A Scoring Efficiency Model v.2

By Cyril Smith

Last week I described a simple scoring efficiency model based on points per minute. As is not unusual in the financial modeling world it promptly went 0 for 4 on the divisional playoff round games. Other models - the Las Vegas line for example - were better in getting at least one game right.
In reviewing the model (which itself was based on data from the 2005-07 regular season and playoff games) it seemed that the weak point was the assumption that each team was roughly equal and that its scoring potential was based on 30 minutes of possession. While this approach had worked reasonably well on past data as well as the wild card round, it did not perform well in the divisional round. There is in fact a great deal of volatility in each team's points per minute and time of possession - volatility which is obscured by using averages. I therefore looked for a way to incorporate this volatility into the model.

At first blush it is apparent that volatility is inversely related to wins. Teams that showed greater volatility in points per minute and time of possession tended to do worse in results. A reasonable hypothesis is that volatility represents weaknesses which a team may not be able to overcome in the playoffs because the opposing team will zero in on those weaknesses. According I took a first cut at combining volatility of points per minute and time of possession, in each case measured by the standard deviation of the series, into the model. The preliminary results look promising. Using the additional input resulted in two changes for the divisional round: Pittsburgh was now favored over San Diego and Baltimore over Tennessee.

Looking ahead the revised model has Philadelphia over Arizona by a point and Pittsburgh over Baltimore by 4 points.

Punting and Field Goals

by Dean Jens

Field Goals

One of the things I often wondered before discovering The Football Project was how the probability of a kicker making a field goal varied as a function of distance. After eyeballing the distributions for a few kickers for the 2005 season, I figured I could try raising a logistic function to some power. For the first several kickers I tried, I found that that power was statistically indistinguishable from 1, so I set about fitting the probabilities to a simple logistic function, i.e. (1/2)(1+tanh((m-x)/w)).†

I had imagined, in the absence of data, that w might be independent of the kicker, and that kickers could be characterized by m, i.e. how far away they are when their percentages drop. This is not the case; w depends on the kicker, with larger values to kickers who tend to miss easy ones and make longer ones, with lower values to more consistent kickers. Olindo Mare missed a few short ones, so his percentages didn't drop off very quickly. Matt Bryant actually had a slight improvement as distances got longer; this would surely change if more statistics were taken at a normal range of distances. On the other hand, John Kasay had a much higher tendency to hit field goals shorter than 50 than if they were longer than 50; of the 8 he missed, the shortest was 42 (he made 24 shorter than that). Jeff Reed had an even sharper drop around 45 yards, missing nothing shorter than 41 and making nothing longer than 47. While I was unable to fairly characterize the best kicker in terms of a drop-off length, I was able to generate a different metric that adjusts for length. By using my logistic fits, I predicted the percentage of field goals a kicker would make if they kicked from a given distance; I then took the 1006 field goal attempts for the season and calculated the percentage of those 1006 field goals that each kicker would have made. I've only included those kickers who attempted more than 4 kicks; the kickers who were dropped were all notably worse than the ones listed.

kicker	normalized score	percentage	number of kicks
racken001	0.963	0.952	42
nednej001	0.917	0.9	30
wilkij001	0.889	0.871	31
dawsop001	0.889	0.933	30
kaedin001	0.866	0.875	24
kasayj001	0.86	0.805	41
vandem003	0.857	0.889	27
stovem001	0.851	0.882	34
grahas002	0.837	0.879	33
hansoj001	0.836	0.792	24
bryanm001	0.836	0.846	26
bironr001	0.835	0.793	29
feelyj001	0.832	0.833	42
linder001	0.819	0.829	35
mareo001	0.815	0.833	30
hallj006	0.81	0.824	17
elamj001	0.806	0.771	35
tynesl001	0.803	0.818	33
akersd001	0.802	0.727	22
brownj018	0.796	0.697	33
petert005	0.794	0.885	26
reedj005	0.785	0.844	32
nugenm001	0.773	0.786	28
vinata001	0.773	0.786	28
carnej001	0.762	0.781	32
longwr001	0.751	0.741	27
gouldr001	0.749	0.786	28
brownk008	0.745	0.765	34
scobej001	0.743	0.75	32
edingp001	0.736	0.735	34
janiks001	0.704	0.667	30
franct001	0.686	0.778	9
cortej002	0.671	0.706	17
novakn001	0.608	0.8	10
cundib001	0.541	0.556	9

