For the past two years or so, Kansas City has been torn about breakfast… Billy “Big Country Breakfast” Butler that is. During this past offseason there were many rumors that the Royals were going to trade him and it seemed inevitable upon entering talks with then free agent Carlos Beltran. Billy Butler is part of the home-grown youth movement in Kansas City with Alex Gordon, and later followed by Salvy Perez, Mike Moustakas, Eric Hosmer, and company. From 2009 through 2013, Billy Butler has offensively been above average, and even great! However, after failing to meet expectations last year, and in some opinion already being in decline at the age of 28, Billy came out and struggled mightily to start the 2014 season.

But he has turned it around somewhat, and with the Royals making headlines this August, Big Country played a big part. So I wanted to look at what he did differently comparing his April dud, to his career average, and to his being a stud again in August. We will measure his overall offensive prowess with WRC+, which in this study would be 50 in March/April, 118 for his career average, and 126 in August. So let’s look at the more telling processing stats.

One of the first things to pop out at you is the BB/K ratio. While under his career margin (and by a decent margin too), his BB/K rate is nearly the exact same in April and August. A lot of times credit for a hitter’s success is given to an increase in the BB% and decrease in the K%, but here Butler cuts down on both, therefore increasing the amount of balls he puts into play bringing us to BABIP. Both his April and August are way below his career norms. Perhaps dealing with a little unluckiness? Or just weak contact? Fact is even with his BABIP down and his home run rate relatively consistent he can still create above average production.

Now comes the most telling rate, which is the type of balls that he hits. As someone who is an AL DH, Billy Butler is not only expected to hit, but to slug. That big goose egg for HR’s in April is just an absolute killer, and the culprit is the GB%. It is no wonder why a big, SLOW (we all know about his base running and uncanny attraction to double plays), gap to gap power hitter has one of the worst months of his career considering his GB% is up almost 12% and his FB% is down nearly 10%. Billy Butler will never be Aoki. He has to get the ball in the air. He lives on hitting doubles into the deep gaps at Kauffman Stadium and with ratios such as those it is no surprise he puts up a WRC+ of 50.

When your BB/K ratio is so nearly identical but yet you put up such drastically different numbers, not to mention the fluctuations in his BABIP, it has to come back to his swing mechanics and getting to a consistently good contact position where he can drive the ball.

Billy’s discipline at the plate has been waning. But the month he really lacked discipline is the same month he did so well in: August. In April he was within his career norms for all of his discipline stats except O-Contact%. Overall he was swinging less and missing less. And that is where the problem may lie! It is not so much that he was struggling with pitch selection, because clearly he was even worse with discipline in August, but the fact that he didn’t miss when he swung.

In a sense Butler was too good at making contact! With his swinging percentage up along with increasingly bad pitch selection, the higher his swinging strike percentage, the better! And perhaps with his swing percentage, his first pitch strike percentage, and his O-Swing percentage all up, he has changed to a more aggressive approach? Again all of this can lead back to the assumption of Butler making poor contact in April. Which leads to the question of what has he done differently, if anything, with his swing?

Now the main reason I bring these stats up is that I am a huge believer in fastball hunting. These charts may not be the most reliable in telling of pitch selection, but they do tell you if he has been seeing certain pitches better and the rates at which he has been seeing pitches.  So I wanted to look closely at his fastball rate in particular just to see if there was anything funky going on. And what was so funky is that in August he was crushing it! The more fastballs you see the better chance you have to hit well. While I am not sure of the exact quantity of fastballs he faced, for the most part he has been seeing the same consistent rate of different pitches he always has and he definitely has done one of his better jobs of taking advantage of the fastballs he has seen. Can a correlation be made between his April failures and August success against fastballs to a possible new approach and/or adjustment in his swing mechanics? Or just unlucky, bad contact?

After searching through the KC Star (hometown newspaper) as well as other media report outlets, I have not been able to find much of anything indicating adjustments being made. There was some talk of just his timing being off, but other than that there are not many clues. I wish I knew how to make video clips of swings and find a couple angles of Billy Butler’s swing in April compared to his swing in August and dissect them both. I would like to see what, if anything, is different. If we could see his timing and especially his bat path, I believe we can tell a lot about what he is doing wrong or right. If anyone can provide those, or teach how to make them, please do and send to me!

However, going off of what I have seen here, everything to me points back to weak contact consistently being made. Whether due to timing or mechanics, I am not sure. Normally I would say this is due to poor pitch selection, but as I showed above, he had even worst discipline and pitch selection in August than April and still put up very stellar numbers. To be clear hard contact is not good enough for a player of Billy Butler’s style. He NEEDS to get air under his pitch. Now they say that this is a game of adjustments. I would love to know what, if any, adjustments Billy “Big Country Breakfast” Butler has made. After all, could it really have just been a string of bad luck?

At the start of the 2013 season, Brett Gardner adopted a new, more aggressive approach at the plate in the hopes of barreling more hittable pitches. Up to that point, the slap-hitting outfielder had been one of the most patient hitters in baseball. Gardner sat out most of 2012 due to injury, but swung at just 32.7% of all pitches seen between 2010 and 2011, the fewest of any player with at least 300 plate appearances. Last year, his swing rate jumped to 40.1%, with most of his new-found aggressiveness focused on pitches located within the strike zone. While his zone swing rate rose by 13 percentage points from 2010 to 2013, his rate for pitches out of the zone only increased by seven.

