Pulling a Rockies Pitching Solution Out of Thin Air

The success of the Colorado Rockies franchise has historically been impeded by air: the thin air of Coors Field and the hot air blown by higher-ups in the front office.

Due in large part to playing their home games in a comically extreme hitters’ park, the Rockies have finished 14th or worse in the National League in runs allowed per game in 21 of their 28 seasons in franchise history. Colorado has finished with a winning record five times in the past 20 seasons, and in four of those they ranked in the top 10 in the NL in RA/G. No, their run prevention as a whole has never been what you would call “good” or even “well above average,” but their only brushes with success have come at times when their pitching ventured beyond putrid.

The adverse effect of the thin atmosphere on pitching is twofold. The more apparent aspect is that it imparts less drag on a batted ball, allowing for fly balls to carry further, resulting in increased slugging at Coors. Perhaps less obviously, movement of pitches due to the Magnus effect is diminished. At the risk of triggering memories of my undergraduate fluid dynamics course, the lift on a baseball (or any spinning sphere) is proportional to the density of the fluid it moves through. Thus, when a fastball is thrown at Coors Field, it has less “rise” (or more accurately, is less affected by gravity) than it would at other major league parks.

Does this mean that every pitcher will perform demonstrably worse if he takes up in-season residence in Denver? Well, yes, but actually no. Read the rest of this entry »

Jake McGee: The One-Pitch Pitcher

One of the newest members of the San Francisco Giants, lefty reliever Jake McGee, is coming off one of his best years in the major leagues throwing one pitch: a fastball. Seemingly by magic, McGee twirled a fastball 97% of the time he threw in 2020 on the way to a 2.66 ERA, 0.836 WHIP, and 11 strikeouts for every walk. I will be taking an in-depth look into McGee’s success and failure over his career, which might give better insight as to how he can continue to perform and how a major league reliever can succeed with only one pitch.

McGee was drafted in 2004 by the Tampa Bay Rays and made his major league debut with them in 2010. After his first full season in 2011, McGee posted extremely strong numbers in 2012, 2014, and 2015 with an ERA+ (it will become clear why I use ERA+) of 148 and a K/BB of 5.02 within those four seasons. After the 2015 campaign, McGee was traded along with Germán Márquez to the Colorado Rockies in exchange for Corey Dickerson and Kevin Padlo.

McGee immediately regressed in Colorado, as his ERA+ went from 163 to 103 (ERA+ adjusts for ballparks, which is particularly useful at Coors Field) and his K/BB sunk from 6 to 2.38 in the transition from the Rays to the Rockies (2015-2016). Of course, some of this decline is attributed to the difficult conditions of Colorado, but there is also additional evidence to show that McGee’s style of pitching contributed to his declined performance. Following 2016, McGee remained a strong-yet-aging reliever and was ultimately released by the Rockies in July of 2020.

Four days later, McGee signed with the Los Angeles Dodgers and proceeded to outperform even his 27-year-old self with an incredible season. McGee finished in the 99th percentile in K%, 96th in BB%, 95th in xERA, and 95th in xwOBA. So what exactly was the cause of this change and what did McGee do to get there? Read the rest of this entry »

Rearing Back: Pitchers’ Effort in Important Situations

Leading 3-1 and one out away from being a World Series Champion, Los Angeles Dodgers pitcher Julio Urías faces Tampa Bay Rays infielder Willy Adames. The first two pitches of the at-bat, fastballs resulting in a swinging strike and a called strike, clock in at 94.9 mph and 94.1 mph. The last pitch of the at-bat (and subsequently the World Series) comes on the third pitch. Urias fires a third straight four-seam fastball, this time for a called strike three at 96.7 mph. This may not feel particularly fast in a day and age in which some pitchers consistently hit 100 mph, but for Urías, there was a little something extra behind that final pitch. Of the 682 four-seam fastballs that Urías threw in 2020, this pitch was the fastest. While it may have been a coincidence that his hardest-thrown pitch was also in the most important situation, I suspect the significance of the moment was a key factor.

