Football Calculus 1

from Hunter Leath


Football Calculus: How I Use Arbitrary Opinions to Prove the NFC West is the Best Division in the NFL

What is it about me that you miss the most friends? Is it my quick wit, my self complimentary nature, my tendency to always list things in threes? Is it my rambling on about topics that you don’t care about 93%, but because you care about 7% you just listen anyway? Is it my propensity to analyze things that only I care about in ways that they should never be analyzed and make you listen all the way? If you have answered yes, boy do I have the column for you. If you answered no to any of those questions, you might want to stop reading at the end of the next paragraph. Not this one, you don’t even know what it is about yet. Are you curious yet? Does this intrigue you? Does another string of three rhetorical questions make you want to hurl yourself down an elevator shaft? All will be explained through the next few pages.

For those of you who have heard me debate between whether or not baseball is a better sport than football, you have heard me use the words “statistical backing” before. Everything in baseball can be backed by numbers and history, whereas football is a game based on luck and whimsy in many regards. I am hereby attempting to remedy that. Given that I have succeeded in one year of high school differential calculus, and I got a 100 on my first STAT 2000 test, I feel I am qualified to do so. As you probably came to expect, this analysis will come in three parts: first I will give you my Power Rankings for week three of the NFL season and also ESPN.com’s rankings, second I will show you statistical evidence based off of those rankings and third I will use my aforementioned system of Football Calculus to all work towards one giant thesis: Despite the fact that it has been nothing but a doormat for the NFL over the past five years, the NFC West has made strides towards becoming the best division in the National Football League.

Part 1: Nick’s Week Three Power Rankings 1. San Francisco 49ers 2. Green Bay Packers 3. Houston Texans 4. New England Patriots 5. Philadelphia Eagles 6. Baltimore Ravens 7. Atlanta Falcons 8. Arizona Cardinals 9. Pittsburgh Steelers 10. Chicago Bears 11. New York Giants 12. San Diego Chargers 13. St. Louis Rams 14. Tampa Bay Buccaneers 15. Washington Redskins 16. Denver Broncos 17. Seattle Seahawks 18. Dallas Cowboys 19. New York Jets 20. Carolina Panthers 21. Detroit Lions 22. Buffalo Bills 23. Miami Dolphins 24. New Orleans Saints 25. Cincinnati Bengals 26. Indianapolis Colts 27. Minnesota Vikings 28. Oakland Raiders 29. Tennessee Titans 30. Jacksonville Jaguars 31. Cleveland Browns 32. Kansas City Chiefs And here is a link to ESPN’s rankings: http://espn.go.com/nfl/powerrankings/_/year/2012/week/3. These will be very important to understanding the rest of this article, please open this in another window and refer to it to clear up any miscommunications that may result from the “brevity” of this column with regard to explanations over the rankings. The only thing I will say with respect to my rankings is that I did it both subjectively and objectively, looking at both degree of competition and points differentials, and also basing it off of who has the most perceived confidence, which teams have the most “talented” nucleus, and which uniforms I think look the slickest.

Part 2: Statistical Analysis of Power Rankings: How the West Has Won Let’s say that someone decided to make their power rankings in the middle of a lecture class they didn’t care about, but did it too quickly and had too much spare time on their hands. That person, hypothetically, would be left no choice except to by hand find the mean score of every division, find each team’s deviation from their divisional mean, find each division’s standard deviation, and z-score every single team based on their divisional mean. And, let’s for kicks, refer to this person as “I.” I then had to figure out what this pile of data I had configured meant to me, and I how I could use this. I then figured it out. All of this data has bearing on playoff projections, and I can use each piece of information to connect the playoffs together, if in fact my views on the best teams in the NFL are correct. I noticed a strange correlation when putting together my divisional means; the divisions I considered to be the best coming into this year, the AFC and NFC Norths, were sixth and third respectively on my list now. How could that be? And how could it be that they were left as third and fourth respectively by ESPN? Let’s start with ESPN. According to ESPN, the best division in football is the NFC East, and the worst is the AFC South. While my data concurs that the AFC South is at least tied with the AFC West for the worst division in the sport, my data spit out the NFC East as second best, and a full 2.5 percentage points below the team ahead of them. Much to my surprise, with a mean score of 9.75, the NFC West had become the best division in the sport. For those who are not grasping this, the division that was easily the worst in the sport at the end of last year now has its average team in the top ten according to me, a full 2.5 points better than the average team in the football factory division of the NFC East. And I am in no way being a wackjob in believing this, as ESPN , the world’s foremost authority on the analysis of football, has the NFC West as the second best division, trailing the NFC East by a measly 1.25 points. How can this have arisen? Is there a way to explain this? I believe I may have found one reason to simply explain it, through the use of divisional standard deviation.