The change seemed to pay off. Gardner posted a career high .143 ISO last season — much better than his career mark of .103 — on his way to a very respectable 108 wRC+. He’s carried that success over to this season as well. With 16 homers, he’s doubled his total from last season — which was already a career high — and with a 119 wRC+, he’s developed into one of the better-hitting outfielders in all of baseball.

But unlike last season, he’s no longer sporting a swing percentage north of 40%. Instead, it’s fallen back to 36.6%, just a tad higher than his 35% mark from 2011. So if Gardner’s back to his old ways of watching two thirds of all pitches go by, how has he managed to keep hitting for power? The answer has everything to do with plate discipline. Gardner’s continued to take advantage of hittable pitches, but has also gotten much better at laying off pitches outside of the strike zone. First lets look at how often he’s swung at pitches inside of the strike zone.

Since adopting his more aggressive approach two springs ago, Gardner’s behavior on pitches in the zone hasn’t changed much. Maybe he’s gotten a little less aggressive over the past couple of years, but for the most part, his swing rates have been pretty consistent. It’s probably safe to say that Gardner’s a guy who swings at about 50-55% of pitches in the strike zone. We see a different story, however, when it comes to pitches outside of the zone.

At least initially, Gardner’s swing rate on balls out of the zone also spiked. He seemingly became more aggressive on all pitches, without discriminating based on location. But that’s changed over the past couple of seasons, as he’s swung at fewer and fewer pitches out of the zone. His O-Swing% dipped below 18% in both July and August — down from around 25% in early 2013 — putting him on par with what he was doing back in 2010 and 2011. Today, Gardner’s been nearly three times more likely to swing at a strike than a ball, up from two times as likely in April of 2013.

Gardner’s improved plate discipline is nothing new. Although his change in approach puts a kink in the trend, Gardner’s been getting better at deciding whether or not to swing since his first days in the big leagues, and probably even longer. Even before he re-evaluated his approach before the 2013 season, he was already starting to transition from a “guy who doesn’t swing at anything” to a “guy who doesn’t swing at balls”.

Coming up through the minors, Gardner didn’t impress many scouts with his tools, and barely even made his college team as a walk-on. Sure, he’s always had plus-plus speed, but that only gets you so far when you’re an outfielder with little power to speak of. Rather than relying on his pure hitting skills, Gardner makes it work with his zen-like plate discipline. By swinging at so few balls out of the zone, Gardner practically forces pitchers to leave the occasional pitch over the heart of the plate, and has just enough pop in his bat to make them pay for it. But most importantly, he’s learned how to take advantage of those mistake pitches, while simultaneously laying off of the bad ones.

Statistics courtesy of FanGraphs.

The Arizona Diamondbacks have the third-worst record in baseball this season, which obviously isn’t a very good thing. But I feel that there are some positive signs for the Dbacks. Or a handful of them, anyway.

Before I begin saying good things about this Arizona team, a disclaimer:

I do recognize that the Los Angeles Dodgers and San Francisco Giants are still in the National League West as well, so it will take a good many things going the right way to make the Diamondbacks do as much as compete with their divisionmates. Even with that, I’m optimistic.

First and foremost: They still have Paul Goldschmidt, and he’s under team control through 2019. Since his first full season in 2012, Goldschmidt has been the second-best first baseman in the bigs. This year, Goldschmidt has been a top-25 player despite missing several games due to injury. Having an All-Star/MVP-caliber/middle-of-the-order-hitting first baseman is a good place to start for a team.

But one excellent player doesn’t make a great team. The old adage is “be strong up the middle,” after all. And Arizona kind of is, or could be.

Of course there is catcher Miguel Montero, who is locked up through 2017. We’ve almost certainly seen the best of Montero already, but he’s still a solid everyday player, at least defensively. And it seems like good defensive catchers pretty much keep being good defensive catchers.

Continuing up the middle, there’s Chris Owings at short. Owings is only 23 and debuted last season. He’s pretty good defensively, has a decent bat with some pop and, despite having only played 72 games this year, has been quite productive.

Again, he’s only played a little more than half a season. But he ranks 14th among all shortstops, and he’s been better than any other one who has played as few games as he has. If we take Owings’ WAR (1.8) for this season and prorate it for a full season (600 plate appearances), he becomes a four-win player. Only four shortstops totaled four wins above replacement last year: Troy Tulowitzki, Hanley Ramirez, Ian Desmond and Andrelton Simmons.

I’m not really trying to suggest that Owings will be as good as any of those four right now or next year or the year after that, but he’s been good so far. And at 23, he’s still got some time to grow.

Center field has been one of the good spots for Arizona. AJ Pollock has been quite good in his limited time, and Ender Inciarte has done well there, too. Inciarte is a defensive wizard, and Pollock was an outstanding hitter this season before going out with a hand injury. We probably shouldn’t expect Pollock to keep this level of offensive production up, but he’ll probably be pretty good. Even if he can’t hit, he put up good defensive numbers last season.

Pollock and Inciarte can play multiple outfield spots, so there’s not a logjam in center, and trading Gerardo Parra away at the trade deadline opened up a spot for the near future.

If Pollock and Inciarte are taking up two spots in the outfield, maybe David Peralta can take the other. Peralta started as a pitcher in St. Louis in 2006, staying in rookie ball for two seasons before eventually blowing out his arm in 2009. From there, Peralta played some independent ball when Arizona discovered him last year. Peralta just turned 27 in August, so he’s still a young guy. Even if he takes a step back in 2015 — and he very well might — he’ll be a piece to have.

