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Christopher Long
"Tick, clong, tick, clong, tick, clong, went the night." - Thurber
"Tick, clong, tick, clong, tick, clong, went the night." - Thurber

Christopher's posts

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What's the Value of a Win?
In a previous entry I demonstrated one simple way to estimate an exponent for the Pythagorean win expectation . Another nice consequence of a Pythagorean win expectation formula is that it also makes it simple to estimate the run value of a win in baseball,...

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A Simple Estimate for Pythagorean Exponents
Given the number of runs scored and runs allowed by a baseball team, what's a good estimate for that team's win fraction? Bill James famously came up with what he called the " Pythagorean expectation " \[w = \frac{R^2}{R^2 + A^2},\] which can also be writte...

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Behind the Speadsheet
In the book "The Only Rule Is It Has to Work: Our Wild Experiment Building a New Kind of Baseball Team" , Ben Lindbergh and Sam Miller recount a grand adventure to take command of an independent league baseball team, with the vision of trying every idea, sa...

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When is a Lead Safe in the NBA?
Assuming two NBA teams of equal strength with \(t\) seconds remaining, what is a safe lead at a prescribed confidence level? Bill James has a safe lead formula for NCAA basketball , and the topic has been addressed by other researchers at various levels of ...

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An Enormous Number of Kilograms
For years the kilogram has been defined with respect to a platinum and iridium cylinder, but this is now no longer the case . Here's a puzzle about kilograms that's easy to state and understand, but the answer is very, very surprising. I've always had a fas...

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Solving a Math Puzzle using Physics
The following math problem, which appeared on a Scottish maths paper, has been making the internet rounds . The first two parts require students to interpret the meaning of the components of the formula \(T(x) = 5 \sqrt{36+x^2} + 4(20-x) \), and the final "...

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Mixed Models in R - Bigger, Faster, Stronger
When you start doing more advanced sports analytics you'll eventually starting working with what are known as hierarchical, nested or mixed effects models . These are models that contain both fixed and random effects . There are multiple ways of defining fi...

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Elo's Rating System as a Forgetful Logistic Model
Elo's rating system became famous from its use in chess, but it and variations are now used in sports like the NFL to eSports like League of Legends . It also was infamously used on various "Hot or Not" type websites, as shown in this scene from the movie "...

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Power Rankings: Looking at a Very Simple Method
One of the simplest and most common power ranking models is known as the Bradley-Terry-Luce model , which is equivalent to other famous models such the logistic model and the Elo rating system . I'll be referring to "teams" here, but of course the same idea...

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Getting Started Doing Baseball Analysis without Coding
There's lot of confusion about how best to get started doing baseball analysis. It doesn't have to be difficult! You can start doing it right away, even if you don't know anything about R, Python, Ruby, SQL or machine learning (most GMs can't code). Learnin...
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