In the Presence of Shadows (Flash Fiction)

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

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.

 

Scales of Unusualness: 2023 MLB Catchers (Defense)

The hierarchical cluster tree, or dendrogram, visualizes the relationships among 2023 MLB catchers based on their defensive statistics. As always, players who are closer together on the x-axis have similar defensive profiles, meaning their statistics in categories like putouts, assists, errors, and caught stealing percentage are more alike. The height of the horizontal lines (distance) indicates how similar or dissimilar players are: the lower the line, the more similar the players are in their defensive performance.

The visualization highlights individual performance and helps teams or analysts compare players across a wide range of defensive metrics. For example, catchers clustered together likely share similar defensive styles or capabilities, making it easier to compare catchers in terms of their effectiveness behind the plate. Furthermore, the dendrogram’s structure shows which players stand out as outliers due to superior or weaker performance compared to their peers, giving teams valuable insights for recruitment, strategy, or training decisions.

Note that J.T. Realmuto is off by himself. Despite not receiving a Gold Glove Award, his defensive performance in 2023 was ostensibly exceptional. In a future post, I will drill down into the advanced metrics to see why he was overlooked. Don’t be surprised if the dendrogram I created in this post is deemed suspect in a few days or so.

 

 

Twilight Embrace (Flash Fiction)

Twilight Embrace

Roland stood on the edge of the pier, the salty sea breeze ruffling his thinning gray hair. The sunset cast a golden glow on the water, turning it into a shimmering mirror. He’d always loved this time of day, when the world seemed to slow down, the chaos of life pausing to catch its breath. But tonight, the sunset was more than just a daily spectacle; it was a backdrop to the thoughts that weighed heavily on his mind.

He heard her footsteps before he saw her, the soft patter of sandals on wood. He didn’t need to turn around to know it was Lila. She had a way of walking that was almost musical, each step a note in a melody that only he could hear. When she reached his side, she leaned on the railing, her youthful face glowing in the fading light.

“It’s beautiful, isn’t it?” she said, her voice as light and airy as the breeze.

Roland nodded, his eyes lingering on the horizon. “It is,” he agreed, though he wasn’t sure if he was still talking about the sunset.

He stole a glance at her, his heart tugging in that familiar, bittersweet way. Lila was young, vibrant, full of life—everything he no longer was. Her hair was a cascade of chestnut curls, her skin smooth and untouched by time. But it wasn’t just her youth that captivated him; it was the way she looked at the world, with wide-eyed wonder and an unshakable belief in endless possibilities.

He’d met her at the community center where he volunteered, teaching a creative writing class. She’d signed up on a whim, she’d said, looking for something to fill her summer days. But from the moment she walked in, Roland had been drawn to her. It wasn’t a sudden attraction, like a lightning strike. No, it had been gradual, a slow unfolding of admiration, respect, and something deeper that he hadn’t felt in years.

They’d spent hours talking after class, about books, music, and the dreams she had for her future. Lila was open, honest, her emotions unfiltered. Roland found himself sharing parts of himself that he’d kept hidden for decades. He felt alive in her presence, like a man much younger than his 63 years.

But as much as he cherished their connection, he couldn’t ignore the nagging voice in the back of his mind. He was old enough to be her father, perhaps even her grandfather. What could she possibly see in him? The thought haunted him, twisting his emotions into knots. Was it wrong to feel this way? Was it foolish?

Lila turned to him, her eyes catching the last rays of the sun. “Roland, you’re awfully quiet tonight.”

He forced a smile, hoping it didn’t look as strained as it felt. “Just lost in thought, I guess.”

She tilted her head, studying him in that way she had, as if she could see right through to the core of him. “You know, age is just a number,” she said softly, as if reading his mind.

His breath caught in his throat. “Lila, I—”

She reached out, placing a hand over his. It was warm, comforting, grounding him in the moment. “You make me happy, Roland. Isn’t that what matters?”

The simplicity of her words hit him like a wave. All the doubts, the fears, the self-recrimination—they seemed to dissipate in that instant, carried away on the breeze. He looked into her eyes, seeing only sincerity there, and something that might have been love.

He squeezed her hand gently. “Yes, Lila. That’s all that matters.”

And as the sun dipped below the horizon, casting the world into twilight, Roland felt something within him shift. He didn’t know what the future held for them, but for the first time in a long time, he was willing to embrace the unknown.

 

Steps Forward (Flash Fiction)

Steps Forward

Sergio stood at the edge of his driveway, phone in hand, staring down the quiet, leaf-strewn road that led to the harbor. The late September air was cool, tinged with the smell of damp earth and the first hints of winter. Lake Erie was only three miles away, a place he’d gone a thousand times before, but tonight was different. Tonight, he needed the walk. He needed the beer.