A piece of what, I’m not sure. He and other outfielder Mark Trumbo have both probably hit their peaks, and the projections just do not care for either of them going forward. I don’t personally know who provides the Oliver projections, but I must presume Peralta and Trumbo have wronged that person/computer in some way.

Veteran Cliff Pennington has been a good at all over the infield this year, and has provided about as much value as Owings in 20 fewer games. He’s 30 now, so he still has some years left and can provide some good defense at a couple of infield spots, at least.

So it’s a good-looking seven players that will head into next year for Arizona. But the problem hasn’t been those pretty good players as much as it’s been the dead weight that Cody Ross, Jordan Pacheco, Trumbo and Aaron Hill have provided this year.

Odds are that we’ve seen the best of Ross and Hill. Both were good players in their primes, but those primes have passed. Ross is locked up through next season, and Hill will be there through 2016. But Trumbo and Pacheco could both be let go after this year.

Sure, there’s value to having Trumbo. He hasn’t hit for much power this year, but that’s been his calling card in the past. But the Dbacks can’t really put him at first because Goldschmidt is there. And if he plays left or right field, Trumbo is taking a spot away from one of those outfielders. Of course, Peralta could have a poor 2015, and Trumbo would fit in left if that’s the case.

I have no idea if that will happen, though. I can’t tell the future.

Trumbo might fit at third, but he hasn’t played there much. Fortunately for Arizona, third base prospect Jake Lamb has already debuted. While he hasn’t been very good at the big league level, he absolutely crushed pitching in Double-A. Lamb is only 23 and projects to be a plus hitter. He’s probably the future answer at the hot corner.

Now for the pitching.

It hasn’t been good. But there’s hope.

Today, we spell hope “A-R-C-H-I-E,” for Archie Bradley, or “B-R-A-D-E-N” for Braden Shipley, both of whom are top 100 prospects, with Bradley being No. 11 overall. Bradley had a little arm trouble this year, but was absolutely lights-out in Mobile last season. Shipley is completing his first full season of professional baseball, and hasn’t been bad at all. Both guys have fastballs in the mid-90s with other offerings that project to be really good.

Relying on prospects is what I meant when I said, “it will take a good many things going the right way” earlier. For the Diamondbacks to have real shots at success, they’ll probably need Bradley and Shipley to pan out. Bradley should be up sometime next year, and Shipley might come just after him.

As far as pitchers already in the rotation, it’s not ideal at the moment. Trevor Cahill has been a bit of a disappointment since coming to Arizona, but he’s only 26. Wade Miley has been pretty unlucky this year and should get a little better, according to his FIP and xFIP. Josh Collmenter pretty much is what he is, and he is a solid starting pitcher when healthy. Collmenter is 28 and Miley is 27, so there’s a chance that they’ll still get better, or at least stay basically where they are.

So that’s it. That’s my case for optimism for the Arizona Diamondbacks. It hinges very much on three good players (Goldschmidt, Montero, Owings) continuing to be really good and several other players (Trumbo, Pennington, Peralta, all the pitchers) just not being awful.

Perhaps I’m looking at the team with Diamondbacks-colored glasses, but I don’t think I am. Maybe I’m expecting too much from the younger guys in the near future.

Actually, that’s probably it. Still, I like their chances.

There’s no doubting that Kevin Gausman is a talented pitcher.  He features a fastball in the mid to upper 90’s, a split-change to fluster lefties with, and a slider with good depth to attack righties.

He even looks the part too, with a 6’3’’, 190 lb. frame, an athletic delivery, and an incredibly fast arm.  And therefore, it was for good reason that the Baltimore Orioles made him the 4^th selection of the 2012 Amateur Draft and he’s risen quickly to the big leagues.

However, Gausman’s career up to this point, at the major league level, has seen its fair share of ups and downs.  He struggled in a brief 47.1 IP in 2013 and in 2014 has hovered around mediocrity.  His ERA is alright at 3.83, but a mere 6.82 K/9 and 3.27 BB/9 is likely not what Baltimore was hoping to see from their former elite pitching prospect.

Heading into the postseason, Baltimore can expect solid performances from Chris Tillman, Bud Norris, and Wei-Yin Chen, but Gausman could be there biggest X Factor.  His stuff gives him a chance to dominate a playoff game and serve as a stopper down the stretch, but he’ll need to be more than a one-dimensional pitcher to get there.

By one-dimensional I’m referring to Gausman’s strong tendency to pitch only down and to his arm-side. See his FanGraphs pitcher heatmaps below vs. lefties and righties.

Notice, despite batter handedness, Gausman’s pitch location tendencies stay the same, as he works down-and-away from left-handers and down-and-in to right-handers.

Some of this is by probably by design. With Gausman and the Orioles trying to expose holes underneath righties hands and staying away from the lefty power zone of down-and-in.

However, a large reason for this tendency is Gausman’s inability to consistently pitch to his glove side.

In the video linked here, watch how Gausman reaches on the back side of his arm action. This reach makes it more difficult for him to command his pitches by limiting his ability to stay tall on his back side, keep a loose arm, and maintain balance.

Second, watch how he steps across his body.  By having a “crossfire delivery”, in order for Gausman to get a pitch to his glove-side, he must over-rotate and power his arm across the rest of his frame.

Gausman has the arm speed to do this, but the process of doing so, inhibits his ability to command pitches to that side of the plate, and he often misses in the strike-zone where hitters can do damage.

A great example of this was during the third inning of Gausman’s start Saturday afternoon versus Tampa Bay.

