We saw the Yankees basically bullpen the AL wild-card game. Sure, it was on accident, but their bullpen pitched 8.2 innings. And they did it well. This made me think about whether a team could put together a pitching staff that is almost completely used for bullpenning for the entire season.

To see if this would be possible, we will look at the Yankees since they are the team most closely equipped for it already. In the wild-card game, they essentially used four relief pitchers (let’s not count the one out Luis Severino had). Chad Green, David Robertson, Tommy Kahnle, and Aroldis Chapman combined for 8.2 innings and one earned run. Clearly, if a team could do this all the time, they would. In that game they did not use other relievers Dellin Betances and Adam Warren, as well as regular starting pitchers Jordan Montgomery and Jaime Garcia, who would have been available that night.

Since we now know what happened in that bullpen game, can we find out if it is possible to do it over a full season? First off, and MLB roster is comprised of 25 men for any given game and an additional 15 that can be called up if needed. An AL team can get by with 12 position players: one for every starting position (including DH) plus a fourth outfielder, utility infielder, and backup catcher.  Let’s say a team’s backups can field multiple positions, like many can. We can get rid of the everyday DH and use one of the backups or starters in that role for a needed day off. That leaves us with 11 position players and room for 14 pitchers.

Many of the Yankees’ own relievers can go multiple innings. Among those pitchers are Chad Green, David Robertson, Tommy Kahnle, Adam Warren, and occasionally Aroldis Chapman and Dellin Betances. Each are effective in their own right. The problem we have to face is the amount of rest needed for these pitchers. The four from the wild-card game each pitched with two days of rest, so we’ll set that as a bench mark. I also don’t want to assume a team needs five pitchers each game like they did in the wild card.

I don’t want to completely get rid of the starting pitcher. It would be dumb to just throw away what Luis Severino and other starters bring to that team. Instead, I want to put a hard limit on how much they pitch each game and how often they pitch. Theoretically, a team could go with a three-game cycle of pitchers. Games are played almost every day during the season, so the two days of rest benchmark will be used here. If we are using four pitchers per game every three games, we need 12 pitchers.

I didn’t make this with any set reason, just the best options the Yankees would have in my view. There are many other options available for them and some may be even better. But, if this is the set of pitchers being used, that leaves two extra spots for our 14 available pitchers. Those two extra spots can be utilized for guys needed for extra innings that can pitch multiple innings, or a guy needed for an inning or two in case one of the above gets into trouble.

If a team were to go by this set of pitchers, the regular starting pitchers would be throwing 162 innings over a season. That would be seen as pretty normal for a starting pitcher over the course of a season and in some cases much less. Severino pitched 193 innings himself. The relievers, however, would see a pretty big bump in action. They would pitch 108 innings in a season, more than any of the pitchers above did last year. However, some of those pitchers were starters to begin their careers. Green, Warren, Betances, and Holder have each pitched more than 108 innings in a season. Now, that could be a reason for their increased effectiveness as relievers, but they would still only be pitching two innings in a game, not five or six.

It is possible to ask these relievers to stretch their arms out to be able to throw that many innings in a season. Relievers do transition to starting and this wouldn’t be quite the workload necessary. If a pitcher needs a break during a cycle through this set of pitchers, that could be what the additional two pitchers on the roster are for, or some of the 40-man pitchers could be called up to give a guy a break. They could also call up an actual starter from the minors to take over for four or five innings after the three-inning “starter” in this example. My point here is that if the relievers get tired over the course of a season, there are ways to give them breaks. Plus, the Yankees have so many resources and available pitchers that they have that capability to give breaks.

If the Yankees wanted to, they could keep Severino, Tanaka, Gray, Green, Warren, Robertson, Kahnle, Betances, and Chapman all on the roster for the whole season. That makes up 3/4 of the necessary pitchers. Shreve, Holder, and Gallegos could each be cycled up and down from AAA with other pitchers like Ben Heller, Domingo German, etc. in order to give breaks to the core nine pitchers. Another solution is to go out and get more relievers who can pitch multiple innings on a regular basis. They certainly have the prospects to do that. Pitchers like Brad Hand, Yusmeiro Petit, and Mike Minor each pitched over 77 innings and were very effective doing so.

