Category Archives: Math

Doctor Obvious Meets Abbie Normal

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Put Away The Bell Curve: Most Of Us Aren’t ‘Average’

For decades, teachers, managers and parents have assumed that the performance of students and employees fits what’s known as the bell curve — in most activities, we expect a few people to be very good, a few people to be very bad and most people to be average.

This isn’t the first time I’ve found that someone is shocked, shocked to find that you have non-normal distributions after you’ve run your sample through some kind of discriminator. Managers don’t tend to hire the unqualified. Students that aren’t college material tend not to go to college, or drop out. If you aren’t good enough to be competitive at a sport you won’t be on the team. Once you have limited your sample in a way that introduces a bias, don’t automatically expect the distribution to be normal.

The Basketball Kama Sutra

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Analytics Reveal 13 New Basketball Positions

For as long as basketball has been played, it’s been played with five positions. Today they are point guard, shooting guard, small forward, power forward and center. A California data geek sees 13 more hidden among them, with the power to help even the Charlotte Bobcats improve their lineup and win more games.

I think it has been long recognized that within any position you can have more of an offensive/defensive prowess, and that there are hybrid positions, regardless of what label you put on them. I’m also not close to being sold on NBA 1st team/2nd team, role-player or one-of-a-kind being a position. (Hey, I’m won the starting job at NBA All-Star on my team!) I think these are ways of categorizing the productivity of players, i.e their roles, rather than defining the position they play. You need a player or players with ball-handling skills, you need ball distribution, you need rebounding, you need scoring ability (interior and perimeter and also free throws), you need defense. How you divvy up those needed skills isn’t fixed, though some pairings might work better than others. This breakdown seems to imply that good players excel at a couple of skills (and the best at even more), or are somewhat less adept at each but possess a wider range of skills, and those pairings/groupings are given.

Now what would be really interesting would be looking at the depth and breadth of coverage of these roles as a function of the teams’ success. The diversity and output of the Mavericks that is shown — does that represent their success as well? Would a cellar-dwellar have the same breadth but simply be at a lower level of achievement, or do they suffer from not having some skill-set combination (e.g. single-skill players, rather than dual-skill), or both?

Mathigami

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Origami exhibit at Cowell College opens April 8 with public talks

A physicist and engineer, Lang is a pioneer of the cross-disciplinary marriage of origami with mathematics. Demaine, a professor of computer science at the Massachusetts Institute of Technology, has done seminal work in the field of computational origami, working with his father, artist and sculptor Martin Demaine, to create abstract origami sculptures representing complex mathematical algorithms.