With 1 out and Ben Zobrist on 3^rd, Gausman tried to beat David DeJesus with a fastball low-and-in.  But Gausman’s fastball was never able to get to the inside part of the plate, and the left-handed DeJesus roped a single.

Now with 1^st and 3^rd, Gausman faced Evan Longoria and after throwing two split-change-ups down, he tried to beat the right-hander away with a fastball. Once again, Gausman couldn’t get the pitch to his glove side and Longoria smoked the ball to center for a sac fly.

Left-handed hitting James Loney came to bat next and immediately lined the first pitch fastball down-and-away to left field for a single.  The ease at which Loney stroked Gausman’s mid to upper 90’s fastball on the low, outside corner to left indicates he likely was cheating on a fastball there.  And judging from Gausman’s heatmaps and the previous two sequences, there was little reason for Loney to believe Gausman was going pitch him anywhere else.

This was a particularly unfortunate series of at-bats for Gausman and there are going to be times he can better locate to his glove-side. He’s a good enough athlete to overcome his delivery and arm action for periods of time, but consistent command to his glove-side is going to be difficult to achieve.

A simple question to ask at this point is why can’t Gausman make the mechanical adjustments to fix these issues?

Yet, changing a pitcher’s arm action and delivery at this stage of his career is extremely difficult. Gausman has likely been pitching this way his entire life and any changes now would probably result in a major setback first before progress could be made (and if progress could be made is even debatable).

This delivery and arm action is what Gausman is comfortable with and it’s worked well enough to make him a successful professional pitcher. Most major league pitchers do not have perfect mechanics, but rather are athletic enough to make up for mechanical flaws.  Gausman fits into this category.

However, there is an adjustment Gausman could make without changing his mechanics, and that’s better utilizing the top part of the strike zone, even if he stays arm-side. Let’s return to the heatmaps shown above once again. Take a look at the red on the bottom part of the zone and blue on the top.

Kevin Gausman has elite fastball velocity and life. His four-seam fastball has averaged 95.9 mph in 2014, which would put him 3^rd amongst starting pitchers if he qualified.  Compare his FanGraphs heatmaps to those of Yordano Ventura and Nathan Eovaldi, the starting pitchers with the most similar average fastball velocities to Gausman.

More-so Ventura than Eovaldi, but see the increased use of the upper part of the strike-zone, as well as the more diverse use of the entire plate. Ventura has been rewarded accordingly as per Brooks Baseball, hitters are only batting .196 against pitches he’s thrown in the top third of the zone in 2014.

At the very least an increased use of the upper third of the strike-zone will give Gausman another dimension to his arsenal. Hitters, like James Loney, won’t be able to cheat to get to certain pitches in specific locations.

Gausman has the dynamic stuff to be a front-line starter, it’s just about expanding the ways he can deploy his weapons and becoming more consistent in his ability to command them.

The Orioles are hoping he can improve at a rapid rate, as he could be the key to their potential success in late September and October.

Stats courtesy of FanGraphs and Brooks Baseball

In this post I use the negative binomial distribution to better model the how MLB teams score runs in an inning or in a game. I wrote a primer on the math of the different distributions mentioned in the post for reference, and this post is divided to a baseball-centric section and a math-centric section.

The Baseball Side

A team in the American League will average .4830 runs per inning, but does this mean they will score a run every two innings? This seems intuitive if you apply math from Algebra I [1 run / 2 innings ~ .4830 runs/inning]. However, if you attend a baseball game, the vast majority of innings you’ll watch will be scoreless. This large number of scoreless innings can be described by discrete probability distributions that account for teams scoring none, one, or multiple runs in one inning.

Runs in baseball are considered rare events and count data, so they will follow a discrete probability distribution if they are random. The overall goal of this post is to describe the random process that arises with scoring runs in baseball. Previously, I’ve used the Poisson distribution (PD) to describe the probability of getting a certain number of runs within an inning. The Poisson distribution describes count data like car crashes or earthquakes over a given period of time and defined space. This worked reasonably well to get the general shape of the distribution, but it didn’t capture all the variance that the real data set contained. It predicted fewer scoreless innings and many more 1-run innings than what really occured. The PD makes an assumption that the mean and variance are equal. In both runs per inning and runs per game, the variance is about twice as much as the mean, so the real data will ‘spread out’ more than a PD predicts.

The graph above shows an example of the application of count data distributions. The actual data is in gray and the Poisson distribution is in yellow. It’s not a terrible way to approximate the data or to conceptually understand the randomness behind baseball scoring, but the negative binomial distribution (NBD) works much better. The NBD is also a discrete probability distribution, but it finds the probability of a certain number of failures occurring before a certain number of successes. It would answer the question, what’s the probability that I get 3 TAILS before I get 5 HEADS when I continue to flip a coin. This doesn’t at first intuitively seem like it relates to a baseball game or an inning, but that will be explained later.

From a conceptual stand point, the two distributions are closely related. So if you are trying to describe why 73% of all MLB innings are scoreless to a friend over a beer, either will work. I’ve plotted both distributions for comparison throughout the post. The second section of the post will discuss the specific equations and their application to baseball.

Runs per Inning

Because of the difference in rules regarding the designated hitter between the two different leagues there will be a different expected value [average] and variance of runs/inning for each league. I separated the two leagues to get a better fit for the data. Using data from 2011-2013, the American League had an expected value of 0.4830 runs/inning with a 1.0136 variance, while the National League had 0.4468 runs/innings as the expected value with a .9037 variance. [So NL games are shorter and more boring to watch.] Using only the expected value and the variance, the negative binomial distribution [the red line in the graph] approximates the distribution of runs per inning more accurately than the Poisson distribution.

