What Happened to the Dodgers?

The once-invincible Dodgers set a LA record by losing 11 games in a row to start September. What was to blame, and what can we expect moving forward? Is it time to temper expectations for a team that seemed destined for greatness only three weeks ago? Let’s take a look at their season to-date in an effort to find out.


The Dodgers won a game.

For the lion’s share of the 2017 Major League baseball season, the above sentence was an apt description of the Dodgers result on an almost nightly basis.  Indeed, as of their off-day on August 28th, the baseball world was talking about the Dodgers — owners of a 91-38 record and a staggering +219 run differential — as worthy challengers to the 2001 Seattle Mariners for the crown of best regular season team in history.  Through that date, the team had already managed to string together multiple 10+ game winning streaks, win 20 games in a month twice, and build an insurmountable National League West division lead.  Sports Illustrated even ran the following cover on August 22:

Dodgers Cover

Since the off-day on August 28th, however, the once-invincible Dodgers have played historically bad baseball, losing 14 of 15 games through September 11 — including an astonishing 11 games in a row.  They were outscored by 53 runs over that stretch, a truly unbelievable fall from grace for a club that was crushing teams for most of the season.  Suffice it to say that it’s a good thing SI included that question mark on their cover.

Interested parties across the country have been pushing the panic button.  Take, for example, Bill Plaschke of the LA Times, who pronounced on September 7th that the Dodgers’ season was “spiraling out of control.”  Similarly, Plaschke’s LA Times colleague Andy McCullough answered fan questions in an article titled, “Dodgers mailbag: It is time to panic.”   McCullough wrote:

It is an abysmal skid, a horrific skid, an embarrassing skid, a confounding skid. I am running out of adjectives to describe it. This is my eighth season covering Major League Baseball. I’ve never seen anything like this — and I used to cover the Mets.

So, what to make of all this?  Is it really time for Dodger fans to panic about a team that seemed destined for greatness only three weeks ago?  Probably not, and let me tell you why.

Observed outcomes and randomness

First, we need a quick refresher.  Every observed baseball statistic (e.g., wins, batting average, ERA, fastball velocity, etc.) has some degree of randomness involved.  A hitter’s batting average, for example, is dependent not only on his underlying ability to hit but also elements of randomness outside of his control such as a weird hop of the baseball or a missed call by the umpire.  Generally, then, observed statistics take the following form:

Observed Outcome = True Talent + Random Noise

Some observed statistics — such as a hitter’s batting average on balls in play or a team’s ability to cluster hits together to score runs — are almost completely random, while others — such as a pitcher’s fastball velocity or a hitter’s foot speed — are almost all talent and have very little random variation.  Regardless of the statistic, over the course of many trials, we expect a player (or team’s) true talent to shine through and for random variation to even out.  However, over a small, arbitrary sample size (e.g., 15 Dodger games in early September), the randomness can cause wild results.  I think most baseball fans understand this.

Here’s the real issue.  Those perplexing, random results often masquerade themselves to us as a pattern, causing both casual fans and more-informed pundits to create a narrative that a structural change in the player or the team is causing the results.  Stanford PhD Ed Fang elaborates:

Humans have an uncomfortable relationship with randomness because we are wired to see patterns, as Daniel Bor explains in his book The Ravenous Brain. It starts with counting by 2 and 5 in the earliest years of grade school and culminates in the technology that puts a computer in our pocket. Humans have this remarkable ability to find patterns even though we can only hold 4 items in our working memory, the same number as a monkey. […] Humans not only find patterns but then tell stories to explain them.

According to Fang, humans are wired to build narratives around patterns that we perceive as being real but that are actually due to randomness.    In my opinion, there is something about sports — perhaps the human aspect — that exacerbates our propensity for building narratives around fake patterns of outcomes.

To illustrate what I mean, I flipped a coin 30 times.  In those 30 flips, I came up with 9 heads and 21 tails.  The coin was very streaky also, landing tails 11 times out of 12 tosses at one point!  Now, I don’t think these results would cause most people to conclude that the coin is weighted or not fair; I feel like most people are very aware of the inherent randomness involved in a small sample of coin flips.  What if, however, we were analyzing wins and losses for a baseball team rather than heads and tails flips of a coin.  In that scenario, you can bet that 9 wins out of 30 games — including 11 losses out of 12 — would cause most fans to search for a story to explain the losing.  The context of sports causes us to forget that randomness plays a role.

So, then, both talent and randomness effect observed outcomes — in this case, the Dodger’s streak of losses.  Has there been a structural change in the Dodgers’ talent (e.g., injuries or fatigue), or have they been victim of some sort of horrible (random) streak of regression?  Let’s take a look at their season to-date in an effort to find out.

Before the off-day on August 28th

The Dodgers were a juggernaut prior to August 28th — thanks in large part to both the hitters and pitchers playing well above their preseason projections.  Preseason projections are never exactly right, but they give a window into industry expectations of a player’s true talent levels.  We would expect players who are playing well above projections to fall back to earth as the season continues.

Below is a graph showing actual minus preseason predicted weighted on-base average (wOBA) for the Dodger hitters through August 28th.  (Projections are per Steamer, and data per Savant.)  As I’ve mentioned before, wOBA is an effective measure of the overall contribution of a hitter.  It is an improvement over on-base percentage because it rewards hitters for the exact run values of distinct offensive events (singles, doubles, walks, etc.) by using linear weights.

Hitters - wOBA actual minus preseason (Pre-Aug 29th)

Red bars indicate those players that were under performing preseason projections as of August 28th, and blue bars indicate those players that were over performing.  As the graph shows, most of the Dodger hitters were — for whatever reason — well outperforming their projections during the first five months of the season; it is natural for hitters like Chris Taylor and Austin Barnes to regress as the season progresses.   This is random variation at work, and we should expect it.  The same is true for certain Dodger pitchers, as shown in the graph of actual minus preseason predicted WAR below.

Pitchers - WAR actual minus Preseason (Pre-Aug 29th)

Again, red bars indicate under performance relative to projections, and blue indicate over performance.  As the graph shows, certain key arms such as first-half stud Alex Wood and reliever Brandon Morrow were punching way above their projections for the first five months of the season.   Just like with hitters, we should expect these guys to come back to Earth.

It seems the Dodgers benefited from a perfect storm of many hitters and pitchers outperforming projections at the same time.  This is what allowed the Dodgers to rattle off a stretch  of winning like they did from May through July.   Regression was inevitable.  Sure, the true talent projections could be wrong; perhaps Chris Taylor is a much better hitter than the industry gave him credit for.  However, I’d also argue that both the hitters and pitchers were getting randomly lucky and that this luck was always bound to reverse.

Let’s look at hitters first.  Below is a graph showing actual wOBA minus expected wOBA for Dodger hitters.  Expected wOBA is a Statcast statistic that measures what the wOBA for a given hitter should have been based on the exit velocity and launch angle of his batted baseballs.  Expected wOBA removes the actual outcome (e.g., single, double, triple) from the equation and rewards hitters for what they can control (i.e., the quality of contact).  A hitter with a large difference between actual wOBA and expected wOBA has gotten lucky.