This obviously does not adjust for wind, and the linemen on both the kicking and defending sides will have some influence on these statistics, but this at least tells which unit is doing better than which other with the confounding variable of distance removed. The average length for a field goal attempt was 36.3 yards; the average for Nick Novak was 33.7, while for Josh Brown it was 41.2. Accordingly the "scores" for these kickers find themselves lower and higher, respectively, than the raw percentage. The scores and the actual percentages have a corelation of 0.8. The means and variances are very similar, though the variance of the raw percentages is a little bit smaller; while the difference isn't statistically significant*, it is what would be expected from coaches deciding to attempt longer field goals with better kickers, and punting or going for the first down with worse kickers. Perhaps looking at all fourth down plays from around the thirty yard line would be a good step for further research.

† This isn't a least-squares fit; I try to maximize the sum of the logarithm of the fitted probability of the actual outcome: for kicks that the kicker makes, P is the fitted probability that the kicker would make the kick, while for those the kicker missed (or were blocked or whatever), it is the fitted probability that the kicker would miss the kick.

* It would be significant at the 25% confidence level on a two-tailed test; arguably a one-tailed test could be used here, but even that isn't going to pass a common significance test. When a team prepares to punt, the punter's statistics are often cited, typically the average length of his punts and the number of times he has left teams behind their own 20 yard line. These seem like kind of strange statistics to me; if I were to take the line of scrimmage and the end position of the ball and plot one against the other, what I would likely expect to see, as a first approximation, would be a 45 degree line† up to a point, and then a horizontal line from there on out. Behind a certain point on the field, a punter would be expected to net a certain length; ahead of that, he would be expected to average a certain level of field position. Grabbing every punt the Packers made that year, I found that the break-point from a least squares fit was very near midfield. Accordingly, it seems to me we ought to characterize the net length of punts from one's own half of the field, and the average final field position for punts from the fifty yard line and beyond.

Punting

Taking the data from The Football Project for 2005, I calculated these statistics for each player who punted. Every player who punted more than twice had at least one punt from each half of the field, so the figures for them are well defined. Remember, the "length" is only calculated for those punts from the punter's own end of the field; the "depth", the name of which is probably more poetically than logically motivated, is the average ensuing field position of the receiving team after punts from the fifty and beyond. I use results net of the return, though using results before the return leaves a lot of what follows more or less unchanged. The players are ordered by length-depth/4, due to the fact that about 4/5 of punts originated from the punting team's side of the fifty.

punter	length	depth	number of punts
moormb001	41.51	13.85	74
jonesd018	41.04	13.35	88
johnsd022	39.78	10.5	42
bergem001	39.69	10.88	75
sauert001	39.38	11.05	83
grahab001	38.84	9.82	75
scifrm001	39.76	14	74
bakerj001	39.55	14.18	88
hentrc001	39.48	14.22	79
mcbrim001	39.16	13.09	85
bidwej001	39.45	15.68	97
hansoc001	38.72	14.52	92
koenem001	38.8	14.84	78
feaglj001	38.02	13.35	78
frostd001	38.21	14.71	91
grooma001	38.89	17.67	12
playes001	36.95	10.5	76
colqud001	37.8	14.14	66
harrin002	36.05	9.71	89
landes001	38.41	20	34
edingp001	35	7	2
maynab001	37.78	18.48	106
leea003	36.44	13.11	110
barkeb001	36.7	14.27	51
gardoc001	36.48	13.95	86
aragul001	37.08	16.4	18
lechls001	36.18	13.08	84
smithh009	35.28	11.08	59
larsok002	36.47	17.73	66
stanlc002	34.81	11.5	79
benned001	34.57	11	8
millej012	36.46	19.1	88
kluwec001	35.21	14.43	75
richak003	34.81	13.17	81
rouent001	34.96	14	76
murphn001	33.5	15	7
sandeb002	33.37	15.4	64
hodger001	32.31	13.92	44
flinnr001	31	23	6
brownj018	NA	11.5	2
cundib001	NA	20	1
dawsop001	NA	6.5	2
ellina001	NA	2	1
gouldr001	NA	24	1
kasayj001	NA	20	1
mareo001	NA	27	1
nugenm001	NA	17	1
roethb001	NA	10.5	2
vinata001	NA	4	1
wilkij001	NA	20	1

