### The (fat?) tails of true talent – Part 4- Results for non-Gaussian True Talent

In parts 3.1 and 3.2 I discussed approximating true talent distributions with Gaussians, and comparing these to data. In this post I will talk about my attempts to model true talent with non-Gaussian distributions. As a reminder, the probability to make an observation x is the convolution of the noise (or luck) distribution, S(x), with … More The (fat?) tails of true talent – Part 4- Results for non-Gaussian True Talent

### The (fat?) tails of true talent – Part 3.2- Results for Gaussian True Talent (Pitching)

In part 3.1 I showed results for comparing a simulated true talent distribution for OBP and wOBA to the data. Here I’ll do the same for FIP-. I looked at ERA- also, but I’m not sure it adds anything over and above looking at FIP-, and I’m less sure about the statistical distribution of ERA-. … More The (fat?) tails of true talent – Part 3.2- Results for Gaussian True Talent (Pitching)

### The (fat?) tails of true talent – Part 3.1- Results for Gaussian True Talent (Batting)

I described the methods I used to estimate true talent distributions in part 2. In short, I determined the maximum likelihood parameters for true talent, assuming a Gaussian distribution, then generated a simulated sample based on that distribution and compared it to data I looked at 4 different quantities; OBP, wOBA, FIP-, and ERA-. All … More The (fat?) tails of true talent – Part 3.1- Results for Gaussian True Talent (Batting)

### The (fat?) tails of true talent – Part 2- The Method

In part 1 I presented a few equations regarding estimating true talent, and using regression to the mean, in a Bayesian framework. In this post I will describe what I did to estimate the true talent distribution, . Given a true talent distribution , the probability to observe a performance is,

### The (fat?) tails of true talent – Part 1- Preliminaries

I’m interested here in looking at the tails of the true talent distribution. My conjecture is that they are fat, i.e., the probability to have a very good level of true talent is greater than implied by a Gaussian (or Normal) approximation. First, a few preliminaries, The model says that true talent, in OBP, wOBA, … More The (fat?) tails of true talent – Part 1- Preliminaries

### Odds ratio method and grading on a curve

The odds ratio method, applied to a binary outcome (e.g, http://www.insidethebook.com/ee/index.php/site/comments/the_odds_ratio_method/), says that is, the odds are the odds(p) times the odds(q), divided by the odds(a). p here represents, say a batters OBP, q a pitchers OBP-against, and a the league average OBP. Applied to grades, one can think of the material as the pitcher … More Odds ratio method and grading on a curve