Ryan's Repository of Random Reflections

The JAX documentation says : einsum is a powerful and generic API for computing various reductions, inner products, outer products, axis reorderings, and combinations thereof across one or more input arrays. In this blog post, we are going to explore the einsum API and utilize it solve marginal inference-type problems.  Basic Examples Suppose we have two $ n \times n $ arrays $A$ and $B$ and we want to compute $$ Y[i, k] = \sum_{j=1}^n A[i, j] B[j, k] $$ This is the basic definition of matrix multiplication, and we can compute it in JAX via jnp.einsum('ij,jk->ik', A, B).  Here the formula 'ij,jk->ik' defines the computation.  Each letter corresponds to a name for an axis of an array.  In this case we have only 2D arrays so each part of the formula contains two axes.  The letters on the RHS of the expression determine which axes will be defined for the output.  Any axes names not appearing in the RHS of the expression will be "marginalized out" via th...

My current best pick selection model for BTS achieves roughly 78% accuracy.  Looking at the table from Day Six , we can see that with an optimal pick selection strategy, my odds of beating the streak are roughly 11,800 to 1, or roughly a 0.01% chance of winning.  In this blog post, I will explore methods for boosting this probability by coordinating picks across multiple accounts (e.g., friends, family, other BTS enthusiasts, etc.) To the non-mathematically inclined, one might think that with $k$ accounts our probability of beating the streak as a group would simply multiply by $k$.  This simple formula is not correct, however, although it is an upper bound.  If each account has a probability $p$ of beating the streak, and there are $k$ accounts, the probability that at least one account beats the streak would be $1 - (1 - p)^k$ if we (incorrectly)  assume independence between accounts .  For small $p$ and small $k$, this is pretty close to to the upper bou...

I recently have been seeing many advertisements for sports betting platforms like DraftKings and Fanduel, and since those are somewhat related to beat the streak, I thought it would be interesting to look into these things a little more. In my search I came across a website that lists Vegas odds for various sports books on various bets.  Among those bets is one highly related to beat the streak: a bet that a given batter will "record a hit" in a given game.  This is exactly the essence of the beat the streak: identifying a batter most likely to record a hit.  In my effort to develop models for BTS, I have several approaches to estimate the probability that a player will record a hit in a given game.   So three natural questions arise: 1. Is Vegas good at BTS?  That is, is the implied probability of a hit given the Vegas odds a better estimate of the true probability than some of the models I've talked about in this blog? 2. Can the Vegas odds be a useful f...

In this blog post, I will talk about a back-testing framework I developed to evaluate the quality of different Beat the Streak pick selection strategies on historical data, including the data sources I use, the evaluation metrics I look at, and some of the baseline models I've considered.  The source code for my back-testing framework is available at  https://github.com/ryan112358/beat-the-streak .  Everything is written in python, and the source code heavily relies on the pandas package for data processing. Data Sources I draw on data from multiple sources, most importantly is statcast data, which I obtain using  pybaseball .  This dataset contains information about every pitch, including the outcome (ball/strike/hit/etc) as well as other characteristics that have expanded over time (pitch type, velocity, spin, etc.).  From this pitch-level data, I derive at-bat level data and (batter, game)-level data.  This data includes many context features that c...