Number one is Brian Moorman, of the Buffalo Bills; second is Donnie Jones. They are the only two punters to average more than 40 net yards from their own end of the field; of punters who punted more than twice, the two who left the ball inside the ten yard line when they punted from midfield or closer were Ben Graham, who had pretty good length as well, and Nick Harris, whose length was more mediocre.

Adding the length and depth for each player with more than two punts, I get a surprisingly narrow distribution. It is centered around 51.4 or 51.5 — 50.5 would be ideal for the use of these statistics — and has a standard deviation of only 3.5 yards. Most punters, then, seem to punt for distance behind their own 49 or so, and for field position beyond there. If I exclude Ryan Flinn, who had six punts (the fewest among those with more than two) for the worst result in both statistics (among those with more than two punts), the correlation between length and depth is 0 to two decimals.* Accordingly, a punter with better length will tend to be affected by the endzone further into his own territory, while a punter who is particularly good at pinning the opposing team against its goal line is more likely to still be punting for length a bit beyond the fifty; there is no unambiguous connection, independent of one's measure of "skill", between a punter's "breakpoint" and the skill of the punter.

It won't come as a great surprise that the length as I measure it and the average length of all punts has a correlation greater than 0.9. It might not be a big surprise either that the percentage of punts to end up inside the twenty has a correlation of -0.4 with "depth", but, interestingly, either length measurement has a correlation of 0.4 with the inside-the-twenty statistic. From a linear regression standpoint, it looks as though the inside-the-twenty statistic is including some length information; 1/3 of the variance can be explained from the two numbers in my table. The median punt to end up inside the 20 starts from 2 yards behind midfield, but 20% come from behind the punter's own 40; some of what is being recorded in that figure is not any deftness in terms of avoiding the touchback or letting one's teammates get downfield, but is simply the ability to kick to the red zone from farther away. This is a nice skill, of course, but it is fully incorporated into the length statistic; the frequency of leaving a punt inside the twenty is a hybrid of skills, and is not the best measure for any of them.

† There is some attempt here to keep the statistics simple. In fact, this line is slightly flatter than 45 degrees because the endpoint is bounded both above and below; punts from behind midfield give a slope of 0.95 that is statistically distinct from 1 at the 5% confidence level.

* This actually is less true without the return; punters who punt the ball farther before the return also tend to punt it closer to the endzone, but not dramatically so. The distribution of punters' depth+length is similar to the results with the return, with several yards simply moved from depth to length.

Is 3rd and 6 a running down in the NFL?

by jjbtnw

This post probably has more to do with an interesting query result than suggesting an alternative strategy for coaches. I was taking a peek at the 2005 play-by-play data that is available on this site (thanks Brian!). I had just separated everything into drives and series. I was wondering what the most efficient pass/run mix was, historically. One of the funny looking query results that I turned up was the following matrix of down-and-distance and conversion percentages. This data is limited to the 2005 data and does not include first downs gained by penalty. Nor does it exclude garbage-time drives or time-pressure drives. It does include playoff games and goal-to-go series.

Down	Distance	Pass Conv%	Run Conv%
3	1	63.5	76.3
3	2	50.8	60.8
3	3	50.8	57.9
3	4	46.9	53.6
3	5	43.1	47.4
3	6	43.2	55.2
3	7	38.7	36.8
3	8	33.9	26.6
3	9	31.1	32.9
3	10	32.2	27.6

To me it is interesting to see that running is a better strategy on
3rd down for distances of 6 yards and less. One of the reasons that running is so effective is that it is apparently unexpected. The next table shows the same down-and-distance situations, and how many of each type of play occurred in the league.

