proud?