Archive for October, 2017

Dryness in Paradise: On Humidors in Spring Training

Spring-training games in the Cactus League are a unique joy, especially for baseball fans (like me) who hail from colder climes. Unlike the Grapefruit League, which features stadiums separated by hundreds of miles of humid Florida air, the Cactus League consists of a compact cluster of stadiums bathed in sunshine and desert-dry air. Spectators and players alike can enjoy the spring conditions (and for some, including myself and Carson Cistulli, Barrio Queen guacamole and sangria) in the Valley of the Sun for weeks before teams return to their home stadiums across the country in late March.

Figure 0: Your author enjoying the 82-degree sunshine (and probably a juicy IPA, not pictured) at Hohokam Stadium, March 2017

Some teams will return to relatively warm and dry climates (Arizona Diamondbacks, who have to trudge the 20 freeway miles to Chase Park), but others will return to retractable domes (Seattle Mariners) or cold conditions where snowed-out games are certainly not out of the question (Cleveland). Given that the point of spring training is to get players ready for 81 games at their home ballpark, are two months of baseball in dry, sunny paradise the best way to prepare players for opening day at home? Short of building exact climate-controlled replicas of Kauffman Stadium and Wrigley Field in the Phoenix Metro, how could teams better prepare their players for the start of the season at their own home ballpark? Enter an unlikely hero, the great “Rocky Mountain equalizer”: the humidor.

Figure 1: Climatology of Phoenix, AZ (Feb-Mar) and the home locations (ICAO Airport codes) of the 15 Cactus League teams (Apr-May)

Just by eyeballing the graphs in Figure 1, without wading into the different lines and the specific airports (some lines switch to larger airports with RH), no stadium’s meteorological conditions are close to those in the Phoenix area. With the exception of the Rangers, no team plays in a stadium with an average May high temperature greater than the average March high temperature in Arizona. And only the “high desert” of Colorado comes close in RH to the dry air in Arizona March. Clearly, the opening day meteorological conditions will be significantly different from those Cactus League players see during spring training (Figure 2).

Figure 2: Changes in climate between April (major airport nearest home stadium) and March (PHX), with larger markers indicating larger temperature differences (dotted markers indicate increased T) and blue markers indicating more humid conditions (orange being drier)

This drastic change in temperature and humidity (Figure 2) is likely to have a major impact on how the ball plays once teams leave Arizona. Like many baseball physics researchers before me, I will once again heavily rely on the work previously done by Dr. Alan Nathan to inform my physical exploration herein. As shown in Nathan, et al. (2011), the two crucial meteorological factors of temperature (T) and relative humidity (RH) have a strong impact on both aerodynamic factors (such as drag) AND contact factors (such as coefficient of restitution, COR) that determine how far a batted ball travels. Rather than run afoul of the copyright of the American Journal of Physics by reproducing the figures here, I highly encourage you to check out Figures 2-4 in Nathan, et al. (2011) to see these relationships.

Equation Block 1: Calculating the effect of COR changes on “effective” exit velocity of a batted ball

The eternally relevant Baseball Trajectory Calculator developed by Alan Nathan has the ability to adjust aerodynamic factors associated with stadium altitude, barometric pressure, temperature, and relative humidity. Combined with the equations from Block 1 above, the changes in COR as a result of meteorological changes can be simply approximated in the Nathan Calculator as a manual change in the rebound (exit) velocity of the ball off the bat.

Great, simply smash aerodynamic and COR changes together and we’re in business, right? Well, almost…it seems every baseball physics article could have all the baseball-specific details stripped out and what would remain is a meditation on linearity and covariance. This example is no different. While we might expect meteorologically-induced aerodynamic and contact factors to vary independently, in real on-the-field situations, balls will be affected by not only their current conditions but also their recent history of past conditions. Absent experimental data on the time scale of such internal ball changes, we can still get a general sense of what could happen when multiple changes overlap. Let’s dive into some colorful 3-D contour plots of results using the default batted ball parameters of the Trajectory Calculator (100 mph pitch, 100 mph exit velocity, 30 degree launch angle) and see what happens!