Down	Distance	Pass Plays	Run Plays
3	1	203	548
3	2	364	260
3	3	423	133
3	4	467	110
3	5	531	95
3	6	526	67
3	7	507	76
3	8	501	64
3	9	396	76
3	10	603	87

On 3rd down and 3, 76% of teams pass instead of run. And thepercentage of passing on 3rd down with more yards than 3 needed for a first down only gets higher. So most defenses on 3rd and 3 or higher will be implementing a pass-oriented scheme and personnel package. And 3 out of 4 times (or even more often) they will be making the correct call. Given those circumstances a run play would be expected to be more successful. And apparently, it is. According to game theory, if coaches were calling the correct run/pass mix, the conversion percentages would be nearly identical. For 3rd and 6 or less, they aren't. So the obvious assumption is that more running plays should be called on 3rd and 6 than are currently being called in the NFL. Of course, this post would need to be backed up by data from more than one year to validate any assumptions made.

Quarterbacks: Starters verses Backups

By Denis O'Regan.

This is a tentative attempt to find a ball park figure for how much a team's chances are compromised when the backup quarterback plays.

Firstly,I collected and combined data for every regular season play since 2007 made by a quarterback who,at the start of the season was considered to be the team's number one quarterback.

I then repeated the exercise for every other quarterback who threw a pass over the same time scale.As I'm initially just looking for a general figure I didn't take any account of how the backup came to be playing.Backups can be under centre for a variety of reasons.They can be mopping up at the end of a large victory or playing out time after a heavy defeat.The best comparison between backups and starters is obviously when the latter is injured and the former starts,but for the moment I've looked at all plays.

I did eliminate passes thrown by non quarterbacks,such as punters or running backs,but I'll present those numbers at the end because they do make interesting reading.

I looked at various passing stats,but I'll be using yards per attempt as the main tool to compare an average backup with an average starter.

Here's the results.

Interceptions.As you'd expect the average starting QB looks after the ball better than his understudy.Backups are intercepted on 3.6% of their attempts since 2007 compared to only 2.8% for starters.

Touchdowns.Starters throw a touchdown on 4.3% of their attempts compared to just 3.3% for backups.

Sacks.Once again starters are better,going down on 5.6% of their total dropbacks compared to 7.3% for backups.However, backups do slightly better by only losing 6.3 yards per sack compared to 6.5 yards for starters.So a small,if insignificant victory,although as we're only looking at two seasons worth of results,this could simply be a sample size issue.

Quarterback rating.I know it's not perfect,but I'm including it anyway.If you take every play made by a starting QB since 2007 and compile a combined QB rating you get 86.0.For backup's it's only 72.4.

Completion percentage.Not surprisingly,backups do poorly compared to starters,not only do they lack the starter's talent,they also get much less time to practise with their receivers.The backup averages a completion rate of 57.9% compared to 62.1%.Breaching 60% completion rates seems to be a factor that defines quality in a quarterback.Eli Manning only hit 56% of his passes in the Giants Superbowl winning season,but on the road,where the trophy was won he connected on 61% of his throws.Prior to Manning you have to go back to the Raven's Trent Dilfer (59%) in 2000 to find a SB winning QB whose regular season completion rate was sub 60%.

Yards/Attempt.This is the stat I'm going to use to estimate a starters worth.Backups pass for 6.26 yards per attempt,very nearly a yard per attempt less than starters,who averaged 7.11 ypa over the two season.These figures don't take into account sacks as failed pass attempts,nor does it subtract sack yards or interception yards,but if you do correct for these occurrences,then the discrepancy in the two figures remains fairly constant.

If you patch all these stats together you find that the 2008 quarterback who comes closest to matching the average stats for a starting quarterback is Denver's Jay Cutler.The pin up guy for the backups based on 2008 is Marc Bulger,which probably says as much about the Rams as it does about Bulger.If you want a player who comes closest to replicating the average backups stats who actually is a backup,try a combination of Brian Griese from 2007 in Chicago and 2008 in Tampa.

Armed with the comparison between yards/attempt for each type of quarterback I next constructed a predictive model based around yards per pass and yards per rush.
I calculated the yards per pass and yards per rush each team had achieved on offense and defense prior to each game from week 4 onwards for the last 7 seasons.I corrected these figures for strength of opponents faced.I then matched each teams offensive numbers with their opponents defensive numbers,and vice versa for every game played and regressed those numbers against the actual result.

