Lucas Duda.  The Dude.  The Big Lebowski.  If there is one player on the Mets who would be most deserving of the title of “Most Underrated” it would be Lucas Duda.  I arrived at this conclusion based on my own subjective, and fallible, perception of the casual baseball fan’s perception about Lucas Duda; which I would assume would be somewhere in the vicinity of none.  Some of his relative underratedness may stem from the fact that he was relatively “streaky” during the course of this regular season, which is an inherent trait of a player who produces a large amount of his value by way of the home run.  Also, after Duda had eight straight hits go for home runs during the course of a seven-game stretch in late July, Yoenis Cespedes caught the eyes of the national media from basically the moment he was traded to New York.  That being said, I think Mr. Duda deserves a little recognition for his solid year, especially since he looms as an important figure in the active World Series.

On the surface Duda has almost exactly replicated his breakout 2014 in 2015.  For reference, this table of arbitrary statistics:

His overall value has remained almost exactly the same over the past two years as he has churned out two straight 3-win seasons.  His walk rate and strikeout percentage have been fairly stable as well, as has his various swing rates.  In this regard Lucas has been remarkably consistent.

However, there is one portion of Duda’s underlying statistics that differed significantly from this year to the rest of his career.  Duda pulled the ball less, and went to opposite field more.  Here is another table to illustrate this fact:

* The table starts in 2012 simply because the prior years don’t really provide any additional insight

And here are the batted-ball maps for 2o14 and 2015 to further illustrate Duda’s change in approach:

It looks as though Duda has tried to make himself a more balanced hitter, and decrease the amount of shifts he faces, as he has made an obvious attempt to go the other way more often this year.  This didn’t result in any additional offensive value this year – as we saw in the first table his overall value stayed steady – as we didn’t even see an increase in BABIP.  Regardless, this seems to be a trend worth keeping an eye on, and worth remembering during the World Series.

In specific regard to the World Series, Duda has a relatively significant platoon split; Career 91 wRC+ vs LHP, 136 wRC+ vs RHP.  With the Kansas City Royals featuring right-handers Yordano Ventura, Edinson Volquez, Johnny Cueto, Chris Young, Wade Davis, Ryan Madson, and Kelvin Herrera, among others, Duda looks to occupy an important role during the series.  With all of Kansas City’s probable starters being right-handed Duda should start every game, and it doesn’t seem like he will be pinch-hit for too often with Kansas City’s three best relievers being right-handed as well.

Lucas Duda; chronically underrated, and under-spoken, might just be the Mets’ most pivotal player during this World Series.  Or not.  Probably not, there are a lot of players on a baseball team, but he will assuredly be a pivotal player.  The Dude Abides.

Let’s look at two pitchers:

________           ERA       ERA+      FIP     K/9     BB/9     HR/9

Jake Arrieta      1.77         222         2.35     9.3       1.9         0.4

Pitcher X               5.23          80         4.75     6.9       4.0         1.2

Pitcher X is not Jake’s long lost brother, but is in fact Jake Arrieta – those are his cumulative stats from 2010-2013, his first four years in the majors. And that’s not a small sample size; Arrieta accumulated 409 innings in his first four years. The top line is from 2015, a season which has put Arrieta within shouting distance of a Cy Young award.

No other pitcher has had a surge like this after floundering so badly for his first four years, but even before 2015, Arrieta was traveling through a baseball landscape witnessed by very few humans. Just 26 pitchers in major-league history have amassed over 400 innings in their first four years and “achieved” an ERA+ of 80 or worse. The list is here. It’s most notable for its lack of notability — an array of names of you haven’t heard of, interspersed with a few modern guys who, for the most part, failed to make an impact.

The other notable thing about the list is how short it is; most teams will have given up on a pitcher this consistently bad long before he’s eaten 400 innings of paychecks. Beside Arrieta, just two of the 26 had successful major-league careers as starters: Bullet Joe Bush and Camilo Pascual. None of them ever came close to Arrieta’s 222 ERA + in 2015; in this respect, Arrieta walks (or rather suppresses walks) alone.

Arrieta came up in 2010 to participate in two 90-loss Orioles seasons, but the Birds were taking flight, and in 2012 they would win 93, before slipping to 85 wins in 2013. These were good teams, patched together with Dan Duquette’s yard-sale bargains and Buck Showalter’s newly humanized intensity.

