This was born in another thread when Relianttexan asked me "If your going to judge the colts run defense on how they played in the playoffs then why not judge our defense in yds allowed the last 13 games of the season in which they were ranked 12th not 23rd.Or how bout we judge them the last 10 games of the season in which they were a top 10 D." I had pretty much ignored that "fact" because I didn't think it was possible that it was true. So this whole post is basically an answer to that question, but because of the scope it entails, I felt it was worthy of its own thread. This post will probably come in several parts because I see it being a lengthy but worthy read.
There is no standard for comparing defenses. You can rank them a number of ways. Ranking them by points allowed doesn't always work because its possible that the team's offense puts them in a bad position. So then you turn to yards. But then you have those bend but don't break situations.
My first inclination, when I read this was to simply take last year’s games, subtract the first 3 games stats from the total stats. Then Divide that number by 13 to get the average of the last 13 games. Then multiply those numbers by 16 to account for a full season. And Yardage wise, I'm proud to announce our Texans would have finished 13th overall in total yards, 14th overall in Rushing yards and an astonishing 11th in passing yards. If only it were that simple.
In some areas of the country, yards do count in the outcome of the game. Certain states will award a win to a team if after an overtime period teams are still tied, they count trips inside the 20 yard line and then total yards to determine the winner of a playoff game. Alas that is H.S. football. In the rest of the football world, the object of the defense is to keep the other team from scoring and if possible score themselves. Since for the most part defensive scores are an anomaly (with a few exceptions) they don’t really figure into the quality of the defense (despite what any fantasy football player would tell you) we will disregard them for this discussion. Points can’t be that determining factor either though. That is because the defense doesn’t play in a vacuum. Some offenses have a tendency to put defenses in a bad situation, or leave them on the field forever. So if you can’t look at yards and you can’t look at points, what can you possibly look at to give you an accurate measure of a defense?
It was no surprise to me that total yards = points. Mathematically that’s easy to prove. That’s probably why it’s not the most useful stat to break down defenses with. But if you split up yards by total rushing yards and total passing yards rushing yards figure into the equation much more heavily than passing yards, in fact Passing yards is around the threshold of the critical value of r – meaning it just barely meets the criteria for a correlation. That is because unlike rushing (in which a failed carry results in negative, or 0 yards) a failed pass attempt doesn’t really show up in the passing yardage. It’s just not a very effective way to measure passing effectiveness (or pass defense effectiveness).
This leaves you with yardage. What do you consider? Total yardage? That doesn't make much sense to me. Especially considering that the Ravens had almost 15% fewer plays on defense than the Titans did. I think that leaves you with yards per play. But I had to look to make sure there was a statistical significance between yan yards per play and points. So here is what I did. I took several major categories and from each team for the 06 season and compared them to points against. I then took the correlation coefficient and ranked them to attain the most relevant statistics. Here is a look at what each of the following statistics tells us and its correlation coefficient:
(note. The closer the number to 0 the lower the correlation. )
Total Yards ( .757) - This obviously has a high correlation to points. But like points it really doesn’t tell us much. Because total yardage is divided into two separate categories and doesn’t measure the importance of run versus pass defense, nor does it tell us what components of each respective aspect of the game are most important. It’s not a bad way to rank total defense but doesn’t account for those defenses that give up a lot of yards while not giving up many points.
Rush yards allowed (.549) /Pass yards allowed (.332) – The odd thing about this is that passing yards had such a low statistical significance. As a sub discussion of total yards they are helpful, but given the difference in plays from scrimmage on one side of the ball or another which isn’t accounted for, they may not be much help either.
Yards / Play (rushing and passing combined) (.772) – This was slightly higher than just total yardage. It tells you on each play what a defense yields. It will tell you, overall how the defense faired. What it won’t tell you is how the run defense faired or how the pass defense faired. It is very similar to total yards in that aspect but it also accounts for the fact that some teams had 800 something plays while others had over 1000.
Yards per Carry (.506) – I split this up from Yards per pass for a reason. It is kind of like the inverse of the whole completion % problem. Teams that allow a team to run the ball for say 3.4 yards, if they give up more rushes will actually stay on the field longer than a team who gives up 4.4 ypc. The whole 3 yards and a cloud of dust, take time off the clock phenomenon may be playing tricks with the numbers here.
Yards per Pass Attempt (.612) – Think of these as the WHIP of football. Statistically almost as significant as total yards by themselves they give you a better idea of what a team does on a per play basis. Ideally you would be able to split them up to where they happen but that involves a ton of work just to collect the numbers. Because yards/catch is so similar among teams Yards/Pass attempt winds up with an almost identical number to comp%.
Comp% (.615) is a little different number. But every bit as valid. Maybe more so. Most teams in the league will rank about the same in completion percentage that they would YPA since most teams are with in 2.5 yards per reception. Completion % though was a huge difference.
There will always be people who rank defenses differently. It is an inherently subjective ranking. You can argue that injuries, or a few bad games, or a few good games will skew the numbers. Between eras it becomes even more difficult. With the passing game having evolved as it has over the last 50 years more plays get run in a game. If you were going to ask me to use two barometers to to rank defenses within a certain year (2006 specifically) I would use the rushing yards against and completion% against numbers. They are specific enough to tell you something about the two different aspects of the defense while being broad enough to be categorized. An example of a stat that doesn't do that would be the yards per catch against. It doesn't take into account the completion% which since each team has a pretty close yards per completion average, is a stat that definitely figures into the effectiveness of any passing game.