For example if team A was averaging 6.5 yards/pass against defenses who were allowing 6.8 yards/per pass,then they were considered below average to the tune of 0.3 yards/pass.If they were matched up against a defense that had allowed 6 yards/pass against offenses that were averaging 6.4 yards/pass,then I considered that the defense they were facing that day was 0.4 yards/pass above average.Combining these two figures gives an overall projected passing capability of team A in this particular game of 0.7 yards/pass below the league average.

I also did this for the projected rushing offense of team A and repeated the process for team A's opponents on that day.

Both teams,therefore had a pregame projected rating for projected passing ability (containing information about their game day opponents pass defense) and rushing ability (containing informtion about their gameday opponents run defense).These four pregame inputs turn out to be statistically significant in predicting the actual game outcome and tests on out of sample games perform to a level similar to the Vegas line.This limited model also suggests that it is much more important to be able to pass the ball than it is to run the ball,which backs the intuitive knowledge that losing your starting passer is a really big deal.

Having produced a serviceable prediction model based on passing yardage all we need to do now to predicted the impact of a backup QB starting is to reduce the expected passing ability by a similar drop to the one seen in the two sets of aggregate stats for starters and backups.

If we do this for every matchup over a series of seasons we find that on average the presence of a backup for the whole game decreases the win probability of that team by about 8 percentage points.In other words a team with a win probability of 58% would turn into a coin toss if they played their backup in that game and their yards/pass numbers were reduced by just under a yard/pass.

So to sum up,in terms of points on the scoreboard a backup QB on average seems to cost a team about a field goal.Individual teams will of course see differences within these averages.Swapping between Manning and Sorgi you would expect would cost the Colts more than the average,whereas the choice between Orton and Grossman may result in little difference.

For completeness,here's the 2007-2008 stats for non QBs passing the ball.They completed 55% of their passes,they were sacked on 14% of their drop backs.They threw 10 yards/attempt and 23% of their passes went for TD's!.They had a combined QB rating of 116.

A Scoring Efficiency Model And The Playoffs

by Cyril Smith

This is the time of year when the NFL really gets interesting.  The ups and downs of the regular season have ended and the playoffs hold the promise of competitive matchups for every game.  I have put together a simple scoring efficiency model for predicting the outcome of playoff games.  I look at the ability of a team to score based on its time of possession, in other words points per minute (ppm). PPM measures not only offense but defense and special teams as well.  Both good defenses and good special teams give the offense good field position, which means less time is needed to score.  A defensive touchdown or a kick return for a touchdown represents scoring with minimal time expenditure.

The model takes the average points per minute for the last nine games.  Each playoff team's ppm is calculated by dividing its aggregate nine game score by its aggregate nine game time of possession.  An assumption of the model is that the playoff teams are roughly equal; accordingly each team's basic score is calculated by multiplying its average ppm by 30. I then make three adjustments: home team gets 3 points; a team whose quarterback has never started a playoff game is docked 3 points; and a team whose average ppm has increased significantly over the past three games compared to games four through six is given 3 points for trend.

How did the model do on the first round of playoffs? It had Arizona over Atlanta by 6 points; San Diego over Indianapolis by 3 points; Miami over Baltimore by 1 point; and Philadelphia over Minnesota by 1 point.

For next weekend the model has Carolina over Arizona by 11; San Diego over Pittsburgh by 4; Tennessee over Baltimore by 3 1/2; and New York over Philadelphia by 4 1/2.

Does Baltimore's Defense Travel?

by Denis O'Regan

This was supposed to be a short piece on home field advantage,but then I caught Boomer Esiason previewing th AFC wildcard weekend on NASN and it turned into something more.

In discussing the Baltimore Miami game Boomer's view was that the Ravens wouldn't be inconvenienced too much by being on the road because "defense travels".
So I decided to see if defense generally and Baltimore's in particular does travel.

Firstly,I compared Baltimore's home and away record since week one 2004,a decent sample size and a period during which their defense has been their dominant asset.

They are 29-12 at home and 15-25 away.If defense does travel I would expect their home and away records to be a lot closer than they actually are.

So next I used a method that gives a reasonable estimation of a team's home field advantage.I'll outline the ideal (but wholly impractical) methodology used and then try to show how you can get reasonable approximations using readily available data.

