Author: RTNM

Analyzing Max Exit Velocity (2020)

In baseball analytics, exit velocity—specifically, the maximum exit velocity—is a critical metric. It measures the speed at which a ball leaves the bat, providing insights into a player’s power and potential impact. I am looking at max exit velocity data from the 2020 season. This visualization offers a clear and detailed view of how max exit velocities are distributed among players and a smoothed density estimate to reveal underlying trends. My first observation is amazement at how hard these balls are being hit. It is truly astonishing.

Forget batting average; this metric is more diagnostic than many others that are typically (especially historically) referenced. If you are putting a team together, you want players who hit the ball hard. And yes, the harder the better. This line of reasoning is all about a player’s ceiling; it has nothing to do with the dribbling groundballs that find a spot between defenders. Such “seeing eye” base hits are of little predictive value.

In 2020, exit velocity data’s importance escalated as teams began using it for more refined scouting and player development decisions. This season saw an exceptionally high interest in advanced metrics, partly because of the pandemic-shortened season. This led teams and analysts to seek more data-driven insights into player performance.

I used a histogram with an overlayed density curve to visualize max exit velocity data. Here’s what each part of this plot conveys:

• Histogram: The histogram separates the exit velocity data into intervals (bins) and shows how many players achieved max exit velocities within each range. Each bar represents a specific range of velocities and provides a quick overview of where most data points (player exit velocities) lie.
• Density Curve: The smoothed density curve overlaid on the histogram estimates the data’s distribution, offering insights into how the data might spread beyond discrete bins. This curve helps us visualize peaks and concentration points without the rigidity of bin divisions.

Key Insights from the 2020 Max Exit Velocity Data

1. Concentration Around the Mean: The density curve reveals a central concentration of exit velocities in the range of approximately 105-111 mph. This concentration suggests that most players in the 2020 season achieved max exit velocities within this range, indicating a consistent performance level among players regarding hitting power.
2. Distribution Shape: The distribution is symmetric, slightly skewed towards higher velocities. This symmetry is typical in sports metrics, where most players fall near the average performance level while a few outliers achieve exceptional numbers.
3. High-End Outliers: The density curve and histogram both suggest that a few players in 2020 achieved exceptionally high max exit velocities, reaching up to 118 mph. These outliers represent some of the league’s top power hitters, whose performances exceed the average exit velocities and pose a significant offensive threat to opposing teams. And in case you were wondering, Pete Alonzo of the New York Mets hit a ball at 118.4 mph to lead the league. If facing such a batter, I would point to first base and take my chances with the next guy. If first were occupied, I certainly wouldn’t put anything over the plate. I wouldn’t even see the line drive coming back at me.

Why This Visualization Matters

A histogram with a density curve provides a quantitative view of max exit velocity data. This visualization helps scouts, coaches, and analysts quickly assess the distribution of max exit velocities across players. The density curve also offers a smooth, continuous view of the data, making it easier to observe trends and concentrations without the constraints of bin width.

Closing Thoughts

This histogram with a density overlay captures a snapshot of the league’s hitting power, revealing the typical max exit velocities and highlighting exceptional outliers.

This exemplifies how data analytics can deepen our understanding of baseball. By looking beyond averages and focusing on distribution, we gain a richer perspective on the league’s players. Whether you’re a data enthusiast or a baseball fan, this analysis offers a powerful glimpse into the metrics driving modern baseball.

 

It was one of those nights when Daniel felt the weight of his existence pressing down on him. Everyone in his circle had conspired to make him feel small and insignificant, and he realized they had won. His guitar, a sunburst Telecaster, sat propped against the corner of his cluttered apartment, its wooden body glowing dimly in the light of a single table lamp. The coffee table was littered with takeout boxes, sheet music, and rejection letters from record labels. He hadn’t played a gig in months, and even when he did, no one cared.

“Just another face in a sea of struggling musicians,” he muttered, kicking an empty can of beer across the room. He knew that when he died, there would be little evidence that he ever lived. He flopped onto his couch, staring at the ceiling.

Daniel had dreamt of being a musician ever since he could remember, but the universe had other plans. The gigs that came through were sparse and unpaid, his songwriting was stagnant and derivative, and his social media accounts were filled with dismal and indifferent silence. He scrolled through his phone, looking at pictures of famous musicians, the people he envied and tried to emulate. Their lives seemed effortlessly glamorous—beautiful women, sleek cars, sold-out shows. How often do those people have to worry about coming up with the rent? What would it be like to be someone like that?

The thought lingered as he set his phone down and reached for his guitar.

The moment his fingers brushed the strings, something strange happened. He felt a jolt of static shoot up his arm. He flinched, shaking his hand, but the sensation faded almost as quickly as it had come. Weird. He shrugged it off and tuned the guitar, plucking each string with expert precision.

The first chord he played was a G major, the quintessential cowboy chord, a familiar sound that usually brought him some comfort. But tonight, it felt… different. The notes hung in the air longer than usual, vibrating through his skull as if the sound had turned physical. It was then that Daniel noticed the room had begun to shift. His fingers kept moving, strumming a melody he didn’t recognize, his body acting independently.

The walls blurred, and his vision seemed to stretch and twist, pulling him through some invisible tunnel. His fingers kept strumming, and he kept playing the unknown song. And then, everything stopped.

Daniel blinked, finding himself standing in the middle of a crowded club. A stage with bright lights. The electric hum of an audience waiting in anticipation. He looked down at his hands. They were gripping a guitar—a Stratocaster that wasn’t his. The strings hummed beneath his fingers, a warm buzz of anticipation. But it wasn’t just the guitar that was different.

He was different.

Daniel stumbled back, his mind scrambling to understand what had just happened. A glance at the mirror behind the bar stopped him cold. He wasn’t looking at his own reflection. Staring back at him was someone else—a man with sharp cheekbones, styled dark hair, and a leather jacket that looked like it cost more than his monthly rent. His hands, calloused and weathered from years of playing, were smooth and adorned with rings.

