football trigonometryPosted by Curt Gebhard on 9/17/2015 11:00:00 AM
The NFL Winning Cycle
by Adrian Nelson III 16 September 2015, 11:50 AMAdrian Nelson - The Sports Quotient
A look at how NFL team success compares to the business cycle.
There are a few basic concepts that everyone who takes Econ 101 generally walks away with, and these concepts can be applied nearly everywhere — even sports! One is the business cycle. In the most basic sense the business cycle is characterized by the old adage of “what goes up must come down.”
The economy goes through periods of growth and decline, and NFL teams are really no different. The NFL has long been called a league of parity. Success is easier to replicate than in a sport like baseball and teams go from worst to first and first to worst seemingly every year.
The rules and structures in place in the league create the conditions for the league to function as it does. Great teams are composed of great players and great players demand high salaries. The salary cap, along with the lack of max contracts, makes it so that when teams are chock full of a lot of amazing players, it will be tough to re-sign them all. They will have to let some go, and in doing so, the team will most likely get worse.
We have already started to see this devaluation with the Seattle Seahawks. After giving hefty extensions to the likes of Richard Sherman, Russell Wilson, and Earl Thomas, the team was forced to let Byron Maxwell walk to Philadelphia and are currently struggling to meet the demands of Kam Chancellor.
In the MLB, the lack of a salary cap allows the teams that have money to spend it. If a championship team wants to retain its pieces, it can. The NBA is somewhere between the NFL and the MLB. The NBA has a cap, but with Bird Rights, teams frequently are allowed to exceed to maintain their own players, although it does come with a hefty tax.
In the NFL, there is no such system. The NBA also has max contracts, which artificially keep the prices of stars down, and make it easier for teams to build squads composed of several superstar level players, like the Miami Heat did just a few years back.
The NFL draft also serves as a way to equalize teams around the league. The worse you are, the better your pick is and the more likely it is that the rookies you draft will be successful in the pros. While this is true of all of the “Big Four,” the salary cap makes the impact of these cheap rookies all the more powerful and valuable.
All the economic checks and balances are there for NFL teams to function just like the economy, and so I wanted to take a look at the results.
For each NFL team, I looked at the last 35 years in their history. I didn’t want to go too far back, hence the 30-year time frame, and I looked at the average of sets of four years to make the data a bit smoother. So, for example, the first data point for the Cardinals averaged their records for 2011-2014, the next data point averaged 2010-2013, and so on.
With this methodology I culled about 30 data points for each NFL team. I then fit the sine curve that was closest to the data. This allowed for me to compare certain attributes, specifically the period of each curve.
For those of you who don’t remember your high school trigonometry (I know, first I’m throwing economics at you, and then trig), the period of the function is how long it takes for a full cycle to complete. So lower periods mean that over the last 30 years a team has displayed a pattern of cycling quickly between success and failure, like the Bengals.
Longer periods mean that a team seems to be going through cycles slowly. It could mean that you’ve been on top for a long time, like the Pittsburgh Steelers …
… or they could have been bad for a long time, like the Redskins.
The graphs for all of your favorite NFL teams are actually pretty cool, and can be found at the bottom of this article, but don’t scroll down just yet.
Overall, the analysis showed which franchises have been the most stable over the past few decades and which have been on a more consistent trajectory (whether good or bad).
Team Period (yrs) Team Period Team Period Team Period Atlanta Falcons 6.8 Arizona Cardinals 13.4 New Orleans Saints 20.7 Tampa Bay Buccaneers 31.7 Cincinnati Bengals 8.4 San Diego Chargers 13.9 Chicago Bears 22.3 Indianapolis Colts 33.8 Baltimore Ravens 9.0 St. Louis Rams 15.7 New York Jets 23.4 Minnesota Vikings 36.1 Jacksonville Jaguars 9.0 Denver Broncos 15.9 Detroit Lions 24.2 Cleveland Browns 43.6 Tennessee Titans 9.0 Seattle Seahawks 15.9 Kansas City Chiefs 25.1 Oakland Raiders 43.6 Carolina Panthers 11.1 Green Bay Packers 16.8 Buffalo Bills 26.4 Pittsburgh Steelers 45.5 Philadelphia Eagles 13.0 Houston Texans 16.9 San Francisco 49ers 28.3 Washington Redskins 51.5 Dallas Cowboys 13.0 New York Giants 19.6 New England Patriots 31.3 Miami Dolphins 61.6
The analysis also showed that the median cycle length for an NFL team is 20.2 seasons. So if your team has been bad for about the last ten years or so, look for the corner to be turned really soon.
Graphs for each NFL team can be found below.
Green Bay Packers
Kansas City Chiefs
New England Patriots
New Orleans Saints
New York Giants
New York Jets
San Diego Chargers
San Francisco 49ers
St. Louis Rams
Tampa Bay Buccaneers
sine termPosted by Curt Gebhard on 1/26/2015 8:00:00 AMhttp://indianexpress.com/article/opinion/columns/for-the-record-in-the-word-sine-we-see-the-interconnection-of-three-mathematical-traditions-indian-arabic-and-european-says-amartya-sen/2/
Astronomy uses trigonometry -- yes, trig is a thingPosted by Curt Gebhard on 12/10/2014 9:30:00 AM
How Do We Measure Distance in the Universe?
When am I ever going to use trigonometry? Farming and hot air ballooning.Posted by Curt Gebhard on 10/26/2014http://www.telegraph.co.uk/earth/agriculture/farming/11166208/Pig-farmer-wins-payout-after-trigonometry-proves-hot-air-balloon-caused-fatal-stampede.htmlThe 40,000 pound question: How high is this balloon?
Interactive Trig websitePosted by Curt Gebhard on 10/13/2014This site has interactive demonstrations.angle - coterminal = 360 degrees reference angle of of 145° is 35°and the graphing app:
Unit Circle Hand TrickPosted by Curt Gebhard on 9/21/2014Trigonometry BlogHere's a neat trick for remembering the (x, y) coordinates of the unit circle using just your hands.