Hitters - wOBA actual minus xwOBA (Pre-Aug 29th)

Red bars in this context mean unlucky hitters, and blue bars indicate lucky hitters.  As the graph shows, through the first five months of the season, almost every Dodger regular posted an actual wOBA higher than would be expected given the quality of the contact.   Some, such as Chris Taylor and Yasmani Grandal, posted significant deltas (above 0.04).  According to Fangraphs, an increase of 0.04 in wOBA can mean the difference between an average season and a great season.  Remember, these differences are due to random variation driven by the positioning of the defense, umpires, weather, etc.  It was inevitable that the luck would turn around.

The same goes for the two pitchers we mentioned above who were uncharacteristically successful in the first five 4-5 months.

Pitchers - wOBA actual minus xwOBA (Pre-Aug 29th)

The luck is less pronounced on the pitchers’ side, yet it’s clear that the results posted by Alex Wood and Brandon Morrow were lucky based on the quality of contact allowed.

After the off-day on August 28th

We’ve seen that both Dodger hitters and pitchers were over performing their projections, thanks in part to random luck.    Since that date, basically every Dodger player has regressed.  The team results speak for themselves, and the media has scrambled to explain the losing.

But that doesn’t mean that the team is any different than the team we were watching three weeks ago!  Indeed, there is evidence that — in this tiny sample size — the hitter and pitcher luck has turned against the team.  Let’s look at the same graphs as above, except this time we’ll filter for games after August 28th.

Hitters - wOBA actual minus xwOBA (Post Aug 29th)

Red still means unlucky, and blue means lucky.  As shown in the graph, the luck has reversed itself in this tiny sample size, as most Dodger hitters have hit the ball better than their results would indicate.   The same goes for pitchers:

Pitchers - wOBA actual minus xwOBA (Post Aug 29th)

Based on the contact allowed, almost every Dodger pitcher has pitched better during the losing skid than their results would indicate.

There’s no way around it: the Dodgers have been playing bad baseball.  But as these two graphs show, they have also been getting unlucky!

Where we stand

Let’s return to our primary question: what explains the observed losing?  Has there been a structural change in the Dodgers’ talent, or has randomness showed up at an inopportune time?

I’d argue a bit of both.  There’s little doubt the Dodgers are fatigued, as every team is to some degree at this point of the season.   Clayton Kershaw and Corey Seager have also missed time due to injury; without those two healthy, the Dodgers are not nearly as good as they could be.   Their psyche is probably a little shaken as well from the last two-weeks of losing.

Yet it’s important to remember that randomness is involved, and I think the panic narrative built by the fans and media alike is foolish.  The Dodgers, perhaps more than any other team, were due for some regression.   Randomness does not explain the entire streak, but it is certainly a contributing factor.

So, what should we expect going forward?  As the late NFL coach Denny Green famously proclaimed, “They are who we thought they were!”  As long as they are healthy, we should expect the Dodgers to get back to their winning ways.  They have a deep lineup and bench, Kershaw and Darvish at the top of a stacked rotation, and enough bullpen arms to match-up with the best of teams.   Their bullpen improved at the trade deadline, and they have strong leadership in the clubhouse.  In short, expect the Dodgers to be the Dodgers.   Mike Petriello, who is a friend of the MIT Sloan Sports Analytics Conference and an overall great guy, said it best when asked what the Dodgers need to do to turn their September around:

The unluckiness will subside, and the Dodgers will get back to winning games.  Of course, this doesn’t mean that they will win the World Series.  If you take away anything from this article, it should be that baseball in small sample sizes — like the postseason — is subject to a ton of random variation.  Yet the Dodgers are in a fantastic position, and I can’t wait to see what happens.

Update: Since I began writing this article last week, the Dodgers have won 3 of 4 games, and the chatter about collapse has predictably subsided.  Pretty soon, the media will be talking about how “hot” the Dodgers are leading into the postseason!  Beware of the narrative.

Modeling a Free Agent Pitcher’s Salary

The following is adapted from an analysis that Chris Bull (MBA ’18), Nehal Mehta (MBA ’18), and I completed as part of an MIT Sloan’s Analytics Edge course. Thanks to them for their help with the analyses, presentation, and write-up.

The Problem

The MLB free agency problem—how teams effectively target the right set of players on the open market for the right price—is an extremely important and costly one.  In 2017, the total contract value of free agents signed was greater than $1.4 billion, a staggering number that actually represents a decrease from the $2.4 billion of total contract value signed in 2016.  These contract values represent a per team average of more than $45 million in 2017 and $80 million in 2016, a significant annual investment made by each team to acquire player services.  Teams incur considerable additional expense to evaluate player talent in hopes of uncovering players they can target in free agency for below-market rates.  As such, acquiring the right mix of talent at the right value is an important and costly task that has critical implications for the success or failure of each franchise.

The Greater Goal

Given the above, we leveraged historic player performance, biographical, and salary data in order to accurately predict what contract value a player will command on the free agent market and what factors are driving that value. In particular, we have focused our analysis on pitchers because our hypothesis was that the market has historically overvalued certain performance measures for pitchers that do not reflect the player’s true contribution to a team’s success (i.e., wins), and therefore the pitching market has some degree of inefficiency.  Gaining insight into what drives free agent contract values, a team can then identify and target future free agents who might be undervalued by the market, given this bias towards inappropriate measures.

The Data

Our primary player performance data source was the Sean Lahman Baseball Database, which is widely regarded as one of the most comprehensive and reputable publicly available data sources in sports; Lahman incorporates baseball statistics dating back to the late 19th century on everything from individual performance measures to end-of-season awards voting. Free agent contract data was compiled from three sources; for years 2006-2010, the data was pulled from ESPN; for year 2011, the data was pulled from MLB Trade Rumors; and for years 2012-2017, the data was pulled from SPOTRAC. Finally, opening day payroll information was pulled from The Baseball Cube.

In the Lahman Database, players are assigned a unique identifier, which normally takes the form “first five letters of last name” + “first two letters of first name” + identifier number (which differentiates players with similar names). Using this identifier, we were able to map salary information and performance statistics to the free agent data, creating a single, comprehensive dataset which would form the base of our analysis.

Model Data Creation

Prior to modeling, we made a number of critical data transformations. These transformations can be broadly categorized as relating either to the individual free agent salary data, to individual measures from the Lahman database, to comparable players, or to payroll size.

Individual Free Agent Salary Data: First, to control for contract length, we calculated the average annual value (AAV) of each contract by dividing total contract size by the duration of the deal. (AAV is a crude, undiscounted dollar figure that treats all future cash flows as the same. Yet we believe it is appropriate to use in this context, given that we don’t have a lens into an appropriate discount rate.) Next, nominal AAV values were inflation adjusted using the Consumer Price Indices (CPI) from the Bureau of Labor Statistics (BLS); this ensured that all salary information was represented in 2017 real dollar terms. Third, non-pitcher and minor league deals were removed from the data in order to isolate Major League pitchers only. The following 641 free agents from 2006-2017 remained in our sample.

Exhibit 1_Count of Major Leaguers

Finally, we log-transformed the AAV variable because of the presence of a number of outlier AAV deals each year. The below pictures present the distribution of nominal AAV and log-transformed AAV by year.