It’s clear that there are a lot of scoreless innings, and very few innings having multiple runs scored. The NBD allows someone to calculate the probability of the likelihood of an MLB team scoring more than 7 runs in an inning or the probability that the home team forces extra innings down by a run in the bottom of the 9th. Using a pitcher’s expected runs/inning, the NBD could be used to approximate the pitcher’s chances of throwing a no-hitter assuming he will pitch for all 9 innings.

Runs Per Game

The NBD and PD can be used to describe the runs scored in a game by a team as well. Once again, I separated the AL and NL, because the AL had an expected run value of 4.4995 runs/game and a 9.9989 variance, and the NL had 4.2577 runs/game expected value and 9.1394 variance. This data is taken from 2008-2013. I used a larger span of years to increase the total number of games.

Even though MLB teams average more than 4 runs in a game, the single most likely run total for one team in a game is actually 3 runs. The negative binomial distribution once again modeled the empirical distribution well, but the PD had a terrible fit when compared to the previous graph. Both models, however, underestimate the shut-out rate. A remedy for this is to adjust for zero-inflation. This would increase the likelihood of getting a shut out in the model and adjust the rest of the probabilities accordingly. An inference of needing zero-inflation is that baseball scoring isn’t completely random. A manager is more likely to use his best pitchers to continue a shut out rather than randomly assign pitchers from the bullpen.

Hits Per Inning

It turns out the NBD/PD are useful with many other baseball statistics like hits per inning.

The distribution for hits per inning are slightly similar to runs per inning, except the expected value is higher and the variance is lower. [AL: .9769 hits/inning, 1.2847 variance | NL: .9677 hits/inning, 1.2579 variance (2011-2013)] Since the variance is much closer to the expected value, hits per inning has more values in the middle and fewer at the extremes than the runs per inning distribution.

I could spend all day finding more applications of the NBD and PD, because there are really a lot of examples within baseball. Understanding these discrete probability distributions will help you understand how the game works, and they could be used to model outcomes within baseball.

The Math Side

Hopefully, you skipped down to this section right away if you are curious about the math behind this. I’ve compiled the numbers used in the graphs for the American League for those curious enough to look at examples of the actual values.

The Poisson distribution is given by the equation:

There are two parameters for this equation: expected value [λ] and the number of runs you are looking to calculate [x]. To determine the probability of a team scoring exactly three runs in a game, you would set x = 3 and using the AL expected runs per game you’d calculate:

This is repeated for the entire set of x = {0, 1, 2, 3, 4, 5, 6, … } to get the Poisson distribution used through out the post.

One of the assumption the PD makes is that mean and the variance are equal. For these examples, this assumption doesn’t hold true, so the empirical data from actual baseball results doesn’t quite fit the PD and is overdispersed. The NBD accounts for the variance by including it in the parameters.

The negative binomial distribution is usually symbolized by the following equation:

where r is the number of successes, k is the number of failures, and p is the probability of success. A key restriction is that a success has to be the last event in the series of successes and failures.

Unfortunately, we don’t have a clear value for p or a clear concept on what will be measured, because the NBD measures the probability of binary, Bernoulli trials. It’s helpful to view this problem from the vantage point of the fielding team or pitcher, because a SUCCESS will be defined as getting out of the inning or game, and a FAILURE will be allowing 1 run to score. This will conform to the restriction by having a success [getting out of the inning/game] being the ultimate event of the series.

In order to make this work the NBD needs to be parameterized differently for mean, variance, and number of runs allowed [failures]. The NBD can be written as

where

So using the same example as the PD distribution, this would yield:

The above equations are adapted from this blog about negative binomials and this one about applying the distribution to baseball. The Γ function used in the equation instead of a combination operator because the combination operator can’t handle the non-whole numbers we are using to describe the number of successes.

Conclusion

The negative binomial distribution is really useful in modeling the distribution of discrete count data from baseball for a given inning or game. The most interesting aspect of the NBD is that a success is considered getting out of the inning/game, while a failure would be letting a run score. This is a little counterintuitive if you approach modeling the distribution from the perspective of the batting team. While the NBD has a better fit, the Poisson distribution has a simpler concept to explain: the count of discrete events over a given period of time, which might make it better to discuss over beers with your friends.

The fit of the NBD suggests that run scoring is a negative binomial process, but inconsistencies especially with shut outs indicate elements of the game aren’t completely random. I’m explaining the underestimation of the number of shut outs as the increase use of the best relievers in shut out games over other games increasing the total number of shut outs and subsequently decreasing the frequency of other run-total games.

All MLB data is from retrosheet.org. It’s available free of charge from there. So please check it out, because it’s a great data set. If there are any errors or if you have questions, comments, or want to grab a beer to talk about the Poisson distribution please feel free to tweet me @seandolinar.

Phil Hughes of the Minnesota Twins and Hisashi Iwakuma of the Seattle Mariners both pitched over the Labor Day weekend and both picked up wins without issuing any walks. While not unusual as single game performances, consider that Hughes now has 15 wins for the season and has allowed only 15 walks while Iwakuma has 13 wins and 13 walks. They both have the opportunity to achieve the rarest of feats if they can finish the season with as many wins as walks. Granted pitcher wins are a poor measure of baseball excellence and are generally out of favor with most readers on this site, but the rarity of their accomplishments are quite astounding and worthy of attention.

