Beginning Monday, we’ll be talking a lot about a variety of different topics in sabermetrics. But before we can even approach any of the topics I (might) have lined up for this course, we should probably first tackle the means through which we will discuss these topics. Of course, I am talking about the terms I’ll be using to lead discussion. There’s a lot of stuff going on in the saber-world today, and it’s difficult enough to try and remember how well players are doing in certain stats, let alone the abundance of other stats that have shown to be useful in evaluating talent and value. So here I’m offering a sampling of terminology that I will be using in the future, with brief explanations and links to articles/posts by people far more involved in the inner workings of these stats.

Pythagorean Expectation

Source: Wikipedia

One of the most important concepts of sabermetrics is considering everything given its context. Wins and losses often come about in fashions that are not conclusive of a team’s talent. Is winning a one-run game in the ninth really worth the same as a decisive five-run victory? How about a shutout loss and that same one-run game, but from the other side? Win-loss records weight these team performances evenly, but it is possible and likely that these wins and losses are in fact different because of the team talent involved.

Once upon a time, a wise man named Bill James found a formula empirically using a team’s runs score and allowed that correlated well with actual wins; later on, this formula was shown to be statistically sound. The formula is as follows:

Estimated Win% = Runs Scored^2 / (Runs Scored + Runs Allowed)^2

Later on, work done by Clay Davenport of Baseball Propsectus gave way to Pythagenport expectation, which changed the exponent from two (2) to (1.5 log((r + ra)/g) + 0.45). Further work done by David Smyth and Patriot yielded the now commonly used Pythagenpat expectation, which changes the exponent to ((r + ra)/g)^0.287).

Run and Win Expectancy

Source: The Book Wiki (see the charts for data for run expectancy from 1999-2002)

Once we’ve determined that runs can be converted into wins using Pythagorean expectation, we can now go about the process of converting events into runs. How can we do that? Well, it seems that, based on the various base/out states that can occur in an inning, there is a certain run expectancy. This can be measured empirically and is shown in the first chapter of The Book: Playing the Percentages in Baseball, which I recommend for all of you as a must-read(it can be found here, in this actual class syllabus; I am in the process of ordering a copy for myself to dig through).

So, for example, in a bases empty, no out situation, teams are expected to score 0.555 runs per game in a run environment of around five runs per game (the math here is obvious: five runs a game, nine innings a game, that becomes your average expectancy per inning without seeing any advancement of the base/out states). But if you followed that up with a double, your run expectancy would jump to 1.189 runs. You can check the full listing of run expectancies based on base/out state between 1999-2002 here.

A similar methodology can be done with wins, forming win expectancy. It and its related concept Win Probability Added are less interesting for context-neutral analysis, but great for managerial strategy.

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