“What the hell?” he whispered, his voice sounding foreign in his own ears.

A voice crackled over the speakers before he could fully process what was happening. “Ladies and gentlemen, give it up for John Wisher!”

The crowd erupted into cheers, and Daniel—or John, apparently—felt his legs carry him to the microphone. His body moved with an effortless swagger as if it knew exactly what to do. Muscle memory. Without thinking, he strummed the guitar, hung down much lower than he was used to, and began to play. The song flowed out of him effortlessly, like he had played it a thousand times before. His fingers danced along the fretboard, and John’s voice boomed through the speakers, captivating the crowd.

For a moment, he was lost in it. The music, the applause, the energy of the room. He felt alive in a way he hadn’t in years. But as the song ended and the cheers died, reality hit him like a punch. This wasn’t his life. This wasn’t his body. He was… someone else.

Panicking, Daniel rushed off the stage, ducking into the club’s back alley. His heart pounded in his chest, his mind racing. How was this possible? Was he dreaming? Was he dead?

He clutched the guitar tightly, his fingers trembling as he plucked the strings again, desperate to find a way back. The same strange melody came to his hands, unwelcome and unintentional, and the world around him began to warp again.

With a rush of sound and light, Daniel was back in his apartment, staring at his reflection. His heart hammered, but the relief was overwhelming. He was himself again.

For days, he avoided his Telecaster, afraid to touch it. The experience felt too real to be a hallucination, but he couldn’t make sense of it. Was it magic? Some kind of curse? He didn’t know. All he knew was that playing those notes had transported him into another person’s life.

But curiosity gnawed at him, whispering to him in the quiet moments. He couldn’t stop thinking about the rush of being John Wisher—the thrill of the crowd, the feeling of success. That was what he had always wanted, wasn’t it? To be someone? To live a life that mattered?

Finally, Daniel gave in.

Sitting on the edge of his bed, he picked up his sunburst Telecaster again, his fingers trembling as he played the same mysterious melody. Once more, the room warped and spun, and when the world settled, he was somewhere new.

This time, he was in a recording studio. His reflection in the glass showed a different man—a polished, clean-cut singer in his mid-30s, headphones around his neck, a crowd of producers nodding in approval from the other side.

The life he’d stepped into was equally glamorous. The day was a whirlwind of recording sessions, photo shoots, and catered dinners at expensive restaurants. For a while, it was everything Daniel had dreamed of. He felt important. Admired. Successful.

But as the days went by, something began to gnaw at him. Each time he returned to his own life, his apartment felt more foreign, more distant. The simple act of waking up as Daniel in his shabby apartment became painful. It was as if he had tasted something sweet, only to have it ripped away again.

He began to spend more and more time in other people’s lives. A rockstar in one life, a wealthy and prominent composer in another. With each guitar strum, he was someone new—someone better. But the more he switched, the harder it became to remember who he really was. He would wake up in a stranger’s body and struggle to recall his own face. His own name.

Soon, the lines began to blur. He would return to his apartment after a week spent as some famous DJ, only to feel like he was stepping into a stranger’s home. He no longer felt like Daniel. He no longer wanted to be Daniel.

One night, after an especially wild show as the frontman of an explosive punk group, Daniel—or the person who had once been Daniel—sat in a luxurious hotel room, staring at the Strat. His fingers trembled as he picked it up again, the strings humming softly. He couldn’t remember the last time he had been himself, and he didn’t want to go back.

His life memories were fading like distant dreams—shadows of another existence. He could barely recall his face in the mirror or the sound of his voice.

As he played the familiar melody, the room began to spin, and he smiled. He no longer cared where the guitar would take him as long as he never had to return to the emptiness of his old life.

The last chord faded, and Daniel disappeared, swallowed by the endless stream of lives he would never fully belong to, lost in a symphony of borrowed faces and forgotten names.

In a state of existential despair, Daniel hoped to “become music” and live an infinite supernatural existence. All I know, all that anyone knows, is that if you visit a run-down building in the southern part of Iroquois County, Ohio, you will find a sunburst Telecaster in the corner of a dusty, abandoned apartment, waiting for its next player.

 

 

Introduction

When I think about baseball, arm strength is one of the first things that comes to mind—especially when comparing players across different positions. Whether it’s a third baseman making a quick throw across the diamond (Brooks Robinson, anyone?) or an outfielder firing a rocket from the warning track (Roberto Clemente was awesome), a strong and accurate arm can make all the difference. Recently, I dove into some data from Major League Baseball covering the years 2020 to 2024 to better understand how arm strength varies by position, and I’d like to share what I found.

Comparing Average Arm Strength Across Positions

I started by looking at the average arm strength for each position. Unsurprisingly, outfielders—particularly those in right field—have the strongest arms, while positions like first base require less power behind the throw.

This bar chart shows the average arm strength for each position (excluding catcher) in miles per hour. Outfielders (RF, CF, LF) clearly lead the way, with center fielders and right fielders consistently throwing the hardest. It makes sense: outfielders must make long throws back into the infield, often in critical situations where arm strength is key.

Are you surprised? I might have thought that shortstops would have edged out left fielders and maybe even center fielders. That said, it is close.

As always, box plots allow us to get a more granular view of the raw data. Here is what I found.

Notice the outliers among first basemen. Lots of them get very little on their throws. That is unsurprising; many players are positioned there for their offense, with defense being an afterthought.

As readers of this blog know, I have a special relationship with violin plots. Here is the same data in that form.

Once again, the poor arms of a select group of first basemen are highlighted. I consider that fact to be a big takeaway from this plot.

Infield vs. Outfield: A Clear Difference

Next, I wanted to break things down further and compare infielders’ arm strength versus outfielders. Unsurprisingly, outfielders, who cover more ground and make longer throws, generally have stronger arms.