Say you've got two teams,we'll call them S and D,S can be the superior team.The first step towards determining HFA for each would be to determine how much better,on average in terms of points S is compared to D at a neutral venue.To do this we'd simply require S to play D,over and over at a neutral spot and average the margin of victory (or the occasional defeat).

We'd then ask the teams to repeat the exercise,with D acting as the hosts.After enough re runs,we would again average the margin of victory or defeat for S and could infer that the amount that this figure had declined compare to S's superiority on neutral turf,would be equal to D's HFA.

Similarly when we played out an extended series at S's home field,the amount that the average margin of victory had increased compared to the neutral figure would be as a result of S's HFA.

Of course none of he above is possible.For a start,aside from the odd trip to London and the Superbowl,hardly any neutral venue games are played.

It does give  clue as to how to approach the problem though.If you take the average difference between the margin of victory with S hosting D and D hosting S,you've got a figure that comprises the HFA of D plus the HFA of S.

There are still problems,even for divisional rivals to get,say 40 pairs of games,you're looking at 40 seasons of results.Teams change,as do likely contributing factors that could affect HFA.

So instead do the next best thing and take,say San Diego's last 40 home and away games (5 years of games).The average margin of victory at home was 10.9 points,away from home it was +3.8 points.That's a spread of 7.1 points.

SD's opponents over those 40 games should represent a fair cross section of the NFL,as should the HFA's of those teams.Therefore,as a good approximation for the HFA of SD's opponents we could use the average HFA for the league over the same period.That figure is 2.5 points.

So subtracting 2.5 from 7.1 gives us SD's HFA over the last five years as 4.6 points.

Do the same for every team and you get.

Team.......HFA (points).
Baltimore    .......8
Arizona...........7.8
Seattle............6.9
Houston..........5.8
St Louis..........4.7
San Diego.......4.6
Jax.................4.3
NYJ................4.3
Tampa............4.1
KC.................4.1
Washington....3.7
Atlanta...........3.7
SF.................3.6
Mini................3
Philly..............2.8
Indy................2.7
Denver............2.5
Buffalo.............2
Dallas.............1.9
Chicago..........1.3
Oakland..........1.2
Cleveland........1.2
Pittsburgh........0.9
GreenBay........0.8
Detroit.............0.5
Tennessee......-0.2
NewOrleans....-0.3
NYG..............-1.7
NewEngland...-1.8
Miami............-1.8
Carolina.........-1.8
Cinci.............-2.1

So over the period Baltimore,as their win/loss record suggests appear to have benefited enormously from being at home and have fared comparatively poorly on the road.Rather than defense travelling well,the reverse could actually be true.

The next step towards perhaps proving that defense doesn't travel involves using a statistics that can represent a teams defensive capability.I used FO's dvoa stats.Their website contains weekly offensive,defensive and special teams dvoa stats from 2004 onwards.

I recorded the offensive,defensive and ST dvoa each team and their opponents took into every game from week 4 2004 to week 16 2006.I regressed these variables against the actual game result.I then ran a real time live test through the 2007 and 2008 season,using the regression line to predict game outcomes.

In short the respective dvoa stats that the home and away teams took into a match up are statistically significant in predicting the outcome of that match up.

The difference between the margin of victory (or defeat) predicted by the regression line and the actual margin averages out at 10.6 points per game over the two seasons of live testing.By contrast the Vegas line is out by on average 10.5 points per game over the same time scale.However,the dvoa based regression shades Vegas overall by being closer to the actual margin of victory in 60% of games.The slightly better average margin of error by Vegas compared to dvoa could be explained by Vegas incorporating readily available team news.

Having,hopefully established the legitimacy of the dvoa  regression line we can now use it to see if it says anything about Baltimore's defense.

To see which of the individual dvoa stats are most important in determining game outcome I standardised the inputs and re did the regression.

The largest contributer to match outcome is the offensive dvoa of the away side,followed by the offensive dvoa of the home side.Because the regression contains a constant that equates to the average home field advantage for the NFL as a whole this tells you that having a good offense helps a team more on the road than at home,but the gap is small.