Figure 3: Effects of meteorological T and RH on fly ball distance, including COR effects equal to ambient conditions (as if balls were kept in the same conditions)


We aren’t too far afield from the basic variables one can change in the Nathan Calculator, so the results from Figure 3 aren’t terribly surprising. Baseballs travel further through warm and dry air. In addition, dry/warm baseballs are bouncier than cold/wet baseballs. It’s unlikely that equipment managers are keeping baseballs outside, so they probably aren’t going to actually experience changes in COR associated with extreme conditions due to the time necessary for water vapor to diffuse into the guts of the baseballs and soften them. But absent a sense of how equipment managers store baseballs, let’s explore the possible impact that a spring training humidor could have.

Figure 4: Effects of humidor-like T and RH on fly-ball distance, with aerodynamic effects equal to PHX March average but COR changing with humidor conditions

Figure 4 shows what would happen if we changed the internal ball T and RH but continued to play in the average Phoenix-area meteorological conditions in March. The weakness of the temperature effect compared to the strength of the humidity effect can be predicted with the slope of each experiment in Nathan, et al. (2011). It’s unlikely, though, that T and RH both have, when combined, a linear effect on COR. For example, it’s unclear whether this linear model captures the hot/wet and cold/dry combinations correctly. This indicates the need to inspect the covarying relationship between T and RH on COR (and therefore, fly-ball distance) more deeply than the simple linear combination I used in this model.

Table 1: Monthly climate, elevation, default fly ball distance using the Nathan Calculator and monthly climate, and scale factors for conversion of March fly ball distance (at PHX) to April fly ball distance (at home).

With the data from Figures 3-4, we can figure out an appropriate scaling factor (Table 1) to translate the dimensions of each team’s spring training stadium and compare them to the dimensions of their home stadium (Figure 5).

Figure 5: Surprise Stadium (KC) and Scottsdale Stadium (SF) scaled to April climatology in KC and SF (no humidor)

After comparing the “effective dimensions” of the Cactus League stadiums to the home stadiums of each team, one can’t help but wonder if the teams had a hand in the way the stadiums in Arizona were constructed. Some teams, such as the Royals, share a stadium with another team (Texas Rangers); therefore, this clearly can’t explain all of the similarities between stadium shapes.

Figure 5 shows that in Arizona during the month of March, the spring training stadiums play much “smaller” compared to other stadiums than their physical dimensions might indicate. By slightly lowering the COR of the ball by using a humidor, teams could cause their spring training stadiums to play with effective dimensions approximately equal to those of their home stadiums. If the Royals were to store their spring training baseballs in a humidor at approximately 70% RH, the differences between the distance up the lines (longer at Surprise than Kauffman) and the distance to straightaway center (shorter at Surprise than Kauffman) would yield around the same “effective surface area” of the scaled outfield.

This analysis, much like my earlier piece on fly-ball precession, neglects many physical variables that would impact the actual games being played. In this example, I have neglected the effects of wind and day-to-day changes in barometric pressure. Prevailing winds due to stadium orientation and location would make this experiment much more realistic. For variations in pressure due to synoptic weather systems (cold fronts, warm fronts, etc.), however, “averages” over an entire month inform us less in terms of the baseline environments of each stadium than monthly averages of temperature and relative humidity. The model also assumes that the balls are essentially stored in temperatures and humidities equal to the ambient conditions in the home stadiums; equipment managers likely store them in some indoor location, but it’s unclear whether they are treated to the exquisite RH control seen with the humidor at Coors Field. Such confounding factors will be explored in future follow-ups to this piece.

In addition to physical assumptions made here, it’s quite possible that baseball operations departments in teams have goals in spring training other than closely approximating the hitting conditions in their home stadiums. But if they want to see who will have power that plays well in their home stadium, the humble humidor could play a key role in moderating the enhanced fly-ball distance that comes naturally with the warm, dry spring air of paradise (Cactus League baseball, that is).

Is Aaron Judge Really Unclutch?

A few days ago, I read an article on FanGraphs that flew in the face of everything I wanted to believe. This article told me that Aaron Judge — the man who holds the record for the most home runs hit in a season as a rookie — was not clutch. As a lifelong Yankee fan, I immediately got defensive. It didn’t matter that I wasn’t really sure that I even believed that “clutch” existed. Or, at the very least, I wasn’t sure we were measuring it correctly.