The box plot below shows the distribution of arm strength between infield and outfield players. Outfielders not only have higher average arm strength, but the range of arm strength is more comprehensive, too. Some outfielders, particularly those in right field, can really get after it when a runner is rounding second.

I would like to tell you something interesting about this plot. Over 35 years ago, I was taught a trick (more properly, a heuristic) at Harvard University. If there is a space between the bodies of the box plots, then the data set is worthy of further exploration. If you look closely, you can see a thin space between the boxes, so I decided to investigate further to see if the differences in arm strength are statistically significant. We will get to that in a bit.

Looking for Patterns: Correlations Between Positions

Before we get to the hard-core statistics, I  wanted to explore whether there is a relationship between arm strength at different positions. For instance, do shortstops tend to have arm strength similar to that of second basemen or third basemen? To find out, I ran a correlation analysis.

This heatmap shows how arm strength at one position correlates with another. There are some interesting patterns here—positions like second base (2B) and shortstop (SS) show a strong correlation, likely because they both require quick, strong throws in the infield. The outfield positions also show high correlations with each other, which makes sense given the similar demands placed on their arms.

Here are the Statistics

The results of the one-way ANOVA test (a comparison of variance amongst means) indicate the following:

• F-statistic: 261.67
• 

Since the p-value is extremely small (well below the typical significance and totally arbitrary threshold of 0.05), we can reject the null hypothesis. This suggests statistically significant differences in arm strength across the different positions. In other words, the differences in arm strength are authentic and valid.

I have never done this before in my blog, but I decided to take an even deeper dive into this data set. I view this blog as more or less an introduction to what I find interesting. I don’t want to get into the weeds; many blogs and websites do that. Today, though, is different. Early this morning, I ran my 4 miles despite not wanting to get out of bed. My hip, which needs to be replaced, barked the entire time. I guess I am in a mood… Here is what I did next.

group1	group2	meandiff	p-adj	lower	upper	reject
arm_1b	arm_2b	4.0267	0	2.746	5.3074	TRUE
arm_1b	arm_3b	8.4252	0	7.1	9.7503	TRUE
arm_1b	arm_cf	12.6281	0	11.334	13.9221	TRUE
arm_1b	arm_lf	11.1761	0	9.9308	12.4214	TRUE
arm_1b	arm_rf	13.3679	0	12.097	14.6388	TRUE
arm_1b	arm_ss	8.977	0	7.6278	10.3262	TRUE
arm_2b	arm_3b	4.3985	0	3.2266	5.5704	TRUE
arm_2b	arm_cf	8.6014	0	7.4647	9.738	TRUE
arm_2b	arm_lf	7.1494	0	6.0686	8.2303	TRUE
arm_2b	arm_rf	9.3412	0	8.231	10.4514	TRUE
arm_2b	arm_ss	4.9503	0	3.7512	6.1494	TRUE
arm_3b	arm_cf	4.2029	0	3.0164	5.3894	TRUE
arm_3b	arm_lf	2.7509	0	1.6178	3.8841	TRUE
arm_3b	arm_rf	4.9427	0	3.7815	6.1039	TRUE
arm_3b	arm_ss	0.5518	0.8486	-0.6946	1.7983	FALSE
arm_cf	arm_lf	-1.4519	0.0019	-2.5486	-0.3553	TRUE
arm_cf	arm_rf	0.7398	0.4534	-0.3858	1.8654	FALSE
arm_cf	arm_ss	-3.6511	0	-4.8644	-2.4377	TRUE
arm_lf	arm_rf	2.1918	0	1.1226	3.261	TRUE
arm_lf	arm_ss	-2.1991	0	-3.3604	-1.0379	TRUE
arm_rf	arm_ss	-4.3909	0	-5.5795	-3.2022	TRUE

These are the results from Tukey’s HSD (Honestly Significant Difference) test results that provide pairwise comparisons between arm strengths for different positions. Yeah, I know your eyes are glazing over, but bear with me. Here’s how to interpret the key columns:

1. Group1 and Group2: These columns represent the two positions being compared. For example, “arm_1b” vs. “arm_2b” compares the arm strength of first basemen with second basemen.
2. Meandiff: This column shows the difference in the average arm strength between the two groups. A positive number means the arm strength of the first group (Group1) is higher than the second group (Group2).
   • For example, the mean difference between first basemen (arm_1b) and second basemen (arm_2b) is 4.03 mph, meaning first basemen tend to have lower arm strength compared to second basemen.
3. p-adj: This is the adjusted p-value, which tests the statistical significance of the difference. If this value is below 0.05, it indicates that the difference is statistically significant.
   • For most comparisons, the p-values are extremely low (0.0), indicating strong evidence that arm strength significantly differs between these positions.
4. Lower and Upper: These are the confidence intervals for the mean difference. It provides a range within which the actual mean difference will likely fall, with a 95% confidence level.
   • For example, the confidence interval for the difference between arm_1b and arm_2b is between 2.75 and 5.31 mph, suggesting that the actual difference lies within this range.
5. Reject: This column tells whether the difference between the two groups is statistically significant. If it says “True,” the test rejects the null hypothesis, meaning the difference between the two positions is significant.
   • In this case, “True” appears in many rows, indicating that the arm strengths differ significantly between most pairs of positions.

Key Insights

• Significant differences: Almost all pairwise comparisons show statistically significant differences. For example:
  • Outfielders (CF, RF, LF) generally have higher arm strength compared to infielders (1B, 2B, 3B, SS).
  • Third basemen (arm_3b) also tend to have higher arm strength than first basemen (arm_1b), as shown by an 8.43 mph difference.
• Largest differences: The biggest differences are between infield positions like first base and outfield positions like right field (arm_rf), where the arm strength difference can be over 13 mph.

Even though my hip is killing me, I feel very good about the results of this study.

Wrapping Up

So, what did I learn from all this? First, outfielders—especially those in right and center field—are in a league of their own regarding arm strength. Conversely, infielders don’t need the same power, but positions like third base and shortstop still require strong arms for those quick, long throws.