The third biggest contributer is home defensive dvoa,but it is followed by the away special teams dvoa and the home special teams dvoa.The smallest contributer to game outcome is the defensive dvoa of the away side.

This is significant to the Baltimore case.The offensive and special teams dvoas merely tweak the built in home field advantage because the relative sizes of their home and away regression coefficients are similar in size.But if you rely greatly on defense,as Baltimore do,the fact that the size of the home and away defensive regression coefficients differ greatly results in a comparatively good predicted home performance and a comparatively poor away one.

So does this predicted home away split occur in practice.

Given the home/away win/loss splits and the apparently large home field advantage,it appears to.But just to be sure,I split Baltimore's 2008 games by venue and looked at the average yards per play allowed through the air and on the ground by the defense.I didn't correct for opponent.

At home the Ravens allowed 4.15 yards per pass and 3.34 yards per run.Those figures increased to 6.12 ypp (increase of 47%) and 3.76 ypr(increase of 13%) on the road.

Spread over the 5 seasons from 2004 onwards,this drop off in defense on the road is still present,albeit less dramatic.Overall Baltimore yields 10% more yardage both to the run and the pass on the road compared to at home.

So to summarise,using dvoa ratings as a measure of team talent,and regressing those ratings against game outcome implies that a good defense is very helpful at home,but performs comparatively poorly on the road.

The really interesting question is why if,Baltimore are typical,do defense reliant teams struggle on the road compared to at home.An obvious cause could be that it's easier for a ref to call pass interference against a road side,but for the moment that's just speculation.Penalty stats are also notoriously difficult to accurately collect.

Another point to consider is that teams that have large home field advantages (for whatever reason,climate being an obvious other factor) are going to be inconvenienced at some stage during the post season.Baltimore are rightly considered to be slight favs even on the road in Miami,but it may be no coincidence that if we look back at the hfa table,all of the Superbowl winners over the period considered had little or no home field advantage.

What Wins Championships?

by Derek Singer

Perhaps the oldest and most revered cliché in all of sports is “defense wins championships.” Play a drinking game based on commentators using that cliché, and you may be dead before the divisional round. Teams such as the 70s Steelers, 2000 Ravens, and 2002 Bucs are often trotted as proof. While the latter two certainly had great defenses backed up by mediocre offenses, the Steelers had several Hall of Famers on offense. The Steel Curtain was complemented with great running and passing attacks. “Smashmouth” football alone didn’t win. The 80’s 49ers were made famous by their West Coast Offense, one built on the passing game. The 90’s Cowboys were best known for the triple threat of QB Troy Aikman, WR Michael Irvin, and RB Emmit Smith. Both dynasties also had good defenses, however, during their championship seasons. The greatest teams, it would seem then, are the best balanced teams. They have good offenses and good defenses. In Football Outsiders’ Pro Football Prospectus 2006, they found that defense does indeed have a higher correlation with playoff success than offense. Correlation not being causation, we have to ask why offense would suddenly become less valuable in the postseason. How is the postseason different than the regular season? The competition is much better. If the proportion of teams with good offenses is higher in the postseason than in the regular season, then the only thing that will separate the best from the good is defense (and special teams to a lesser extent).

	Total Teams	Playoffs	Playoff %	Conf. Champs	Conf. Champ %	SB Champs	SB Champ %
pass off. >5%	167	115	68.86%	25	14.97%	13	7.78%
pass off. >10%	105	81	77.14%	19	18.10%	11	10.48%
pass off. >15%	60	49	81.67%	14	23.33%	7	11.67%
pass off. >20%	24	20	83.33%	7	29.17%	4	16.67%
run off. >5%	161	76	47.20%	14	8.70%	9	5.59%
run off. >10%	87	44	50.57%	9	10.34%	6	6.90%
run off. >15%	52	25	48.08%	4	7.69%	2	3.85%
run off. >20%	24	10	41.67%	3	12.50%	1	4.17%
pass def. >5%	158	101	63.92%	18	11.39%	11	6.96%
pass def. >10%	67	53	79.10%	11	16.42%	7	10.45%
pass def. >15%	21	17	80.95%	5	23.81%	4	19.05%
pass def. >20%	4	3	75.00%	1	25.00%	1	25.00%
run def. >5%	159	70	44.03%	19	11.95%	11	6.92%
run def. >10%	80	37	46.25%	10	12.50%	5	6.25%
run def. >15%	35	14	40.00%	4	11.43%	1	2.86%
run def. >20%	15	4	26.67%	2	13.33%	1	6.67%