Arrieta had a quiet breakthrough in 2012, his third year with the Orioles, when his K/9 spiked at 8.7, while his BB/9 plunged from over 4 down to 2.7. These front-line starter numbers were buried by his 6.20 ERA, which in turn stemmed in part from a high homer rate (1.3/9). The Orioles understood that beneath the ERA there was progress, and did not trade him.

In 2013, Arrieta gave most of his gains back. The strikeouts remained, but he began walking the house. Even FIP began to have doubts, and on June 17 they shipped him to the Cubs (along with Pedro Strop, now a competent set-up man) in exchange for backup catcher Steve Clevenger and 90 mediocre innings from Scott Feldman. It looks like a disastrous trade now, but at the time it seemed suicidal for a contender to hand Arrieta the ball every fifth day.

Perhaps the Orioles’ inflexible approach to pitching mechanics impeded Arrieta’s development. Perhaps he developed a new pitch, or refined an old one. Maybe he needed a change of scenery. Whatever the case, Arrieta didn’t become Jake Arrieta with the Cubs right away. He brought the walks and homers with him in his carry-on luggage when he touched down in Chicago in late June. His strikeout rate actually dropped. But perhaps most importantly, his WHIP plunged, from over 1.7 with the Orioles in 2013 to just over 1.1 with the Cubs. Both rates were BABIP driven: in Baltimore, .343, in Chicago, an equally unsustainable .190. But Arrieta took advantage of his luck, using the emotional breathing space the sudden drop in traffic provided to focus on developing his devastating sinkerslidercutterwhatever. In this case the change of scenery provided an immediate and positive, if accidental, dividend. Arrieta’s BABIP has since returned to a normal neighborhood: .274 in 2014 and .246 in 2015. (His success this year was only partially BABIP-fueled, a fact that should the scare the pine tar off the bats of NL Central hitters.)

Although no one on the List of 26 is really a comp for Arrieta, Pascual probably comes closest, thanks to his dominating stuff. Featuring a knee-buckling curve, Pascual achieved strikeout rates that wouldn’t look at all out of place in today’s game. From 1958-1964, Pascual K/9 never fell below 7; this in an era when league strikeout rates were typically in the 5s. Wildness and gopheritis plagued Pascual in his early years, but he became a rotation mainstay for the Senators in ’58, and stuck with the franchise until 1966, a year after the now-Twins went to the Series.

Pascual had a quiet breakthrough in 1956, his third year with the Senators. His strikeout rate spiked at 7.7/9, while the walk rate dropped to a (still high) 4.2. Victimized by a ghastly 33 homers, his ERA was awful, but there were signs of promise. In 1957 it all went backwards. His ERA peaked at an eye-watering 6.11 on May 4, and after ebbing somewhat, reached another appalling summit at 5.49 on June 22, about the same time in the season that Arrieta’s career ended in Baltimore.

But the Senators did not blink. It was around this time, in the sweltering 1957 summer, that Camilo Pascual became Camilo Pascual. The strikeouts came back, the homers did not. He finished with a respectable 4.10 ERA, a figure he would easily beat for the next 8 years.

Pascual was only 23 during his Crossroads Year; Arrieta was 27, a much easier age for a team to give up on a player. Arrieta has Scott Boras as his agent; Pascual had the reserve clause as his ankle bracelet. Perhaps most importantly, the 1957 Senators were simply abominable. They would lose 99 games (out of 154!) in 1957, and indeed would exceed 90 losses during every season from 1955-1959.

In 2013, the Orioles couldn’t risk nine more Jake Arrieta starts if they hoped to contend; In 1957, the Senators wouldn’t contend until 1962, by which time they had moved to a different time zone. The 2013 Orioles’ team success produced a roster assembly failure, while the 1957 Senators’ team failure produced a roster assembly success.

Pascual was very good for several years. Arrieta has been outstanding for two. His FIP has been very consistent in his two full years with the Cubs: 2.26 in 2014, and actually slightly higher (2.35) in 2015.  Arrieta’s remarkable climb has reached the top rung; it remains to be seen how long he can stay there.

No this isn’t a piece for accountants so please don’t give up on it or go to sleep!  It is an MVP discussion, and there is always a lot to talk about with the MVP, the very definition of which is vague, entitling anyone to interpret it how they wish.  There are perpetual questions– is it for an outstanding player or one who can meet some criteria of clutch?  Can a pitcher be more valuable than an everyday player?  Must a candidate play on a contender?