Clearly there is much more that would be needed to make this a reality, and I don’t have the resources to know if it is even possible. Maybe these guys simply couldn’t pitch that many innings over a full season or they would lose too much velocity of break on their pitches from fatigue. But I saw David Robertson pitch 3.1 masterful innings in the wild-card game and pitch another 1.2 innings three days later. Obviously that is only two outings, but he was nevertheless effective in doing it, and I believe if any team could make this happen, it would be the Yankees.

In the NLDS, Stephen Strasburg was absolutely brilliant for the Nationals in his two starts. Due to an injury to Max Scherzer, Strasburg got the ball for Game 1 and was dominant. He threw 5.2 innings of no-hit ball before giving up back-to-back RBI singles to Kris Bryant and Anthony Rizzo that allowed two unearned runs to score thanks to a rare error by Anthony Rendon. Strasburg finished with an impressive line of 7 IP 3 H 2 R 0 ER 1 BB and 10 K in a losing effort. Although his outing was ruined by the unearned runs and Kyle Hendricks’ outstanding start which shut down the Nationals offense, Strasburg made the Cubs hitters look foolish all night long. Getting the ball once again with his team down 2-1 in the series, Strasburg turned in another absolute gem in Game 4. In a 5-0 victory, Strasburg threw seven shutout innings, scattering three hits while walking two and striking out 12. In his two starts combined, Strasburg threw 14 innings without allowing an earned run, while only giving up six hits with three walks to go along with 22 strikeouts.

The dominance on display by Strasburg is nothing new. Despite being the second-best pitcher on his team, Strasburg is an ace and finished second (behind Scherzer) among NL pitchers with 5.6 WAR. When Strasburg come to mind, the immediate thought goes to his power fastball. It’s one of the main reasons why the Nationals selected him with the first overall pick in the 2009 draft. He throws the pitch with an average velocity of 95.6 MPH good for fifth among qualified pitchers. Yet, Strasburg also loves to throw changeups, especially to right-handed hitters. Throughout the course of the regular season, Strasburg threw 16.3% changeups to right-handed hitters. This is an absurdly high amount for a power pitcher like Strasburg. Typically right-on-right changeups are primarily thrown by low-velocity sinkerballers, since changeups typically have the same movement as their sinker despite being thrown 5-10 MPH slower. Conventional wisdom has dictated for years that power pitchers should throw fastballs and curveballs (or sliders) to the same-handed hitters while throwing fastballs and changeups to opposite-handed hitters. The idea behind this is to throw a breaking pitch with movement that breaks away from the hitter, making it harder to hit. Right-on-right changeups were regarded as a dangerous pitch since a mistake almost always ended up with the pitch being barreled.

In 2013, Ben Lindbergh wrote an article for Baseball Prospectus about the Tampa Bay Rays (because who else besides Joe Maddon and Andrew Friedman) and their increased usage of same-sided changeups (this article includes left-on-left changeups as well). However, the team refused to recognize this increased same-sided changeup usage as an intentional move, but rather tried to classify it as an increase in the emphasis on throwing changeups to all hitters regardless of handedness. As a team in 2013, the Rays led the league in percent of same-sided changeups, as 15.9% of all pitches thrown to same-sided hitters were changeups. The league average was 5.4%. This league average has held relatively constant over the last four years. Using Statcast data from 2017 for all right-on-right pitches thrown by starting pitchers, 6.6% of all right-on-right pitches were changeups.

Back to Strasburg. Throwing his changeup 16.3% of the time to right-handed hitters, he generated a whiff rate of 27.2% while only allowing five hits and 13 other balls in play, on 213 changeups. Four of those five hits were singles, while the other was a home run hooked down the line by Josh Harrison (hit probability of 13%). He used his changeup primarily as an out pitch, as most were thrown down and in with two strikes. It totally makes sense for Strasburg to use his changeup so much, as it is one of the best pitches in baseball, and it really is its own animal. It’s unique because he throws it really hard. It was the second-hardest changeup among qualified starters, coming in at an average of 88.7 MPH. Despite throwing it so hard, it was 7 MPH slower than his average fastball, right in the ideal range of velocity differential. It also has a decent amount of arm-side run to go along with late and sharp drop (as can be seen here). According to the Pitch Values assigned by FanGraphs, Strasburg’s changeup was fifth best among qualified starters in total value, and 10th best on a per-pitch basis.

