Ryan's Repository of Random Reflections

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 am going to show why the work I did on  Day Three  is so important, and how using the strategy I outlined in that post can improve your odds of beating the streak by a factor of 5-10!  On day three, I analyzed the situations under which you should select a player who you think will get a hit, as opposed to not selecting that player, and instead maintaining your current streak until the next day.  In summary, I found that your decision should be guided by your current streak, the number of games left in the season, your confidence in the player (how likely is he to get a hit?), and the distribution of likelihoods across all games in the season.  After solving for the optimal strategy, I was able to approximate the probability of winning under that strategy by making some simplifying assumptions about the probability distribution of the best player getting a hit on a given day. I'm not going to get too deep into the math in this blog post, b...