This article lays out a framework for quantifying these issues.   As described, a definitive answer requires a little more data than we now have, but it’s possible to have this data for an interesting quantitative measure of the MVP.

Let’s start with principles:

• The objective is to win a championship. I don’t expect this to be controversial, is it?  As we’ll get into, this doesn’t mean a non-contender can’t win, but it will be more difficult for them to do so.
• Context and chances matter. We aren’t trying to pick the best player, we’re trying to pick the most valuable.  We’re not trying to forecast the future, we’re looking back at the past.  Whether a player benefits from the luck of situations or of opportunities, the player who capitalizes upon his luck seems to this author to have been more valuable than an unlucky player who doesn’t have as many such opportunities.  Dave Studeman and Dave Cameron have written well on this topic.  If you don’t agree, take it up with them.  (For future research – must an author’s first name begin with the letter “D” to believe this?)  Further, the context of a player’s team matters – clinching a pennant on the last day is more valuable based upon context than an April rout or a meaningless September game between call-ups.

Introducing CPA

Accordingly, we’ll take something old, Win Probability Added, (WPA) and dust off and tweak something else old, Championship Leverage Index (CLI) to make up a new statistic to measure value – Championship Probability Added (CPA).  Our formula is CPA = sum of all daily WPA x CLI.

The facets of WPA are discussed thoroughly in another Studeman article.  Suffice to say, it captures a hitter’s or pitcher’s contribution to the probability of his team winning a game, which we can take as a player’s value to his team in the particular game.

As for the importance of the game to the team, Studeman and Sky Andrecheck have developed a measure of the game’s importance, the Championship Leverage Index, how the outcome of a game affects a team’s championship probability, but, as Studeman pointed out in his WPA article, the new wild-card format makes calculation of CLI difficult.

Fortunately, FanGraphs has a big part of the answer in their playoff probability table, which daily measures a team’s playoff and championship probabilities.  The day to day changes in these probabilities are indicative of each game’s importance, although a full measure of a game’s importance would require running the simulations 15 more times to determine the change in probability for each game’s alternative outcome.

There are different measures of championship probability in these tables based upon projections or upon random (coin toss) probabilities for a season’s balance.  The projection-based probabilities may be more accurate, but, for our purpose, measuring the value of each game, the coin toss probabilities are more useful.  1) The projection-based probabilities are more volatile early in the season as they vary not only with the game’s outcome, but with players’ individual performance which in turn affect his team’s projections.  Thus early-season games are weighted more highly than late games.  2) A player’s individual impact can be diminished because it already has been factored into a team’s projections.

The 2015 MVP Race by CPA

For now, without the complete probabilistic simulations, we’ll try to approximate the value of a game by taking the absolute value of a daily change in a team’s championship probabilities.  We use the absolute value of the daily change since it measure’s the game’s importance whether or not a team wins.  Without this, a player would be penalized if his team loses a game, even if he has a big (valuable) game (high WPA).

For now, the daily changes must be recorded from FanGraphs by hand, so we’ll run with an illustrative example rather than a definitive analysis.  Let’s start with the top two players by WAR in each league:

In the AL, both the Angels and Jays were in contention, although, the Jays’ chances became markedly better later in the season.

While the Angels had a low probability, there was still a lot of opportunity for Mike Trout to benefit from swings in their chances in the end, but he couldn’t make up all the ground on Josh Donaldson’s high WPA during the Jays high CLI second-half run.

On the NL side, WAR leader, Bryce Harper, had his CPA affected by the Nats dropping out of playoff contention.

Harper’s early-season lead fell by the wayside as Kershaw’s performance improved from its negative start and the Dodgers remained in the championship hunt.

So, definitive MVP stat?  Not yet, but hopefully a step in that direction.  Calculating a probabilistic CLI would be a big help.  Improvements to WPA to incorporate base running and fielding would help too.

Thoughts?

My name is Rich Rieders and I am a 2015 graduate of Rutgers Law School. Over the winter, I participated in Tulane University’s 9th Annual Baseball Arbitration Competition and we finished in 2nd place overall out of 40 teams.

In order to prepare for the competition, I created a database (going back to 2008) consisting of all arbitration awards and players who signed 1-year contracts avoiding arbitration along with their respective statistics. Using regression analysis, I was able to determine which statistics correlate most with salary. In turn, I have created a projection system that can accurately predict arbitration salaries. My projections are more accurate than the ones featured on MLBTradeRumors.

