For those unfamiliar with Joe Peta’s groundbreaking 2013 book Trading Bases, the author is a successful financial analyst and former Wall Street trader. Seriously injured in a traffic accident, Peta’s long and painful recovery included employing his professional skills to develop a baseball wagering methodology. His book is about more than that though, including observations about the 2008 economic meltdown and sports wagering writ large. Peta’s anecdotes alone make it worth the read — imagine being hit by a NYC ambulance and then being billed by the city for the ride to the hospital.

At its highest level, the Peta methodology is based on the utilization of a team’s previous season performance adjusted for cluster luck (a regression of OBP/SLG/ISO to arrive at “hits per run”) and WAR, as well as upcoming-season projected WAR. Arriving at an estimate of a team’s season win total, it is then used to identify and capitalize on inefficiencies between the model’s estimates and wagering lines.

Peta’s work produces two products: a season-long projection of wins (the long game) and the ability to handicap individual games through adjustments to each team’s lineup, starting pitcher, and home field. While conceptually straightforward, it is time-consuming to operate, requiring familiarity with Excel (particularly the ability to link sheets). In lieu of Peta’s regression calculation of cluster luck, I utilized FanGraphs’ calculation of BaseRuns, convinced of its utility as a proxy after reading a 2019 article at samkonmodels.com arguing it was one of a number of comparable and readily available such calculations. Read the rest of this entry »

While it might not appear so, baseball games constantly portray economic thought, such as in the mathematical model of game theory. There are many ways game theory takes place, but a classic example is the prisoner’s dilemma. Imagine a police officer is interrogating two suspects of robbing a bank together. The police officer has some evidence to put them in jail, but a confession would go a long way. Each suspect is contemplating confessing to the crime. If both suspects keep quiet, they will each receive five years in jail. If one suspect confesses and the other keeps quiet, the one who kept quiet will receive 20 years in jail while the suspect who confessed will receive just one year. If both confess, they each receive 10 years in jail. The logical choice for each suspect is called the dominant strategy. The end result, or the combination of each suspects decision, is called the Nash Equilibrium. By using game theory, we come to the conclusion that each suspect should confess to the crime, meaning they will each get 10 years in prison. I won’t go much into why this is the case, but feel free to research more about game theory and the Nash Equilibrium on your own.

What does this have to with baseball? We can think of each pitch as game theory, with each suspect as the pitcher and batter. Instead of confessing to a crime, the pitcher is contemplating throwing a ball in the strike zone while the batter is contemplating swinging. While the prisoner’s dilemma has a Nash Equilibrium, not only does a pitch to a batter not have a Nash Equilibrium, but the combination of decisions is constantly changing. If the batter’s dominant strategy is to swing, then pitchers will throw more balls outside the batter’s reach. If the pitcher’s dominant strategy is to throw a ball, then the batter will take more pitches.

We could observe this thought process for every pitch thrown. However, let’s look at one type of pitch: 3-0 counts. If you are the batter, it might seem obvious to take the pitch. The worst-case scenario is you end up with a 3-1 count. If you are the pitcher, it might seem obvious to throw an easy strike. You do not want to walk the batter, and you know the batter doesn’t want to swing and risk giving you an easy popup to get out of good count. So I guess the batter should take every pitch and the pitcher should throw the ball right down the middle every time. Read the rest of this entry »

Introduction

For quite some time, wOBA has been used as a well-known, all-around statistic for measuring the output of a hitter. wOBA doesn’t treat the many different ways of getting on base equally. Instead, it gives credit to the hitter for the value of each outcome, whether that be a single, home run, or walk. For more information, FanGraphs goes more in-depth here.

With the emergence of Statcast, xwOBA has been introduced. xwOBA uses launch angle, exit velocity, and sometimes sprint speed of the batter to give an expected value of wOBA on batted balls. xwOBA can tell us at what exit velocity and launch angle the most meaningful outcomes are produced. That is important to know because we can now see if specific teams or players are underperforming, overperforming, or are performing as expected based on these two stats. wOBA and xwOBA are not in perfect correlation for hitters with at least 50 plate appearances in 2019, but they still have a very strong relationship (r = 0.918). As plate appearances increase, the two should eventually level out to be the same. At what amount of plate appearances that occurs at, I don’t know.