Running the ANOVA and Tukey’s test confirmed that these differences in arm strength are not random results due to the vagaries of sampling. Understanding these variations can be crucial for teams looking to optimize their defensive lineups or scout new talent.

Examining the data and seeing how arm strength varies across MLB positions was fascinating. I hope you enjoyed it. I am going to grab a beer and contemplate the disappointment of my team, the Cleveland Guardians, disastrously ending another year. Meh, what else is new?

Catcher defense, especially the ability to block pitches, can often go unnoticed but significantly impact the game. Preventing wild pitches and passed balls can save crucial runs and give pitchers confidence to throw in the dirt when necessary. In 2023, several catchers distinguished themselves as exceptional blockers. Let’s take a look at some of the data.

This analysis uses metrics like “blocks above average,” passed balls/wild pitches (PBWP), and more to examine the best catchers at blocking pitches during the season. Below, I break down the data to highlight the elite performers.

1. Top 10 Catchers by Blocks Above Average

“Blocks above average” is a critical statistic that tells us how much better (or worse) a catcher is compared to the league average at blocking pitches. Here’s a look at the top 10 catchers based on this metric:

As shown, Sean Murphy from the Atlanta Braves leads the way with 16 blocks above average, followed closely by Alejandro Kirk and Nick Fortes. These catchers were above average in keeping pitches in front of them, saving runs for their teams.

2. Actual vs. Expected PBWP

Next, take a look at the actual vs. expected number of passed balls and wild pitches (PBWP). The scatter plot below visualizes this comparison:

Catchers whose actual PBWP is lower than expected (below the red line) performed better than average. Catchers like Sean Murphy and J.T. Realmuto are among those outperforming expectations, while others are closer to the expected values. Note that the majority of catchers were about average.

3. Blocks Above Average Per Game

Another critical metric is the rate catchers accumulate blocks above average per game. This accounts for differences in playing time and offers a normalized view of performance. Here’s a look at the top 10 catchers:

The usual suspects are once again prominent. Notice that Yainer Diaz ranked number one in the league in this critical category.

4. Comprehensive Heatmap

To better understand each catcher’s performance, I’ve compiled several blocking metrics into a heatmap. This chart includes statistics such as catcher blocking runs, blocks above average, actual vs. expected PBWP, and blocks above average per game:

The heatmap above gives a comprehensive view of the top 10 catchers. The varying shades show how these catchers compare across multiple metrics, with Sean Murphy, Alejandro Kirk, and Nick Fortes again emerging as the top performers. This heatmap allows us to see the nuances in their blocking ability, with some excelling at reducing passed balls. In contrast, others are better at blocking above average on a per-game basis.

Conclusion

Nuance and subtlety are the operative words here. Asking who was the best defensive catcher in 2023 has as complex and interesting answer. What should we value in a catcher’s defense? Which metric is more important to winning than the others? Can you settle for a below-average pop time if your catcher is brilliant at framing pitches? Lots of great questions that require thoughtful answers. Stay tuned; I will continue posting my analyses. And yes, I do intend to publish some (hopefully) thoughtful conclusions.

 

In baseball, a catcher’s Pop Time can be the difference between catching a base-stealer and letting them slide in safely. Pop Time measures how quickly a catcher transfers the ball from their mitt to second base, factoring in the catcher’s footwork, exchange, and arm strength. This metric provides a more comprehensive assessment of a catcher’s defensive capabilities than arm strength alone, making it crucial in evaluating how effectively a catcher can control the running game.

This post explores the distribution of pop times among various MLB catchers, with visualizations such as a histogram, Kernel Density Estimate (KDE) plot, violin plot, and box plot. We’ll also examine some key summary statistics and update the analysis with the best pop times recorded during the 2023 season.

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What is Pop Time?

Pop Time is the time it takes for a catcher to throw the ball to second base during a steal or pickoff attempt. It measures the time elapsed from when the pitch hits the catcher’s mitt to when the throw reaches the center of the base. MLB’s average pop time for a throw to second base is 2.01 seconds, but elite catchers are significantly faster.

Pop Time considers three main factors:

• Footwork: The catcher’s ability to quickly get into a throwing position.
• Exchange: How fast the catcher transfers the ball from the glove to the throwing hand.
• Arm Strength: The velocity and speed of the throw.

Catchers with exceptional Pop Times obviously offer a much higher probability of recording an out.

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Best Pop Times from 2023

Below are the best average Pop Times to second base on stolen-base attempts (minimum 15 SB attempts) from the 2023 MLB season:

• J.T. Realmuto: 1.90 seconds
• Yan Gomes: 1.93 seconds
• Jorge Alfaro: 1.94 seconds
• Austin Hedges: 1.94 seconds
• Manny Piña: 1.94 seconds
• Gary Sánchez: 1.94 seconds

These elite catchers consistently post Pop Times well below the league average, making them highly effective at throwing out would-be base stealers. J.T. Realmuto, whose reputation proceeds him, leads the pack with an impressive 1.90 seconds.

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Pop Time Distribution: A Closer Look

To better understand how Pop Times vary among catchers, I visualized the distribution using a histogram:

The histogram shows that most catchers’ Pop Times cluster around 1.95–2.0 seconds, with very few recording times below 1.90 seconds. The majority of catchers are near the league average of 2.01 seconds, but the elite catchers separate themselves by consistently being faster than this threshold.

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Kernel Density Estimate (KDE) Plot

A Kernel Density Estimate (KDE) plot smooths out the distribution to provide a clearer picture of the underlying trends:

The KDE plot highlights the peak of Pop Times around 1.95 seconds, confirming that most catchers perform near this time. The data skews slightly to the right, indicating that a few catchers have slower pop times exceeding 2.0 seconds, but most fall below this threshold.