I decided to go a different route. I decided to go back in time, and replace Aaron Judge with a completely league average player…in every situation he was in. I took every plate appearance, from every base-out situation from 2014 through 2017, and averaged some random samples to find out exactly how many runs a hitter was expected to generate (xRBI). How many more runs did Aaron Judge force across the plate than the average player (RBI – xRBI)? So I calculated some xRBIs…because I like to pluralize RBI. My distribution of dRBI was a bit skewed — so I adjusted for HRs (high HR rates would inflate your RBI over your xRBI…but solo shots are still valuable things), and SOs (because strikeouts provide essentially no opportunity to bring in a run). Now, my distribution looked more normal.

And here we have it! Aaron Judge’s 2017 ranks….879th out of 954 hitter-seasons with 350+ PAs?! Dammit. Apparently Aaron Judge, based on the base-out opportunities he’s been provided, drove in 10 fewer runs than we should have expected. Womp womp.

What does this tell us? You know…I’m not really sure. Here’s the top 15 player-seasons:

         name      Season  PA   OBP HR  K.rt RBI   xRBI  dRBI
1  Miguel Cabrera    2014 685 0.371 25 17.08 109  83.03 25.97
2  Nolan Arenado     2015 665 0.323 42 16.54 130 106.55 23.45
3  Mike Trout        2014 705 0.377 36 26.10 111  88.87 22.13
4  Robinson Cano     2014 665 0.382 14 10.23  82  61.04 20.96
5  Michael Taylor    2015 511 0.282 14 30.92  63  43.13 19.87
6  Devin Mesoraco    2014 440 0.359 25 23.41  80  60.15 19.85
7  Nolan Arenado     2017 654 0.369 35 15.90 126 107.23 18.77
8  Giancarlo Stanton 2014 638 0.395 37 26.65 105  86.28 18.72
9  Ryan Braun        2014 580 0.324 19 19.48  81  62.53 18.47
10 Justin Morneau    2014 550 0.364 17 10.91  82  64.13 17.87
11 Matt Kemp         2015 648 0.312 23 22.69 100  82.15 17.85
12 Paul Goldschmidt  2014 479 0.392 19 22.96  69  51.28 17.72
13 David Ortiz       2014 602 0.355 35 15.78 104  86.35 17.65
14 Yoenis Cespedes   2014 645 0.301 22 19.84 100  82.69 17.31
15 David Ortiz       2016 626 0.401 38 13.74 127 109.82 17.18

They’re all pretty good. Were these the most clutch guys? I’m not really sure where I’m going with this. I’m not even sure if I’m going anywhere with it. I guess it’s just a different way to think about clutch. My process doesn’t take the game score into consideration. It doesn’t take into consideration whether or not a player is playing at home, or any other context for that matter. But in trying to quantify a relatively subjective stat…should any of that matter?

Let’s Make Four Radical Changes to MLB and the Playoffs

Hello, I’m so glad you’re here. And since you’re here, you’re either open to fantastically wild ideas, or you’re a traditionalist who still can’t believe we have interleague play, wild-card teams, and one-game playoffs. You’re either more than happy to discuss why the DH should be universally adopted, or you’re here to tell me why the NL brand of baseball has “more strategy” because of all the situations regarding when to go to your bullpen instead of letting this happen.

Let me begin by saying that I too used to be, or maybe still am, a baseball traditionalist. I have great respect for the history of the game, but I’d also like to embrace the things that make it great and that can make it a better product for the future. This isn’t about mindlessly making changes to the status quo; rather, it’s choosing the best of what baseball has to offer and featuring it as much as possible.

With that in mind as the backdrop, here are the four radical changes I’d make to Major League Baseball to deliver on what I already see as being the strengths of the sport. At the same time, I propose these changes will minimize the things that are bad for the sport. And yes, the Sawchik Playoff series will be part of the solution in the wild-card round.

MLB Should Universally Adopt the Designated Hitter

Yes. They should. I hear your argument against it. Strategy, right? Or tradition that the pitcher should hit?  It’s a quaint notion. I respect your opinion, but thoughtfully disagree.