Individual Measures from the Lahman Database: We created rate statistics from count statistics (using total batters faced as the denominator) in order to control for differences in aggregate output between free agents. We also calculated other metrics such as ERA, WHIP, and Fielding Independent Pitching (FIP). For each of these measures, we incorporated time series lags for each of the two years prior to free agency to account for a pitcher’s most recent performance heading into his free agent winter. In addition to these single-season lagged variables, we created cumulative counts for number of innings thrown in a pitcher’s career, total All-Star appearances, and cumulative wins. We added an indicator variable to separate relief pitchers from starters, and we calculated each pitcher’s age at the midpoint of the season immediately following their free agent winter. Finally, we added each player’s log-transformed salary in the previous season; if previous year salary was not available in the Lahman database, we used the last salary recorded for that player.

Comparable Players: For each player-year observation in the database, we modeled the supply of comparable free agents in that year by calculating the Euclidean distance between a given free agent and every other free agent in the market. The analysis was done separately for starting pitchers and relief pitchers. For starters, distance was calculated based on age, lagged wins, and lagged FIP; for relievers, distance was calculated based on age, lagged saves, and lagged FIP. The threshold distance for “comparable” pitchers was chosen based on a sensitivity analysis whereby we inspected the distribution of total comparables across years under varying threshold levels. The below picture presents the average comparables per person by year for both starters and relievers.

Exhibit 3_Average Comparables by Year

There are more relievers in the market generally, and clubs also view free agent relievers as more interchangeable than starters; thus, it is appropriate that relievers have more comparables than their starter counterparts on average.

Payroll Size: Payroll varies widely between clubs in Major League baseball. Thus, for each player-year, we added the opening day payroll size of the acquiring club for that year to reflect the differences in team spending habits.

Exhibit 4_Boxplot of Opening Day Payroll

Opening day payrolls were also inflation adjusted to represent 2017 real dollar terms.

Modeling Free Agent AAV

After gathering, cleaning, and transforming the data, we performed three continuous modeling techniques: linear regression, CART, and random forest. We trained our models using the free agent data from 2004-2014, and we held out 2015-2017 data in order to test our models’ out-of-sample performance. Based on our data and modeling, we found that the linear regression and random forest models had comparable accuracy, though the linear regression model was clearly more interpretable.  Each method is described in greater detail below:

Linear Regression

As noted above, linear regression offered the greatest combination of accuracy and interpretability.  We initially started with a data set of 35 potential independent variables; however, we noticed a very high degree of correlation among certain variables (i.e., Wins and Innings Pitched), so we excluded certain highly-correlated variables to reduce multicollinearity.  We next removed insignificant variables one-by-one based on significance and intuition, resulting in the model included below.

Linear Output

As we hypothesized, recent opportunity-based performance measures (wins and saves) as well as factors that are more reflective of a pitcher’s individual talent (strikeout percentage and walk percentage) are both heavily weighted by the market. Interestingly, including lagged FIP, a pitcher’s weight, and/or a pitcher’s handedness in the model did not improve the performance. The cumulative measures (wins, All-Star appearances, total innings pitched) also were not helpful.

Our linear regression model performs fairly well out-of-sample, with an out-of-sample Root Mean Squared Error (RMSE) of 0.61 ($1.84M), an out-of-sample Mean Absolute Error (MAE) of 0.48 ($1.62M), and an out-of-sample R-squared (OSR-squared) of 0.61. The below picture presents a scatter plot of predicted versus actual contract values for the 191 players in our test set.

Actual vs. Predicted

As shown above, our model performs adequately with small to medium AAV players, but it tends to under predict AAV for bigger money pitchers (especially starters). That our model systematically underestimates expensive starting pitchers means that we likely are not accurately capturing how teams financially differentiate between starters and relievers; for instance, teams deeply value a starter’s durability—which we have not explicitly included here—in addition to his performance metrics.


In the interests of delivering the most interpretable possible model which could serve as a simple guide for managerial decision-making, we next built a CART model.  Given a set of user-defined parameters, a CART model builds a tree by splitting the data on certain independent variables. CART models are highly interpretable given that they provide simple rules to determine the prediction; the output is a decision tree-type picture like the below.

As expected, our CART output proved to be highly intuitive, with premiums paid for pitchers with more than 8.5 wins and high strike out percentages.  (Outcomes in the tree below are log AAV.)

Cart Tree

After the initial split on last year’s wins, premiums were paid for closers, and large market teams also evinced the ability to pay higher premiums for free agents. Predictably, despite this highly intuitive result, the CART model fared poorly during validation on the test set, yielding an out-of-sample RMSE of 0.72 ($2.05M), an out-of-sample MAE of 0.59 ($1.80M), and an OSR-squared value of 0.45.

Random Forest

Since our goal was predictive accuracy, we elected to fit a random forest model to our data to assess whether or not we could increase our accuracy over a simple linear regression. At a high level, random forest models take advantage of the “wisdom of crowds”: the idea that the predictions of a group outperform those from any one person. A random forest model is a combination of many CART models; each CART model is trained with a random subset of observations and variables from the training data, and each fitted CART tree makes a prediction given the values of the independent variables in its subset.  Because each CART model is trained on different subset of observations and variables, each model uncovers slightly different patterns. When combined, random forest has the ability to find complex patterns in the data that a simple linear model would have missed.  The one big drawback to random forest is the lack of interpretability; a random forest model is more or less a black box that often delivers very accurate predictions.

We started with the same set of data above and conducted out-of-bag cross-validation on our training data to determine the appropriate MTRY value. (The MTRY value controls the number of variables examined at each split of the fitted CART trees.)  Based on this analysis, we determined an MTRY of 10 variables resulted in the lowest mean absolute error, so that was the value we used in our final random forest model.

Similar to the linear regression model, the random forest model assigned high value to recent opportunity-based measures of performance, including last year’s salary, wins, innings pitched, and saves.  The top eight measures are included in the table below:

CART Importance

Our random forest model was fitted with an out-of-sample RMSE of 0.62 ($1.86M), an out-of-sample MAE of 0.50 ($1.65M), and an OSR-squared of 0.60.

Comparison of Models

The below table depicts a consolidated comparison of the out-of-sample performance for each of the three models.


Interestingly, the linear regression delivered the highest OSR-squared and lowest error values of all three potential models. The CART model’s performance likely suffered on account of overfitting to the training data; this result was manifest despite multiple adjustments to the breakdown between training and test population sets. While intuition may have suggested that the random forest model would always outperform the other two options, our empirical observation suggests that the model struggled to improve on the linear model on account of the relatively small data training set.  (Random forest would almost certainly have outperformed the linear model if we had millions of data points.)

Just for fun, let’s take a look at some of the best and worst predictions using the coefficients from the linear model.  These players are from the test data set, so their data was not used in model estimation.

Predictions (Good and Bad)

Interestingly, we were very close on two of the highest paid starters in the game: Zack Grienke and David Price.  This is despite systematically underpredicting expensive starters, which can be seen in the fairly horrible predictions for Jeff Samardzija, Wei-Yin Chen, Johnny Cueto, and John Lackey.

Challenges in Modeling Free Agent Pitcher Salaries

Forecasting MLB player salaries is a challenging proposition that we believe is complicated by four main factors.  First, team plans and market forces are unclear and difficult to model. As constructed, our model fails to account for team need, which means we fail to capture a team’s willingness to pay. Similarly, many teams plan to trade for players or target players next year instead of pursuing free agents this year, which impacts the competition for player resources. To refine the model, we would seek to better account for team needs and market characteristics, though the appropriate approach to take remains unclear.

