This week, we plan on explaining what the Fundamental Theorem of Calculus is and what it means, including why it is important, by using a specific example from baseball to illustrate our point.
As the name suggests, the Fundamental Theorem of Calculus is, well, fundamental to calculus and its applications. Naturally then this theorem was discovered and proved before calculus was even invented, by a famous Isaac, but not the one you think.
This week, we chose to get a little philosophical and discuss the construct-measurement gap in statistical data gathering, or surveys, and in particular the creation of sample statistics in baseball.
The famous scholar Alfred Korzybski once asserted that, "the map is not the territory and the name is not the thing named" to encapsulate his world view that a human abstraction or construct derived from a physical object or consequent reaction thereof is not the same thing as the object itself. His assertion comes as a response to his observation that many people confuse models of reality with its actuality. Korzybski’s legacy includes generations of social scientists conjuring up his name when talking about the "gap" between a construct and measurement.
This is post is the finale of our study of probability by examining the popular casino game, roulette. In case you missed either of our first two installments, here is our introduction to probability in roulette and here is our analysis of your expected winnings in playing roulette.
As we have mentioned over the last two posts, gambling strategies are popular in casinos to “skew the odd” in a gambler’s favor. A popular strategy for roulette, that is also widely used in currency trading, is The Martingale. And if you are like us and thought that was also a popular bird, we are afraid that you are actually thinking of that feathery troubadour, the Nightingale.
This post is a continuation of our study of probability by examining the popular casino game, roulette. If you missed it, check it out here.
Although the study on independence, and lack thereof, in roulette spins and bets is fascinating, personally we find the examination on the expected values of the main bets more elegant, and beautiful in their inerrant equivalence.
With the Super Bowl between the Patriots and Falcons coming up on Sunday, the internet is flooded with probabilities of which team will win as well as a myriad of other prop bets. Currently, the Patriots are favored by three points and the predicted score is estimated to be around 28-25.
Nate Silver of the FiveThirtyEight blog, using a pretty intense simulator, has the Patriots at 61% of winning the Super Bowl with the Falcons consequently at 39%. His forecast is based on 100,000 simulations of the season with updates after every game. His model uses Elo ratings, a complicated measure of strength based on head-to-head results and quality of opponents, to calculate a team’s chances of winning their next game.
To check these probabilities, we developed a basic simulator incorporating only the final scores from games played by the Patriots and Falcons during the regular season and playoffs so far.