Categories
Statistics

The NFL Draft: Shopping for Bargains!

Last week, the NFL player draft took place over 3 days in New York City, and now the annual exercise of “grading” each team based on their draft haul commences.  It’s a fun debate, with grades often based more on feel or perceived value, rather than any real analysis.

There are many ways to evaluate draft results, but from a purely mathematical standpoint, I like to look at value.  Which teams  got the best “bargains”, and which teams went out on a limb?  If you had the 20th pick in the draft, did you get the 20th best player?  Or did you draft a lower-ranked player.

I took all of this year’s 254 players drafted in the NFL draft, and compared them to their draft ranking, according to CBS Sports.  The only real reason I have for using CBS as opposed to the many other draft rankings out there, is that it was easy to pull their data out into a spreadsheet.  From there, I computed the “value” of each pick.  If a team drafted a player above his rank, this is negative value.  If a team drafted a player after his rank, this is a positive value.  Some examples:

Geno Smith was drafted with the 39th pick, but was ranked 21st by CBS Sports, so his value was +18

Meanwhile, E.J. Manuel was drafted with the 16th pick, but was ranked 40th, for a value of -24.  

Some players represented great values for the teams which picked them:

Cornelius Washington, Chicago Bears (pick 188, ranked 82, +106)

Andre Ellington, Arizona Cardinals (187, 88, +99)

Jordan Poyer, Philadelphia Eagles (218, 119, +99)

While other players could be considered “reaches”:

B.J. Daniels, SF 49ers (pick 237, ranked 818, -581)

Jon Meeks, Buffalo Bills (143, 834, -691)

Ryan Seymour, Seattle Seahawks (220, “1000”, -780).  Ryan is the only drafted player who did not appear in CBS’s top 1000, so I just assigned him #1000.

There is a bit of un-fairness here, as many teams will use later picks on “projects”, players who have little expectation of making the team, but who seem to have a particular upside, so there was much volatility in the later round values.

From there, I simply added up the value scores for the players drafted by each team, and found an overall value score.  So, which teams earn the best grades?  Only 3 teams earned overall positive scores.  This is understandable, as it is much easier to earn negative scores than positives, especially in the later rounds.

THE TOP 3:

Minnesota Vikings (+187)

Chicago Bears (+51)

Philadelphia Eagles (+25)

THE BOTTOM 3:

Buffalo Bills (-836)

SF 49ers (-1097)

Seattle Seahawks (-1571)

For math class, have your students think of other ways to measure draft success.  Is the value measure here valid?  How can the method be adjusted?  How do some of the huge negative numbers in this data influence results?  Feel free to download and toy around with the data in my draft value tracker, and let me know what you come up with!

Categories
Statistics

Monopoly Math

The big Monopoly battle is coming near its end, and the iron and racecar are battling for Monopoly supremacy.

Monopoly Board

Both players own properties on the next block, and have some spaces they’d like to avoid.  For the car, here are the spaces he’d like to avoid.

Car Spots

And for the iron, there are a few spaces to avoid.

Monopoly - Iron 1

Since there some houses and hotels on some of the spaces, they are worth different amounts.  Below, here is how much each player will have to pay if they land on the “bad” spaces.

Car Board B

Monopoly - Iron 2

So, here’s the question:  which player is in “worse” shape?  Which player should be more worried about their upcoming turn?

Let this stew with your classes, and would enjoy hearing some class reflections.  The big reveal will come in a few days.

Categories
Algebra

Linear Programming with Friends

An early morning post from Nik_D from the UK led to sharing class activities for linear programming, and provided a great example for me to share with colleagues on the value of twitter:

The activity on Fawn’s blog invites students to build Lego furniture and find the combination which will maximize profit.  I love the idea of handing students baggies with the “supplies” and having students build the chairs and tables.  But, without having Legos around, both Nik and I sought a way to approach these linear programming problems with a different hands-on approach.  In previous years, I had used sticky dots to help students visualize constraints and a fesible region.  Nik posted about his experiences last week, and now I am happy to share the U.S. point of view

Here, I worked with a freshman-year teacher who was eager to try something different to open linear programming.  As students wandered into class, they were given the initial problem.  The Powerpoint slides are available for you to use.

LP1

The class worked in teams to consider the problem.  Many start off by making data tables of the possibilities.

Student work 1

As the teacher and I circulated the room, we found that eventually, students consider algebraic models.

Student work 2

There was agreement on solution: 2 chairs and 2 tables are ideal.  The teacher asked students to share their ideas, which were written on the board, and led to new vocabulary: constraints, profit function.  We’re now ready to tackle our next challenge:

LP2

Many groans were heard, as students understood that “guess and check” would no longer be a great idea.  Note that the chair design also changes, which a student cleverly noted was from the “Game of Thrones” collection.

First, the class agreed on the constraints:

Then, for this part of the activity, the class is split into two groups, one for each constraint, which both the lead teacher and I worked with to explain the guidelines.  A spreadsheet with 50 identical “strategically selected” points were given to both groups, along with a pack of stickers.  The group task: test each of the points for their given constraint, and place a sticker on the wall if it satisfies the constraint.  The “small block constraint” group was given blue dots, while the “large block constraint” group had red dots.  After a few moments of organizational chaos, leaders emerged, and points were distributed nicely to the team.  Soon, dots made their way to the board.

Dots1

After both groups were satisfied with their work, the teacher (Joe, below) discussed the dot patterns.  Where do the dots share space?  Where are there only reds, blues?  What parts of their graph are most important for this problem?  Then, I grabbed Nik_D’s idea by turning on the Desmos calculator and super-imposing  the inequalities onto the graph.  There was some prep work needed here, as Joe and I made sure the grid paper was placed nicely on his SMART board.  Also, please note that I seem to suck at taking clear pictures….it’s a probem.

Joe G.

One thing we would do differently here is letting students see the inequalities.  We hid them, so as to maximize screen space.  This would allow the teacher to turn the inequalities on or off, and emphasize where the colored dots reside.

The class discussion continued with an argument of how to identify the “maximizing” point, and the corner-point principle.

One last thought here.  The power of Desmos is evident for linear programming problems.  The teachers I work with agree that having students graph these sorts of problems by hand is not only time-consuming, it is silly.  By letting students experience the Desmos calculator, not only can we have real discussions of problems, we can tackle problems which may not be so graph-friendly.

Thanks to Nik D. and Fawn for the sharing!