Second, become teams pay for future performance, the model should incorporate performance projections rather than actual observed performance. Though this creates a “model of models” scenario, each team’s willingness-to-pay is based on their expectation of how a player will perform. Of course, the historical performance indicators are baselines for projections, but they deviate from projections in that they do not include the vital regression to the mean component. To better reflect what the market value is likely to be for a player, we would seek to incorporate some form of consensus projections to address this.

Third, the market for pitchers is not an independent marketplace. Teams have limited resources to spend, and money spent on non-pitching staff clearly impacts the resources available to pay free agent pitchers.  Our model currently fails to account for these measures, so we would seek to model their impact in a future forecast by incorporating data reflecting the size and competitiveness of the overall free agent market—not just the free agent market for pitchers.

Finally, the huge influx of cash from local TV deals has perhaps translated into salary inflation above and beyond the CPI that we used to inflation-adjust our salary data. Because this is a fairly recent development, there may be a structural break between the data we used to fit the model (years 2006-2014) and the data after that period.  A sharper model might better account for baseball-specific inflation rather than using the CPI only.


Though the specified MLB pitcher salary model has room for improvement, it provides a reasonably accurate prediction of the average annual contract value a MLB pitcher is likely to command upon entering free agency.  Using this prediction output—and more importantly understanding the factors driving the market’s value in our model—teams can identify strong performers who are expected to command lower prices, most likely those who have lower opportunity-based performance measures like wins or saves.  We would recommend teams with limited budgets leverage our model assessing projected cost alongside more traditional scouting analysis to focus their limited resources on potentially undervalued free agents that address team needs.

The Curious Case of Jason Heyward

Jason Heyward’s first year with the Cubs was certainly a year to forget. So should we expect more of the same in 2017? Let’s take a look at Heyward’s career and comparable players in an attempt to find out.

The night was October 26, 2016.   Game 2 of the World Series,  and the Chicago Cubs were down 0-1 to the Indians in their chase for the city’s first title in over 100 years.  And where was the Cubs’ highest paid hitter, Jason Heyward?  Riding the pine for the second straight game, benched because of an inability to produce at the plate.  To a large extent, Heyward must have been thinking: how the hell did I get here?  Meanwhile, the Cubs front office was concurrently wondering whether they fantastically overvalued their prized off-season acquisition.

To answer these questions, let’s examine Heyward’s superstar pedigree, his spectacularly bad 2016 offensive performance, and his prospects for next season.  (Spoiler alert for 2017: he’s going to bounce back.)

A Cant-Miss Prospect

A first-round pick by the Atlanta Braves in 2007, Heyward tore up the minors for three seasons before forcing his way onto the Big League team to begin 2010.   Heyward was the consensus number one prospect in baseball at the time, generating sentiment like the following scouting report from MLB.com:

There’s little Heyward can’t do. He’s got great bat speed, with the ability to hit for average and power. He has an excellent knowledge of the strike zone. He’s got a plus arm from the outfield, runs well and is an excellent base-runner. His makeup is off the charts. Oh, and he’s only 20…

Heyward owns a slightly unorthodox swing: his hands start very low and close to his body, he has a bit of a hitch, and the swing has very little loft.  From where I sit, the swing seems to lack the fluidity exhibited by other superstar left-handed batters.


The lack of loft means that he likely will never tap into the massive home run power that normally comes with that type of bat speed, and the hitch means he may have trouble getting to inside pitches with authority.  Nevertheless, based on his superb minor league results and first-round pedigree, expectations across the industry were sky-high for the talented, young left-hander.

Major League Ready

Heyward announced his arrival on the world stage in 2010 by launching a home run to the right field seats in his first Major League at-bat for the Braves.  He would ultimately play five seasons for Atlanta, putting up solid — albeit at times not spectacular — offensive numbers to go along with excellent defense.  While his offensive prowess may not have quite lived up to immense expectation, his defense and base running made him one of the most valuable outfielders in baseball during the Atlanta seasons of 2010-2014.  Still just 25, Heyward was set to cash in as a free agent after the 2015 campaign.

Fully aware of how expensive Heyward would be as a free agent, the Braves decided to  include Heyward as the centerpiece of a blockbuster deal with the St. Louis Cardinals for Shelby Miller before the 2015 season.  Heyward was extremely valuable during this only season with the Cardinals, pairing his usually stellar defense with excellent offensive production.  All told, he was the 11th most valuable player (regardless of position) according to FanGraphs in 2015.  The below chart shows that Heyward was consistently above-average offensively during his time in Atlanta and St. Louis:


Due to his track record and his young age, Heyward commanded a massive deal after the 2015 season; he ultimately parlayed his performance into a hefty 8 years / $184M contract with the Chicago Cubs.

New Contract, New Town, Terrible Time

Yes, the Cubs won the World Series.  But on a personal level, the slugger’s first year with the team was a year to forget.  His offensive production dropped off a cliff, as shown in the below graph:


Heyward was mightily below-average at the plate last season; indeed, of the 394 players who registered over 150 plate appearances, Heyward ranked 321 in wOBA.  We might expect a precipitous decline like this from a hitter in the twilight of his career.  But for a player with his offensive track record, athleticism, and age to be so inept at the plate?  That is a massive deviation from expectation.

So, what happened at the plate last season?  To investigate, let’s examine a few groups of heat maps (courtesy of FanGraphs) to see if there are any glaring differences between 2015 and 2016.  First up is swing percentage; the top set of images is against left-handed pitchers, and the bottom set of images is against right-handed pitchers.

The charts lump all pitches together, so they would change if we subset by pitch type.  But in the aggregate, the graphs appear to show that Heyward swung at more inside pitches from left-handers and more up-in-the-zone pitches from right-handers last season than in 2015.

So, maybe Heyward was being slightly less selective.  How often did he make contact with these pitches?  Below is a comparison of Heyward’s contact percentage between 2015 and 2016, separated by pitcher handedness.

It’s tough to glean any glaring difference from the contact percentage graphs, as it appears that Heyward made a lot of contact in both 2015 and 2016.

But was it weak contact?  To answer that question, let’s look at his Isolated Power.  Isolated power is a measure of a hitter’s ability to hit for extra bases as opposed to singles, and I show the heat maps here as a proxy for hard contact.

You’ll notice a glaring difference in ISO between 2015 and 2016; compared to 2015, Heyward made significantly less hard contact against both lefties and righties.  Put all the heatmaps together, and it looks like Heyward made a great deal of weak contact in 2016.

But there’s one (huge) piece of the puzzle that we’re missing: luck!  Take a look at the following graph showing Heyward’s batting average on balls in play (BABIP) between 2010 and 2016:


As noted by FanGraphs, a high or low BABIP is not necessarily a sign of luck, but a BABIP that is substantially different from a player’s career mark usually is.  Heyward’s average BABIP from 2010-2015 was .305, and his BABIP in 2016 was .266.  Perhaps Heyward was simply unlucky.

This next point is key.  Think of player performance like a bell curve distribution, with some mean (i.e., the player’s true talent level) and some standard deviation of performance.  Any observed performance of that player is a random sampling within that player’s performance distribution.   We expect a player to perform at their true talent after a huge number of trials; yet over an arbitrary number of plate appearances (say, for a season), there is a chance that the player significantly over or under performs their true talent level.  This variation in observed performance is due to chance alone; Heyward simply had a year in the (very) bottom tail of his performance distribution.