I will be releasing my 2016 projections once the season is over and all awards are announced.

The goal of this article is to properly explain how arbitration salaries are determined and how to choose the best comparative baseball salaries (comps) as outlined in Article VI, Section E, Part 10(a) of the CBA. You can think of the comps as legal precedent. The closer the comps are to the player’s stats, the more comps you have and the more recent those comps are, the stronger your argument.

First and foremost, the purpose of the arbitration process is to compensate the player for his actual results on the field, not to give him a salary based on what we expect he will produce in the upcoming season. We concern ourselves with only the traditional stats. I know this is a complete departure from the way we normally think here on FanGraphs, but salary arbitration is a completely different animal. In essence, arbitration salaries are determined by the accumulation of traditional counting stats.

For our purposes, there are six types of players who are up for arbitration in a given offseason and each type has its own separate valuation. The six types of players are:

(1) First-year-eligible SP

(2) SP who have previously been through the arbitration process

(3) First-year-eligible RP

(4) RP who have previously been through the arbitration process

(5) First-year-eligible position player

(6) Position players who have previously been through the arbitration process.

I will explain, in detail, how to properly choose player comps for each of the six group of players. In this segment, we will focus just on the starting pitchers.

For a SP who is arbitration eligible for the first time, here are the statistics that correlate most with eventual salary:

Platform IP: 60.83%

Platform GS: 57.59%

Platform SO: 54.41%

Platform W: 53.12%

Career IP: 50.56%

Career SO: 47.45%

Career W: 42.76%

Career GS: 37.10%

When initially looking for player comps, these are statistics we are going to focus on. Keep in mind that although ERA is not listed, it is nonetheless important as ERA is still one of the default statistics during a hearing and the first basis for comparison. Note that rate stats almost always have a very low correlation since rate stats do not take into account playing time.

Let’s use Atlanta Braves starter, Shelby Miller, as an example of a first-year-eligible SP.

Shelby Miller is arbitration-eligible for the first time going into 2016 with 3 years and 30 days of service time (3.030). In his platform season (2015), Miller made 33 starts recording 6 wins, 171 SO with a 3.02 ERA in 205.1 IP. Over his career, Miller has compiled 575 IP, 32 W, 483 SO with a 3.22 ERA in 96 GS. The objective here is to find the players who avoided arbitration by signing a 1 year contract with statistics that are most similar to Miller’s. The more recent, the better. The best way to do that is to set a floor and a ceiling and then work your way towards the middle.

From Miller’s perspective, let’s look at Miguel Gonzalez’s 2014 platform season. Like Miller, Gonzalez posted a low win total despite a very strong ERA. Gonzalez made 26 starts, recorded 10 wins, 111 SO with a 3.23 ERA in 159 IP. Over his career, Gonzalez compiled 69 starts, 30 wins, 308 SO with a 3.45 ERA in 435.2 IP. Although their ERA and win totals are extremely close, Miller bests Gonzalez in all the most important categories and has significantly more playing time and strikeouts. Therefore, we can definitively state Miller should receive more than Gonzalez did. As such, Gonzalez’s 2015 salary of 3.45 million should be the floor.

From Atlanta’s perspective, let’s look at Chris Tillman’s 2014 platform season. Like Miller, Tillman pitched a similar amount of innings and games with a pretty low ERA. In his platform season, Tillman made 34 starts recording 13 wins, 150 SO and a 3.34 ERA in 207.1 IP. Over his career, Tillman compiled 45 W, 680.1 IP, 511 SO with a 4.00 ERA in 118 GS. Although Miller has the better ERA, Tillman is superior in all the other major categories. Hence, we can conclude that Miller will receive less than Tillman. We can use Tillman’s 2015 salary of $4.315 million as the ceiling.

Given the above, Shelby Miller is likely to receive somewhere between $3.45 million and $4.315 million. Now that we have a range, let’s find someone towards the middle.

In 2011, Justin Masterson made 33 starts with 12 W, 158 SO, 3.21 ERA in 216 IP. Over his career he made 87 starts, with 28 W, 485 SO, 3.92 ERA in 613.2 IP. Those numbers are quite similar across the board with Miller having a better ERA, but fewer IP. Masterson’s 2012 salary was $3.825 million. Alex Cobb ($4.0 million in 2015),  Travis Wood ($3.9 million in 2014) and Steven Strasburg ($3.975 million in 2014) are all good comps as well.

