Hey everyone, I'm part of the International Baccalaureate (IB) program at my high school, and in order to graduate with our IB diploma we have to pass written papers exploring different subjects. In Calculus, my assignment was to apply mathematics to an area that interests you. So of course I'm going to do mine on APBRmetrics. The topic needs to be advanced enough so that I can bring calculus into it, but I think I can do that through scatter plots and lines of best fit and other descriptive statistics with the data I collect.
I have a few ideas for my paper:
How do players effectiveness in their last year of contract vary to the next season.
How is mathematics used in the NBA to help teams win more game.
I don't have anything I really like yet, so I was hoping for a little help. I'd want to do it on something that could be explained to a person easily as well. Thanks.
Research Ideas for Calculus Paper
Re: Research Ideas for Calculus Paper
If your topic is literally calculus it is hard to think of applications. Probability and statistics have a lot more applications to basketball, as does data analysis in general.
Calculus does come in handy for deriving fundamental statistical properties. There are advanced ones such as least squares regression and maximum likelihood estimators, but deriving them is usually done in mathematical statistics classes, which most students don't take until their senior year of college, if they take such a class at all. A better topic might be cumulative distribution functions, their derivatives i.e. density functions, and application of those concepts to hypothesis testing or to analysis of different random variables.
All of those involve utilizing calculus to learn about statistics, rather than basketball. But I can't think of any direct applications of first-year calculus (or second-year for that matter) to basketball.
Calculus does come in handy for deriving fundamental statistical properties. There are advanced ones such as least squares regression and maximum likelihood estimators, but deriving them is usually done in mathematical statistics classes, which most students don't take until their senior year of college, if they take such a class at all. A better topic might be cumulative distribution functions, their derivatives i.e. density functions, and application of those concepts to hypothesis testing or to analysis of different random variables.
All of those involve utilizing calculus to learn about statistics, rather than basketball. But I can't think of any direct applications of first-year calculus (or second-year for that matter) to basketball.
Re: Research Ideas for Calculus Paper
trying to think of something where calculus is kinda related, you could look at how both the expected fg% and expected value of a shot change as the shot clock goes on for different type of shots/players and then look at how the marginal rate of effectiveness is changing over time. i believe somebody has already done something like that on here, but I doubt your hs paper has to be completely original
Re: Research Ideas for Calculus Paper
Here's an idea: shot clock optimization stuff.
Perhaps you could build on Brian Skinner's work: http://arxiv.org/abs/1107.5793
Or perhaps go to his blog for other ideas: http://gravityandlevity.wordpress.com/t ... analytics/
Perhaps you could build on Brian Skinner's work: http://arxiv.org/abs/1107.5793
Or perhaps go to his blog for other ideas: http://gravityandlevity.wordpress.com/t ... analytics/
Re: Research Ideas for Calculus Paper
Christopher D. Long @octonion
" A great choice for basketball and calculus involves optimal shot angles based on position relative to the basket."
" A great choice for basketball and calculus involves optimal shot angles based on position relative to the basket."