Predicting Heyward’s 2017

So, given the above, what can we expect from Heyward offensively in 2017?  Has he completely lost his ability to hit?  Or should we expect a rebound season at the plate?

These days, publicly-available player predictions are easy to find.  Steamer, ZiPS, and PECOTA are three of the most well-known systems, and while each varies in complexity, they generally rely on (at least) weighted past performance, league performance, and age/athleticism.   For simplicity, we’ll just look at Steamer here.

And guess what?  Heyward’s projected wOBA for 2017 is .333.  Not .282 like his 2016 season, or league-average at roughly .310, but above-average at .333.   Why is the prediction so bullish on Heyward’s chances of a return to form in 2017?  The short answer: because that is what other players have done.

This is a key point about predictions: our best guess for Heyward’s offensive performance next season is based on comparable players.  In essence, there is nothing particularly special about Jason Heyward individually; we’d expect him to do what every other hitter with a similar profile has done before him.

To find comparable players, I built a database containing offensive statistics for every player-season from 1985 through 2016.   I subset the database to isolate those players with four consecutive years of offensive performance within +/- 0.02 of Heyward’s wOBA.  This means, essentially, that each of the players in the sample had three good years of offensive performance followed by one bad year.  We’re interested in how these players performed in the year following their bad year:


Weighting by plate appearances, we get a .325 wOBA across the entire sample of comparable players.  This is above league average; clearly, more often than not, the player returns to form after his bad year.

This is a good start, but this list includes athletes that are not comparable in age to Heyward.  The below table subsets the sample further to include only those players that are closer to Heyward on the age curve:



Aha!  Again weighting by plate appearances, these players posted a .337 wOBA in the year immediately following the bad performance.  By isolating those players that are on a similar portion of the age curve, we have come very close to replicating Heyward’s 2017 Steamer projection.  As we can now see, the projection systems predict that Heyward will bounce back precisely because that’s what comparable hitters tend to do.

There are rumblings of Heyward making major changes to his swing this offseason. However, when Heyward returns to his former self at the plate, don’t be too quick to attribute the success to the new swing.  Rather, remember that Heyward is due for a great deal of regression towards his true talent level, which means a bounce-back season is in order.  And what welcome news that must be for both Heyward and the Cubs!


How on Earth Did He Hit That?

Gary Sheffield was incredible to watch at the plate, with lightning quick hands that even the casual baseball fan could recognize with the naked eye. With Sheffield making his annual Hall of Fame ballot appearance, which current hitters have quick enough hands to mash the fastballs that the Sheff used to feast on?

A certain type of Major League slugger fascinates me more than the rest.  He’s the dude who stands up there, waggles his bat aggressively, has an extreme leg kick, and then still manages to pull a high-grade fastball.  These guys are seemingly on one leg as the pitch is hurled at them and still manage — somehow —  to be ready to hammer it before it crosses the plate.

The slugger that immediately comes to mind is Gary Sheffield.  The Sheff, who clubbed 509 home runs over his 20+ year career, possessed the most notorious and aggressive waggle of them all; the cap of his bat would be pointed almost directly at the pitcher as the ball was coming at him.  Yet because of his other-worldly hand speed, Sheffield was still able to get the barrel of the bat to the baseball.  Check this out to see what I mean:


Sheff manhandled inside fastballs thanks to some of the fastest hands in the game.  In honor of his third appearance on the Hall of Fame ballot, I thought it would be fun to find out which hitters used their lighting fast hands to mash the hardest inside heaters in 2016.

What pitches meet the criteria?

Over 700,000 pitches were thrown across the Major Leagues in 2016.  To investigate the idea posed above, I subset the database to include only those pitches which were (1) thrown over 95 MPH by the pitcher, (2) located on the inner 15% or further inside of the plate, and (3) swung at by the batter.   Below is a strike zone plot of those pitches; the red dots correspond to the fastballs that were contacted in play for a hit, and the gray dots correspond to those balls that were either swung at and missed, foul tipped, or put in play for an out.

All pitches on the graph are inside: the right side of the graph shows inside pitches to lefties, and the left part of the graph shows inside pitches to right handed batters.  Left handed batters accounted for only 40% of total pitches seen in 2016, so it makes sense that there are generally fewer dots on the right hand side of the graph.


First, the graph shows that hitters swung at some wildly inside pitches this season.  Those 95 MPH+ inside pitches, located a foot above the zone?  Might want to lay off those. Same to the fastballs that almost hit the ground and the ones that are about a foot inside.

You’ll also notice that, predictably, the farther inside the fastball, the less likely the hitter is to have success.  But there’s also a significant amount of red on that graph,  both for lefties and righties, meaning that certain hitters — at least every once and a while — had success by swinging at these pitches.   So, the next question is:

Who saw the most of these pitches, and who swung most often?

Let’s see which hitters bite at these pitches most often.  Below is a table that shows the list of the hitters who saw these pitches the most and their corresponding number of swings.


Because the criteria for inclusion in this analysis are restrictive, the “Total Pitches Seen” number for any given hitter is not particularly high.  (A starter might see over 2,500 pitches in a season.)  However, there are a number of hitters that, when these types of pitches come their way, don’t seem able to keep from swinging.

Perhaps these are the hitters we are looking for!  One might hypothesize that the guys who swing the most at these pitches have the most success, and that they have success because they have fast hands.  The first few guys on the list — Abreu, Bryant, and Donaldson — certainly pass the eye test.  To find out, let’s take a look at another piece of the puzzle.

Who had success on these pitches?

My thought with this exercise was not to see who swung at these pitches, or even who collected hits on these pitches in 2016; it was to see who could hit these balls hard — like Gary Sheffield.  In order to isolate “hard” hits from the bloop singles, I removed all hits where the word “soft” appeared in the event description contained in the raw data.

This distinction is subjective and predicated completely on the manually-recorded description of the event in the data.   Of course, batted-ball exit velocity would make this a much more exact science, but MLB hasn’t released individual at-bat tracking data to the public.  So, for this analysis, “hard” hits are considered singles/doubles/triples/home runs that do not include “soft” in the event description.  (There are other hard hit events, such as line outs, that are more difficult to detect in PITCHf/x and have been excluded here.)

Below is a replication of the same table, but with an added column for Total “Hard” Hits.


The hitters who swung at these pitches the most did not necessarily have much — or, interestingly, any “hard” hits on these baseballs in 2016.  For example, reigning NL MVP Kris Bryant did not record a “hard” hit on any of these pitches last year.  So, who were the leaders in “hard” hits?  Below is another table which shows the 2016 league leaders in “hard” hits off of 95 MPH+ inside pitches.


Importantly, no hitter was successful very often; that’s to be expected since these pitches are hard to hit.  But we’re getting somewhere, since we’ve appeared to isolate (1) a group of good fastball hitters and (2) a number of hard hit baseballs.  The 22 home runs definitely fit that bill.

Of the “hard” hits, which were on the wildest pitches?

Let’s further dig into the location of some of the wildest “hard” hit balls.   Below are two tables, one for all “hard” hits and one for home runs only, by notable accomplishment.


There are some pretty good fastball hitters listed on these tables and the ones above.  For example, Ryan Howard has a notoriously quick bat, and although he’s not nearly the hitter he used to be, still managed to collect a hit on a 101.5 MPH inside fastball this season.

