It’s been quite a week for the WAR stat. Since Jeff Passan dropped his highly controversial piece on the metric on Sunday night, the interwebs have been abuzz with arguments both for and against the all-encompassing value stat. One criticism in particular that caught my eye came from Mike Newman, who writes for ROTOscouting. Newman’s qualm had to do with a piece of WAR that’s often taken for granted: the positional adjustment. He made the argument that current WAR models underrate players who play premium defensive positions, pointing out that it would “laughable” for Jason Heyward to replace Andrelton Simmons at shortstop, but not at all hard to envision Simmons being an excellent right fielder.

This got me thinking about positional adjustments. Newman’s certainly right to question them, as they’re a pretty big piece of the WAR stat, and one most of us seem to take for granted. Plus, as far as I’m aware, none of the major baseball websites regularly update the amount they credit (or debit) a player for playing a certain position. They just keep the values constant over time. I’m sure that whoever created these adjustments took steps to ensure they accurately represented the value of a player’s position, but maybe they’ve since gone stale. It’s certainly not hard to imagine that the landscape of talent distribution by position may have changed over time. For example, perhaps the “true” replacement level for shortstops is much different than it was a decade or so ago when Alex Rodriguez Derek Jeter, Nomar Garciaparra, and Miguel Tejada were all in their primes.

I decided to try and figure out if something like this might be happening. If the current positional adjustments were in fact inaccurately misrepresenting replacement level at certain positions, we’d expect the number of players above replacement level to vary by position. For example, there might be something like 50 above-replacement third basemen, but only 35 shortstops. Luckily, the FanGraphs leaderboard gives you the ability to query player stats by position played, which proved especially useful for what I was trying to do. For each position, I counted the number of plate appearances accumulated by players with a positive WAR and then divided that number by the total plate appearances logged at that position. Here are the results broken out by position for all games since 2002.

Based on this data, it seems like the opposite of Newman’s hypothesis may be true. A significantly higher portion positive WAR plate appearances have come from players at the tougher end of the defensive spectrum, which implies that teams don’t have too difficult of a time finding shortstops and center fielders who are capable of logging WARs above zero. Less than 13% of all SS and CF plate appearances have gone to sub-replacement players. But finding a replacement-level designated hitter seems to be slightly more difficult, as teams have filled their DH with sub-replacement-level players nearly 30% of the time. Either teams are really bad at finding DH types (or at putting them in the lineup), or the positional adjustments aren’t quite right. The disparities are even more pronounced when you look at what’s taken place from 2002 to 2014.

The share of PAs logged by shortstops and center fielders hasn’t changed much over the years, but the numbers have plummeted for first basemen, corner outfielders, and DH’s. From Billy Butler and Eric Hosmer, to Jay Bruce and Domonic Brown, this year’s lineups have been riddled with sub-replacement hitters manning positions at the lower end of the defensive spectrum. Meanwhile, even low-end shortstops and center fielders, like Derek Jeter and Austin Jackson, have managed to clear the replacement level hurdle this season if we only count games at their primary positions.

The waning share of above-replacement PA’s coming from 1B, LF, RF, and DH has caused the overall share to drop as well, with a particularly big drop coming this year. Here’s a look at the overall trend.

And here it is broken down by position…

And just between this year and last…

Frankly I’m not sure what to make of all of this. I’m hesitant to call it evidence that the positional adjustments are broken. There could be some obvious flaw to my methodology that I’m not considering, but I find it extremely interesting that there’s been such a shift between this year and last. We’re talking an 8 percentage point jump in the number of PAs that have gone to sub-replacement-level players. Maybe its been spurred the rise of the shift or maybe year-round interleague play has something to do with it, but it seems to me that something’s going on here. And I’m interested to hear other people’s thoughts on these trends.