In his Game 1 start, Strasburg threw six right-on-right changeups out of 45 pitches (13.3%) and generated four whiffs with zero balls in play. This was right in line with his season averages, which would’ve been expected to continue in Game 4. But this was not the case. It was reported on Tuesday that Strasburg was sick and would not pitch on Wednesday despite being on regular rest after the rainout. Yet, on Wednesday morning, plans changed and he was announced as the Game 4 starter with the Nationals season on the line. As mentioned earlier, he did his job by turning in a spectacular start, and the Nationals’ season lived to see another day. However, in Game 4 Strasburg decided to get funky. He threw 16 right-on-right changeups out of 45 pitches, equal to a whopping 35.6% of the time, and generated eight whiffs with one ball in play hit at 27.7 MPH. His changeup and its increased usage was no doubt a huge factor in shutting down the Cubs once again (as can be seen here, here, and here). Who knows why he decided to go to it so much more often. Maybe he saw the success he had with it in Game 1, or maybe that pitch was the most comfortable for him to throw while supposedly not feeling well (his average fastball velocity of 95.4 MPH suggests he was feeling just fine). No matter what it was, it doesn’t matter. Strasburg has proved that the right-on-right changeup can not only be an effective pitch, but an absolutely devastating one. A pitch that can even be used over a third of the time. Let’s see if hitters will be able to adjust.

Although this season for Giancarlo Stanton was one for the record books, this monumental display of power should not be enough to warrant a spot in the top 10 of baseball’s best position players.

While Stanton did have an impressive season to say the least, and with an NL MVP seemingly locked, he wasn’t even the best in the NL alone. With the NL being the easier of the two leagues, most certainly, it seemed that Stanton had every advantage there could’ve been given — aside from playing in Coors for 81 games.

Here’s how his 2017 season fared:

59 HR and 132 RBI paired with 32 2B. with a .281 / .376 / .631 slash line (1.007 OPS) 6.9 WAR / and a whopping 156 wRC+

Mind you, these numbers are indeed phenomenal, but they are not deserving of being named “Top 10” in baseball, let alone “NL MVP.” Giancarlo did what no one had done in over a decade, and that is hit 59 homers (Ryan Howard hit 58 in 2006). He surpassed every personal best of his entire career, and rewrote his own book — which was filled with injury questions, as well as his inability to hit for average.

However, factoring in the huge increase in the amount of home runs hit this season, Stanton’s monumental 59 is slightly less impressive.

% OF RUNS OFF OF HR

2017- 42.3 % (+2.1 %)

2016- 40.2 % (+2.9 %)

2015- 37.3 % ( / )

NUMBER OF HR HIT

2017- 6,105 (+495)

2016- 5,610 (+701)

2015- 4,909 ( / )

With this being known, there were 41 players with over 30 homers, as well as Kris Bryant, Bryce Harper, Jose Ramirez, and Mike Napoli being notched with 29.

Giancarlo Stanton’s career numbers should not boost him to the top-10 consideration, so why would one season justify such? Stanton is a career .268 hitter, and never hit more than 37 homers in a single go (although yes, he never played more than 150 games). Even with his AS recognition in 2014, in which he slugged 37 to pair with a 6.3 WAR season, he wasn’t even considered top-5 then. The drastic injuries that Stanton has faced, as well as his lack of defensive abilities and base-running abilities, mean his value is hurt. Even for the 2017 NL MVP, Stanton shouldn’t win.

59 HR- 1st in NL

132 RBI- 1st in NL

.281 AVG- 24th in NL

.376 OBP- 14th in NL

.631 SLG- 1st in NL

6.9 WAR- 2nd in NL

156 wRC+- 2nd in NL

Although Stanton did indeed have the edge in the majority of these categories, it is seen that aside from his impressive slugging percentage, he was not even top-10 in any other categories. If we’re being honest with each other, Anthony Rendon, Justin Turner, and Joey Votto all put together more impressive and stand-alone seasons.