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Violin Plot: Visualizing Distribution and Density

I also created a violin plot, which combines the features of a KDE and a box plot to visualize both the distribution and the density of pop times:

The violin plot shows that most catchers fall within a narrow range of 1.90 to 2.00 seconds. The distribution is dense around 1.95 seconds, with fewer catchers having significantly faster or slower times. This plot also highlights that catchers like J.T. Realmuto are outliers, excelling well beyond the typical range.

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Box Plot: Highlighting Key Statistics

The box plot below offers a simple yet informative view of the data, focusing on the central tendency and spread of Pop Times:

Key points from the box plot:

• Median Pop Time: 1.97 seconds
• Interquartile Range (IQR): Most pop times fall between 1.93 and 1.99 seconds.
• Outliers: A few catchers have slower times above 2.0 seconds, but these are rare.

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Summary Statistics

The summary statistics for Pop Times further illustrate how closely clustered most catchers are around the league average:

• Mean Pop Time: 1.96 seconds
• Standard Deviation: 0.051 seconds (indicating low variability)
• Minimum Pop Time: 1.83 seconds
• Maximum Pop Time: 2.09 seconds
• 25th Percentile: 1.93 seconds
• 50th Percentile (Median): 1.97 seconds
• 75th Percentile: 1.99 seconds

These statistics show that most catchers perform within a narrow band, with the elite catchers falling below 1.90 seconds.

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Conclusion

Pop Time is a critical metric for evaluating a catcher’s ability to control the running game. While arm strength is important, Pop Time provides a fuller picture by incorporating footwork and exchange speed. This type of analysis also lets us ignore the pitcher and focus exclusively on the catcher’s skills.

Our analysis of Pop Times using visual tools like histograms, KDE plots, violin plots, and box plots shows that most catchers fall within a narrow range of 1.95 to 2.0 seconds, with a few standout performers excelling beyond this. The data from the 2023 season illustrates how slight differences in Pop Time can significantly impact a catcher’s effectiveness at throwing out base stealers.

For catchers, a fast Pop Time can be the difference between a successful defensive play and allowing the opposing team to gain momentum on the bases. I hope you are enjoying this deep dive into the nuances of catching; I certainly am. It is fascinating, isn’t it?

In baseball analytics, understanding a player’s whiff percentage—the rate at which they miss the ball when swinging—can offer key insights into their performance. A higher whiff percentage suggests a tendency to miss pitches, while a lower percentage indicates better contact with the ball.

In this post, I explore whiff percentages from both leagues across several years using three different visualization techniques: box plots, violin plots, and a line plot of medians. Each method offers a unique perspective on the data, and together, they help paint a comprehensive picture of trends in whiff percentages from 2015 to 2023. All players with approximately 200 plate appearances in that given year are included in the study.

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1. Box Plot: Visualizing the Distribution by Year

A box plot is a simple yet powerful tool to summarize the distribution of whiff percentages each year. It shows the median (the line within each box), the interquartile range (the box itself), and any outliers (the dots outside the whiskers).

This box plot gives us several insights:

• Consistency: In certain years, the boxes are tightly grouped, indicating less variation in whiff percentages (e.g., 2015).
• Outliers: Some years have extreme values, shown as dots, which highlight players who either significantly outperformed or underperformed compared to the rest.
• Year-to-Year Comparison: The height of the boxes gives a sense of how spread out the whiff percentages were for each year, helping to identify years with more variability in player performance.

Why use a box plot? Box plots are ideal when you want to compare distributions without being distracted by individual data points. It provides a clean, uncluttered view of how the overall performance fluctuated from year to year, and highlights outliers effectively.

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2. Violin Plot: Adding Depth to Distribution Analysis

A violin plot enhances the box plot by providing additional information about the shape of the distribution. It combines aspects of a box plot with a kernel density estimate, which helps visualize the probability distribution of the data. I will mention once again that I invented these plots, much to the chagrin of my peers, many decades ago. See my “A Crush, A Data Viz, and a Book Long Postponed” post for that tragic tale.

This violin plot offers some extra depth:

• Distribution Shape: You can see how the whiff percentages are spread out within each year. Some years have narrow violins, suggesting that most players had similar whiff percentages, while others are more spread out, indicating more variability.
• Density: The wider sections of the violin show where most data points are concentrated, allowing us to see not just the range but also the density of players’ performances in each year.

Why use a violin plot? Violin plots are particularly useful when you want a more nuanced understanding of the data distribution. While box plots are excellent for a high-level summary, violin plots allow us to see the underlying density, which can reveal patterns not visible in box plots alone.

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3. Line Plot of Medians: Tracking Trends Over Time

Finally, to understand the overall trend in whiff percentages, I created a line plot of the median whiff percentage for each year. The median is a robust measure of central tendency, making it ideal for highlighting general shifts without being overly influenced by outliers.

This plot shows us:

• Overall Trend: The line plot helps reveal whether the median whiff percentage is increasing, decreasing, or remaining stable over time. If the line rises, it suggests that players are missing more swings as the years progress, while a falling line indicates better contact rates.
• Key Years: Significant upward or downward trends in specific years are easily spotted. These could prompt further investigation into why such changes occurred, whether due to rule changes, player performance shifts, or other factors.

Why use a line plot? A line plot of medians is the best way to capture the long-term trend. It smooths out individual variations and provides a clear picture of how the “middle” of the data is changing over time.

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Conclusion: Insights from Multiple Perspectives

By using these three visualizations—box plots, violin plots, and line plots—we gain a multi-dimensional understanding of whiff percentages in baseball:

• The box plot provides a clean, high-level comparison of distributions across years, highlighting outliers and general performance variability.
• The violin plot offers a deeper look at how player performances are distributed within each year, revealing the shape and density of the data.
• The line plot of medians shows the overall trend, capturing how the middle of the distribution shifts over time.

Each plot tells a part of the story, and when combined, they provide a comprehensive view of player performance over the years. Whether you’re a data enthusiast, baseball analyst, or interested bystander, these tools can help unlock valuable insights into the game. And yes, I find the trend reversal after the 2020 season curious. The great thing about Exploratory Data Analysis (EDA) is that it can strongly suggest what questions must be asked in subsequent stages of analysis. That is certainly what happened here.