How rare? It’s rarer than a perfect game, a 4-homer game, an unassisted triple play, and a batting triple crown. The last time a qualified starter had as many wins as walks was Carlos Silva of the Twins in 2005. Silva recorded only 9 wins in his best pro season by WAR, but he also walked only nine batters. And it wasn’t a small sample size situation either. The dude started 27 games and pitched 188 innings. Unfortunately his team didn’t reward him very often in the win column. Amazingly, 2 of his 9 walks were intentional.

Before that, Bret Saberhagen recorded 14 wins and allowed a mere 13 walks with the New York Mets in 1994. Interestingly, Saberhagen’s season included zero intentional walks while Iwakuma and Hughes have both issued one IBB so far, which leads one to wonder how many walks by these control artists were actually due to wildness (or a stingy strike zone) and how many were because they were merely pitching around a batter? There could literally be zero wild walks by these four, but it’s hard to even estimate without analyzing all the gifs and then guessing.

Also of note, Hughes has hit 3 batters so far this year, which has the same effect as a walk, while Iwakuma hit 2 all season. Both of Iwakuma’s HBPs actually happened in the same game, against Boston in his 24 August start, against back-to-back batters. Silva hit a surprisingly high 3 batters in his 2005 season and Saberhagen hit 4 in 1994. Again, it’s hard to say which of these HBPs were due to wildness and which were statements or retaliation although I personally watched Iwakuma’s two HBPs on MLB.TV and they were definitely not intentional.

Prior to Saberhagen? You have to go all the way back to Slim Sallee in 1919 to find someone with as many wins as walks. Remember him? Me neither. He had 21 wins and 20 walks that year for the Cincinnati Reds over 228 IPs. In baseball terms, 1919 was before Babe Ruth became a Yankee.  He was still pitching for the Red Sox and now he’s extremely dead.  So in the last 95 MLB seasons, among thousands of qualified starting pitchers, only four people have had as many wins as walks, and two of them are doing it this year! Here’s the all time leaderborad going back to 1900 sorted by wins minus walks.

Table 1: MLB Single Season Control by Qualified Starters Ranked by Wins-Walks, 1900-2014

Christy Mathewson is the clear stud in this statistical category with a +4 in 1913 (with zero hit batters) and +1 the following year. Look at all the hall of famers like Cy Young, Walter Johnson and Greg Maddux mixed in with guys that had great control but less than HOF careers like Bob Tewksbury, Babe Adams, Jon Lieber and La Marr Hoyt. Now look at and appreciate some of the innings pitched by these early control artists, led by Cy Young’s incredible 380 IPs in 1904 with only 29 walks.

This being a sabermetric site, the more generally accepted advanced baseball metric for pitcher control is probably BB/9 which takes the subjectivity of wins out of the equation. By that measure, here’s the all time leaderboard since 1900.

Table 2: MLB Single Season Control by Qualified Starters Ranked by Walks per 9 Innings, 1900-2014

Who would have ever guessed that the ALL TIME LEADER in single season BB/9 is Carlos Silva in 2005? By a significant margin! Notice also that even with the elimination of wins from the discussion, Hughes and Iwakuma are still having truly historic seasons, tied for eighth on the all time list. It’s time they start getting some recognition for their accomplishments. Miguel Cabrera won the Triple Crown in 2012 and rightfully received notoriety for achieving a traditional statistical feat. Hughes and Iwakuma are on the verge of doing something similarly extraordinary and deserve some credit as well. I for one am going to watch closely and root for them to continue their excellence and go into the record books with at least as many wins as walks.

* Intentional walks weren’t recorded as an official statistic until 1955

If you’ve been on the internet in the last few weeks (or within earshot of a Michigander) you may have heard about the Tigers. Specifically, you may have heard about how the odds in favor of a Detroit appearance in the 2014 ALDS dropped from 21-to-1 on July 25 to under break-even by August 23 before a slight rebound to finish out the month. Even more specifically, you may have read Mike Petriello’s article about that on this very website. Or at the very least, you may have heard their struggles described in a less quantitative fashion. Regardless, the month of August was not kind to the Bengals.

As Petriello pointed out, this has been less of a Tigers collapse than a Royals surge. But there’s still something to the idea that the Tigers were playing worse in August than they had been previously. Let’s start with the basics:

In August, the Tigers scored fewer runs, allowed more runs, and won fewer games than in the first half. On some level, that’s all that really matters. On another level, something else is different about August for these Tigers.

Back on July 14, Buster Olney and Jeff Sullivan both wrote articles about schedule strength. Olney called the Tigers’ schedule the second-most difficult of 17 “contending” teams (paywall), while Sullivan said it was the easiest in all of MLB. One of the key reasons for the discrepancy was that Sullivan was using projections to determine the difficulty of a particular opponent, while Olney was using actual results. Score one for Sullivan. Another key difference was that as of July 14, the Tigers were about to play 55 games in 56 days, which did not factor into Sullivan’s analysis.

A point for Olney? Perhaps. But first, what would we expect to see if this was a result of schedule fatigue? Or put another way, which groups of players might be hurt most or least by not having a day off? Based on conventional wisdom, the bullpen would probably be the most affected, and the starters the least. So how does this match up to the Tigers? Read the rest of this entry »

Brandon Moss has wielded an immensely potent bat since joining the Athletics’ lineup in June of 2012. Between 2012 and 2013, he hit a remarkable 146 wRC+, and clubbed a homer once every 15.7 PA’s, placing him third in baseball behind Chris Davis and Miguel Cabrera over that span. Moss kept up the hot hitting to start the 2014 season, as well. The 30-year-old 1B/OF/DH posted a 162 wRC+ in the season’s first two months, further establishing himself as a key cog in one of baseball’s most potent lineups.

