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 »

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 »

Much criticism has been levied onto baseball managers and their inability to see past the archetypal dominant closer who closes pitches in save situations. Writers in the statistical community have observed and critiqued the many flaws which come with the save statistic and how it’s perceived by fans, managers, and baseball decision-makers as far back at least 2008 ^[1]. Accumulating saves is a function of opportunity and degree of difficulty that is certainly not the best way to get at a relief pitcher’s ability to get outs. More objective methods such as ERA and its estimators, like Fielding Independent Pitching (FIP) and Skill-Interactive Earned Run Average (SIERA). are better ways to evaluate a pitcher’s talent, and Win Probability Added (WPA) is better for measuring a pitcher’s importance to winning specific games. This criticism has definitely been heard in the intervening years by people running ball which, can be shown by the number of pitchers who are getting saves on each team and the variance of save totals for a given team.

A team with high variance in their save totals means that there is one player who accumulates a lot of saves and some number who have very few, opposed to lower variance representing a more even distribution of saves among pitchers. This variance metric is heavily negatively correlated (-0.74) with the number of pitchers a team has record a save in a given season. This means the more pitchers recording a save on a team, the more likely the distribution is to be equitable and the insistence on using your best pitcher in only a save situation is lower. Based on this analysis, somewhere between 2008 and 2011 was the peak on the capital “C” Closer in the majors. A rather precipitous drop occurred in 2016 and has continued on a downward trajectory to the point where last year saw the most equitable distribution of saves among teams since 1987, excluding the lockout-shortened 1994 campaign. Read the rest of this entry »

The Louisiana State University Shreveport Pilots are an NAIA team in Shreveport, Louisiana competing in the Red River Athletic Conference. This article was written by Brent Lavallee and David Howell. Brent Lavallee is the Head Coach of the Pilots and David Howell is the Director of Player Development, Director of R&D, and Assistant Pitching Coach.

Introduction

With the rise of affordable bat sensors, we no longer have to rely on only the eye test when it comes to evaluating swings. Gone are the days of attempting to evaluate a hitter’s progress based on the small sample of fall games, or how well they seem to be hitting flips at the end of the season. Even the days of measuring exit velocity during tee work with a radar gun are comparatively basic with what can be accomplished with a sub-$200 Bluetooth sensor.

At LSU Shreveport, we started using Blast Motion sensors this fall, which are placed on the knob of a bat and measure metrics such as bat speed, attack angle, rotational acceleration, and more. The sensors work by taking into account the characteristics of a bat (length, weight, etc.) and derive swing metrics when hitters make contact. Read the rest of this entry »

With the 2019 season firmly in the books and the expanded offering of spin-related pitching data now readily available across the internet, I decided it was time to take a hard look at every team’s pitching staff. The hope in doing so was to identify a trend, if any, within the spin metrics of the best clubs. Do any staffs have a noticeable tendency to use pitchers with a specific spin profile?

To answer this, I pulled together every pitcher and their average spin metrics for each pitch type that they threw a qualified amount of times (30-plus in most cases) in 2019. This meant ignoring splitters because of sample size considerations. I was also tempted to use Bauer Units — a proxy for spin rate divided by velocity, as well as a nod to Trevor Bauer — to control for velocity in this study, but I decided to keep this post more straightforward. The study instead uses raw spin rate, horizontal and vertical movement, and spin efficiency as reported by Baseball Savant. I then aggregated the players’ data by the team they finished the season with to create an average spin profile for every team. This team profile weighs all of their qualified pitchers equally.

Once I was able to establish what the normal team looks like across those categories, I wanted to identify any clear outliers to possibly show where organizations consciously emphasized certain metrics. To do that, I produced league rankings and standard deviations for each category based on the team averages. Read the rest of this entry »

It’s the bottom of the sixth inning at Minute Maid Park. Down 3-2 in the series and facing elimination, the Yankees are trailing the Astros, 4-2, in Game 6 of the 2019 American League Championship Series. Facing Yordan Alvarez with two out and nobody on, Tommy Kahnle needs to keep the game within reach to give his offense a shot at coming back. After falling behind 2-0 to Alvarez, Kahnle comes back and gets a strike looking on a changeup up in the zone. On 2-1, Kahnle throws a changeup below the zone and gets Alvarez to swing through it for strike two.

After getting a swinging strike and with the count now at 2-2, what does Kahnle do to try to get Alvarez out? Does he attempt to repeat the previous pitch after successfully inducing a swinging strike, or does he throw a different pitch in anticipation that Alvarez is expecting the same pitch? Kahnle repeated the changeup below the zone and got Alvarez swinging on strikes to keep the Yankees within two runs.

Pitch sequences like these are very intriguing because of the variety of factors that affect the at-bat, such as the pitcher and hitter’s game plans, game situations, and recent performance. It is a big reason organizations carefully study pitch sequencing. I wanted to quantify and analyze the effectiveness of situations like Kahnle’s against Alvarez. That is, I wanted to determine the most effective two-strike strategy for the pitcher after the batter swung and missed on the previous pitch. Organizations can then share these findings with their pitchers so that they have better success as a staff. Read the rest of this entry »

The NLCS had a weird feel to it from the get go. The Nationals’ pitching was stupendous, balls hit off the bat that sounded like towering home runs were dying on the warning track, and of course, the Cardinals bats never woke up. This was a bit unexpected considering the club’s monster first inning in Atlanta during game 5 of the NLDS. We were all waiting for the Cardinals offense to appear, but it never showed up, as they only scored six runs in a four-game sweep by the Nationals.