This study uses data from the 1990-2007 seasons culled from pro-football-reference.com. The main statistic used is percentage over league average of yards per play. From year to year, the average yards gained per pass play hovers around 6, while the average for run plays stays around 4. So an offense gaining 6.6 yards per pass play would be around 10% over league average. A defense allowing 5.4 yards per pass play would be around 10% over league average (i.e. >0% means the defense is above average, <0%>10% above average, 11 won the Super Bowl (13.6%).
Of the 44 postseason teams with a run offense >10% above average, 6 won the Super Bowl (13.6%).
Of the 53 postseason teams with a pass defense >10% above average, 7 won the Super Bowl (13.2%).
Of the 37 postseason teams with a run defense >10% above average, 5 won the Super Bowl (13.5%).

	Avg.	Max.	Team with Max.	Min.	Team with Min.
Pass Off	11.197	30.739	STL 1999	-11.152	BAL 2000
Run Off	3.6846	22.536	STL 1999	-18.314	NE 2003
Pass Def	8.5432	22.304	TB 2002	-1.5238	NE 2001
Run Def	4.3924	34.174	BAL 2000	-28.287	IND 2006
Conf. Champions (% above league avg)	Avg.	Max.	Team with Max.	Min.	Team with Min.
Pass Off	10.804	34.146	STL 2001	-11.152	BAL 2000
Run Off	2.7994	22.536	STL 1999	-18.314	NE 2003
Pass Def	6.4548	22.304	TB 2002	-5.5967	TEN 1999
Run Def	4.3563	34.174	BAL 2000	-28.287	IND 2006
Playoff Teams (% above league avg)	Avg.	Max.	Team with Max.	Min.	Team with Min.
Pass Off	6.803	41.785	STL 2000	-17.34	TB 2005
Run Off	1.5066	38.559	DET 1997	-25.13	NE 1994
Pass Def	4.5736	22.904	NO 1992	-13.531	WAS 2005
Run Def	1.218	34.174	BAL 2000	-33.141	IND 2005

The second table shows that teams that make it deeper into the playoffs are better in all four phases of the game on average. All of the last 18 Super Bowl champions have been above average in at least one phase, with 15 being above average in three phases. Only one champion has been less than 5% above average in all phases of the game: the 2001 Patriots. Sixteen of the last 18 champions were at least 5% above average in two phases of the game. Ten have been at least 10% above average in 2 or 3 phases (none in all 4, seven in only 1). A team that excels in one area can make the playoffs. Championship teams, however, excel in more than one area. In general, they are balanced teams in that they are great at one or two things and terrible at very little. Only the 2001 Patriots were more than 5% below average in two phases (run offense and run defense).

Team	Seed	Pass Off	Run Off	Pass Def	Run Def
TEN	1	-4.93	2.94	15.09	11.37
PIT	2	-0.34	-12.63	28.03	21.71
MIA	3	13.00	0.70	-1.03	0.71
SD	4	23.30	-2.50	0.06	4.35
IND	5	6.91	-18.12	4.43	0.95
BAL	6	-0.93	-4.55	16.82	15.40
NYG	1	-1.15	19.29	4.66	5.55
CAR	2	16.53	14.99	7.11	-5.25
MIN	3	-0.09	6.86	0.59	21.16
ARI	4	13.34	-17.61	-4.60	5.73
ATL	5	17.43	3.75	1.88	-16.90
PHI	6	-1.41	-5.49	15.24	16.63

Applying these ideas to the 2008 playoffs, the Carolina Panthers emerge as the favorites to win it all. They are more than 5% above average in pass offense, run offense, and pass defense. Four of the other five NFC teams are more than 5% above average in two areas. The Steelers look like the favorites in the AFC, with an exceptional defense and average passing game. Baltimore, Tennessee and Pittsburgh all have very good defenses and mediocre offenses this year. On the flipside, Miami, San Diego, and Indianapolis have good pass offenses but unexceptional running games and defenses.