Rendon- .301 / .403 / .533 slash with a 6.9 WAR and a 143 wRC+ over 605 PA at 3B

Turner- .322 / .415 / .530 slash with a 5.1 WAR and a 151 wRC+ over 533 PA at 3B

Votto- .320 / .454 / .578 slash with a 6.6 WAR (1B gets brutalized for WAR) and a 165 wRC+ over 707 PA (record number for walks taken in a season)

However, this discussion is not about whether or not Stanton should win MVP. It is whether or not Stanton should be considered a top-10 position player in the game of baseball. In my opinion the list currently stands as such:

1. Mike Trout
2. Jose Altuve
3. Bryce Harper
4. Paul Goldschmidt
5. Kris Bryant
6. Joey Votto
7. Josh Donaldson
8. Manny Machado
9. Buster Posey
10. Daniel Murphy

(with Rizzo, Judge, Lindor, Gary Sanchez, Freeman, Corey Seager, and Nolan Arenado in the territory)

The reasoning behind this list is both the strength of their position, as well as their career history and trajectories. Trout is easily the greatest player in the game, and shows no signs of slowing down. Altuve is the best infielder in the game right now, and I don’t see him ever hitting under .300 for the rest of his career. Harper is younger than Trout, and has already accomplished things that no player can imagine, and possesses five tools to his game. Goldschmidt, like Votto later on, is the epitome of consistency. Bryant, Donaldson, and Machado are all in a different breed of third basemen (Nolan not far behind) with their amazing offensive production, and defensive splits. Posey is the best catcher in baseball, and hits supremely well for average. And Daniel Murphy is the same as Posey, where he is a phenomenal contact hitter, with the power upside. With the other players in the area, all of them are young with upside, and their minor-league track records mixed with their current production at the major-league level lead me to believe they’re the real deal.

Stanton may barely crack T20 in my eyes. With the fact that he is too slow and lumbering in the basepaths, mixed with his horrid defensive splits (10 DRS, below average/ 6.7 UZR, below average/ -.5 dWAR), he’s a one-dimensional player. Stanton clearly is a generational talent, and possesses power like no other in baseball, but with his poor attitude and colossal contract, he should be labeled overrated. He is making nearly 30 million dollars per year, and for a player who has only surpassed a 6 WAR twice over his eight seasons, it makes you question how truly valuable he is.

According to Marlins new CEO and part owner, Derek Jeter, the Marlins are “in a rebuilding process,” which Stanton responded to with “I want no part in a rebuild.”

What does the future hold for Giancarlo Stanton and his massive $220 million that is due? The world will just have to sit back, relax, and enjoy the show.

Let’s set the scene here. Top of the fifth inning, two out, two on. Your ace has come into the game, and given up the lead. All you’re looking to do is to minimize the damage. Just when it looks like you’re out of the jam with a big strikeout from Scherzer, the ball scoots between Wieters’ legs, and heads to the backstop. The one wrinkle, you might ask? Oh yeah, Wieters gets hit on the backswing by Baez. Now, there was no doubt in anyone’s mind that Baez hit Wieters, or so we think. The average casual baseball fan might be wondering if something could be called.

Some more experienced baseball fans may be inclined to say that was unintentional backswing interference, but in this scenario, that is wrong. Some may think that since Baez didn’t hit him intentionally, there should be no penalty.

Now for the good stuff. In the Official 2017 MLB Rulebook, the comment under rule 6,01 a) states:

“If a batter strikes at a ball and misses and swings so hard he carries the bat all the way around and, in the umpire’s judgment, unintentionally hits the catcher or the ball in back of him on the backswing, it shall be called a strike only (not interference). The ball will be dead, however, and no runner shall advance on the play.”

and the PBUC manual even goes slightly further to elaborate on this. On top of the official MLB ruling, it adds, “If this infraction should occur in a situation where the batter would normally become a runner because of a third strike not caught, the ball should be dead and the batter declared out.”

So was Wieters right to be frustrated with the non-call? Absolutely. Should Dusty have tried his case a bit further? Probably. Jerry Layne and his crew missed a call that ended up costing the Nationals two runs in a game that they ended up losing by a single run. If Layne gets this call right, does Scherzer get another inning? Does getting out of a jam wake up the Nationals’ bats for a big inning to propel them to the NLCS? I guess we’ll never know.

Everyone knows the strike zone alters based off the count. It shouldn’t, but umpires can’t help but be biased. If the count is 3-0, the strike zone will be more forgiving to the pitcher. If the count is 0-2, the zone will be more forgiving to the hitter. What does the zone look like for each possible count? Using Statcast detailed zones, let’s look at the called-strike rate on the corners for the last five years.

As expected, the lowest rate comes from 0-2 counts, and the highest rate comes from 3-0 counts. But the difference is shocking. A pitch in the same location is called a strike 26.46% more often, just because of the count. Here is the same table, ordered by increasing rate.