But Brandon Moss hasn’t been himself lately. Since his last home run on July 24th, he’s only managed three extra-base hits, resulting in a laughable .168/.317/.198 batting line. Moss’s slump has also coincided with a change in his hitting approach. Moss appears to have gotten a bit more passive at the plate, swinging at way fewer pitches both inside and outside of the strike zone. This new-found passivity took a turn for the extreme once the calendar turned to August, when his O-Swing% and Z-Swing% fell to 27% and 65%, respectively — both around six percentage points lower than his career norms.

Moss’s decision to lay off more pitches has unsurprisingly lead to a spike in both his walk and strikeout numbers, but it’s also resulted in his power completely flat-lining. Moss has basically been Adam Dunn without the power these last couple of months. That’s a pretty terrible hitter, and is part of the reason why the A’s went out and got the real Adam Dunn to help their sputtering offense.

The new swing profile is something that’s recently changed, making it the obvious culprit for Moss’s drop-off in production, but we shouldn’t immediately rule out the possibility that pitchers have changed the way they’re approaching him. It could just be that he’s swinging at fewer pitches because he’s getting fewer pitches to hit. That doesn’t seem to be the case, though, as Moss’s zone breakdown from August looks nearly identical to what it was over the season’s first four months. For whatever reason, Moss just isn’t swinging as often as he used to.

It’s not entirely clear what’s spurred Moss’ sudden reluctance to swing the bat, but all indications are that it’s done a number on his offensive performance. Unlike the Brandon Moss that — up until recently — could be counted on for a wRC+ north of 130, this latest iteration seems to be letting a few too many hittable pitches float down the heart of the plate. And based on what’s transpired over the last month or two, Moss’s best bet is probably to re-discover the more aggressive approach that’s worked so well for him in the past.

Statistics courtesy of FanGraphs; Zone breakdowns courtesy of Baseball Savant.

Coming into this season, the Boston Red Sox had high hopes. Obviously, they were coming off a World Series title, and they had every reason to expect that they could contend again. Jarrod Saltalamacchia was gone, but he could be replaced by A.J. Pierzynski; the drop-off there wouldn’t be too large. Ryan Dempster was gone, but the Red Sox’s rotation of Jon Lester, John Lackey, Clay Buchholz, Jake Peavy, and Felix Doubront was what they had gone with during last year’s stretch run anyways. Jacoby Ellsbury was gone, but Jackie Bradley Jr. (and Grady Sizemore!) should have been able to play well enough to make his departure bearable. And Stephen Drew was gone, but uber-prospect Xander Bogaerts was ready to take over the Red Sox’s shortstop position and dominate the league.

Needless to say, none of those really worked out like the Red Sox and their fans had hoped or planned. Boston currently resides in the AL East cellar, all but certain to go from first to worst just the year after they had done the very opposite. And perhaps no individual part of that failure this season has been a bigger disappointment than Bogaerts. Instead of being the hitter he was supposed to be, he has struggled mightily at the plate, to the tune of a .223/.293/.333 slash line — good for a 74 wRC+ (as of September 1) and a major contributor to his negative WAR.

Where do we start in trying to assess the reasons for Bogaerts’s struggles? Well, time-wise, we can place a pretty neat cutoff point at June 4: That is when Bogaerts started to slump (I think I cursed him). For the first two months of the season, actually, Xander was quite good: he had a 140 wRC+ through April and May, and that figure would have been higher if not for a mini-slump that came towards the very beginning of the season. He was drawing walks roughly 11% of the time (above average) and striking out at a clip a shade below 22% (not much below average). And then came June. It started out OK — he went 4-for-13 in his first 3 June games. But after that, for the rest of the month, he recorded a mere 9 hits and 3 walks in 88 plate appearances. July was better, but not good: Bogaerts managed just a .228/.253/.342 line, and now through most of August he has been even worse than he was the previous two months, with a paltry .123/.195/.164 triple slash.

His wRC+, by month:

Yeesh. Not the way you want to be trending. So what happened? Well, the easy answer is to point to BABIP:

This looks right, right? His best month by wRC+ was his best month by BABIP. His worst month by wRC+ was his worst month by BABIP. And the same can be said for every month in between. But that, of course, doesn’t tell the whole story. Why is his BABIP from the first two months so much higher? What can he do to fix it? Will he fix it? Can he? Let’s explore.

A .364 BABIP like Bogaerts had in April is unsustainable. The .421 BABIP he had the following month is way too high for even the best players to keep up. So naturally, we would expect some regression from him. But his batted ball profile did suggest a decent BABIP – high line drive rate and low popup rate. The only thing overly suspect was his 17.1% infield hit rate in June. Nothing there would suggest such an outrageously high BABIP for the first two months, but nothing would suggest the low BABIPs that were to come later either. So something must have changed. What was it?