This exercise came to mind because I loved watching Sheffield hit.  Thus, the best part about identifying these unusual events is marveling at them on video.  However, since videos of singles — like Howard’s single on a 101 MPH fastball — are hard to come by on the internet, we’ll have to settle for watching the home runs that we’ve identified as particularly rare.

Here’s that Denard Span home run — which happened to be a game winner — where the heater almost hit the ground.  Those are some fast reflexes!

Next, here’s that Evan Longoria dinger on the 97 MPH pitch located at the inner top of the strike zone.  That pitch probably breaks most hitters’ bats, yet because of a short, ultra-quick swing, Longoria hit it for a dinger.

And finally, here’s the Joc Pederson home run from September 10, which was both the most inside and the hardest thrown home run in our sample.  Somehow, Pederson was able to keep this ball in fair territory:

We endeavored to identify the hitters who have fast hands by isolating those players who enjoyed success on hard, severely inside pitches in 2016.  To some degree, I think we accomplished that.   The group of hitters listed throughout this article — Piscotty, Betts, Pedroia, Hosmer, and the like — are, by and large, excellent fastball hitters who pass the eye test for having lightning quick hands and bats.  Hosmer and Pedroia even throw in excellent leg kicks!

But there are certain other factors at play that tamper with the results, the most relevant of which being a hitter’s ability to guess.  A hitter might rely on his ultra-quick hands to catch up to the inside fastball thrown over 95 MPH, or a hitter could have average bat speed and simply guess correctly on that particular pitch.   Joc Pederson can hit any pitcher’s fastball, but I would imagine he did a bit of guessing on the home run shown above.  We don’t have the data to know for sure, so this simple caveat will have to do.

But overall, the hitters we’ve identified are those types that I’ve admired since I was a little kid: unafraid — like Gary Sheffield — to swing violently in an attempt to punish hard, way-too-inside heaters.

How Do Pitchers (Try To) Get Corey Seager Out?

Corey Seager’s breakout 2016 performance cemented his position as the Dodgers’ shortstop of the future. Let’s take a look at how pitchers tried — often unsuccessfully — to get Seager out last season.

Corey Seager is a budding star.  A former North Carolina high school baseball standout, Seager was selected 18th overall by the Dodgers in 2012 and hasn’t looked back, tearing his way through six levels of the minor leagues before earning a September call up in 2015.  The rookie with the calm demeanor performed very well during his late-season stint with the Major League club, starting over veteran shortstop Jimmy Rollins in the playoffs and convincing management in the process that he was ready to be the 2016 every day shortstop.

The 22-year-old wunderkind certainly lived up to the hype during his first full season in the Major Leagues.  Seager stayed injury free, playing in 157 regular season games and finishing in the top-7 in wins above replacement (according to both the Baseball-Reference and Fangraphs versions of the statistic).   What’s more, Seager played surprisingly good defense over a full season at shortstop.  Standing at 6-4, Seager is one of — if not the — tallest shortstop since Cal Ripkin Jr., and the popular scouting narrative has been that his height would force a move to third base in the big leagues. (Third base requires less range and lateral quickness than shortstop and is thus easier to handle for taller players.)  Perhaps the move will eventually happen, but it certainly wasn’t necessary in 2016 as Seager played above average shortstop defense according to prominent defensive metrics.  The fact that he’ll be staying at shortstop for the foreseeable future is welcome news for the Dodgers; shortstop is a more important defensive position than third base, and Seager is thus more valuable as a shortstop than he is as a third baseman.

Unfortunately, MLB doesn’t publicly disclose player tracking data, so we’ll have to save an analysis of his defense for another post.  Instead, let’s take a deep dive into the PITCHf/x data to see how pitchers tried — often unsuccessfully — to get Corey Seager out in 2016.

Consistent Corey Seager

Most rookie hitters experience extended slumps in their first season in the big leagues. Compared to the minor leagues, the majors feature not only the world’s best pitching but also improved scouting, more travel, a longer season, and more pressure, all of which can make for a harsh environment for newcomers.   Knowing this, my initial thought with this exercise was to compare slumping Seager to non-slumping Seager in an effort to analyze how pitchers attacked him over time.  But this turned out to be a fruitless endeavor, because Seager didn’t experience a prolonged slump during 2016.  Check out Seager’s  weighted on-base average (wOBA) by month last season:


One quick note regarding the usage of wOBA instead of mainstream statistics like batting average or slugging percentage.  wOBA rewards hitters for the exact run values of distinct offensive events (singles, doubles, walks, etc.) by using run environment-specific linear weights.  This is an improvement over other rate statistics like batting average — which weights all offensive events equally and does not reward walks — or slugging percentage — which arbitrarily weights different offensive events without regard for their actual run values.  For example, slugging percentage weights a home run as three times more valuable than a single; in reality, this isn’t the case.

Back to the charts. The wOBA of the league-average hitter is typically around .320 (according to Fangraphs), and a fantastic wOBA is above .400, so Seager was consistently excellent against right handed pitchers and league-average against left handed pitchers.  The small month-to-month variation is to be expected, especially with small sample sizes.  Remember, any given month is a random sample — with arbitrary end points — of Seager’s true (i.e., mean) talent level.  The sample is therefore subject to the same type of random variation around the mean associated with typical sampling of a distribution.  The fact that we don’t see a precipitous drop means it’s safe to conclude that he was consistent on the whole, especially for a rookie getting his first taste of starting in the big leagues.  This speaks not only to his talent but also to his makeup and willingness to make adjustments, two qualities which bode extremely well for his long-term development.

What types of pitches did Seager see?

So, Corey Seager didn’t exactly slump in 2016.  But let’s still examine pitcher strategy, even though the strategy was not successful for prolonged periods of time.

First, let’s investigate the types of pitches Seager saw.  The below depicts the percentage of each pitch type faced by Seager in 2016 (by month and pitcher handedness).


You’ll notice (1) that Seager saw about half as many pitches from lefties as he did from righties and (2) that the Seager pitch mix shifted throughout the year.  Seager saw more curveballs and fewer sliders from lefties as the year wore on, and he saw fewer fastballs and more changeups from righties towards the end of the season.

With a bit of league-wide context, these charts are convincing evidence that pitchers attacked Seager differently than they pitched the average hitter.  Using the graph on the left, Seager saw a breaking ball (i.e., slider or curveball) from lefties about 35% of the time.  Of the hitters that saw at least 100 pitches from lefties this season, the league-wide average breaking ball rate was 24% (with a standard deviation of roughly 9%), showing that Seager saw a significantly higher percentage of breaking balls than the rest of the league.

Similarly, the right graph shows that Seager saw a changeup roughly 20% of the time from righties. (The actual figure is 18%.)  The league-wide average changeup percentage (among hitters who saw over 100 pitches from righties) was 9% with a standard deviation of 4.4%.  This means that Seager saw changeups at a 2+ standard deviation higher rate than the rest of the league.  Indeed, Seager faced the second highest number and fifth highest percentage of changeups across the entire Major Leagues last season.

Where were those pitches located?

We’ve seen from the above that lefties attacked Seager primarily with a combination of fastball-breaking ball, and righties attacked Seager primarily using a combination of fastball-changeup.  In an effort to complete the picture, let’s take a look at the last piece of the puzzle: where those pitches were located.