Bullpen strategy in baseball is evolving quickly to a point where this decision of “when to pull your starter” very rarely coincides with the decision of whether or not you want him to hit this inning. Reliever specialization and matchup-based decisions are more often than not the tipping point rather than a decision around whether or not to let your starting pitcher hit one more time. There are more frequent decisions around how long can I let a particular reliever pitch, should I use this reliever for more than three outs, or can this reliever pitch for a third consecutive day?

As for the tradition argument, I’d argue that most pitchers stopped trying to be professional hitters decades ago and it’s time we recognize this for what it is: a dying notion. This is about having the best product on the field for fans to watch. Pitchers in 2017 collectively hit .125/.163/.164.  This is bad for baseball.

Try this as a thought exercise. You’re already thinking about him — Madison Bumgarner. He’s a pitcher who can hit and hit home runs. Or if you prefer, Adam Wainwright. Take your pick! In the hypothetical world where the DH exists in the National League I’d argue you could let either of them DH — if you really wanted to see them hit. Would the Giants or Cardinals ever do this? The answer is no. They wouldn’t want to risk injury to a player whose primary role on the team is to take the ball every five days and throw it. So why are we still making them hit?

MLB Should Abolish the National and American Leagues

Now that we’ve universally adopted the DH, we don’t really need the distinction between the National and American League. We already have interleague play every day of the season. There are no NL and AL umpires. There isn’t an AL-only players union. We already associate all-time records with all of MLB and not league-only specific records. This gives us the freedom of making sensible decisions around radical re-alignment.

MLB Should Have Four Divisions and Make the Pennant Race Meaningful

Traditionalists will argue that the current playoffs no longer guarantee that one of the best teams will win the World Series. They’ll argue that the wild card has diminished the meaningfulness of winning your division. They’ll argue that interleague play is silly. I agree with them, but let’s embrace the fact that these things are not going away. What can we do to build upon these ideas and make them better?

First of all, interleague play and its “natural rivals” approach is very flawed from a competitive-balance perspective. I don’t want to eliminate it; rather, I want to embrace it and make it part of the landscape. The best part about baseball are the rivalries and traveling to ballparks in (and outside) of your area to watch teams play. Mets/Yankees? Royals/Cardinals? Yes please! But we can do better through radical geographical re-alignment to enhance these rivalries. At the same time, through natural geographical selection we pit market-size rivals against each other as well.

MLB East (7):  Mets, Yankees, Red Sox, Orioles, Phillies, Nationals, Blue Jays

MLB North (8): Cubs, White Sox, Brewers, Twins, Tigers, Reds, Indians, Pirates

MLB South (7): Marlins,  Rays, Braves, Astros, Rangers, Cardinals, Royals

MLB West (8): Dodgers, Angels, Padres, Diamondbacks, Rockies, Giants, Athletics, Mariners

This setup allows us to retain the geographic rivalries. The seven-team divisions can play each division rival 14 times. The eight-team divisions can play each division rival 13 times. This allows for a single series against every other team in baseball. If you were worried that the Cubs/Cardinals series was going away, it’s not. They still get to play every year.

This is a more balanced approach to scheduling and allows each team to see the game’s star players. Why should Twins fans only get a chance to see Giancarlo Stanton mash 500ft monster blasts once every blue moon? Does a Pirates fan even know who Mike Trout is? Why are we hiding the stars and confining them to their leagues and divisions? Let the fans see and appreciate all the star players.

This format will allow for four division winners, who will all be granted a bye in the first round of the playoffs. This will make for meaningful pennant races and bring back the excitement of winning your division. Winning a division against four other teams and playing those four teams nearly 80 times isn’t exciting. As a Brewers fan, by the time we get into August and September it’s all I can do to watch another series against the Reds or the Cardinals. At the same time, because you’ll only play four series against your divisional foes, it will make those four series just a little more meaningful – especially for the teams battling atop the divisions.

MLB Should Expand the Wild-Card Round To Eight Teams and Adopt the Sawchik/KBO Playoff Format

Travis Sawchik opined that MLB should adopt the KBO playoff format for the wild-card round. This is something I can support.