I doubt this claim comes as much of a surprise to anyone. Most people in crucial situations will push a little harder to ensure the outcome is in their favor. To test the theory, I examined pitch velocities from the 2019 regular season. I chose 2019 rather than 2020 to ensure the situations were most similar to a normal year in case any of the irregularities of baseball during COVID influenced the data. In general, it appears that two-strike fastballs are thrown harder than fastballs in other counts. I graphed the respective densities of fastball velocities below. Read the rest of this entry »

Modeling the Effect of Deadening the Baseball

Much has been made of the “juiced ball era” which we currently inhabit. Decreased drag on the ball along with an increase in-ball bounciness means that fly balls are carrying further, rewarding hitters with more home runs than ever before. This change has coincided with increases in strikeout rates which can be partially explained by pitchers throwing harder, but also may be due to more hitters selling out for a home run. There are now fewer balls in play than ever before, and many fans no longer enjoy this Three True Outcomes style of baseball.

Deadening the ball is a proposed solution to ballooning home run rates. Introducing a deadened ball along with measures to limit the dominance of pitchers (such as shrinking the strike zone) could increase the number of balls in play, improving the aesthetic value of baseball for many viewers as discussed on this site in a recent article. But what would baseball with a deadened ball actually look like? How much would the ball have to be deadened to return home run rates to those seen in past years? Would deadening the ball disincentivize strikeouts more strongly than the juiced ball? Which hitters would be the biggest winners and losers in a season with a deadened ball?

I aim to investigate all these questions in this article, so without further ado, let’s dive right in. Read the rest of this entry »

Pound the Knees, Steven

After the Toronto Blue Jays traded for left-handed pitcher Steven Matz, he is projected to slide into the bottom of the starting rotation and pitch about 115 innings this year. Matz’s 2020 was a year to forget — join the club, Steven — but let’s take a look at who Matz is as a pitcher and why a change in fastball location is something the Jays coaching staff might consider.

Matz pitched only about 30 innings last year, so in the interest of sample size, I will also be using statistics from 2019 and 2018. Here is what those last three seasons looked like, courtesy of Baseball Savant: Read the rest of this entry »

Extracting Luck From BABIP

Balls in play are subject to lucky bounces, bloops, and exquisite defensive plays. Are some great hitting seasons and breakout performances just a player getting lucky on more than their fair share of balls? Is there any way to tell if a player is truly lucky or good, or if his batting average on balls in play is higher than we would expect? Could building a better expected BABIP help us find over- or undervalued players?

In the hopes of better understanding players’ true abilities, I looked specifically at the correlation between BABIP and launch characteristics. A player’s BABIP viewed across a short timeframe, such as a single season, can be highly influenced by luck. BABIP doesn’t converge well over a small sample. Using the law of large numbers, we know that given enough balls in play, a player’s BABIP should converge to their “true” BABIP. Fortunately, other launch characteristics like exit velocity and launch angle (both vertical and horizontal) converge more quickly. My goal was to build a model for expected BABIP based on those launch characteristics that removes as much luck as possible and more closely reflects a player’s true skill.

This project started as work I did along with Eric Langdon, Kwasi Efah, and Jordan Genovese for Safwan Wshah’s machine learning class at the University of Vermont. We were using launch characteristics (exit velocity, vertical launch angle, and derived horizontal launch angle) to predict if balls would land for hits or not. We initially tried using a support vector machine classification but found that a random forest model delivered more accurate predictions. Read the rest of this entry »

Analyzing the Draft

Ever since the MLB draft was created in 1965, teams have been searching for any competitive edge to separate themselves from the rest of the league. After all, it is one of the best ways to acquire young affordable talent for your organization. Not picking the best players available is a huge missed opportunity for any club and can set the organization back for years. It can also exasperate even the most devoted fans. It is imperative to have successful drafts every year, but what constitutes a successful draft? How many major leaguers are available in a draft and where can you find these players? These are some of the questions I hope to answer.


Much of my analysis in this article will include references to team-controlled WAR. I calculated each draftee’s WAR total by summing their pitching and hitting WAR totals for the first seven years of their career to estimate the amount of value they provided their clubs before the players were eligible for free agency. This method is not perfect, because it does not consider demotions to the minor leagues, and it incorrectly assumes that every team would keep their prospects down in the minors to gain an extra year of control. However, I believe that the first seven years of WAR in a player’s career is a valid estimation of the value a player provides his organization before he exhausts his team-controlled seasons.