To do this, I created a strike zone heat map by grouping each of Seager’s roughly 2,700 pitches seen into equally sized buckets.  The heat map shows the relative location of all pitches which satisfy a given combination of outcome, month, pitch type, pitcher handedness, and count.  The heat map is drawn from the perspective of the catcher, and the coordinates of the top and bottom of the strike zone are specific to Seager.

A static shot of the heat map is pasted below, but please go play around with the tool on Tableau Public! (Unfortunately, WordPress would not let the workbook be directly embedded in this post.)


Using the heat map, we can see that left handed pitchers attacked Seager with breaking balls away and fastballs middle-away; they had the most success when their fastball was elevated in the zone and when the breaking balls were thrown down and away (especially when Seager was behind in the count). As for righties, the heat map shows us that pitchers had success when they threw changeups down and away and breaking balls down and in.  Finally, and not surprisingly, Seager had success against both righties and lefties when pitches were thrown in the middle-inside part of the strike zone.

Put it all together, and we have a bit of a lens into how pitchers approached Corey Seager in 2016 and what we might expect in 2017.  Seager saw a below average percentage of fastballs from both lefties and righties; lefties attacked Seager instead with a heavy dosage of breaking balls, and righties attacked Seager with a league-leading number of changeups.

We can expect more of the same next season.  Seager has proven that he can hit the best fastballs in the world, especially those in the middle-third of the plate, so he should expect to continue to see a heavy dosage of off-speed pitches away — in all counts.  Changeups like this nasty one from Kyle Hendricks are something that Seager will have to continue to deal with moving forward.


But the smart money is on him to figure it out. He is an extremely balanced hitter who is rarely fooled, and he possesses a veteran-like demeanor that will serve him extremely well moving forward as pitchers adjust their game plan.

Best of all from the Dodgers’ perspective?  He isn’t arbitration eligible until 2019, and he’s under team control until 2022 when he finally becomes a free agent.  Based on his 2016 performance, it sure looks like the Dodgers have found their shortstop of the future.

In Praise of the Rich Hill Curveball

Journeyman Rich Hill has enjoyed a resurgence in recent years, thanks in large part to his devastating curveball. In honor of his free agency, let’s take a detailed look at one of the most versatile pitches in baseball.

For a marquee free agent, Rich Hill has had an atypical Major League career.  He’s bounced around the league since debuting for the Chicago Cubs in 2005, and he can proudly say he’s worn the jersey of eight Major League teams after getting traded to the Dodgers this past summer.  He’s had mixed results throughout his career, due in no small part to his inability to stay healthy.  Plagued with back, leg, shoulder, and elbow issues, Hill has spent a good part of the last decade on the disabled list.  The 37-year-old doesn’t have a particularly flashy or deep pitch arsenal like his former Dodger teammate Clayton Kershaw, and he averaged a pedestrian 90 mph on his fastball in 2016.

So, why then do we love watching Rich Hill pitch?  Well, first, he’s kind of nuts.  To say he wears his emotion on his sleeve is an understatement, and over the course of his summer with the Dodgers, he showed a propensity to scream and fist pump regardless of score or inning.   Indeed, he sometimes would celebrate so hard that I feared he might hurt himself.  Do you, Rich.


But there is a second reason Hill is amazing to watch: he’s the owner of a majestic curveball that often makes hitters look silly.  He throws the pitch from various arm angles, with fluctuating velocity and break, which makes it an exceedingly difficult pitch to hit with any success or regularity.   For example, check out these two Hill curveballs:



The top pitch is thrown at 64 mph from a high arm slot with a big break, and the bottom pitch is thrown nearly 10 mph harder from a sidearm delivery with sideways action.  Hill throws some type of curveball roughly 50% of the time (more than any other big league pitcher), and his ability to vary the speed and break of the pitch is a huge key to his success.

In honor of Rich Hill’s free agency, I thought it would be interesting to compare Mr. Hill’s breaker with the curveballs of the rest of the league.  Again, we turn to MLB’s PITCHf/x data for insights.

Rich Hill’s Curveball is Different

PITCHf/x tracked over 63,000 curveballs in 2016 (of which 1,007 were from Rich Hill), and the data gives us a wealth of information about the velocity, spin rate, break angle, and break length of those pitches (among many other variables).  For the purpose of this analysis, we isolated curveballs based on the “Pitch Type” classification contained in the raw data.  Generally, we should be wary of using the Pitch Type classification because the same pitch can often be classified a number of ways (e.g., curveballs and sliders are similar).  Yet, because PITCHf/x classified nearly all of Rich Hill’s 2016 breaking pitches as curveballs (rather than sliders or a mix of the two), we are confident that the Pitch Type classification will work for this analysis.

Anyway, let’s get to the fun stuff.  Below is a series of scatter plots which compare Rich Hill’s 2016 curveballs to the league average in terms of velocity, spin rate, break angle, and break length.  Some rather technical definitions are necessary before we proceed.  According to Mike Fast’s PITCHf/x glossary, break angle is the angle at which the ball breaks from the catchers perspective; the greater the number, the greater the horizontal break.  Break length is the largest deviation from a straight line between the pitchers release point and when the ball crosses home plate.  The actual numbers aren’t hugely important; just remember that all else equal, the greater the break angle and length, the more the pitch moves.

The red dots are Hill curveballs that were either (1) called a strike or (2) were swung at and missed by the batter.  Combined, these two defense-independent outcomes are my indicator of a successful Hill curveball.

One theme is apparent from the pictures: Rich Hill throws many different types of curveballs, evidenced by the fact that the pitches don’t heavily cluster around a particular velocity, spin rate, break angle, or break length.   You’ll also notice that Rich Hill throws his curveball slower than the average pitcher yet with a bigger break and much more spin.  The effect is a devastatingly big breaking ball that tumbles down on the hitter at the plate.

Which Hill Curveball is Most Successful?

The graphs above prove that Hill throws many different types of curveballs, and the red dots show that he has success — at times — with just about all of them.   But which type of Hill Hammer is successful most often?   To find out, I grouped each of Hill’s roughly 1,000 curveballs into velocity, spin rate, and break angle buckets, and then created heat maps showing the relative success of each.  As above, success is defined as those curveballs that were either called a strike or swung at and missed by the batter.  The top table shows the success percentage for a given bucket, and the bottom table shows the number of pitches thrown by Hill contained in that bucket.


You’ll see immediately that success (as we define it) is fairly spread out across the various  velocity and spin rate buckets.   That said, there are still some interesting takeaways.  Namely, Hill throws most of his curveballs between 73-75 mph, but he often has good success when he’s able to throw the pitch a bit harder.  Further, he threw a high portion of his pitches with a spin rate between 1,725 and 2,135 rpm, but he had above-average success when he was able to spin the ball either faster or slower than his normal curveball.   Granted, the number of pitches in these other buckets are small, but they provide interesting observations nonetheless.

Next, let’s take a look at spin rate and break angle.


Again, you’ll notice that success is not heavily clustered around a specific spin rate or break angle range.  That said, Hill throws the majority of his curveballs with a break angle between 11-15 degrees, but he also has a good success when he throws the pitch with shorter break (between 9 and 11 degrees) and with less spin than average.

Let’s look at our last combination, a heat map for velocity and break angle.