I haven’t run the numbers yet to see where the Texans stand in those categories (to eliminate bias when I finally answer the question) but I will in the morning and then I’ll finally answer the question I started out trying to answer.
Mike
There is no standard for comparing defenses. You can rank them a number of ways. Ranking them by points allowed doesn't always work because its possible that the team's offense puts them in a bad position. So then you turn to yards. But then you have those bend but don't break situations.
My first inclination, when I read this was to simply take last year’s games, subtract the first 3 games stats from the total stats. Then Divide that number by 13 to get the average of the last 13 games. Then multiply those numbers by 16 to account for a full season. And Yardage wise, I'm proud to announce our Texans would have finished 13th overall in total yards, 14th overall in Rushing yards and an astonishing 11th in passing yards. If only it were that simple.
In some areas of the country, yards do count in the outcome of the game. Certain states will award a win to a team if after an overtime period teams are still tied, they count trips inside the 20 yard line and then total yards to determine the winner of a playoff game. Alas that is H.S. football. In the rest of the football world, the object of the defense is to keep the other team from scoring and if possible score themselves. Since for the most part defensive scores are an anomaly (with a few exceptions) they don’t really figure into the quality of the defense (despite what any fantasy football player would tell you) we will disregard them for this discussion. Points can’t be that determining factor either though. That is because the defense doesn’t play in a vacuum. Some offenses have a tendency to put defenses in a bad situation, or leave them on the field forever. So if you can’t look at yards and you can’t look at points, what can you possibly look at to give you an accurate measure of a defense?
It was no surprise to me that total yards = points. Mathematically that’s easy to prove. That’s probably why it’s not the most useful stat to break down defenses with. But if you split up yards by total rushing yards and total passing yards rushing yards figure into the equation much more heavily than passing yards, in fact Passing yards is around the threshold of the critical value of r – meaning it just barely meets the criteria for a correlation. That is because unlike rushing (in which a failed carry results in negative, or 0 yards) a failed pass attempt doesn’t really show up in the passing yardage. It’s just not a very effective way to measure passing effectiveness (or pass defense effectiveness).
This leaves you with yardage. What do you consider? Total yardage? That doesn't make much sense to me. Especially considering that the Ravens had almost 15% fewer plays on defense than the Titans did. I think that leaves you with yards per play. But I had to look to make sure there was a statistical significance between yan yards per play and points. So here is what I did. I took several major categories and from each team for the 06 season and compared them to points against. I then took the correlation coefficient and ranked them to attain the most relevant statistics. Here is a look at what each of the following statistics tells us and its correlation coefficient:
(note. The closer the number to 0 the lower the correlation. )
Total Yards ( .757) - This obviously has a high correlation to points. But like points it really doesn’t tell us much. Because total yardage is divided into two separate categories and doesn’t measure the importance of run versus pass defense, nor does it tell us what components of each respective aspect of the game are most important. It’s not a bad way to rank total defense but doesn’t account for those defenses that give up a lot of yards while not giving up many points.
Rush yards allowed (.549) /Pass yards allowed (.332) – The odd thing about this is that passing yards had such a low statistical significance. As a sub discussion of total yards they are helpful, but given the difference in plays from scrimmage on one side of the ball or another which isn’t accounted for, they may not be much help either.
Yards / Play (rushing and passing combined) (.772) – This was slightly higher than just total yardage. It tells you on each play what a defense yields. It will tell you, overall how the defense faired. What it won’t tell you is how the run defense faired or how the pass defense faired. It is very similar to total yards in that aspect but it also accounts for the fact that some teams had 800 something plays while others had over 1000.
Yards per Carry (.506) – I split this up from Yards per pass for a reason. It is kind of like the inverse of the whole completion % problem. Teams that allow a team to run the ball for say 3.4 yards, if they give up more rushes will actually stay on the field longer than a team who gives up 4.4 ypc. The whole 3 yards and a cloud of dust, take time off the clock phenomenon may be playing tricks with the numbers here.
Yards per Pass Attempt (.612) – Think of these as the WHIP of football. Statistically almost as significant as total yards by themselves they give you a better idea of what a team does on a per play basis. Ideally you would be able to split them up to where they happen but that involves a ton of work just to collect the numbers. Because yards/catch is so similar among teams Yards/Pass attempt winds up with an almost identical number to comp%.
Comp% (.615) is a little different number. But every bit as valid. Maybe more so. Most teams in the league will rank about the same in completion percentage that they would YPA since most teams are with in 2.5 yards per reception. Completion % though was a huge difference.
There will always be people who rank defenses differently. It is an inherently subjective ranking. You can argue that injuries, or a few bad games, or a few good games will skew the numbers. Between eras it becomes even more difficult. With the passing game having evolved as it has over the last 50 years more plays get run in a game. If you were going to ask me to use two barometers to to rank defenses within a certain year (2006 specifically) I would use the rushing yards against and completion% against numbers. They are specific enough to tell you something about the two different aspects of the defense while being broad enough to be categorized. An example of a stat that doesn't do that would be the yards per catch against. It doesn't take into account the completion% which since each team has a pretty close yards per completion average, is a stat that definitely figures into the effectiveness of any passing game.
I haven’t run the numbers yet to see where the Texans stand in those categories (to eliminate bias when I finally answer the question) but I will in the morning and then I’ll finally answer the question I started out trying to answer.
Mike
