Now that the NCAA basketball tournament is over and sadly my pick of UK lost (my dad went to UK so don’t think that I just jumped on the bandwagon this year), I started thinking about how I could apply math to the tournament. To celebrate the beginning of March Madness, we played “trashketball” one day in class a review game (little did they know, this effectively helped me get them away from sneakily watching the games on the ESNP app from their phones). However, I am sure there are more complex things we could do for some hands on applications.
There’s so much hype around a perfect bracket, so we could definitely explore the odds of getting a perfect one. Thinking through the odds we can note that each team has 1 of 2 options in the game…winning or losing. There are 64 teams in the tournament and therefore, to create a perfect bracket you would have 2^63, or one in 9.2×10^18 (9.2 quintrillion), chances of getting a perfect one. Of course that’s if you predict like a coin flip…heads or tails…but we know there is a lot more that goes into basketball. Just calculating that is a good exponential application for students and might be a cool way to open the exponents unit that we do around this time of the year, but could we do more?
Students could watch the games and pick out any key vocabulary they see during the games…parabolas, circles/polygons/curves/lines on the court, spheres…but, hmm what else…
Maybe we could look at statistics: Students could pick a player and follow their stats. They could watch for points, assists, rebounds, blocks, field goal %, and steals (I might have to have a coach come in or a kid on the team explain how to track stats like this to some students). Then students could compare what they find to ESPN’s calculations. Or, students could team up and find the stats of an entire team vs. another team. We could do this before the tournament and then using those predictions calculate which team they think would win. Granted a lot of other factors are involved in winning a game, but I think player’s individual stats could be a good start. I’d love to talk to a statistician and get some more ideas…! Maybe students could even write in to ESPN or our local news and give their own feedback on how their player/team did…they’re always looking for more commentators right?!
We could also use regressions with our statistical data: We could take a team’s win-loss history and run a linear regression to graph the data and find trends. We could compare the prediction to what happens in the tournament or even compare the seed rankings to our predictions.
Or maybe we could relate it all to quadratics: I am thinking students could take a picture of a shot attempt that did not go in and analyze the parabola. A few years ago, my dean and I used Logger Pro to analyze a thrown ball. The program will calculate the equation and from there you can find key points along the parabola (this is what I did for the “Saving the World with Math” project here). I bet we could do a similar thing with a video of a shot attempt, or maybe just with a printed out picture, to analyze why the shot did not go in. Students could put their video/picture on a graph, find the equation and certain points on the graph like the vertex and x-intercept. Then, by seeing if the point of the basket is along their parabola, they could calculate why the ball didn’t go in. From there, students could correct the equation for an accurate basket to be made.
Does anyone do anything in their classrooms related to March Madness?
I guess I have a whole year to think about this…in the mean time, go Spurs go!