While we’re at it, let’s face it, the best team is probably not going to win the World Series anymore. Once we stopped playing for a league pennant and had one World Series to crown the best American baseball team, we introduced the idea of the best team not winning the title. It’s a fact that the regular season no longer has much of an impact on the playoffs. We’ve established this.

Joe Sheehan recently wrote in his newsletter that each team in the 2017 playoffs, through expected value calculations, would be expected to have a 4-3 record in any seven-game series, and a 3-2 record in any five-game series. More specifically, he wrote:

“It’s not that the postseason is ‘luck’ or ‘random.’ It’s simply that it’s short, too short for the true differences in ability among baseball teams to play out. You’d rather have the better team, but over five or seven games, ‘better team’ is an almost meaningless distinction except at the extremes.”

The playoffs are simply a tournament for the “better teams in baseball to determine a league champion.” If we wanted the best team to be the champion we’d quit after the regular season and see who had the most wins. It’s for this reason I’ve been suggesting that we as baseball fans #embracethetournament.

Top 12 Teams In Wild Card Era
Rank 2017 2016 2015 2014 2013 2012
1 104-x 103-x 100-x 98-x 97-x 98-x
2 102-x 95-x 98-y 96-x 97-x 97-x
3 101-x 95-x 97-y 96-x 96-x 95-x
4 97-x 94-x 95-x 94-x 96-x 94-x
5 93-x 93-x 93-x 90-x 94-y 94-x
6 93-y 91-x 92-x 90-x 93-x 94-y
7 92-x 89-y 90-x 89-y 92-x 93-y
8 91-y 89-y 88 88-y 92-y 93-y
9 87-y 87-y 87-y 88-y 92-y 90
10 86 87-y 86-y 88-y 91 89
11 85-y 86 85 87 90-y 88-x
12 83 86 84 85 86 88-y

I’m not as radical as you think. I’m not telling MLB to change the rules to let the 12th-best team into the tournament — they already do that (2012 Cardinals). I’m not telling MLB to change the rules to let a wild-card team win the title — they already have (2014 Giants). I’m not telling MLB to change the rules to allow an 85 or 86-win team into the playoffs — they already have (2017 Twins, 2015 Angels).

What I am suggesting is that the expanded playoff pool would increase the popularity of the tournament, and allow MLB to showcase their star players more. The wild-card round could certainly feature the KBO playoff format where the 4-8 seeds host the 9-12 seeds for a best-of-two home playoff series whereby the home team needs to win only one game and the away team needs to win both to advance. We won’t need any Game 163s because teams will have already all played each other three times during the regular season and we can break ties head-to-head.

In this format, this is what the 2017 playoffs would have looked like:

#1 Seed – MLB West Champion – Los Angeles Dodgers
#2 Seed – MLB North Champion – Cleveland Indians
#3 Seed – MLB South Champion – Houston Astros
#4 Seed – MLB East Champion – Washington Nationals

(#12) St. Louis Cardinals @ (#5) Boston Red Sox
(#11) Minnesota Twins @ (#6) Arizona Diamondbacks
(#10) Milwaukee Brewers @ (#7) Chicago Cubs
(#9) Colorado Rockies @ (#8) New York Yankees

I’d prefer seven-game series for the Divisional round, Final Four and World Series, but could live with five-game series for the Divisional and Final Four rounds because, at the end of the day, it doesn’t really make it any more or less random.


Major League Baseball has a solid product, but it could be better. By allowing more playoff teams, even if for just one or two games, it creates a chance to see more of the league’s stars in the national spotlight. This is also achieved by letting every team in baseball play every other team in baseball each year (though I concede I don’t know the effects on scheduling). By re-aligning the divisions, MLB can emphasize the natural geographic rivalries without a hokey home-and-home interleague series, while these larger divisions bring back some meaningfulness to the term “pennant winner” by including a bye. Finally, the removal of the American and National Leagues allows for re-seeding of all the playoff teams based on record in each round (if #12 advances, they’d play #1 in the divisional series), and allows both leagues to play under a common DH rule. Don’t misunderstand my grasp on reality here; I understand this would likely never happen — but why not? Can you come up with a reason other than tradition?