As for my model, Miller projects to receive $3,859,816 +/- $145,351 which is perfectly in line with the comps above. MLBTradeRumors projects him at $4.9 million, which is not only significantly higher than the above comps, but would beat the record for a first-year player by nearly 600K.

For a player who has already been through the arbitration process before, the valuation is completely different as career statistics are no longer used the 2nd, 3rd, 4th, etc. time around (except in a few rare cases). This group of players are the most difficult to project since we use fewer variables due to the exclusion of career stats and how there are fewer SP across the league than relievers or position players. Nonetheless, we can still get a pretty good idea what their eventual salary will be.

For an SP who has previously been through the arbitration process, the stats that correlate most with eventual salary are:

(1) Platform W: 69.12%

(2) Platform RA9-WAR: 64.04%

(3) Platform SO: 60.97%

(4) Platform fWAR: 58.93%

(5) Platform IP: 58.34%

(6) Platform GS: 49.75%

For example, let’s look at Angels SP Garrett Richards who is arbitration eligible for the second time going into 2016. As a Super-2 going into 2015, Richards received a $3.2 million salary. That figure includes everything he had done in his career up to that point. Thus, when determining his 2016 salary, we don’t need to focus on previous seasons. We need only determine what his 2015 season was worth and give him a raise. In his platform season (2015), Richards made 32 starts recording 15 wins, 176 SO, 3.65 ERA, 2.5 fWAR and 2.8 RA9-WAR in 207.1 IP. We want to find the players whose stats are most similar to Richards.

First let’s discuss Matt Garza’s 2010 platform season (a bit old, but still useful) where he made 32 starts recording 15 wins, 150 SO, 3.91 ERA, 1.9 fWAR and 2.8 RA9-WAR in 204.2 IP. Other than the strikeout numbers, we have a virtually identical season. As such, Richards is likely to receive a raise higher than Garza’s $2.6 million raise going into 2011. We can consider a raise of $2.6 million to be his floor.

Next let’s look at C.J. Wilson’s 2010 platform season (again old, but useful still) where he made 33 starts recording 15 wins, 170 SO, 3.35 ERA, 4.1 fWAR and 5.1 RA9-WAR in 204 IP. Wilson has the same amount of wins and virtually the same number of SO although Wilson has a clear advantage in fWAR and RA9-WAR with a slightly better ERA so it’s pretty safe to say that Richards is likely to get a raise lower than Wilson’s $3.9 million raise. The $3.9 million should be the ceiling.

Homer Bailey’s 2012 platform season is a great final comparison. Bailey made 33 starts recording 13 wins, 168 SO, 3.68 ERA, 2.7 fWAR and 2.8 RA9-WAR in 208 IP. Both players are virtually identical statistically. Bailey received a raise of $2.925 million so Richards is likely to receive a very similar raise himself. Shaun Marcum ($3.1 million in 2011), Jordan Zimmerman ($3.050 million in 2011) and Max Scherzer ($2.975 million in 2013) are all good comps as well.

Therefore, we can be certain that Richards will receive a raise somewhere between $2.6 million and $3.9 million. As for my model, Richards projects to receive a raise of $2,923,484 for a total salary of $6,123,484+/- $336,500 and, unsurprisingly, that is perfectly in line with the comps above. MlbTradeRumors is projecting a raise of $3.6 million for a total salary of $6.8 million which I think is a bit generous given the comps we have at our disposal, but not unreasonable.

Next up: Relief Pitchers.

We’ve come to the end of the 2015 regular season and it’s time to start looking towards the playoffs. As with every year there have been surprises and disappointments. One of the most anticipated events of each season is the debut of rookies and how they will perform throughout the year. Big things were expected from Kris Bryant this year and he definitely did not disappoint. Originally drafted by the Blue Jays in 2010 in the 18th round (546th overall), he was committed to the University of San Diego and the Jays didn’t offer enough to sway him. In 2013, the Cubs drafted him 2nd overall and he did nothing but climb the ranks until he made his MLB debut on April 17, 2015. His first game didn’t go as well as he hoped, going 0-4 with 3 K’s, but debuts mean nothing except for a little extra media hoopla. He cruised the rest of the way through the season on his way to one of the most impressive rookie seasons in recent memory, posting the 3rd highest WAR of any rookie since 2001. Only Mike Trout (10.3 WAR in 2012) and Albert Pujols (7.2 WAR in 2001) posted higher better WARs in their rookie campaigns.