It wasn’t Bogaerts’s average flyball distance; that stayed more or less intact. But he did start hitting many fewer line drives…

…and started striking out more, which didn’t affect his BABIP directly but did have an impact on his overall hitting (somewhat astonishingly and coincidentally, his K% has been the exact same – to one decimal – each of the past 3 months):

And in the same vein, he walked much less, which helped contribute to his very low wRC+ as well:

So while it may be easy to ascribe Bogaerts’s recent struggles to his abnormally low BABIPs, there is more to the story. He simply isn’t hitting anywhere near as well as he did earlier in the season. I can think of a few potential reasons for this:

1. Pitchers are pitching to him differently, and he will have to adjust

2. He is in a prolonged slump, and will snap out of it eventually

3. He isn’t actually that good, and his first few months were just very lucky

4. He was playing third base

I think we can ignore the last two. Bogaerts, after all, was ranked a top-5 prospect coming into the season by almost anyone worth listening to, and he has hit very well in the majors before; he’s almost certainly not actually bad at hitting. As for the last one — that was a theory many people floated out when Bogaerts stopped hitting well at almost the exact same time as Stephen Drew returned and kicked Bogaerts over to third. The argument was that since short was Bogaerts’s natural position, and he felt most comfortable there and could focus on his hitting, he would do better when playing there.

And that theory holds some water: this season, his wRC+ as a third baseman is 37 (in 180 PA), and as a shortstop it is 95 (in 312). That is too large of a difference to dismiss offhandedly. But here’s the problem: when Drew was traded, and Bogaerts returned to shortstop, he continued to hit poorly. In fact, throughout the entire month of August, Bogaerts played shortstop, and he had a -3 wRC+. I am going to say that that theory, while compelling, doesn’t really explain Bogaerts’s struggles at all. He’d tell you that himself.

So what does? Pitchers pitching him differently? Yes, to an extent. Here is how Bogaerts has done all season long against certain pitches:

And here is how he has been pitched:

The pitches in that gif are ordered by how many runs above average Bogaerts has been against them, descending. You can see that from June 4 (the date of the start of Bogaerts’s extended slump) on, he has seen many fewer fastballs and many more sinkers and sliders than before. That could be the cause of his BABIP, strikeout, and general hitting struggles since he excels against fastballs and cannot hit sliders or sinkers (sliders more so).

But there’s only one issue: the problem isn’t that Bogaerts is getting fewer pitches he can hit, it’s that he’s not hitting the pitches he used to. Here’s Bogaerts against four-seam fastballs (from Brooks Baseball; BIP means balls in play):

He’s cut down a bit on his swings and misses, but everything else looks bad. He’s drastically decreased his line drive rate and drastically increased his popup rate. His groundball rate has gone down a bit, which can be good or bad (in this case I don’t think it’s had a huge effect on anything), and his flyball rate has gone up a lot — which could be good, but Bogaerts is averaging a mere 266.75 feet on his fly balls — 230th out of 284 qualified hitters. So how has this changed his results? Again, Bogaerts against fastballs:

Wow. That is quite the drop in production. League average wOBA against four-seamers this year is .416 (which makes you question why they are thrown so much, but that’s a different article) and so Bogaerts’s wRC+ relative to other fastballs went from a 113 to a 61 in those two timeframes (park-unadjusted).

And look where Bogaerts is hitting balls, too. The following charts aren’t only fastballs — it’s all balls put in play by him. In the beginning of the year, he was sending line drives to all fields, getting grounders through the infield, and pulling balls deep. In the second part, you see lots of shallow line drives and fly balls — in fact, in the three months covered in the second half of the gif, there are all of TWO ground balls that make it through the infield, and only one opposite-field line drive that makes it to the outfield. There are more popups, too, and the fly balls seem to be shallower generally.

Now, some of the things you’re seeing here could be a result of teams shifting on him more as the year goes on, which is why no ground balls are getting to the outfield. But more likely it is Bogaerts making weaker contact and allowing fielders to get to his ground balls; in addition, he isn’t hitting many ground balls up the middle, where you’re more likely to get hits.

Take a look at the gif above. What you’re seeing is the same thing as the last one, only with the at bat result instead of the batted ball type. In the first part of the year, you see Bogaerts getting lots of hits to all parts of the outfields, including deep balls that end up in home runs or doubles. Then, many more balls end up in the infield and most of his hits are shallow balls to the outfield.

This doesn’t look good, especially since it’s been going on for so long. I’m no expert in swing mechanics, so I can’t tell you why Bogaerts has suddenly stopped hitting everything, fastballs especially. My guess is that it’s just a long, long slump that is happening because he’s only 21 years old. I don’t think this means that we should give up on him. He has already proven that he can hit, albeit in a very small sample.

Take a look at the list of all the players who had a wRC+ below 100 in a year where they were listed as top-10 prospects by Baseball America (since 1997):

There are a lot of really good players on that list. Bogaerts is one of the worst there in terms of wRC+ that year, but he’s also younger and higher-ranked than most. That doesn’t concern me. What concerns me is that almost all of the ones on that list from the past few years haven’t succeeded: all of the ones that have are from 2009 or earlier. This is consistent with semi-recent findings by Jeff Zimmerman that the aging curve is changing: hitters don’t improve with age anymore. Further research by Brian Henry shows that players who start in the big leagues at 21 tend to stay steady with their production for a while, then decline at around 30. This does not bode well for the young Red Sox shortstop.

But who knows? If I had to guess, I would say that Bogaerts regains his stroke and starts driving the ball more. He’s too good of a hitter to be so bad against fastballs. After all, he is only 21 years old. Plus… I mean, look at that swing. Number two prospects go far. All the prospects on the list above ranked first or second had some degree of success in the majors, with the exception of Rocco Baldelli, who was good until injuries ruined his career. (Brandon Wood didn’t have enough plate appearances to qualify for the list.) If he was playing a little over his head in April and May, he’s been playing well below his feet for the past three months, and those kinds of things tend to right themselves in time.

Note: This was written before Bogaerts played today, Monday 9/1. He went 1 for 4 with a double and two strikeouts.