What I want to know is what goes into a team’s defense if they are allowing a larger xwOBA than wOBA. That would mean they are taking expected hits for the opposing team and turning them into outs. I got to thinking about this idea while watching the ALCS between the Tampa Bay Rays and the Houston Astros, specifically Game 3, and I have now had time to dive deeper into my initial question. The Rays put together a beautifully played defensive game while their offense seemed to struggle outside of Randy Arozarena.

In Game 3, the Rays pitching staff combined to give up an xwOBA of 0.337, but they only allowed a combined wOBA of 0.300. Their defense saved 0.037 points of wOBA from the Astros to take a commanding 3-0 lead. Read the rest of this entry »

In what feels like interminable scrolling of the internet this offseason waiting for something to finally happen, it occurred to me to ask, does any of this rumor-mongering actually tell us anything? It is certainly strange that we as consumers of baseball, a modified game of tag with hitting and throwing a ball, care so much about the internal machinations of billion-dollar organizations and the personal decision-making calculus of people we will never meet. Regardless of this peculiarity, I myself still spend hours a week wondering if George Springer would be willing to play for a team who doesn’t have a guaranteed home stadium for the foreseeable future and subsequently will be located in a foreign country in Canada.

This interest is what feeds the North American baseball media ecosystem and employs thousands of people, from reporters to web designers, social media managers to news aggregators, and many more. I wouldn’t necessarily argue that this content holds no value if it is biased or inaccurate, because the time we spend consuming this offseason content really just satiates our longing for baseball when we can’t watch our favorite teams live. But the question remains, does this content hold any predictive value, or are we just fooling ourselves?

This article is based on data scraped from MLB Trade Rumors, the leading aggregator of rumors around baseball, on December 9, 2020. I pulled the last 2,000 posts that each team was tagged in and analyzed what information we’re actually getting from reading and discussing the rumors and reports inside the baseball media ecosystem. To begin, we can observe the volume of rumors for teams by seeing how many days one would have to go back to reach a cumulative 2,000 posts. Read the rest of this entry »

As Major League Baseball prepares for 2021, teams are bracing for another season of COVID-19 related financial problems. There will undoubtedly be a smaller-than-usual capacity of fans at ballparks nationwide, and depending on the municipality, there might not be fans at all. Teams are hoping 2021 is not as bad as 2020. According to an analysis by the Tampa Bay Business Journal, the New York Yankees missed over $437 million in expected income. Near the bottom of the list, the Tampa Bay Rays lost only $67 million in expected income.

But the pandemic affected the Rays in additional ways, some of which could impair the ability of the team to stay in Tampa Bay. As the Rays recently appeared in the World Series, it is important to explore how the pandemic could impact the long-term sustainability of baseball in Tampa Bay.

In 2019, the Tampa Bay Rays won 96 games and made the playoffs for the first time in six years. Their series versus the Astros was the Rays’ first postseason under Kevin Cash and their first since Joe Maddon and Andrew Friedman left the organization following the 2014 campaign. After three mediocre seasons, the Rays had increasingly improved under the radar of all but the most dedicated baseball fans. Read the rest of this entry »

A recent post in the Effectively Wild Facebook group sparked my curiosity. A poster named Tim wrote: “Record I’d like to see set that isn’t inconceivable: Player gets 5 HR in a single game.” That record is not inconceivable, because it has been accomplished at least five times in the minor leagues.

In fact, the professional baseball record is eight home runs in a single game, set by catcher Jay Clarke of the Corsicana Oil Cities in a 51-3 win over the Texarkana Casketmakers in a Texas League contest in 1902. The last minor leaguer to hit five homers in a single game was Dick Lane of the Muskegon Clippers in 1948.

But of course the poster was in all likelihood talking about the MLB record of four in a game, which has stood since 1894. But it was a commenter on the post that really piqued my interest. They simply asked: “Would a team really continue pitching to a guy who’s already had 4 HR in a game though?”

It’s a valid question to ask, and it set me down a rabbit hole of seeing just how many players had a plate appearance with four homers already in a game, and how those plate appearances went. Looking back at history isn’t necessarily the best way to predict future behavior, but it is a fun exercise if nothing else, because frankly, before conducting this research I had no idea how many players ever had a crack at a fifth home run. Read the rest of this entry »

Everyone knows that a strong farm system is key to the long-term success of a major league organization. They make it possible for clubs to field competitive teams at affordable salaries and stay beneath the luxury tax threshold, but how much value can an organization truly expect from their farm system? How much more value do the best farm systems generate compared to the worst ones? I decided to take a closer look.

