Modeling Strikeout Rate with Plate Discipline Part 1: Hitters

Strikeout and walk rates are perhaps the most popular and widely used peripheral statistics, particularly for pitchers. However, with pitch level data, these statistics now have “peripherals” of their own. I was curious if I could create an accurate-yet-interpretable model using FanGraphs’ plate discipline metrics that could offer insight on what drives the differences in strikeout and walk rates between players.

While many have noted individual correlations between a single statistic and strikeout rate, I have not seen many unifying models that incorporate several plate discipline metrics. For the first part in this study, I will focus on hitter strikeout rate, but I intend on also looking at walk rate and, later on, pitchers’ strikeout and walk rates.

If you are not a fan of mathematical details, feel free to skim or skip these next few sections to get to my overall conclusions.


Plate Discipline Flash Card 12-29-15

Note: I used BIS discipline statistics rather than PITCHf/x. I do not think this made a significant difference, but I think it is important to keep in mind.

FanGraphs gives us nine plate discipline statistics to work with. However, several of them can be removed as they can be derived using the other statistics. In a regression setting, this phenomenon is called perfect multicollinearity, which is when an explanatory variable can be perfectly formulated by other explanatory variables. With a high degree of multicollinearity, it can be extremely difficult to tell which particular variable is responsible for a change in the response variable, which is problematic for inference. Using some basic dimensional analysis, I found formulas for all three of these: Read the rest of this entry »

Finding Ray Fagan: A Minor League Mystery

Sometimes numbers tell a story. Sometimes that story is a mystery.

I came across the Baseball-Reference page for Raymond Fagan and was stunned by what I saw. It says Fagan went 13-0 with a 1.16 ERA for the Class D Oklahoma City Senators in 1915. Now the stunning part – it says it was his only professional season. Despite those dominant results, it appears Fagan never pitched again.

What happened to Raymond Fagan? Did he suffer a career-ending injury? Did he get into legal trouble and change his name? A Google search yielded no answers. This mystery required a deeper dive. Read the rest of this entry »

Third Grader Hits the Library: An Origin Story

We usually think of origin stories as the province of fictional superheroes or the real-life super rich. It could be an ordinary boy bitten by a radioactive spider or arriving on earth as refugees from an annihilated planet. Perhaps we think of a nearly destitute J.K. Rowling toiling away at her first novel in a coffee shop, or Jeff Bezos creating an empire from scratch on a computer in his living room. Yet many of us who came from humble origins and went on to live simple, unremarkable lives also have a narrative that informs who we became. Mine happened in third grade.

I am a husband, a father, and a teacher. To these three descriptors of my identity I would add one more, just slightly less central. I am a baseball fan.

I am not one of the true obsessives who grew up playing Strat-O-Matic and graduated to planning his whole calendar around the SABR conference or spending countless hours with multiple fantasy leagues (two is my limit). But I have been a fantasy league commissioner since 1992, and the majority of text messages that my adult son and I exchange have some connection to the top Atlanta Braves prospects for the coming year. I also get to sleep most nights not by counting sheep, but by silently reciting World Series winners backward from 1970.

Baseball, its present and its past, is deeply ingrained in my outlook on life. My bookshelf is 70% baseball, 30% history and politics.

Baseball on the field was part of my youth, first as a fourth-rate Little League catcher and then as a minor league batboy for the Class A Lynchburg Mets.

Family vacations have often included trips to Baltimore or Atlanta for games. My son’s youth and high school games with me as spectator, coach, or scorekeeper were part of the rhythm of our family life for over a decade. Our baseball bond defines our relationship.

As the immortal lyric of David Byrne plaintively asks, “well, how did I get here?” Read the rest of this entry »

Why Most Fans Blame the Players

I imagine most people reading this have a favorite team. And over time, you’ve likely had numerous players on that team whom you particularly enjoyed watching play. But when push comes to shove, who receives your greatest loyalty, the team or the players?

I’m a Cardinals fan, and I greatly enjoyed Albert Pujols‘ contributions to the Redbirds’ success during his 11 years wearing the birds on the bat. Since he’s left St. Louis? Sure, I’ve been happy for him when he’s done well — getting his 3,000th hit as well as his 500th and 600th home runs — but it’s not the same. He’s an Angel now, not a Cardinal, so I’m simply not as invested in his accomplishments.

This stance is probably understandably similar for most of you. Teams are (mostly) eternal, while players are ephemeral. Can I name the starting eight position players for the 2011 Cardinals? Probably not, but I still know they won the World Series that year.