I was looking over Bryant’s stats and his K% really jumped out at me. Although Bryant hit 26 home runs on the year, I began to wonder if there were any comparable seasons. Now the only criteria I used for comparison was: (1) as many or more home runs (26) and (2) equal or greater K%. Only 13 other players met this criteria since 2001 and they are listed in the table below.

Besides an awfully high K%, for which he ranks 23rd overall since 2001, out of all the players on this list, he posted the most impressive WAR. He’s also in some pretty elite company with respect to power hitters. There are four 40+ home run seasons on that list and many 30+ homer seasons. In addition to providing value with his bat, he also provided a positive UZR rating at a highly demanding defensive position. This combination is what made Kris Bryant so attractive to teams since the 2010 draft.

Using the same player list as above, I looked at their seasonal BABIPs, and I found one particular season of interest. Bryant’s 2015 season. Bryant posted a 0.381 BABIP this year, and the next-closest player on the list was Mark Reynold’s 2009 season at 0.338 which is still quite a difference. Looking at Mark Reynold’s seasonal stats from 2008 to 2011, his batting average follows the same pattern as his BABIP.

And a plot showing the relationship between AVG and BABIP (data from 2001 to 2015). There is an increasing relationship between the two, but there is some pretty wide variation. Nonetheless, I’ve highlighted Bryant’s data point from the 2015 season in red and it’s pretty clear that it represents an outlier for his batting average.

If we consider that the players listed in the tables above are from the same pedigree, their career BABIPs average out to around 0.298. Now I’m not saying Kris Bryant is going to follow the same trend, but based on the strikeout rate he posted this year he’s very aggressive at the plate and I know we are going to expect that inflated BABIP to come back down to Earth so I think we can expect some regression next year. As a reference Danny Santana posted a BABIP of 0.405 in 2014 only to drop down to 0.290 this year which saw his WAR plummet from 3.3 to -1.4. I looked at the relationship between HR, SB and a few other stats and batting average showed the highest correlation with BABIP from the stats I looked at. Based on this I expect his batting average will be the most likely to be affected with a downfall of BABIP. I really don’t think the home runs are going to go anywhere, but I think we can likely expect to watch that batting average fall. It remains to be seen how this will affect his peripheral stats, but as long as he continues providing solid defense at the hot corner he is going to provide lots of value on a major-league roster. I’m sorry to say Cubs fans I think you should expect some offensive woes next year.

Now that the regular season is over, it’s time to talk about awards. I mean people were already talking about awards, but now it’s time to really start talking about awards. Perhaps the most hotly contested award this year is the NL Cy Young. Clayton Kershaw, Zack Greinke, and Jake Arrieta are in three-headed race for the award, and they’re all incredibly close in terms of quality of performance, making it nigh impossible to pick a single winner. So I thought I’d give picking one the old college try. For simplicity reasons I decided to only compare Kershaw and Arrieta, who seem to be the two most often pegged as deserving in the sabermetric community. So, let’s dive in.

First things first, Kershaw has a pretty significant advantage when it comes to FIP metrics. His 29 K-BB% is seven percentage points higher than Arrieta’s 22%. Kershaw’s huge lead in strike-zone control more than makes up for the fact that he’s let up home runs a bit more often than Arrieta (10% and 8% HR/FB rate respectively). Boiling it down, Arrieta’s 61 FIP- trails behind Kershaw’s (52) by almost ten points.

Where things start to get murky is when one looks into their contact management ability. On the surface it appears Arrieta has a leg up here. Their IFFB% is basically identical. But as I mentioned before Arrieta has given up a few less home runs, and has also induced more groundballs.

Arrieta’s production on groundballs is also much better: he’s allowed a .377 OPS on grounders to Kershaw’s .468. Although it’s not that simple, because all defenses are not created equally, and the quality of the fielders behind you can have a big effect on the production of the groundballs you induce. So in that respect it’s worth noting that the Cubs ranked 6th in UZR/150 among all teams, while the Dodgers ranked 13th.

But there’s other ways of determining groundball production. Grounders that are pulled, generally, are more likely to turn into outs than grounders hit to the opposite field. Thus, it would make sense that a pitcher who gets batters to pull their grounders more often would have better production on their grounders, regardless of the quality of his team’s defense. So who’s induced pulled grounders more often? It turns out Arrieta – although only by the slightest margin. He’s induced a pulled groundball on 0.052% of his pitches, while Kershaw’s done the same on 0.047% of his.