In football, I use standard deviation to explain how close divisional races can be; a smaller value will result in more teams being in the hunt for the division title and vice versa. The NFC West, with a value of 6.90 in my rankings, second smallest among divisions (9.29, third smallest in the ESPN PR), looks to be a close division, which is one thing we already seemed to know. It has always seemed like every team was close to as good as both the team ahead of it and the team below it. Now, while everybody is obviously chasing the San Francisco 49ers (explained in the next paragraph), these teams barely deviate from one another. Can this mean that competition breeds talent? In other words, can simply playing other teams at or around your skill level frequently eventually lead up to all of the teams being good? This is tough to say, but the numbers themselves don’t lie. The toughest division to win according to my deviation and ESPN’s deviation (5.62 and 6.13 respectively) is also considered by most to be the toughest division to win every year by logic: the NFC East. Yes, the division that sent a 9-7 team to the Super Bowl last year and came out hoisting a Lombardi Trophy. Yes, the division that is the only one in football to boast a 2-0 team but no 0-2 team. Yes, the division that historically holds 12 of the Super Bowls won, best of any division. So, in some ways, talented competition can create talented teams. But, does that make the converse true? According to my rankings and ESPN’s, the division with the high standard deviation is the AFC South. Yes, this division features the youngest team in the National Football League, but that is the team that looks to be the best, the only one even sniffing the teens in either set of rankings. But following that is the AFC North, a both traditional and current powerhouse of football. How could this be? Look at each division. In the case of the AFC South, it is a no brainer in the minds of most that the Houston Texans will walk through that division like preschoolers through a puddle. No other team in that division (sadly) looks to have any legitimate chance of making the playoffs. Although outliers are impossibilities in the NFL, the Texans seem to be one in the AFC South. Similarly, the AFC North has a large disparity between good and bad. While the Ravens are number six and the Steelers are number nine in both polls (weird), the Browns and Bengals have average scores of 31.5 and 20.5 respectively. Think about this giant gap and also the implications it has for the NFC West. This is a division that produced three playoff teams last year, one who was a dropped pass and/or a missed field goal away from probably winning the Super Bowl. Yet, if any case, the bottom teams have gotten worse, with the Browns considered by apparently everyone but me to be the worst team in football and the Bengals only able to beat them by one touchdown. In this case, it seems that competition has broken down the talent in a division. Could this mean doom for the case of the NFC West, or am I simply forgetting to mention that standard deviation does NOT measure how good a division is, but rather how CLOSE teams in the division are to each other. So, there is no proof that the AFC North is declining, but rather that its disparity is increasing, much like how the gap is closing on the west coast of the Senior Circuit.

But that isn’t all that can be learned from an examination of Power Ranking statistics. No, I have gone much further into how teams and their playoff possibilities are structured. As I assume most of my readers know, a z-score is how many standard deviations a value is from the average. In essence, to apply that to this situation the z-score is how good or how bad a team’s chances of being the winner of their division are. For example, the team with the best chance of winning their division right now, with a value of -1.49, in the Houston Texans, closely followed by the -1.47 of the New England Patriots. To stick with these two divisions, the next closest team to the Texans has a value of .31 and the next closest AFC East team has a score of .23. This literally means that the Texans are .74 standard deviations better than the next best team in their division and the Patriots are .84 standard deviations better than their bet opponent in division. (Note that all of these values are based off of my rankings and not off of ESPN. I don’t have that much free time to freehand z-score 64 different values.) What does this mean for the division we are examining? The z-scores for every single team are: San Francisco -1.27, Arizona -.25, St. Louis .33, Seattle 1.05. These numbers can be interpreted many different ways, but the simplest inference to be made is that the 49ers are the team to beat. And there is no sense beating this into the ground, they are a good football team that are supremely well coached. I realize now that up to this point I have been stat geeking it up and haven’t given any literal football insight, so I’ll take this time to talk 49ers football, the rest will be discussed in length later. The reason for this team’s success can be seen in three ways: coaching, emotional progress, and badassedness. The coaching is easy; Jim Harbaugh is a massive upgrade from Mike Singletary and Mike Nolan before him. The lift he has given this team has shown in a few too many ways, the first being the attitude they come into every game with; they don’t think they will win, they know they will win. The emotional progress I speak of lies all in the throwing arm of Mr. Alex Smith. He has finally reached a point in his career where he is playing like Vince in Recess: School’s Out. (Yes, I just made that reference.) He has finally stopped listening to what the external influences of coaches and media and plays his game. In other words, he is aiming it not throwing it. Finally, and most importantly, the 49ers are built entirely around badassedness. Their defense is really freaking good at being really freaking intimidating. Their attitudes, built around the play styles of Patrick Willis, the Smith Brothers, and DaShon Goldson, beating the other team down to a pulp and then exploiting their tiredness. Needless to say, if you have the best coach, a confident quarterback, and a violent defense, you should succeed in the National Football League. That is why they are number one right now.