Once again, success percentage is fairly spread out across the buckets.  Yet as we saw above, Hill had good success in 2016 when he threw his breaking ball a bit harder than average and with a little less break than average (i.e., more like a slider than the big, looping curveball).   This suggests that Hill might benefit from throwing a harder, shorter-breaking version of the pitch more often.

The above is merely food for thought.  It is not, however, a call for Hill to alter his approach.   He is a master of varying speed and break, and his ability to adjust his curveball based on feel and the game situation is why he will soon sign a big (albeit short) contract.   Further, his ability to induce weak contact with his curveball is a huge piece of his success; that piece of his game is not captured by this analysis because I’ve chosen to focus only on those curveballs which were not put in play.  If anything, the above numbers indicate that Hill should continue to vary the look of his curveball as much as possible, since the data confirm that he can be successful across a very wide array of curveball types.

In other words, keep doing you, Rich.  I’ll be rooting for you.


What Happened to Invincible Aroldis Chapman in Game 7?

With Aroldis Chapman on the verge of landing a monster free agent contract, let’s take a look back at that fateful Game 7 outing in the World Series.

Aroldis Chapman is the most coveted reliever in this free agent class, and it’s not particularly difficult to see why.  Armed with the most explosive fastball in baseball, the four-time All Star has dominated hitters since arriving in the big leagues in 2010, striking out almost 15 batters per nine innings pitched.  He stands 6-4, has very long limbs, and owns a sweeping delivery that makes most left-handed batters wish they had never stepped foot in the box.  Put it all together, and Chapman is in line to become the highest paid reliever in baseball next season.   Of course, this presupposes that a team will look past Chapman’s domestic violence history.   The Yankees and Cubs were able to rationalize that away in 2015, and while his past may scare some off this winter, there is almost no doubt that a team will break the bank for Chapman’s age 29-34 seasons.

Yet the last time we saw him on a mound, Chapman was anything but dominant.  Summoned by manager Joe Maddon to protect a 6-3 lead in the 8th inning of World Series Game 7, Chapman promptly surrendered a double to Brandon Guyer and a game-tying, two-strike home run to Rajai Davis.  Chapman was noticeably fatigued, pitching on no rest because Maddon had used him with a five run lead in Game 6.  Indeed, TV commentators Joe Buck and John Smoltz commented in real time that Chapman’s fastball looked different than usual.

But just how different was “Game 7” Chapman versus “Normal” Chapman?  To more rigorously answer this question, we turn to MLB’s glorious PITCHf/x data.

“Normal” Chapman

Even the most casual baseball fan can pick up on what makes Chapman a nightmare for hitters: he throws hard.  Incredibly hard.   To put his fastball in context, I thought it would be useful to compare the velocity and spin rate of every Chapman fastball thrown in 2016 to the league-wide average fastball.   Spin rate is measured in revolutions per minute, and it’s an important metric because all else equal, the faster a ball spins, the harder it is to hit.


The league-wide average lines are calculated using data from both starters and relievers, so the picture would look slightly different if we subset the data to include only relievers (since relievers throw harder on average than starters).  But further subsetting the data wouldn’t change the primary takeaway: the vast majority of Chapman’s 2016 fastballs were thrown harder and with more spin — often considerably so — than the league average fastball.

PITCHf/x tracked nearly 1,000 fastballs thrown by Chapman in the 2016 regular season and postseason.  Below are the probability distributions of velocity and spin rate, along with the mean and standard deviation of each, for the portfolio of Chapman fastballs in 2016.

The left picture shows an incredible result: Chapman’s fastball velocity averaged over 100 mph this season.  Averaged!  Remember, the league average velocity on fastballs this season was roughly 93 mph, and the league average spin rate on fastballs was roughly 2,100 rpm.  Using the above probability distributions, there is virtually a 100% probability that a given Chapman fastball will be thrown harder than the league average, and a 95% probability that a given Chapman fastball will spin faster than the league average.

The data confirm what we already intuited was the case.  Chapman throws an absolutely monster heater.

“Game 7” Chapman

So what happened in Game 7, then?  How was the baseball equivalent of a fire breathing dragon reduced to tears after giving up the tying runs in the biggest game of his life?  Well, because baseball, for one.  But also because “Game 7” Chapman might not have been the same as “Normal” Chapman.

Chapman threw 21 pitches in that painful eighth inning, 19 of which were fastballs.  Those 19 pitches are isolated below, along with Chapman’s 2016 average fastball velocity and spin rate.


You’ll notice immediately that every eighth inning fastball was either average or below average in terms of velocity, and most were below average in terms spin rate.  Granted, a slightly slower Chapman fastball is still harder than the vast majority of pitches thrown in the Major Leagues, and thus incredibly hard to hit.  But the point is that they were not Chapman-esque fastballs.

Let’s highlight the Rajai Davis at-bat, in which Davis sent a 2-2 fastball to the concourse to tie the game at six apiece and send Cleveland into a (temporary) frenzy.


The black dots are the fastballs that Chapman threw to Davis, and the purple dot is the fastball that Davis rocketed down the left field line for the home run.  The blue and red shaded regions represent one standard deviation from Chapman’s mean velocity and spin rate, respectively, and the gray region represents two standard deviations from Chapman’s mean velocity.

This graph proves what we suspected.  The gopher ball Chapman threw to Davis was highly abnormal; it spun more than one standard deviation slower than average, and it was thrown with two standard deviations less velocity.   How odd statistically is the pitch Davis hit into the seats?  Based on the rest of Chapman’s 2016 fastballs, there was only a 14% chance he would throw a fastball that spun that slowly, and a 3% chance he would throw a ball with that velocity.  3%!  Clearly, Chapman wasn’t Chapman.

Of course, Davis still had to make it happen.  He still had to get the barrel to a middle-in fastball thrown over 97 mph in Game 7 of the World Series.  That’s incredibly difficult!  In fact, the pitch location wasn’t actually that bad, as shown below.


As the graph shows, the purple home run ball was a middle-in, down strike.  Not great location, but not horrible by any stretch.  It’s the type of pitch that doesn’t usually hurt Chapman.  But in this instance, Davis had a better than average chance to barrel up that baseball because Chapman was not his normal, rested self.

Joe Maddon typically gets a lot of credit for being a great tactical manager.  However, his decision to use Chapman in Game 6 with a five run lead was highly suspect at the time, and it almost cost the Cubs the World Series.  Of course, we must evaluate Maddon on his thought process rather than the observed outcome.  Yet this move is fair game because it was highly questionable at the time.

Did Chapman know he wasn’t his normal self?  Maddon — showing an extreme lack of faith in the rest of his bullpen — sent Chapman back out for the ninth inning.  And something odd happened.  Of the 14 pitches Chapman threw in that inning, 9 were not fastballs (or roughly 65%).  To see how abnormal that is, I looked at every inning (and partial inning) that Chapman threw this year to investigate whether he ever threw that high a percentage of non-fastballs.  The answer is no.


That’s right: the owner of the hardest heater in the world was reduced to throwing slider after slider to get through his last inning of the World Series.  And you know what happened?  Three up, three down.  Because, again, baseball.

Aroldis Chapman will be an even richer man very soon.  A team will — somehow — look past his history of domestic violence and rationalize paying him something on the order of $100 million.  Yet on the night of November 2, in the biggest situation of his life, he looked anything but worth it.