So the difference between their pull rates is essentially negligible. But there’s more ways yet to evaluate groundball production. For instance, the velocity on those groundballs. Logic dictates that it’s easier to field a slow-moving groundball than a fast-moving one. After all, slow things are generally easier to pick up than fast things. Thus a pitcher who is more disposed to generate grounders of modest velocity is more likely to have better production on those groundballs, once again regardless of defense.

To figure out who had been better at coaxing soft grounders, I employed Baseball Savant’s PITCHf/x search tool. I set the batted-ball type to groundballs for obvious reasons. I set the maximum batted-ball velocity at 80 MPH because I couldn’t find the league average and 80 seems like a reasonable number. As it turns out, Arrieta has produced soft grounders on a greater number of his pitches than Kershaw (4.4% to 3.6%). Again the difference isn’t huge (the separation between the best and the worst in this particular metric is only about 4.5%) , but further implicates that Arrieta has been the better manager of contact. To sum it up, It does appear as though Arrieta has an advantage in the contact-management department, but not as large as it looks at first glance.

At the end of the day, these are two similarly great pitchers having two great similarly great seasons, and both should be celebrated as such. But if I had to pick one for award purposes, I think I’d go with Kershaw. If only because I believe more in his strike-zone-control numbers than Arrieta’s contact-management ones.

The news that Barry Zito has been called up to start against Tim Hudson, with Mark Mulder in attendance, has rightfully thrown the baseball world into a mini-frenzy. Jonah Keri covered the meat of it spectacularly here. Here’s a dirty secret though: as we evaluate pitchers today, they weren’t great pitchers. An even dirtier secret: I don’t think it matters.

Zito, Hudson, and Mulder were undoubtedly good pitchers, racking up a Cy Young trophy and four more top-10 finishes in their time in Oakland. But were they great pitchers? Let’s take a look at their FIP- during their Oakland careers:

At their peak, they were well above-average pitchers, but, combined, they only had two top-10 finishes in FIP-, with Mulder finishing 10th in 2001 and Hudson 10th in 2004. Good, but not transcendent. If that’s worse than you remember, it’s probably because their ERAs consistently undershot their FIPs:

The Big Three were among the last players before sabermetrics exploded in popularity with casual fans, and our analysis of them reflects that. If they had come up today, would we label them as three guys who are above-average, rather than the cultural phenomenon they became? It’s very likely. That the cultural relevance of the Big Three has carried into the sabermetric era is a delightful reminder of how recently we crossed the frontier.

Does the fact that their accomplishments don’t hold up as well in the FIP era diminish their place in baseball history? I say no. Even though baseball has seen a number of better three-man rotations, the “Big Three” label feels at home in Oakland. In 2008, Dan Haren, Brandon Webb, and Randy Johnson, averaged a 76 FIP- for the Diamondbacks, better than any year of the real Big Three. But would Dan Haren starting against Brandon Webb on Saturday be a headline event (forgetting about the medical miracle required)? I doubt it. Zito, Hudson, and Mulder evoke something in us beyond their raw performance.

I always recited the order as Zito, Hudson, Mulder. Zito always comes first because as a fellow lefty who didn’t throw very hard, but thought he had a big hook, I emulated him both in real life and in MVP baseball, where I spent countless hours dropping his curve in against hapless computer foes. Zito was my guy and Hudson and Mulder fell in line after. Everyone had their own order relative to their personal biases. The combination of youth, talent, and personality made them relatable in a way that other greater pitchers just weren’t.

The Big Three were also the rock on which Moneyball was built. For fans of small-market teams, they represented what was possible. If your team scouted, drafted, and developed well, you too could have your own set of homegrown stars. The 2001 A’s-Yankees ALDS was, in my opinion, the pinnacle of the era. Zito, Hudson, and Mulder combined to throw 28.2 innings and give up just five earned runs, but it wasn’t enough. The 2001 A’s were one of the most likable teams of all time and the Big Three were the dominant reason why.

Although they had their best years in Oakland, when they were forced to move on, there was a sense when that they were headed for greater things. The potential they left behind in Oakland still tantalizes. Although the greatness never materialized in their new homes, it still feels like they left something on the table when they left. We never had the closure of seeing them grow old and decline together which is why finally getting our closure on Saturday feels so comforting.