He scrolled through his contacts, hoping someone might answer, someone who could drive him down to the old pub by the harbor—Murphy’s Place. It was a spot he’d frequented in better days, back when life felt less like a cage. But now, it was just a distant reminder of the way things had changed.

The first call went to voicemail. “Hey, this is Dan. Leave a message.” Sergio didn’t bother. He tried a few more numbers—each one met with the same silence, or a polite but firm excuse. “Busy tonight, Sergio. Maybe another time.”

He let out a long sigh, shoving the phone into his jacket pocket. No one was coming. It seemed fitting, really. In the last year, most of his friends had drifted away, and those who hadn’t were more like acquaintances now—people with lives too busy for someone who’d become a shadow of his former self. It was easy to let that happen, Sergio thought, when you spent more time with a bottle than with people.

He started walking, his footsteps heavy on the pavement. The streetlights were spaced far apart, leaving long stretches of darkness between them. Sergio welcomed it. The shadows felt like a shroud, something to hide in, away from the prying eyes of a world that no longer made sense.

As he walked, the memories crept in. The accident. The year he’d spent trying to piece his life back together after losing his wife, Ellen. The guilt, the what-ifs that gnawed at him day and night. He’d been driving that night, too tired from work, too stubborn to admit he needed rest. And then the truck, the blinding lights, and the sound of metal tearing like paper.

They told him it wasn’t his fault, that it was a freak accident, but the words never reached him. They couldn’t undo the damage, couldn’t bring her back. So, he’d let the grief consume him, finding solace only in the numbness that came from a bottle.

The harbor came into view, its lights flickering in the distance like tiny beacons. Sergio felt a pull toward it, like it was calling him, offering some small comfort. He reached Murphy’s Place, its neon sign buzzing in the dark. Inside, the warmth and noise greeted him like an old friend. He ordered a beer, the bartender nodding as if he knew. Everyone knew, in a place like this.

But as Sergio lifted the glass to his lips, he paused. The walk had stirred something in him, something he hadn’t felt in a long time. A small, insistent voice that whispered: enough.

He set the beer down, untouched, and walked out of the bar. The night was cold, the air sharp in his lungs as he headed back the way he’d come. Each step felt lighter, the darkness less oppressive. He didn’t know what tomorrow would bring, didn’t have any grand plans to turn his life around. But as he walked back toward his empty home, Sergio knew one thing: he was done running.

The walk had changed something in him, something vital. It wasn’t about the beer, or the harbor, or the friends who no longer answered his calls. It was about the simple act of moving forward, one step at a time. And for the first time in a long time, Sergio felt like he could keep walking.

 

Pitching is (or was) more Important than Hitting? Who knew?

 

This analysis examines the relationship between a team’s On-base Plus Slugging (OPS) and their total wins in Major League Baseball (MLB) over a five-year period from 2004 to 2008. OPS is a key statistic in baseball that combines on-base percentage and slugging percentage, providing a comprehensive measure of a player’s (or team’s) ability to get on base and hit for power. The scatterplot visualizes this relationship, with each point representing a team’s OPS and corresponding number of wins for a particular season. The data points are colored by year, allowing us to observe any patterns or trends across the seasons. That factor proved not to be very useful.

A linear regression model was applied to determine if there is a significant correlation between OPS and team wins. The analysis revealed an R-squared value of 0.196. The R-squared value indicates that approximately 19.6% of the variance in team wins can be explained by their OPS, suggesting a moderate correlation. While OPS is a useful statistic, the relatively low R-squared value implies that other factors, such as pitching, defense, and managerial decisions, also play a significant role in determining a team’s success over a season.

The analysis covers data from five consecutive MLB seasons, providing a broad overview of the relationship between OPS and wins over multiple years. The consistency of the trend line and equation across the years indicates that the OPS-wins relationship is relatively stable during this time period.  However, given the moderate R-squared value, this analysis suggests that while OPS is an important metric for assessing team performance, it should be considered alongside other variables for a more comprehensive understanding of what drives a team’s success.

In a recent post, I demonstrated that WHIP is much more predictive of a team’s record than OPS, at least in the mid-2000s. I don’t think anyone will be surprised to learn that pitching is more important than hitting if you want to win baseball games. There will be more on that and related topics coming soon.

 

Now, Isn’t This Interesting?