Rockies outfielder Corey Dickerson is quietly having an excellent season at the plate. Believe it or not, the 25-year-old is hitting an impressive .315/.371/.577, which even after adjusting for the effects of Coors Field, is still good for a 144 wRC+ — 13th highest among players with at least 400 plate appearances. Dickerson’s batted pretty sparingly against lefties, which has certainly played a role in his gaudy stat line, but platoon or no platoon, a .405 wOBA is certainly nothing to sneeze at.

While Dickerson’s out-of-the-blue breakout is interesting, the approach he’s used to get there is what makes him truly unusual. Since debuting last season, he’s swung at 62% of pitches inside the strike zone and 42% of pitches outside of it, making him about 1.5 times (62%/42%) as likely to swing at a strike than a ball. This is the lowest such ratio of any player with at least 600 PA’s these last two years. Dickerson’s not a free swinger, per se — his overall swing rate of 51% is 38th out of 251 players with at least 600 PA’s — but he just doesn’t discriminate based on whether or not a pitch is in the strike zone. Here’s a look at the hitters with the lowest Z-Swing%/O-Swing% these last two seasons:

Dickerson’s contact rates tell a similar story. Just like his overall swing rate, Dickerson’s contact rate of 81% isn’t all that interesting. Here, he checks in at 151 out of 251. But also like his swing rate, it doesn’t change very much depending on a pitch’s location. He’s put wood on 83% of pitches he’s offered at in the zone, compared to 74% outside of it, making him 1.1 times as likely to connect on a pitch within the zone — fourth lowest out of 251.

Multiplying these two metrics (Contact% x Swing%) gives us Dickerson’s contact rate over all pitches seen, regardless of that pitch’s location. Lets call this AllContact% to distinguish it from the traditional Contact%. This number shows just how much of an outlier he really is. For the average major league hitter, a pitch thrown in the strike zone results in contact 2.9 times as often as one outside of it, but for Dickerson, a pitch in the zone is less than 1.7 times as likely. Even if we set the bar as low as 70 plate appearances to include 577 players, this is still the lowest in baseball since the start of 2013.

And unsurprisingly, he also the all-time leader since 2007 (the earliest year with PITCHf/x data). Dickerson had the lowest among all players with 100 PA’s here, but I set the threshold to 600 PA’s to avoid having leader board filled with obscure players like Jesus Feliciano and Jordan Brown. In case you were wondering, Vladimir Guerrero checked in at 2.13.

Dickerson’s indifference to a pitch’s location means its probably only a matter of time before pitchers just stop throwing the ball in the strike zone, especially if he keeps slugging well above .500. So far this year, opposing pitchers have thrown Dickerson a strike just over 45% of the time. This is lower than the league average of 49%, but isn’t exceptionally low, especially for a free-swinging power hitter. Guys like Jose Abreu, Carlos Gomez, and Pablo Sandoval see strikes around 42% of the time, so pitchers could almost certainly get away with throwing Dickerson a few more balls. Sure, he’s shown that he’s able to hit those pitches, but even for a player like Dickerson, chasing after bad pitches is still a recipe for lots of swings and misses. His 74% O-Contact% is well above the league average of 63%, yet still lower than the overall Contact% of 80%.

Dickerson’s one-size-fits-all approach to swinging has worked well so far, but it remains to be seen what will happen when pitchers start exploiting it by throwing more balls out of the zone. Maybe he’ll be unfazed and keep on raking. Maybe he’ll turn into a strikeout machine, who needs to refine his approach to even stay in the big leagues. Either way, Corey Dickerson’s a fascinating player, who’s unlike any we’ve seen in recent years, and it’ll be interesting to see if he’s able to keep succeeding going forward.

The Stolen Base

Some consider the stolen base a “lost art.” Gone are the days of Vince Coleman’s back-to-back-to-back 100+ stolen base seasons of Whitey-ball folklore. Teams are stealing at the lowest rates (per game) since the 1950’s.

Aside from the 2011 outlier, stolen base rates have trended downward at a serious pace, but stolen bases still have their place in the game, especially in increasingly shrinking run environments, but at what point is the value added from a stolen base worth the risk of an out?