Four of the first five are two-strike counts, where umpires seem to favor the batter. The average rate in those zones in the past five years, regardless of count, is 22.45%. The rate on all two-strike counts is 13.16%, a good bit below the overall average. Hitters ahead in the count have nearly twice as many strikes called on them in the corner zone, as the rate spikes from 13.68% when they are behind to 25.99%.

What stands out is how much one strike can affect the umpire. The last four are all no-strike counts, and there is an over 10% difference between 3-1 and 3-0. One strike significantly changes how the zone is called. Balls, on the other hand, do not have the same effect on the zone. Two-ball and three-ball counts are up and down the list. The amount of strikes controls the way the zone is called.

It’s a given that the zone will expand to favor pitchers when they are behind, but the difference is surprising. A first-pitch strike is always preferred, but pitchers also get a significant amount of leeway as they fall behind.

I researched a potential cost of elevating before. I found a small but not significant correlation of launch angle and strikeout rate, and also a hint that hitters who elevate more might suffer in BABIP, especially if the guys pull a lot. That makes sense, since the BABIP on balls above 25 degrees is just 0.093. Some of that is pop-ups as sometimes FB hitters tend to hit more pop-ups, but even just looking at non-popped-up higher FBs (25 to 40 degrees), the BABIP is just 0.167. Even subsetting that for balls hit at 100+ MPH, the BABIP still is only .233, so that doesn’t help much.

However, that is not the whole story, as HRs are hits too. The BABIP might suffer, but if you hit a lot of homers, that can offset some of that. You can calculate that pretty easily. If the BABIP of higher FBs above 25 is 0.093, that means you need a HR/FB of around 20% to hit for a true average in play of .300. If you look at guys who hit no pop-ups, that requirement lowers to about 18% (.114 BABIP on balls between 25 and 60 degrees as non IFFBs). That doesn’t even really change for harder hitters, as the BABIP between 25 and 60 with 95+ MPH still is only .130, so HR/FB remains the limiting factor. High-pop-up hitters might require higher minimum HR/FB threshold to keep the OBP up.

A good example is prime Pujols. He was no Bautista/Dozier HR-or-out type of elevator, but his BABIP was only around league average while his average was higher than his BABIP, due to low K and high HR/FB rates. Thus, he could hit for the same average as Miggy, who routinely had .330+ BABIPs but slightly worse K and HR/FB rates.

Here is a table showing wOBA for different LA/EV combinations. I used 87 as a cutoff because that was the 2017 league average. Minus 10 to plus 5 was taken as more “line-drive grounders” while <-10 was used for chopped grounders and anything above 60 as a pop-up, so I did not divide that more. Keep in mind those are all hits and not hitters/average EV.

You can see that higher EV guys have a higher effective LA range. The very soft group actually was a little less sensitive for EV in FB angles, probably because there are a lot of bloopers in that range. Thus that might not apply that much for guys who routinely hit that soft, and thus are played shallower.

The slightly below average group was effective between 5 and 25 and then had a sharp drop-off. With the slightly above average group, the grounders get a little more effective, the peak at the line-drive angles gets a little higher, but there still is a big drop-off around 25 degrees, actually even starting above 20 degrees.

Now it really changes in the hard-hit range (95+) and especially the really hard-hit balls (100+, 110+). The really hard hitters stay effective until almost 45 degrees, meaning they do much better in the non-popped-up but high outfield fly balls (pop-ups are not sensitive to EV and always produce nothing). Those real power hitters (not the Murphy/Altuve type elevators, but guys like Gallo, Sano, Stanton, Judge who can really hit it) thus should hit a lot of fly balls to the OF.

The slightly above average power guys can still benefit from elevating, but then a few things must be true:

1)at least low-ish K rate. This is seen with Altuve and Murphy who don’t hit super hard but for great production

2) The elevated balls shifted towards the LD range and away from the high OF FB range, i.e. a very narrow LA range. Murphy here ideally is again a prime example because he hits very few grounders without a really high FB rate

3) Ideally a low pop-up rate

So it really depends on the type of hitter how they should approach. The hard hitters are always quite effective, even with grounders, but still they need to elevate since the grounders are only around average, but they usually have low defensive value and high Ks and thus need to compensate something. The really hard hitter is rarely truly terrible even as a grounder machine (see Christian Yelich), but if there are higher Ks and no defensive value they might still be bad players. Also despite grounders being less bad, the gap between grounders and FBs is still getting larger, so they have more to gain by elevating. Thus it makes sense for them to go into the OF FB range.

