Archive for the ‘Math of Sports and Games’ Category

First week of school

One week (a partial week) is in the books, and this school year looks to be an interesting one.   I introduced SBG to my Calculus class.  We haven’t yet taken a standards assessment (it will be next Tuesday), so they haven’t made any real judgments on the system.  They seem skeptical, but we’ll see how things go.   I’m not used to giving assessments as often as it will be needed with SBG, so it will be different for me as well.

The Math of Sports and Games class has been pretty fun so far.  On the first day of class, I presented them the classic Monty Hall problem. I asked them what they would do, and I then showed them this video clip from the movie 21 (by the way, that’s the best website for math video clips anywhere, so check it).

They were skeptical even after watching it.  The guy sounded smart, but they weren’t sure what to make of it.  I made no comments on anything at this point in time.

At this point, I WANTED to have the kids use their iPads to perform a simulation of the Monty Hall question (I like to program).  However, they decided not to give iPads to the iPad-centered class, so we couldn’t do it.  Instead, I gave them 3 post-its and a little piece of paper and had them simulate it in a “hands-on” method with another classmate.

They recorded their answers and we pooled the results to discuss.

It went pretty well, but the fact that a fellow classmate was choosing where to put it gave us some skewed results (since it wasn’t truly random).

Lebron James vs. Michael Jordan


Who is the better NBA player?


Students discuss in their groups how/if we can determine this with math.   Their goal for this discussion with their groupmates is to create a plan on how to determine which athlete is the better athlete.  I’ll have them record their plan and we’ll come back together and share ideas.

Questions that I hope will come up:

How do we define “better”?  How do we quantify a player’s value?   How do we compare players from different eras/different skillsets?

The key question that will help us determine which is the better athlete is “How do we quantify a player’s value”.

I think it would be a good idea to get the students to come up with their own way (using common stats) of ranking players.

Not all students will know the ins-and-outs of basketball.  I may need to do a primer (read…. “go to gym and play some basketball”) on the different statistics available.

There’s a few useful things I’ve found out there.  Chapter 29 of an excellent book entitled Mathletics by Wayne Winston has a nice discussion on the NBA efficiency rating (points per game + rebounds per game + assists per game + steals per game – turnovers – missed FG per game – missed FT per game) as compared to a much more complicated player efficiency rating abbreviated PER (see the wikipedia page).  They state that the correlation between the NBA’s efficiency rating and PER is at 0.99.  Moral of the story, complicated does not always equal better.

We might decide as a group to come up with our own efficiency rating.  I’ve got a few ideas of what this could look like, but I don’t want to be a “provider of information”.

I liked what Mr. H over at Mathing did in a Tyson Chandler versus Steve Novak argument, and I think it could fit into this discussion quite easily.

When all is said and done and we use an efficiency rating of sorts to compare the two players, I want them to discuss (and this may be difficult without them knowing the sport very well) what the problem(s) are with using an efficiency rating like this to compare two players.   Wayne Winston does a good job of this in Mathletics.

Another good reference for what I’ll call “extended NBA statistics” is 82games.

I see this project hitting on the following math topics:
z-scores, standard deviation, correlation, evaluating expressions

Most importantly, it will hopefully develop problem solving skills in the students.

I thought about having them go through this Lebron vs MJ argument, and then assigning them to pick their own two athletes to compare of any sport (perhaps I could exclude the NBA since that would be too easy after the MJ vs LJ argument).  They then would have to create their own SportsCenter segment similar to my intro piece comparing the two athletes.

Any thoughts on how to improve upon this very rough outline of a project?

Math of Sports and Games description

Since I’ll be referencing it a lot in some of these blog posts, I wanted to share what my Math of Sports and Games course actually is.

Here’s the course description that I wrote for our program of studies:

Mathematics of Sports and Games
Prerequisite: Pass Algebra, Functions, and Data Analysis OR Algebra 2
Standards of Learning Addressed: Various standards will be addressed found in the following courses:

Credit: 1 elective credit
(actually, we were able to modify this to provide an actual math credit to students)

Course Description:
This course will investigate the mathematics behind sports and games. Our investigations will apply the principles of functions, probability, statistics, geometry, and equations to sports and games. This course is designed to strengthen a student’s mathematics skills while looking at practical applications of mathematics as it applies to sports and games.

This next year, I will be teaching the course as part of a pilot program.  We have chosen a group of about 20 students that show academic promise, but perhaps do not believe in themselves.   Kids that need a push.  As part of this program, each kid will be given an ipad for the year, so I’m hoping to be able to come up with some ideas to use those (once they come in, and I can start playing with it).

I wrote up a short blurb to give the kids (or probably their parents) an idea of what’s going on in this course.  It reads as follows:

Is there really such thing as home field advantage?  Can we predict the performance of players?   What strategies should we employ that would give our team the highest possibility of success?  What strategies should we use that would give us the best possibility of success in a particular game?

In math of sports and games, students will examine question such as these and the mathematical relationships that exist within the realm of sports and games.  Students will develop problem solving skills while working collaboratively with peers.  This course will help students develop the critical thinking skills (as well as mathematical content knowledge) necessary to be successful in their future endeavours in further education.

I don’t really know what all will happen in this course.  I know that it will be project driven.  The math content will come as the projects dictate.  I won’t be presenting math content as much as providing math content as they realize the need for it.  I could easily turn this course into a very statistic heavy one, but I’d like it to be more of a balance of statistics with their other mathematics knowledge.

I’ll share some of my project ideas as time goes on.