When it gets flipped, however, is when we go off the playing field and into the negotiating room. When the owners and players are battling over matters of the game — particularly the divvying up of the loot — I largely stand behind the players. The owners become the faceless, monolithic corporations that extort billion-dollar ballparks from their communities and work extremely hard to give the players as small a portion of the pot as possible, while the players have short careers and are positioning themselves to take care of their families as much as possible before their careers end.

Of course, it’s not that cut-and-dried. Both sides have their virtuous and unseemly characteristics. Each group is willing to put their interests before others.

But regardless of who sticks it to whom for their own benefit, it’s largely the players who suffer the vitriol of the fans and media when the two sides clash. The question is, why is that? The answers actually make a lot of sense — even if they really don’t. Read the rest of this entry »

All Stolen Bases Were Not Created Equal

Fielding percentage is often criticized for the selection bias introduced by a player’s range (good defenders attempt more difficult plays, leading to more errors). A similar issue of selection bias is present in stolen bases. On any given pitch, it is at the sole discretion of the runner if he will steal a base or not. Naturally, the runner will only attempt a stolen base when he believes he has an advantage over the pitcher and catcher.

Ivan Rodriguez caught 46% of base-stealers throughout his career, topping out at a 60% caught stealing rate in his prime and leading the league in CS% in nine seasons. Knowing that stealing against Pudge is little more than a pipe dream for most, only the best baserunners would dare to attempt a steal. If this assumption holds, Rodriguez’s CS% would in fact be far more impressive than initially reported due to the level of competition he faces relative to a typical catcher.

To adjust for selection bias in stolen-base attempts, I developed an ELO model. For those unfamiliar, ELO ratings are a method of calculating the relative skill levels of players in zero-sum games. You might recognize ELO from chess rankings or FiveThirtyEight’s sports prediction models. These ratings can be used to directly estimate the probability of winning a match between two individuals or teams. The ratings change after each match, rewarding a win by an underdog more than a win by the favorite.

On a stolen-base attempt, the runner, pitcher, and catcher all play a major role in the outcome of the play. An argument could also be made for the importance of the fielder receiving the throw, especially when considering the select few who can make tags like this: Read the rest of this entry »

Examining Mike Trout’s Perfect Swing

Sir Isaac Newton’s second law of gravity tells us exactly how much an object will accelerate based on the given net force.

For baseball hitters, this is directly applicable considering the goal to hit baseballs as hard and far as possible. And when it comes to generating net force against baseballs, Mike Trout is an expert. He has been crushing baseballs with the league’s elite since he became a full-time regular at age 20 in 2012. Trout’s offensive production, in particular, has gone to another level over the course of his career. The following table breaks up his career into two distinct parts. The numbers show Trout’s production compared to league average, with a mark of 100 denoting exactly average.

A Tale of Two Trouts
Years wRC+ BB%+ K%+ Pull%+ Cntr%+ Oppo%+ FB%+ GB%+
2011-15 170 159 115 93 100 112 110 89
2016-19 180 222 91 100 102 98 121 78

Trout has always produced elite offensive numbers, but he’s at an entirely different level now. He has transformed into baseball’s best hitter by walking more, striking out less, and pulling more hard-hit baseballs in the air. Trout is both barreling up more baseballs and raising the launch angle of his batted balls. Unsurprisingly, he had baseball’s second-best sweet-spot percentage in 2019. Trout has talked about a gap-to-gap approach in the past but recent trends show him moving away from hitting balls the other way. Read the rest of this entry »

2021 Arbitration Preview: Lucas Giolito – Chicago White Sox

With the 2020 Major League Baseball season on hiatus due to the Coronavirus, one can’t help but wonder of a season that could have been. Do the Nationals, after losing slugger Anthony Rendon to the Angels, have what it takes to repeat as World Series champs? Can Pete Alonso be this season’s home run champion again? Will Trout win another MVP?

Hopefully we will know sooner rather than later. In the meantime, I took the liberty of looking at players who will become first-time arbitration eligible following the 2020 season, focusing on Lucas Giolito of the Chicago White Sox.

Rather than conduct an analysis based off of career numbers (excluding the vacant 2020 season), I utilized The BAT Projection System by Derek Carty, which is part of FanGraphs, to fill in the gap for 2020 season statistics.

The BAT is a standard projection system that predicts outcomes in accordance with basic factors such as hitter and pitcher, park quality, umpires, weather factors, and more. Read the rest of this entry »

The Effect of Umpires on Baseball: Umpire Runs Created (uRC)

It’s a cool and breezy April afternoon down by Baltimore’s Inner Harbor, and the mid-rebuild Orioles are taking on the division-winning and record-breaking Minnesota Twins. Trying to salvage the final contest of a three-game series, the O’s — to no one’s surprise — find themselves trailing in the bottom of the ninth. But not all hope is lost. The Twins’ lead is small — two runs — and the Orioles have some of their best players due up. Out of the gate, Twins pitcher Taylor Rogers hits the first Orioles batter, Joey Rickard, in the foot. Then, after a Chris Davis lineout, Jesús Sucre resurrects the inning with a single to left that advances Rickard to third. The comeback is on.