 

I took a deeper dive into MLB Catchers for the year 2023. I found lots of interesting stuff. Let’s get to it.

In this post, I decided to focus on catcher framing. Some catchers are better than others in fooling umpires that a ball is a strike. That is what catcher framing is all about. This may surprise some of you, but all this data is now readily available. Every pitch is tracked with impressive accuracy, with terabytes of data generated for each game played.

I created this figure to illustrate the standardized zones used for pitches thrown to home plate. The following is taken from the perspective of the catcher and home plate umpire.

Take Zone 11, for example. The reams of data tell us the percentage of pitches in that area that are taken and called strikes. In 2023, 19.2% of all pitches thrown into that zone were called strikes. Austin Hedges, then a catcher for the world-champion Texas Rangers, managed to get 27.6% of those pitches called strikes by the sweaty man crouching behind him. Get the idea? Hedges’ strike rate for that zone led all of MLB.

Hedges’ work in Zone 13 was even more impressive. The league average for pitches thrown up and away to right-handed batters was 23.6%. Hedges managed to get strike calls on 42.2% of those pitches. Extraordinary.

I ran a Cluster Analysis of all the framing data across all the zones to recognize the top ten catchers in MLB in 2023. Hedges and Patrich Bailey of the San Francisco Giants stand apart based on their superior performance.

And, yes, what is a top ten list without a bottom ten list? There might be a name or two on there that will surprise you.

In a previous post, I had identified J.T. Realmuto as having an outstanding defensive season in 2023. Regarding pitch framing, he ranked a ridiculous 63^rd. I admit, I found that unexpected.

Now, we can move on to something very cool. I have known what heatmaps are for a long time, but I have never needed to create one. It simply never came up. Guess what is next; go ahead.

I want to point out one aspect of this map: Hedges was well below the league average regarding framing pitches in Zone 14. I must admit, that is curious. I do not know why he would be so bad in that area and excel in all the other zones. I have no explanation for that anomalous chunk of data.

And, yes, I also generated a heatmap for the bottom ten catchers in 2023.

Another strange fact is that Martin Maldonado was very good at getting strike calls in Zone 11 but well below average in all the others. Does that have something to do with the pitchers on the Houston Astros in 2023? That line of reasoning might lead to a possible explanation.

I thought that was the end of this post, but I decided to test the new AI release that ChatGPT just dropped. I asked it for recommendations on how it would display this data. It offered up something very cool. Here are Radar Plots of the top 5 and bottom 5 catchers for pitch framing for the 2023 season.

Note that Hedges in Zone 13 and Miguel Amaya in Zone 17 stand out.

These plots are beautiful, but I haven’t decided on their utility. Are they diagnostic enough to merit their use? We will look more into that question in future posts.

At least for now, the takeaway is that determining the best defensive catcher in 2023 is much more subtle and nuanced than one might have imagined. Stay tuned; there is more to come.

 

The Unopened Letter

 

A soft thud echoed from the hallway. Marie looked up from her computer screen, her glasses slipping down the bridge of her nose. The mail had arrived. She sighed and went to the front door. Bills, advertisements, a postcard from some real estate agent—nothing unusual.

But there was one letter that caught her eye.

It was different. No return address, no postage stamp. Just her name scrawled in a familiar hand. Her hand. Marie’s breath hitched in her throat. She turned the envelope over, but it was sealed shut with an embossed wax stamp. Her intuition told her this wasn’t some prank. She had written the letter. But how? When?

She stepped back inside, the world outside the door suddenly too sharp, too loud. Sitting at her kitchen table, she stared at the envelope, her fingers tracing the edges of the paper. The handwriting was unmistakable. The way her “r” curled slightly, the way she looped her “e”—it was her own. But she hadn’t written a letter to herself, had she?

Marie’s heart quickened. The edges of the world seemed to blur, like reality had bent just slightly. The envelope weighed heavier in her hand than any ordinary letter should.

The air in the kitchen felt stifling. Her fingers twitched, wanting to tear it open and read the words. Yet, something held her back. Fear. What could it say? Was this some kind of cruel joke, was her intuition deceiving her, or was it… something more?

She shook her head. This was ridiculous. Letters didn’t just appear out of nowhere. There had to be a logical explanation. Maybe she’d written it and forgotten, right? But then how did it get delivered?

Her phone rang, her boss demanded a report be submitted by the end of the workday. Marie knew it was due, and she had already done much of the work, so she quickly hung up and went into her home office.

The end of the day was approaching when Marie got another call. The main office needed numerous items added to the report. She took a deep breath and worked late into the night.

The following morning, Marie was awakened by her phone. A text message from Greg:
Hey, are we still on for dinner tonight?
A normal text. Everyday life, pulling her back into routine. She swallowed, glancing between her phone and the letter on her nightstand.

Yeah, she typed back, 7 p.m. at Luca’s, right?
Right.

She felt relieved by the prospect of a night out. She picked up the envelope and brought it into the kitchen. She picked up a butterknife to use as a letter opener but quickly put it back. Her fingers hovered over the edge of the envelope once more before she tucked the letter into a drawer. Later. She would deal with it later. She wasn’t ready now. It can wait.

But Marie couldn’t forget the letter.

Back at work, she found herself distracted, staring at her computer screen but seeing only the envelope. During her lunch break, she examined her desk, half-expecting the letter to have magically appeared. She had to consciously stop herself from running into the kitchen, tearing it open, and confronting whatever lay inside.

The anxiety clawed at her all afternoon. What could the letter say? How did it end up at her door? The thought gnawed at her, and by the time she had finished the day’s tasks, it was all she could think about.

When she turned off her computer, the first thing she did was head to the kitchen drawer. She stood there, staring at it for a long time, her hand resting on the handle. Slowly, she opened the drawer and pulled out the envelope. Her heart hammered in her chest as she sat down with it again.