For the really low power hitters it doesn’t really matter unless they slap it straight into the ground, which still is a bad idea for them.

And the average power hitters should shoot for the low-line-drive range unless they are able to have a very narrow range and avoid the high OF FBs; then they can elevate up to the 15-20 range without a penalty (Daniel Murphy type).

Watching the Yankees and Twins playoff game last week, I noticed that it seemed the strike zone was pretty tight. This was just one playoff game and a few pitches, but I thought of the possibility of a shrinking strike zone in the playoffs, as umpires may be less forgiving.

Baseball Savant would not let me run a query for all seasons, so I divided my data queries into three-year increments, dating back to 2009. First, for each three-year set, I found the total called strikes and balls (pitches not swung at) and calculated what percentage were called strikes for the regular season and the playoffs.

The zone grew a little from the regular season to the playoffs in 2015-17 and 2009-11, but shrunk a little in 2012-2014. So no indication of any sort consistent strike-zone change.

Using the Statcast detailed strike zones, I looked at the same called-strike rate on zones 11, 13, 17, and 19. These zones are the corners of the strike zone, with half of the area in the zone and half outside of it.

There is a clear change here, and not in the direction I thought it would. There is a 3% average increase of called strikes on the corners here. Not a huge change, but certainly a difference-maker. Looking at just this season, the called-strike rate on the corners has increased from 21.88% in the regular season to 24.14% in the postseason.

Let’s look at the rest of the edges of the strike zone (area between the corners).

Not nearly the difference of the corners, but an average of a 1.58% increase. There is definitely a trend of strike-zone expansion.

This also begs the question of whether Rob Manfred’s initiative to raise the bottom of the strike zone has had any effect. There was worry that umpires had become too trigger-happy with pitches around the knees. Looking at only pitches in the bottom edge of the strike zone, the called strike rate in 2014-16 for the regular season was 34.78%. In the 2017 regular season, it was 33.85%. So it appears there was definite change. But has Manfred’s wish stayed consistent in the playoff?

The called-strike rate in the zones bordering the bottom of the strike zone (through October 9) is 37.38%, nearly four percentage points higher than the regular season. So umpires are not meeting Manfred’s hopes in the playoffs thus far.

We can’t be sure of how this affects playoff games, but Dustin Pedroia struck out looking on a bottom-corner pitch barely in the zone with the bases loaded. Maybe if it were like the regular-season strike zone, we would be talking about an Astros and Red Sox Game 5. Obviously we cannot assume anything, but it’s hard to argue this does not change the game at least a little.

Clearly, my initial inclinations watching the Yankees and Twins play were wrong. I was surprised to discover the zone actually expands, not shrinks, in the postseason. In a climate that is already more difficult for hitters, as most teams are pitching their best stuff, it is only making postseason hitting even more difficult.

Since the dawn of baseball, fans and coaches alike have debated whether or not pitch count and days of rest affect a pitcher’s health status and performance. This ongoing discussion has led to a close examination of how to best manage the health status of a pitcher. Should you give your starting pitcher that extra day of rest or can you pitch him in the big game today? The question of how to manage your starting pitcher can make or break a season, and, therefore, certainly merits the amount of attention and debate it has received.

Major League Baseball’s adjustment to the age of big data has reshaped the way in which we view these age-old debates. Nowadays, there are public databases that allow hobbyists and students of the game to query their own data and investigate their own theories. Baseball Savant and Baseball Reference are the two main public databases in use, and are the two databases that will be utilized for this study. The data being queried is rest days and runs scored per inning pitched for starting pitchers in Major League Baseball in the last five full seasons.

Problem Definition

In this study, I will look at the effect that the number of days of rest has on the performance and health of a starting pitcher in Major League Baseball. More specifically, I will investigate whether or not fewer rest days are correlated with poor performance and poor health status. Not only does this study have the potential to save millions of dollars for the baseball industry, but it could also provide starting pitchers with more knowledge on how rest days between starts affects their health and performance. The predictor “Runs Scored per Inning Pitched” will be evaluated to determine performance. Although there is a significant amount of noise (i.e. many factors contribute to the outcome) in the runs scored predictor, it seems like the best way to determine a pitcher’s performance on a game-by-game basis. Ultimately, the number of runs scored is the difference between winning and losing, and therefore should be the main criteria used to judge the performance of a starting pitcher.