Hanser Alberto then plunges the Orioles hopes back down to earth with a swinging strikeout that gives his team just one more out with which to work. But then comes Jonathan Villar, who rips a double to deep left, scoring Rickard and advancing Sucre to third. The Twins lead is cut in half. After an intentional walk to Trey Mancini that loads the bases, the game now rests in Pedro Severino’s hands. With two outs and the bases loaded, still down by one, Severino manages to work the count to 3-0. His team is one pitch away. The crowd is on its feet. Rogers winds and delivers his pitch. It’s outside! “Ball 4!” the commentator exclaims. The fans cheer, Severino begins to walk towards first, and the tying run starts his trot towards home. But suddenly, the umpire punches his arm through the air. He called it a strike. Severino walks back towards home plate, distraught. He pops up the very next pitch, and just like that, the game is over.


Using data from Baseball Savant’s pitch-by-pitch library, we can begin to understand the role that these incorrect calls play in baseball. By matching up the database’s pitch locations to the calls associated with those pitches, we can see which calls were supposedly correct, and more importantly, which were not. The results are pretty astounding. Last year, by this data, MLB umpires made a total of 33,277 incorrect calls. That’s good for 13.8 per game, or just over 1.5 per inning. While not every bad call is a comeback-killer, these mistakes have the ability to greatly alter an at-bat, a game, and maybe even a season. Read the rest of this entry »

Sabermetrics, the Sound off the Bat, and a Bit of Phenomenology

Baseball as a sport, like most activities of daily life, is one which we consume primarily through our eyes. While I’m certain some people still enjoy it by listening to the radio (a mode I’m still partial to), I think you would be hard-pressed to that argue baseball is not visual. That’s not to say we don’t listen to the sounds (personally I find baseball on mute to be close to a kind of torture). However, our judgments of the game, and more importantly our judgments of the players in it, are based on what we see visually. We don’t know Mike Trout is good just because the announcer tells us he is good, we know he is good because we can see how good he is. We can see the balls he snatches away as they clear the fence, as well as the balls he smashes over them.

There are other methods we can use to see that Trout is good as well. Sabermetrics and Trout have seemingly been tied together in their emergence into the public baseball consciousness. As he blossomed into a star, so did Sabermetrics as it rose to the forefront and into the view of the average fan. Like Trout, the way we digest sabermetrics is in a sense almost purely visual. We come to FanGraphs, and we read a stat line off the screen. When we look at exit velocity or launch angle, we’re looking at metrics we’re aware of because a computer system visualized them for us.

To a large extent, what I’ve said above is simply a result of us privileging sight more than our other senses. Baseball utilizes the other senses as well. We all likely have memories tied to the smell of the stadium or a leather glove. Maybe every time you go to a game you get a hot dog, and that taste is as connected to baseball as the sound of a cheering crowd. Baseball at its best is a palimpsest of all of these senses working together to create our experience. Read the rest of this entry »

The Tino Martinez All-Stars – Pt. 1

Excitement. Disappointment. Tradition. They make baseball great! Following your favorite team for six months a year will cause any halfway-devoted fan to learn more about the 25th man on the roster than will ever be necessary. It also might mean that fans could always recite the name of the prospect that never was, even years after the fact. And if those fans continue to follow that same team for many seasons, the list of players that they remember will continue to grow. Not all the memories are pleasant, however. That’s not how life works. In fact, the not-so-happy moments from the playing field tend to be what most fans remember the most. It’s those memories of a certain type of player type that live on in the collective mind of fans everywhere, and it’s those types of memories that I will be delving into in this piece.

A recent Grant Brisbee piece at The Athletic set out to create an all time team of “lightning rod players” he loved from the San Francisco Giants, and I felt it was a delightful read. It seemed like a lot of fun to dig in on all those players, and as a Cardinals fan, it made me think about what a similar team of St. Louis players would look like. What follows is my detour down the cul-de-sac of memory lane that many would rather soon forget, an imaginary lineup dubbed the Tino Martinez All-Stars.

Let me be clear — this will not be a scientific process. There will be a statistical element, but it will not be a “who was the worst player at every position” contest. Maybe the players were overrated, maybe they are overpaid, or maybe they were just overplayed. The bottom line is, apathy is the enemy! Also, I was born in 1983, so the team I’ll be picking will undoubtedly be influenced by the Cardinals clubs I have seen the most. You have been warned. Read the rest of this entry »