Methodology

The first thing I did was gather the player information and rankings from the Baseball America’s Prospect Handbooks from 2001-14 and entered them into a database. I then found players’ total fWAR produced over the next six seasons, and I added them together to find the values that each farm system produced. I chose six seasons to ensure that teams wouldn’t get credit for a player’s non-team-controlled years, since the value produced would not be guaranteed for the player’s current organization. This method will reduce the total value produced by players that are further away from the majors, but the purpose of this analysis is to focus on the value of the entire farm system and not an individual player’s value over the course of their career.

Let’s look at the 2014 Minnesota Twins as an example. Below is a list of the thirty players that were ranked and the amount of WAR that each player has produced by season. Read the rest of this entry »

This article is a casual version of my paper “Challenging Nostalgia and Performance Metrics in Baseball” published in Chance which showed, among other things, that wins above replacement (WAR) and the wide class of “versus your peers” statistics are incapable of accurately comparing players across eras. In particular, it was shown that WAR exhibits a very strong bias toward baseball players who played in earlier seasons. A collection of resources and an interactive web app within this framework can be viewed here.

How We Came To This Conclusion

In our research, we split baseball data into time periods and show that WAR includes players from the older era in its all-time rankings. Specifically, the older time period is defined by players who started their career in 1950 or before, and the newer group is defined by players who started their career after 1950. The split date of 1950 corresponds to the US Census that is closest to the integration of baseball in 1947. Prior to 1947, Major League Baseball was a largely all-white segregated sports league, but it slowly but surely integrated in America and the has steadily risen in popularity abroad. All the while, the world populations continue to grow as time progresses. Simply put, there are far more people in the baseball-eligible talent pool post-1950 than before.

We find that roughly 20% of the “realistic historic talent pool” belongs to the pre-1950 group. By “realistic historic talent pool” we mean the cumulative population of men ages 20-29 collected every 10 years arising from baseball playing countries (men ages 20-29 serve as a proxy for a concept of talent pool that is otherwise not well-defined). Before 1950, this population is basically just white American men. After 1950, this population includes all American men, as well as men from a plethora of baseball-playing countries. Read the rest of this entry »

There are 24 different “states” in baseball. The three bases can be filled in eight different ways, and there can be 0, 1, or 2 outs at any given moment. Each of these 24 base-out states has an expected run value associated with them. Each value represents the average number of runs that the team is expected to score by the end of the inning. These values change each season depending on the run environment, but they generally don’t vary much.

Consider the following situation: Lorenzo Cain is on first base with two outs. Now consider two possible hitters, one being Christian Yelich and the other being Ryan Braun. According to the 2019 averages, the run expectancy in this base-out state was 0.24, regardless of the hitter. While both players had impressive seasons, Yelich is unquestionably the superior player at this point in time.

As a result of their differences, the run expectancy should be higher when Yelich is at the plate. Consequently, the benefit Milwaukee gets from Cain attempting to steal second base should be adjusted as well. Why is this the case? Given Braun’s inferior power and hitting ability, there is more to gain from Cain putting himself in scoring position, but more importantly, there is less to lose if he were to get caught. On the other hand, Yelich is much more likely to drive the ball. With Yelich at the plate, the increase in run expectancy from a stolen base is slightly smaller than if Braun were hitting. However, the decrease in run expectancy from being caught is significantly greater. This is why we need RE+. Read the rest of this entry »

The 2020 season brought unprecedented rule changes, one of the most puzzling among them being the “extra inning runner.” Ostensibly in an effort to reduce the spread of COVID-19 and speed up play, commissioner Rob Manfred decreed that once a game progresses past the ninth inning, a runner would be placed at second base to begin the frame.

Manfred’s blatantly obvious motives turned baseball fans — a demographic notorious for their acceptance of changes to the national pastime — against it. If there is any defense to be made for the addition of the extraneous runner, it’s that shorter games helped save pitchers’ arms in what’s already been an utterly brutal season for pitcher injuries.

This seismic rule change also created a correspondingly large shift in how teams strategized after a game surpassed nine innings. Teams, even the more sabermetrically inclined among them, began to employ traditional tactics. In order to determine how clubs played with a free runner, I charted every extra inning of the 2020 season. Read the rest of this entry »