Results

I determined that there is a significant difference between a pitcher’s performances on a specific number of rest days versus the others. However, there is no significant difference in starting a pitcher on “short rest” (1-3 days) versus “normal rest” (4-6 days) versus “extended rest” (7+ days).

This is an extremely important result considering that starting pitchers are usually employed on three, four, or five days of rest. Currently, starting pitchers are believed to perform at the highest level without the added possibility of injury with this amount of “normal rest.” However, this study shows that there is no significant difference in starting your pitcher on short rest vs. normal rest vs. extended rest. While there is a correlation in the specific number of rest days and performance of a pitcher, there is no significant difference in starting your pitcher on short rest vs. normal rest vs. extended rest.

This study shows that each of those extra off days could not only make a significant difference in pitching performance but also could make a difference in health status for pitchers. There is a fine line between getting the most out of your starting pitcher, and overusing him.

Data Analysis and Tests

In order to determine if there is a significant difference between runs scored per inning pitched and the number of rest days, a non-parametric ANOVA test is needed. The results are as follows:

Reject Ho at alpha=. 05, the Runs Scored per Inning Pitched rate is significantly different for at least one of the number of days of rest. The number of runs scored per inning pitched is significantly different for at least one of the numbers of rest days.

However, we want to know if having your starting pitcher pitch on “short rest” is significantly different than having your starting pitcher on “normal rest.” In order to do this, the data was split into number of days of rest 1-3 and days of rest 4-6. Zero days of rest was eliminated, as these numbers typically only apply to relief pitchers. Then, a non-parametric rank sum test was conducted to determine if performance on “short rest” is significantly different than performance on “normal rest.” The results are as follows:

Do not reject Ho at alpha=. 05, the Runs Scored per Inning Pitched rate is not significantly different for “short rest” and “normal rest.” There is no significant difference in performance between pitchers on “short rest” and “normal rest.”

Last, “extended rest” was looked at to determine if runs scored per inning pitched was significantly different than “short rest” and “normal rest.” “Extended rest” includes all rest days of 7 and over. The results are as follows:

Do not reject Ho at alpha=. 05, the Runs Scored per Inning Pitched rate is not significantly different for short rest, normal rest, and extended rest. Therefore, there is no significant difference in performance between short rest, normal rest, and extended rest.

Recommendations

The first recommendation I would make would be to look at pitchers coming off the disabled list and starting. Starting pitchers can definitely be skipped in a rotation when a team has an off day. This causes there to be much more time between starts.

If possible, data that tracks rest time between pitcher’s starts up to the hour as a continuous variable would be ideal. This could provide more insight into the effect of rest on performance of starting pitchers, and it would provide more of a continuous variable for analysis instead of treating all rest days equally.

Another recommendation for the study would be to use a different predictor for performance. Finding a public database that included days of rest data for each start was tough, and finding one that had days of rest data for each start along with the predictors that were sought after was even tougher. Ideally, an advanced statistic like FIP or weighted On-Base Average would be used, but these predictors are very difficult to calculate for over 1300 data points.

As long as there are starting rotations in baseball, the question of how off-days affect the performance and health of starting pitchers will be studied. Another potential study would be to look at the pitch count of starting pitchers. This could have a similar effect as rest days when looking at performance. With the recommendations made in this study, a future study to determine if performance is affected by pitch count and days of rest would be extremely beneficial.

Now, with the 2017 MLB regular season behind us, the offseason frenzy is in full swing already for those teams that didn’t make the playoffs. The biggest glaring issue that was noticed by millions of fans nationwide, appears to be the inconsistency, and overall treachery of the St. Louis Cardinals’ bullpen arms. Now, coming out of this season, in which they missed the playoffs, questions are asked about the abilities of their bullpen arms, as well as the consistency of all of them. The acquisition of Brett Cecil at the beginning of the year had looked as if it could be a great signing; however, he was anything but that. Let that segue into today’s discussion, Trevor Rosenthal.