“Okay,” she whispered to herself. “Okay.”

Her thumb slid under the flap of the envelope, and—

A knock at the door startled her so badly that she dropped the letter.

Marie stared at the door, her pulse racing. She wasn’t expecting anyone, was she?

Another knock, this one more insistent. The letter lay on the floor, unopened.

She left it there and crossed the room cautiously. When she opened the door, Greg was standing on the porch, his hands stuffed in his jacket pockets. His smile wavered as he took in her frazzled expression.

“Hey, you okay? You didn’t respond to my last text. I thought I’d just come by and make sure we were still good for dinner.”

Marie blinked, her mind whirling. She had completely forgotten.

“Yeah, dinner. Right.” She glanced over her shoulder at the letter on the floor, still sealed. “I… uh… just lost track of time.”

Greg raised an eyebrow but didn’t push. “You sure you’re alright? You look like you’ve seen a ghost.”

“I’m fine,” she said quickly, rubbing her arms. “Just… distracted.”

His eyes followed hers to the envelope on the floor, but he didn’t comment. “Okay, well, if you need to reschedule…”

“No,” she interrupted, forcing a smile. “Dinner sounds great. Let me just grab my coat.”

Throughout dinner, Marie tried to push the letter from her mind, but it was impossible. Greg’s voice became background noise as she ran through every possible scenario. If she had sent herself a letter, it had to be important. Urgent. But what if opening it changed everything? What if reading the letter caused something terrible to happen?

“Marie?”

She blinked, suddenly aware that Greg had been talking to her. “Sorry, what?”

He frowned. “You haven’t heard a word I’ve said, have you?”

“I’m sorry, I just—” She paused, lowering her fork. “Something weird happened yesterday.”

Greg leaned forward. “Weird, how?”

“I got a letter. From me.”

His brow furrowed. “From you?”

“Yeah, like… it was in my handwriting. My name, no return address. It just showed up, and I have no idea how.”

Greg sat back, his face a mix of confusion and mild amusement. “Maybe it’s some kind of prank?”

“I thought of that, but… I don’t know. It felt too real.” She shook her head. “I haven’t opened it yet.”

“Why not?”

“Because… because what if it’s something I’m not ready to know? What if it’s a warning or…” Her voice trailed off, her chest tightening.

Greg was silent for a long moment. “Marie, if you wrote this letter to yourself, there’s a reason. Maybe it’s something you need to hear.”

She stared down at her plate, her appetite gone. “I’m scared.”

“I get that,” Greg said softly. “But maybe the fact that you’re scared means you need to read it.”

That night, Marie sat on her bed, the letter resting in her lap. The edges of the envelope were soft now from all the times she’d handled it, but it was still sealed. Still waiting.

She took a deep breath, trying to steady her nerves. Her hands trembled as she finally slid her finger under the flap and tore it open. A faint yellow glow surrounded her hands as she removed the sheet of paper.

The letter inside was short, only a few lines. Her heart pounded as she unfolded the paper and began to read.

In her own handwriting, the message was simple:
Don’t open the door tomorrow.

The words blurred before her eyes as the realization hit her like a punch to the gut.

Tomorrow.

 

In the Presence of Shadows

 

When Jacob first woke, the air in his bedroom felt thick, like a smothering weight pressing down on him. His eyes blinked open to the familiar shape of his bedside lamp, the faint glow of morning just barely filtering through the curtains. But there was something else.

Someone was standing at the foot of his bed.

His heart leaped into his throat. A tall, shadowy figure, darker than the rest of the room, seemed to loom over him. Jacob froze, his body paralyzed with a cold, creeping terror that crawled up his spine. He tried to blink it away, telling himself it couldn’t be real. His fingers clutched the sheets, the pulse in his ears deafening.

But the figure didn’t move.

A breath caught in his throat, sharp and painful. Then, in an instant, like a trick of the light, the shadow was gone. There was nothing there—just the familiar shapes of his dresser, the door slightly ajar, the room as it always had been. Jacob sat up, swallowing hard, his hands trembling as he dragged them through his sleep-tousled hair.

It was a hallucination, just a figment of his groggy, half-asleep mind. It had to be. He’d been stressed—work had been hell lately, and his sleep schedule was a mess. This kind of thing could happen to anyone, right?

He swung his legs over the edge of the bed and planted his feet on the cool hardwood floor. He rubbed his face, trying to shake off the lingering unease. He’d been on edge for days, running on caffeine and fumes. The vision had been a warning from his overworked brain, no more, no less.

Jacob stood, stretched, and padded toward the bathroom. The rest of the morning was supposed to be mundane—shower, shave, breakfast—but as he went down the hallway, he felt… off. His steps seemed too loud on the floor; his skin tingled like it didn’t fit quite right. The quiet of the house had a strange weight to it, like it was watching him.

Shaking his head, he tried to dismiss the thought, but the sensation persisted, an inexplicable tightness in his chest.

When he stood at the kitchen counter, pouring himself a cup of coffee, the unease had settled into something more tangible. Every so often, he’d catch a flicker of movement from the corner of his eye—a shadow darting across the wall, a figure slipping behind a corner. His head would snap toward it, only to find nothing there. Empty spaces. Ordinary silence.

Jacob clenched his jaw, forcing himself to focus. “Get it together, man,” he muttered, gripping the coffee mug too tightly, his knuckles going white.

The momentary distraction helped. He busied himself with making toast, methodically buttering the bread, the warmth of the kitchen offering some comfort. But as he reached for the silverware drawer, his hand brushed something cold.

Startled, Jacob looked down. His fingers had grazed the handle of a knife, but the metal felt icy, far colder than it should have been. He pulled his hand back, and in the reflection of the knife’s blade, he saw something move behind him.

He whirled around.

Nothing.