 

This scatterplot visualizes the relationship between a baseball team’s WHIP (Walks plus Hits per Inning Pitched) and the number of wins they achieved during the seasons from 2004 to 2008. I included both the AL and NL in this analysis. Each point on the graph represents a team in a specific year, with the color indicating the corresponding season. The WHIP is plotted on the x-axis, while the number of wins is plotted on the y-axis. This visualization allows us to observe if there is a pattern or trend between these two variables across different years.

A trendline, represented by a solid red line, has been added to the scatterplot, which provides a general indication of the relationship between WHIP and wins. The slope of the line suggests that as WHIP increases, the number of wins tends to decrease. The strength of this relationship is indicated by the R-squared value of 0.49, meaning that WHIP accounts for approximately 49% of the variability in the number of wins. This moderate R-squared value suggests a fairly significant correlation between the two variables.

In summary, the scatterplot illustrates a moderate negative correlation between WHIP and team wins, indicating that WHIP is a meaningful factor in a team’s success, though not the sole determinant. Including both leagues from 2004 to 2008 allows for an interesting, if limited, analysis over multiple seasons, with the trendline and R-squared value providing insights into the overall pattern between these two metrics. This plot highlights the importance of WHIP in predicting team performance while suggesting that other factors certainly contribute to a team’s total wins.

Here is a scatterplot illustrating wins in terms of team ERA (earned run average). When I was a kid, I didn’t think ERA was very valuable, and the following plot shows that it has less explanatory value than WHIP.

As we saw in a previous post, payroll differences explained approximately 19 percent of the variability in win totals. Team ERA explains about 44 percent of the variability, while the WHIP metric has more explanatory value (49 percent) when determining what leads to wins in major league baseball. I will keep posting more information as my research progresses.

 

2018 AL WAR vs OPS

 

The scatterplot titled “2018 AL WAR vs OPS (Colored by Position)” visually explores the relationship between Wins Above Replacement (WAR) and On-base Plus Slugging (OPS) for players in the American League during the 2018 season. Each point on the plot represents a player, with OPS on the x-axis and WAR on the y-axis, and the points are colored according to the player’s position. This allows us to observe how players across different positions performed in terms of their offensive output and overall contribution to their teams.

Notably, the plot highlights standout players such as Mookie Betts and Mike Trout, who are positioned in the upper right corner, indicating their exceptional performance. Betts, then an outfielder for the Boston Red Sox, and Trout, still a center fielder for the Los Angeles Angels, both had extremely high OPS and WAR values. Their positions in the plot underscore their status as two of the most valuable players in the league during the 2018 season.

In contrast, Chris Davis, a first baseman for the Baltimore Orioles, is positioned in the lower-left corner of the plot. Davis had one of the lowest OPS and WAR values in 2018, indicating his struggles. The spread of points across the plot also reveals how different positions cluster in certain areas, with players like Davis standing out as outliers in underperformance. At the same time, Betts and Trout exemplify top-tier performance. This is a pretty cool visualization of this type of data. I find scatterplots useful.

 

Here’s a Little 3D For You

 

How is this for a different perspective? The 3D Cluster Analysis of 2023 National League (NL) shortstops visually represents player performance using an extra dimension, highlighting their key differences and similarities. Using a sophisticated technique called Principal Component Analysis (PCA), the high-dimensional performance metrics of the shortstops were reduced to three principal components, which encapsulate most of the variance in the data. This dimensionality reduction (or expansion, if you prefer) allows for a clear visualization in three-dimensional space, where each player’s metrics reflect their overall performance. The players are grouped into three distinct clusters, each represented by a different color, providing insights into how these athletes compare to one another based on their statistics.

The clusters were determined using the K-means clustering algorithm (much more of that down the line), which groups players with similar performance metrics into the same cluster. As earlier, the plot reveals three main clusters: Cluster 1 in blue, Cluster 2 in green, and Cluster 3 in red. Each cluster represents a subset of players with comparable performance profiles. For instance, the player in Cluster 3 (Mookie Betts), shown in red, exhibits stronger or more consistent performance in certain areas, distinguishing him from those in the other clusters.

Unsurprisingly, Betts is once again highlighted in the analysis. Notice that he is off by himself in red, focusing our attention. This emphasis allows for a closer examination of where Betts stands relative to his peers in the 2003 NL shortstop group. While I do believe that the two-dimensional plot from the last post is more diagnostic, no one can deny how cool the 3D plot looks. And that is why I published this post.

 

Scales of Unusualness: Offensive Production of NL Shortstops in 2023

To the surprise of no one, Mookie Betts was, by far, the most unusual offensive performer last year among NL shortstops. If you study the plot, you can follow the line connecting Betts to the other players.

 

Betts is a cluster of one. His offensive production was so far above all the other shortstops that no one could cluster with him. And that, I must say, is highly unusual.