2017 Sabermetric Awards

To wrap up the season, let’s take a look at the winners of leaders of some interesting sabermetric categories. Not all of these are meant to be indicative of a player’s skill; rather just interesting notes. First, hitters:

Three True Outcomes

To measure this, I added players K%, BB%, HR/PA, and HR/H together.

  1. Joey Gallo, 1B/3B, Texas Rangers
  2. Aaron Judge, RF, New York Yankees
  3. Chris Davis, 1B, Baltimore Orioles

This leaderboard surprises no one. It’s essentially Gallo, then Judge, then everybody else. Davis is in third, but he has Giancarlo Stanton and Khris Davis right on his heels.

Good Contact

I utilized Statcast’s xwOBA and players’ Hard%, while also setting contact minimums, to calculate a measure of guys who make consistent, hard contact.

  1. Paul Goldschmidt, 1B, Arizona Diamondbacks
  2. Corey Seager, SS, Los Angeles Dodgers
  3. Nelson Cruz, DH, Seattle Mariners

Two stars and then an aging former star.

Plate Discipline

Z-O Swing% was used to measure discipline.

  1. Joey Votto, 1B, Cincinnati Reds
  2. Jed Lowrie, INF, Oakland A’s
  3. Freddie Freeman, 1B/3B, Atlanta Braves

Votto has long been one of the kings of plate discipline, and he’s still getting better. Lowrie is quite a surprise, but Jeff Sullivan recently dubbed him as one the league’s most improved players.


I used O-Contact% + Z-Contact% to give more weight to making contact outside of the zone.

  1. Melky Cabrera, LF, Chicago White Sox/Kansas City Royals
  2. DJ LeMahieu, 2B, Colorado Rockies
  3. Joe Panik, 2B, San Francisco Giants

All of these guys are sticking with career norms as contact hitters.


Z-Swing% + O-Swing% to see who hacks at everything.

  1. Corey Dickerson, OF, Tampa Bay Rays
  2. Avisail Garcia, RF, Chicago White Sox
  3. Adam Jones, CF, Baltimore Orioles

Dickerson and Garcia opened the season with impressive breakouts that slowly diminished throughout the year. Jones kept doing what he does.

Now, the pitchers:

Contact Managers

Looking at GB%, IFFB%, soft contact rate, and xwOBA allowed.

  1. Dallas Keuchel, SP, Houston Astros
  2. Brad Peacock, SP, Houston Astros
  3. Corey Kluber, SP, Cleveland Indians

Keuchel has established himself as the ground-ball king. Kluber and Peacock are fourth and eighth in K/9, so their inclusion is impressive.

Swing Generators

Z-Swing% + O-Swing%

  1. Masahiro Tanaka, SP, New York Yankees
  2. Madison Bumgarner, SP, San Francisco Giants
  3. Jake Odorizzi, SP, Tampa Bay Rays

Tanaka had a rough season, while Bumgarner did not play much of the season. Odorizzi was quite terrible, posting a 5.34 FIP.

Whiff Generators

Z-Contact% + O-Contact%. Lower is better.

  1. Robbie Ray, SP, Arizona Diamondbacks
  2. Corey Kluber, SP, Cleveland Indians
  3. Max Scherzer, SP, Washington Nationals

These guys are two, four, and three in starter strikeout rate.


Lowest walk rates.

  1. Josh Tomlin, SP, Cleveland Indians
  2. Jeff Samardzija, SP, San Francisco Giants
  3. Clayton Kershaw, SP, Los Angeles Dodgers

Tomlin did not pitch well all year, but he quietly posted an incredible 0.89 BB/9.


Guys who threw the highest rate of off-speed pitches.

  1. Lance McCullers, SP, Houston Astros
  2. Jordon Montgomery, SP, New York Yankees
  3. Madison Bumgarner, SP, San Francisco Giants

McCullers’ crazy curveball throwing is well known. Montgomery features a lot of curveballs and changeups, while mixing in sliders. Bumgarner throws a heavy dose of sliders, and includes curveballs every so often.

There isn’t much to this. I’m sure there are many categories I could have added. I just wanted to throw out some information that people might be interested in.