The kitchen was empty, just as it had been. His eyes scanned the space, his heart hammering in his chest. His mind was playing tricks on him, indeed. But the knife…

He stared down at the butter knife. It was just a regular utensil sitting innocently on the counter. Maybe the air conditioning had kicked on. Maybe—

A sharp pain shot through his right hand, causing him to drop the knife with a clatter. He gasped, clutching his hand, his pinky throbbing like he’d jammed it in a door. He flexed his fingers carefully, but something wasn’t right. The pinky seemed… off. It was bent at an unnatural angle, swollen and discolored.

“What the hell?”

His breath came faster now. He hadn’t hit it on anything. He hadn’t even touched anything hard enough to break a bone. Panic began to bubble up inside him, mixing with the strange, disorienting feelings that had been plaguing him since he woke. His skin felt too tight again, his thoughts scattered.

Something was wrong. Really wrong.

The coffee mug slipped from his grasp, shattering on the floor. The sound rang in his ears, louder than it should have been, like a gunshot. Jacob flinched, his pulse racing.

It was enough. He grabbed his phone, fumbled for his car keys, and within minutes he was out the door, driving with one hand while his broken pinky throbbed in time with his heartbeat.

The fluorescent lights buzzed overhead at the emergency room, casting a sterile glow over the rows of plastic chairs and the low hum of chatter. Jacob sat with his right hand cradled in his lap, his mind still spinning. He kept running his thumb over the curve of his pinky, feeling the break, the way the bone didn’t line up quite right anymore.

A nurse finally called his name, leading him into a small exam room. The doctor arrived soon after—a tall, wiry man with graying hair and a kind smile. He introduced himself as Dr. Fields, gave Jacob’s hand a cursory glance, and immediately ordered an X-ray.

That creeping sensation returned as Jacob sat on the examination table, waiting for the nurse to return with the X-ray machine. The room felt too cold, and shadows seemed to pool in the corners where the overhead light didn’t reach.

He glanced toward the open door and saw something. A figure, tall and thin, standing just out of sight in the hallway.

His chest tightened. He could barely breathe. His vision wavered, like heat rising off asphalt. He blinked, and the figure was gone, swallowed by the sterile white light of the hospital.

The nurse wheeled in the X-ray machine, oblivious to the tension thrumming through him. He forced himself to sit still, to focus on her instructions as she positioned his hand for the scan. But his heart wouldn’t slow down. His mind raced.

The hallucinations were getting worse.

The scan took only a few minutes, and soon, Dr. Fields returned with the results. He slid the black-and-white film onto the lightbox and flipped the switch, illuminating the delicate bones of Jacob’s hand.

“Well, Mr. Hale,” Dr. Fields said, his brow furrowed as he examined the X-ray. “It’s definitely broken, but… it’s odd.”

“What do you mean?” Jacob asked, his voice tight.

“This kind of fracture is more common in crush injuries or severe trauma. It’s clean, but with enough force applied directly to the bone to cause significant displacement.”

Jacob swallowed. “But I didn’t do anything to it. I mean, I didn’t hit it or crush it or anything.”

Dr. Fields looked at him thoughtfully, concern flickering in his eyes. “You don’t remember any impact at all? No recent accidents?”

Jacob shook his head. His hand throbbed again, the pain sharp and insistent.

“I’ll put a splint on it for now,” the doctor said, “but I’d recommend seeing an orthopedist in the next few days. This isn’t a typical break.”

Jacob nodded, barely hearing him. As the doctor left to retrieve the splinting supplies, Jacob’s gaze drifted back to the X-ray film. His bones seemed fine, normal, except for the fractured pinky. But behind the bright white lines of his skeleton, deep in the shadows of the film, something strange caught his eye.

There, nestled between the bones of his hand, was a faint, dark outline. It was almost imperceptible, but once Jacob saw it, he couldn’t unsee it.

A shape. Like a hand—thin and skeletal—resting over his.

A shiver ran down his spine. His breath caught in his throat.

He stared at it, unblinking, as the cold hospital room grew darker around him.

 

Baseball Has a Strange Math Issue

My last post was about the defensive capabilities of MLB catchers in 2023. I mentioned that there was more to come. As I was researching the follow-up post, I came across something bizarre. As soon as I stop violently shaking my head back and forth, I will show you what I found.

This post was supposed to be about framing pitches. Some catchers are very good at fooling umpires into calling strikes on pitches that are actually balls. There is lots of excellent data to quantify the ability of any catcher to do this. As you might guess, this is a precious skill that any team would want to have in their catcher.

As I reviewed the data and put together a strategy to analyze and visualize it for the post, I realized that I needed to draw pictures of home base, more commonly called home plate. Why home base, then? That is what it is called in the official baseball rule book. How did I end up on a web page showing those rules? That is an excellent question.

I searched for the dimensions of home plate; it wasn’t something I had committed to memory. Trust me, I know the numbers now, and I doubt I will ever forget. Here’s why…

The following paragraph is taken from Official Baseball Rules, 2024 edition, published by the Office of the Commissioner of Baseball.

2.02 Home Base. Home base shall be marked by a five-sided slab of whitened rubber. It shall be a 17-inch square with two of the corners removed so that one edge is 17 inches long, two adjacent sides are 8½ inches and the remaining two sides are 12 inches and set at an angle to make a point

So, what’s the big deal? The rule book describes an impossible figure. The shape described does not, and cannot, exist. Unbelievable, isn’t it? Look at the drawing I conjured up.

 

Figure 1. Home plate as it should be and home plate as described in rule book.

 

I suppose a lawyer could litigate this. It seems that the intent was for the angle formed at the point to be 90 degrees, which it clearly is not when following the description from the rule book. It takes slightly more than 12 inches to meet the requirements of Pythagoras and his ubiquitous theorem. Is Major League Baseball concerned about this? Apparently not. Am I concerned that they have fudged a famous trigonometry theorem? I’ll crank up some Mozart and mull it over for a bit. My guess is I won’t lose much sleep.