David Blackwell

David Blackwell was a highly-regarded statistician and mathematician who taught at UC Berkeley for 30 years.  Apparently he was the kind of mathematician who could become interested in a new topic, learn about it, and then quickly produce profound results.   Then he’d move on.  Blackwell died on July 8th:  his obituary in the NYT can be found here.

Among other things, Blackwell was a strong proponent of the Bayesian approach to statistical inference, and he produced results in Game Theory regarding bluffing and dueling.

By patrick honner, ago

On Flyswatters

Designing a flyswatter is an interesting exercise in optimization.

You want it have enough holes so that it can quickly achieve swatting speed, but you don’t want it to have so many holes as to substantially decrease the chance of actually making contact with the pest.

I wonder if there is an industry standard for a flyswatter’s empty-space-to-surface-area ratio.

By patrick honner, ago

Measuring Mortgage Defaults

According to a recent study the default rates for mortgages over one million dollars is nearly twice as high as the default rate for mortgages under one millions dollars (14.3% to 8.3%).  A default on a mortgage essentially means that the home-owner stops making mortgage payments and the bank takes possession of the home.

There are a lot of interesting mathematical, sociological, and perhaps ethical questions here, but I wanted to point out that although the above probabilities are interesting, the number and total value of the mortgages in question are probably more relevant data to consider.

For example, if only 1/10 of all mortgages are over a million dollars, then this statistic might not be that important; on the other hand, if a good number of defaults are way over a million dollars, than this statistic isn’t telling the real story either, but in a different way.

As an aside, renting vs. owning is a general and interesting mathematical question to explore in a variety of different contexts.

By patrick honner, ago

Paul’s Perfect Prognostication

Paul the octopus must be enjoying his 15 minutes of fame for correctly predicting the outcomes of eight World Cup matches in a row.  In fact, a stamp in his honor is currently available at the Shanghai World Expo.  This must be a welcome relief from the death threats that followed his [ultimately accurate] prediction of Spain over Germany.

Assuming that the outcome of every match was equally likely (what if you don’t?), then Paul had a 1/256 chance ( that is, (1/2)^8 ) of nailing all eight predictions.  That’s roughly a .4% chance, on the order of getting dealt a straight in a five-card poker hand, or rolling a six three times in a row on a fair die.  Or, if you prefer, exactly equal to the likelihood of flipping a coin and getting Tails (Arms?) eight times in a row.

Apparently octopi have short lifespans, so it doesn’t look like Paul will be around in 2014 to put his record on the line.  At least he’ll go out on top.

By patrick honner, ago

Visual Representations of World Cup Final Stats

The NYT’s soccer blog (I can start calling it soccer again, right?) has a nice selection of tools to analyze the stats from yesterday’s World Cup Final:

http://goal.blogs.nytimes.com/2010/07/11/world-cup-live-netherlands-vs-spain/

The default is the “Heat Map”, which attempts to show the region of play minute-by-minute.  That’s not nearly as interesting to me as the the “Passes” tab, which appears to detail each possession with an undirected graph, connecting two players with an edge if a pass occured between them (How do we know who passed to whom?  What if two players passed back-and-forth to each other? Why not indicate turnovers in this manner?).    Using a graph like this could certainly help an analyst determine the worth of a player on the field.

There’s also a sidebar that shows various stats from the game.  For example, you can see that the seven players with the highest number of “Touches”, and the top eight in “Passes”, were all Spaniards.  This supports the general description of their style of play (a lot of passing and waiting, I guess).  After looking at those stats for a bit, I couldn’t help but laugh when I pulled up the list for “Goals”.

There’s a lot of statistical analysis here for a game that was tied at zero for two hours.

By patrick honner, ago
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