Nobody could seem to get anything going offensively. Instead of searching for answers for all the Cardinal batters, let’s just look at one. While Paul Goldschmidt had his worst season offensively with a .346 wOBA, he is still the thunder in the St. Louis lineup. How exactly did the Nationals pitch to Goldschmidt, and why couldn’t he succeed in the series?

On one hand, the Nationals pitchers were outstanding. They were putting pitches right on the edge of the plate and mixing their pitch selection well. When you have Max Scherzer, Stephen Strasburg, and Patrick Corbin in your starting rotation, your opponent is going to have a difficult time. Additionally, Anibal Sanchez had a great game. Meanwhile, Goldschmidt went 1-for-16 with nine strikeouts in the series. He did seem to experience a little bit of bad luck with a few hard hit balls. In Game 4, he hit a ball 101.4 mph that went 340 feet, and he had another two hard-hit outs in Game 2. One traveled 316 feet that was hit 95.9 mph off the bat, and another traveled 284 feet that was hit 108.1 mph. That may not make him feel tons better about his performance given the nine strikeouts.

It is not surprising that Anibal Sanchez was able to succeed in his three times facing Goldschmidt in Game 1. Sanchez used the cutter and sinker well in that game. While his sinker generated an unimpressive .387 wOBA this year, his cutter was lethal with a .260 wOBA. Goldschmidt had a .350 wOBA against sinkers and a .317 wOBA against cutters. Those numbers are going to add to some underwhelming results. Sanchez utilized the sinker and cutter well and put them in difficult locations against Goldschmidt. During the second at-bat, Sanchez generated similar results. Read the rest of this entry »

Each play in the playoffs holds extra weight compared to the regular season. An error can change a game, and a loss can doom a series. In close games and series, it is often the team that executes the small plays that comes out on top.

A particular play in Game 2 of the NLDS between Washington and Los Angeles stood out in this context: Asdrúbal Cabrera singled to right field, driving in Ryan Zimmerman. However, the throw from the outfield held up Kurt Suzuki at third base, and Cabrera was thrown out trying to advance to second base on the throw. Although the Nationals still won the game, the baserunning error was not inconsequential in the series.

Evaluating the Result with WE and RE24

Two statistics – Win Expectancy and RE24 – can be used to show why trying to advance was a bad decision.

Win expectancy (WE) is the probability a team will win given the specific circumstances. Greg Stoll’s Win Expectancy Calculator [1] shows how potential baserunning outcomes by Cabrera change Washington’s win expectancy in Table 1 below.

The Nationals’ win expectancy before Cabrera’s single was 82.7%. The highest WE is 93.4% and results when Cabrera gets to second base, however, staying at first only decreases Washington’s win expectancy by 0.9%. In comparison, getting thrown out decreases their chances by 6.7% compared to staying at first. A 0.9% increase in WE is probably not worth risking 6.7%, especially in a playoff game where you have the lead. Read the rest of this entry »

If you’ve ever looked at Mike Trout’s Baseball Reference page, you’ve seen a lot of black ink, indicative of leading the league in some offensive category. Trout is currently leading the league in a lot of such categories — and he has done so in the past. He’s likely to lead the AL in homers for the first time this year, and as noted recently by Ben Lindbergh, that would be the 10th category out of 17 basic ones at Baseball Reference that he’s led the league in at least once in his career. Only about two dozen players have led the league in more of these 17 categories at some point in their careers.

Trout is also leading the league in another category that would also be a first for him: hit by pitch (HBP). He’s been plunked 15 times this season (editor’s note: now 16), one more than Shin-Soo Choo as of this writing. HBP is not what you would call a sexy stat, but it does have value. It’s as valuable as a walk — in fact, per FG’s linear weights, a little more so, apparently because it occurs slightly more in base-out states that have higher run expectancy (RE) than average.

HBP, like walks, are valuable because they put a runner on base, where he has a chance to score, while simultaneously avoiding an out, thus giving another batter a chance. They’re a good thing. But they also come with a risk. If a batter is hit by a pitch, he could suffer a significant injury and miss time. The resulting lost time is lost value. This raises an obvious question: is the increased value gained by getting hit by pitches greater than the potential risk of losing value to injury? If it is — and one would assume that in this stat-savvy age, it would have to be — by how much? Read the rest of this entry »

While there have been similar articles about the advantages of pulling the ball in the past, I wanted to do some new research based on the changed ball as well as player development.

Recently, there has been a lot of discussion among hitting coaches about pulling the ball. Traditionally, batting coaches usually suggested going gap-to-gap, which means basically hitting where the ball is pitched and mostly trying to stay in the middle of the field between the middle infielders. However, recently this has changed and more and more sabermetrically leaning coaches suggest focusing on pulling the ball because they think that this will create more power.

Let’s look at some pros and cons of pulling the ball using 2019 data, starting with the cons. Read the rest of this entry »