Being a Cardinals fan definitely has its ups and downs, and like most, I ride high with the ups, and fall hard with the downs. Trevor Rosenthal has always been a well-liked player of mine, and one that I not only love watching, but also feel is a vital piece to the Cardinals’ puzzle. After Trevor’s tumultuous 2016 season, and his bounce-back 2017 season, eyebrows are still raised over the 27-year-old’s future with the team. Rosenthal was placed in the bullpen, and used as a mid-innings guy, usually when the game was out of reach for either side in 2016. Again, he did not impress whatsoever, and the offseason that followed would be a “make it or break it” one for Trevor Rosenthal. 2017 was a different story for him, however. He was able to find himself, show his life and velocity on his fastball, clocking over 100 mph multiple times a game. Cutting his ERA down to a solid 3.40, with a 2.71 FIP. His K/9 rose from a 12.5 to a 14.3, and his BB/9 dropped from 6.5 to a 3.8. His abilities to strike out batters at an extremely efficient rate, and his cutting down on H/9, led him to regain the closer role on the team, especially with Oh’s horrendous season. Yet having to undergo Tommy John surgery ended Rosenthal’s season, and ultimately the Cardinals’ bullpen as a whole.

When Rosenthal was placed on the 10-Day DL, on August 16th, the Cardinals record stood at 61-59. They finished the season at 83-79, going 22-20 over their last two months of the season. Of those 20 losses, 13 of them were due to bullpen implosions. They clearly struggled mightily, and finished the year with a team bullpen record of 22-29, and a combined ERA of a 3.81, with the 12th-highest WAR (4.4). Although these stats may not seem out of line or too terrible, when watching the game itself, you could visibly see the struggles. Their starting pitching vastly outperformed that of their bullpen, and the tumultuous headlining of Oh among the others.

Now, my main debate here is to address the following question that is in the back of my mind, and one that I certainly feel is understandable in many ways, more so than most would think and see…

Is Trevor Rosenthal the Cardinals’ most valuable player?

Rosenthal is a guy who, as mentioned prior, was crucial to the Cardinals success. Yet saying the words “most valuable player” means that he was not literally their best player, but instead their most valuable. While their best player this season had to have been Tommy Pham on the offensive side (.306/.411/.520 slash with a 5.9 WAR and 148 wRC+), with their best on the pitching side being either Lance Lynn (11-8, 3.46 ERA, 7.39 K/9 over 186.1 IP) or Carlos Martinez (12-11, 3.64 ERA, 9.53 K/9 over 205 IP), it is still bold to say that none of them are the most valuable to the team. With Rosenthal, the Cardinals clearly relied heavily on him, as he appeared in 50 games, pitching 47.2 innings. With his fireball abilities, and fantastic strikeout ratio (again, 14.6 per nine), and his 1.6 WAR. Rosenthal’s importance cannot be simply stated with statistics. Watching him pitch, his demeanor and influence on the game is virtually unrivaled. When Rosenthal was brought on, the team and fans felt safer. He often came on, threw 12 to 18 pitches, and got the three outs needed. Despite this, his ERA was an inflated 3.40. His xFIP counters this at a more-than-respectable 2.55. When opponents got a hit off of him, it was most of the time lucky (.337 BABIP against a .206 BAA), and he rarely gave up the long ball (0.57 per nine, down from 0.67 the year before). So this leads you to believe that he was their savior, or their Andrew Miller even. Rosenthal’s value for the Cardinals will be truly tested come this offseason, as they gauge whether or not to gamble on their star bullpen arm, being that he is a free agent, or if they ride the roller coaster that is their current pen.

The reason behind Rosenthal’s team MVP claim is that despite Pham’s remarkable season, and even DeJong’s and Jose Martinez’s, they did not truly impact their team. The Cardinals offense ranked 13th in runs (761), 18th in home runs (196), and 9th in team offensive WAR (0.6). When it came down to it, their contributions weren’t enough to propel the Cardinals to a ton of runs per game, and they certainly did not do enough to lead the team to the playoffs. When Rosenthal was told he would miss the season, the whole fan base felt a seemingly sharp pain in their stomach. The Cardinals were still very much in the playoff picture, sitting only 4.5 games back of first in the NL Central, yet now the team and fans knew it was going to be a much rockier go at things. Rosenthal is the Cardinals’ hardest thrower, and has the best K/9 on the team. His contributions, and ability to get the team out of sticky situations, would no longer be usable, and his elbow is now going to be a question for the future. Yet, if you’re the St. Louis Cardinals, do you re-sign your clear-cut best bullpen arm, despite the TJ surgery? If not, who do you call upon or sign to replace him? Rosenthal is not a simple piece to replace, and his value is not matched by anyone else in the pen.

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).