Run Expectancy

Tom Tango’s handy-dandy run expectancy chart can give us this answer. In his run expectancy matrix, we can see how run expectancy can change from one state to another from a series of events. The basic guide that saberists abide by is that you should be able to steal bases twice as much as you get caught trying to steal to break even in expected runs, but every situation is different. With runners on first and third and two outs, you would actually have to steal bases at an almost 6:1 ratio to break even.

This is because of three factors: you are not adding any value to the runner that is already on third, making an out takes the bat out of someone’s hands, and making an out with someone already in scoring position is the most detrimental kind of out. Also, in any given situation, you are facing a battery with different characteristics. Stealing a base off of Kyle Lohse and Yadier Molina was nearly impossible back in 2011. On the other hand, stealing a base off of John Lackey and Jarrod Saltalamacchia would have been a lot easier. Accounting for the risk of your own baserunner, the defense, league rates, and base-out situation will lead to the most informed decision.

In the tool below, begin by picking your situation (the strings go: out, first base, second base, third base where “x” means no runner and a number means a runner occupies that base e.g. 0x2x means no outs and runner on second base). Then evaluate your baserunner’s steal rate against an average opponent (Steamer’s updated projection gives Kolten Wong a 21/24 chance of stealing a base). After that, evaluate your opponent’s steal rate against (lefty or righty pitcher, strong armed catcher). Then plug in the league average steal rate, and you should have an expected stolen base percentage for your given situation and the given change in run expectancy (RE24).

LINK

As of this writing the MLB K/9 stands at 7.7, the highest in recorded history.

>> Here is a list of HOF pitchers with a career K/9 over 7.7:

Nolan Ryan        9.55

Sandy Koufax   9.28

Yep, that’s it.

>> There are 27 active pitchers with at least 1,000 IP and a career K/9 over 7.7.

>> There have been 643 seasons in MLB history in which an ERA-qualifying pitcher put up 7.7 K/9.  Just under half of those (315) have occurred since 2003.

>> The five best 7.7+ seasons by FIP (FIP,ERA,ERA+, K/9):

Pedro Martinez             1999         1.39/2.07/243       13.20

Dwight Gooden             1984         1.69/2.60/137        11.39   19 years old

Clayton Kershaw          2014         1.89/1.70/2.11        10.74   MVP. Yes, I said it.

Sandy Koufax                     1965          1.93/2.04/160       10.24   26 HR allowed

Tom Seaver                      1971          1.93/1.76/194          9.08

>> The five worst 7.7+ seasons:

Brandon Duckworth    2002          4.39/5.41/72          9.22    26 HR allowed

A.J. Burnett                      2007          4.33/3.75/119         9.56    had winning record

El Duque                            2006           4.24/4.66/96         9.09

Tim Lincecum                 2012            4.18/5.18/68          9.19     lead league in losses

Jonathan Sanchez         2009          4.17/4.24/100        9.75

>> The major league strikeout rate has continuously been:

above 7 since 2009

above 6 since 1994

above 5 since 1982

above 4 since 1952

above 3 since 1930

>> The strikeout rate hasn’t decreased since 2005.

>> If the season ended today:

5 playoff teams would have a team K/9 over 7.7

Dodgers        8.4

Angels           8.2

Mariners       8.0

Nationals      7.9

6 playoff teams would have a team K/9 below 7.7

Cardinals      7.6

Athletics        7.5

Giants            7.5

Pirates           7.3

Royals            7.2

Showalters    7.1

>> From 2000-2008, only one World Series champion had a K/9 over 7.7: the 2001 Snakes at 8.0. Since 2008, only one world champ has had a K/9 under 7.7: the 2011 Cardinals (6.8).

I’m not sold on the idea that all these strikeouts threaten Our Way of Life (indeed, this is far more dangerous). But it will be fascinating to learn if some GM will be able to find an underpriced competitive advantage in scouting and developing guys whose bats can locate the ball more often.

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.