The drafts being examined are the drafts that took place from 1965 to 2004. I chose to stop at 2004 because that was the last year that had every player in its draft class exhaust his team-controlled seasons. If I were to include more recent drafts that still have active players, I could draw erroneous conclusions, since these players still have time to make their major league debuts and accumulate more WAR in their team-controlled seasons. Read the rest of this entry »

Maybe It’s Better To Never Swing at Shane Bieber’s Pitches

You don’t need me to tell you how effective Shane Bieber was in 2020. He led the majors in ERA, FIP, K/9, overall strikeouts, and of course was the unanimous winner of the AL Cy Young Award. The underlying pitch-tracking data all back up the quality of his skillset. He’s very good. So you’re probably wondering how this all jibes with a title suggesting it may be better for hitters to not swing at Bieber’s pitches, right?

I’ll start with this: Bieber’s 34% zone rate ranks 316th out of 323 pitchers who threw a minimum of 20 innings in 2020. That’s dead last among qualified starters. How is this possible? The simple answer is that, once again, he’s very good. The slightly less simple answer is that batters swing at unhittable pitches and don’t swing at hittable pitches. Bieber throws almost twice as many pitches out of the zone as he throws in the zone, so what if hitters just stopped swinging at his offerings? Surely he would just change his approach if a batter didn’t swing at his pitches, right? Read the rest of this entry »

Calculating the Odds of Mike Brosseau’s Magic Moment

After watching the great matchup between the Yankees and Rays in the 2020 ALDS, including Mike Brosseau’s epic at-bat against Aroldis Chapman in the deciding Game 5 of that series, I couldn’t help but take a look at the characteristics of the pitch he hit. Chapman is known as having one of the best fastballs in the game and a long track record of success as a closer. After battling back from 0-2, on the 10th pitch of the at-bat, Brosseau hit a 100.2-mph fastball thrown with 2386 rpms and 7.4 feet of extension over the left-field wall, allowing the Rays to advance to the ALCS.

This pitch was 6.9 mph, 80 rpms, and 1.1 feet above the average velocity, spin rate, and extension for four-seam fastballs in 2020. Given the same location, if the pitch was a little faster, had more RPMs, or was thrown even closer to home plate, would the result have changed? The aim of this article is to create a model to determine what the exact chances were of Mike Brosseau hitting that home run.

Using Baseball Savant and its wealth of Statcast data and more typical statistics, we can select all the four-seam fastballs thrown in 2020 and their related metrics. The data was cleaned for missing values, four-seam fastballs thrown by position players, eephus pitches, and four-seamers that may have been mislabeled as sliders or changeups. For the latter category, a minimum velocity of 87 mph was used to remove these potential label errors, and pitches with negative pfx_z values were removed as four-seam fastballs are expected to drop less relative to gravity. For pfx_x, the absolute value of the given value was used, as I want to look at the magnitude of the horizontal break as opposed to which side of the plate the movement is going towards. Read the rest of this entry »

A Lineup Construction Experiment

Who should bat second? This question has been debated quite a bit in recent years, as the modern approach has become to slot the best hitter in the 2-hole to increase their total plate appearances in a season. Others argue that the second hitter, like the leadoff man, should be a table-setter and the goal should be to get the best hitters to the plate with runners on base. So which is more valuable: getting your best hitter to the plate with men on or getting them to the plate more often? A simple experiment suggests that we are wasting a lot of energy arguing either side, and it would be time better spent thinking about other elements of lineup construction.


I created nine fictional players that will be referred to by position. I arbitrarily provided probabilities for the players based on seven possible plate appearance outcomes: single, double, triple, homer, walk, hit by pitch, and out. To simulate the lineup playing a game, I used a simple base-to-base style (the runners on base move up the same number of bases as the batter). An oversimplification of play to be sure, but the goal is to get an approximation of potential lineups relative to each other. Each lineup “plays” 100,000 nine-inning games so that the run distribution is virtually identical on multiple simulations. Read the rest of this entry »