Part Three: Football Calculus: How to Derive and Integrate the NFC West to Predict Future Performance It is very complicated to say that you can use differential calculus to predict performances in the NFL, because I don’t think you can. But, it is the principles of calculus that need to be examined to show why the NFC West has done what it has in the first two weeks of the season. The 49ers have trucked through the Packers and the Lions, the Cardinals have won close games against the superior Patriots and the arguably superior Seahawks, the Rams have played it close against two teams that are obviously more skilled than they are, and the Seahawks lost a close one to the Cards and dominated the Cowboys on both sides of the ball. That should be enough. Analysis shouldn’t be necessary to explain this; they played well in both of the first two weeks and there is no telling whether or not it will continue. I’m going to try and change that no telling into telling, I’m going to derive the NFC West. Basic fundamentals of calculus dictate that the acceleration function is the derivative of the velocity function is the derivative of the position function. Let’s for the rest of this column call the position function either “the now” or “the present.” We will refer to the velocity as “recent performances” or “the past 32 games.” And the acceleration will be “front office performances”, “recent offseasons”, or “draft prowess.” We will start with the niners since they are the easiest to describe. The 49ers are at what can only be assumed to be their maximum, the peak of their now. The present is brighter than any other present, mostly because of a positive sloping last 32 games. The failures under the previous regime under Coach Singletary sent the team spiraling into a minimum on the recent performances graph. The hiring of Coach Harbaugh sent this team in a positive direction (pun), which correlated to the team crossing into the positive axis of perceived team success. (Harbaugh’s hiring is on the front office performances graph. I forgot to make that clear. It sent the past 32 games in a positive slope, which is now commemorated on the now graph. You have caught up.) The only concern that fans should have is that they seem to be having an extended peak caused by a weak draft class this year, AJ Jenkins in the first round, and the necessary coordinator purging that should occur at the end of the year. Enjoy it while it lasts 49ers fans. No one can play this well for too long. Ask any fan of the Patriots about 2007. Now you feel bad. The Cardinals are a tricky team to describe right now. Let’s start at the start of the modern Arizona Cardinals, the retirement of Kurt Warner. Next thing you know, Anquan Boldin is a Raven, Karlos Dansby is a Dolphin and DRC is an Eagle. This team was in a massive front office downswing. But wait. Throw in a Patrick Peterson selection, a true QB controversy, a Michael Floyd selection, a healthy Ryan Williams, and a great fourth quarter football team and you have a team with a massive upswing to end their last 32 games. This positive slope taken by the team continued into this season, but they are obviously not peaking as they still don’t have a great quarterback. This means we have a very flawed football that is coming off of a victory over the poster boy of the NFL. Just wait until their best offensive lineman, Levi Brown, returns from injury. This team will start turning the present into a point so high in the positive axis they will compete for a wild card position. The Rams are a curious team, as their present graph is obviously still below the x axis, but their front office graph is reaching a peak and the last 32 games is increasing as a result. The hire of Jeff Fisher was a great stride for this young team, spiking their recent offseasons into a skyrocket. Last season ended on a negative note, dropping their recent performances graph, but their draft this year spiked the integral futures graph too high due to the stockpiling of RGIII picks they have. Not to mention that this is a team that has invested recent first round picks in Sam Bradford, Chris Long, Robert Quinn, Michael Brockers, and the never should be mentioned Jason Smith. Going what I believe will be 4/5 on 5 first rounders is not a bad thing. Don’t forget the value they can get out of late round picks they took from this year like Isaiah Pead and Janoris Jenkins, not to mention Cortland Finnegan and his immediate impact on this defense. This is a team that is still below the good team threshold, the x-axis, but rapidly increasing towards it. The Seattle Seahawks are the wrench in my plan, the bane of my theory, the Bane to my Batman, and the Bain Capital to my presidential run. Look at their recent first round picks and free agent acquisitions. Bruce Irvin? James Carpenter? Matt Flynn? Tarvaris Jackson? Terrell Owens? This is a team that doesn’t look like they got everything together, but they are playing well enough to be noticed by everyone from me to you. Tell me you hadn’t thought at one point this season “Why are we sleeping on the Seahawks?” The only two explanations are a) this is a half baked theory and football cannot be defined in mathematical principles, or b) Russell Wilson defies logic. I think it is the former, but genuinely hope it is the latter, because he has a trait that I can only describe as “Favrian.” They are definitely, like the Rams, below the threshold, but approaching it quickly. What does all this mean? I have mentioned the integral of the now is that word everyone overuses in football: the future. What does the future hold for these teams? What does the future mean, is it next season or this year’s playoffs? What I think it means is that if you were to integrate the perceived present graph of every team in the NFL, the NFC West would be the only division without a negative graph. And that scares me as an AFC fan, I can’t even fathom the NFC. The only explanation I can give for this long ramble about the curious nature of this experiment is the NFC West has looked good this year and looks like it can keep on looking good. I will track this phenomenon through the entire season and keep you posted with both more statistical (POWER RANKING REGRESSIONS MOFOS!) and belief based reviews of what the NFL season is and is becoming. I am so ashamed that I am going to make this a recurring column, but it is going to be my first. Expect a new Football Calculus every week, but don’t worry, more public interest stuff will come to. I send my regards to all fortunate enough to have the time to read this. Peace out.


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