You will note that Keri’s article does not once mention FIP. It’s a defensible choice because that’s not how we evaluated them at the time so it’s not how we remember them now. None of the reasons why we loved them are because they were the very best pitchers in the game or sabermetric darlings. It was a confluence of harder-to-quantify factors.

Baseball is a funny game. None of the Big Three ever had a season as good as Jake Arrieta’s this season. But ask me who I’m going to remember in 20, 30, 40 years? No contest. Baseball is an analytical nostalgia factory, a game that runs on both numbers and feelings without ever feeling like it contradicts itself. Perhaps no one represents that dichotomy better than the legendary Big Three.

Baltimore Orioles first baseman, Chris Davis, is in the final year of his contract where he is making $12 mil/yr. At age 29, Davis has had a roller-coaster of a career starting in Texas where he burst onto the scene hitting 17 & 21 homers in his first two seasons. After which, he declined dramatically the next season hitting just under .200 for Texas. The following season he was traded to Baltimore where he revived his career and met his long-awaited potential. Today, Davis is one of the biggest power hitters in the game. He hit 53 homers in 2013 and 43 homers thus far in ’15. With Davis on the market we know clubs will be interested in his bat along with some other big FA names such as Yoenis Cespedes, Justin Upton and Alex Gordon.

The problem with Chris Davis is that he’s somewhat inconsistent. As a power hitter we can take a look at his slugging percentage, which will give us a better indication of his extra-base hits and power numbers. In seasons with at least 300+ at-bats he slugged an average of .507 but has a standard deviation of .091. It seems he has struggled to find consistency with his hitting, especially last season when he hit .194, with 23 homers and a slugging mark of .404. Compared to his .286/53 HR/.634 campaign in 2013, it is a huge difference.

If we take a look at a similar power hitter in Nelson Cruz, in his seasons with at least 300 ABs he slugged a similar average of .515 with a SD of only .04. Cruz is more of a model of consistency and has been less risky than Davis. Besides his one season of slugging .460, Cruz was always in the mid-.500s. Which is great for a power hitter. This is a big reason I am not a huge fan of Chris Davis. He just hasn’t shown a high level of consistency.

Another is his strikeout rate, which is extremely high. Since his first full season in Baltimore, Davis struck out 169, 199, 173, 182 times over the last 4 seasons. That’s good for a 31% K-Rate. Easily one of the worst in the league. His 196 strikeouts this season also happen to lead the league! Although he strikes out a ton, he gets the job done by driving in runs. Which at the end of the day could be seen as more important. Davis drove in 138 runs in 2013, 86 in ’14 and so far 110 in ’15. Did I mention he’s also eighth in the league with 118 runs created. A stat used to measure how valuable a player is to contributing runs to his team. So with great power comes great responsibility. Davis may strike out but he can really drive the ball. To me, he’s a high-reward/high-risk guy.

Interested teams:
Chris Davis is so valuable to the Orioles in terms of producing runs it’s hard to imagine him being let go without a fight. I think the Orioles will absolutely make him an offer. He’s already making $12m/yr and the O’s have a lot of money coming off the books this winter (Orioles’ Payroll). Only $41m is committed to next season ($119m payroll this year). So I can see them raising their price tag to about $18m/yr. The O’s are in a position to win now with Machado/Jones and a fairly young team so if they aren’t getting Davis they will no doubt be spending on others.

Other teams I can see having interest in Davis would be Seattle, San Diego, and Houston. Seattle is the kind of team to pay up for hitting; I could see them doing that with Davis as they did with Cano/Cruz. They need offense but they already have Trumbo at first base who has been decent. If they could move Trumbo I could see them making a play for Davis. Having Cano-Cruz-Davis would be quite powerful. They’re losing some money with Rodney & Jackson coming off the books. Seattle could be really interesting to watch.

The Padres I could see showing some interest but only if they lose Justin Upton and keep Wil Myers in CF. I think they’ll try to re-sign Upton who has had a good year playing in Petco Park. They’ve played Myers at 1B occasionally because of his injury concerns. With no DH, it’s harder to maneuver players around. Yet, again, AJ Preller is a magician so no one can really predict what he will do next. I think the Padres’ concern would be as Davis gets older he could regress on the defensive side of the ball and offensively. Petco Park is a pitcher’s palace so if Davis’ power dropped off his value would really take a hit. Putting Davis in as a full-time DH later in his career would help him maintain his power and consistency like it has for David Ortiz and A-Rod.

The Astros are a wild card I think. I said in the Cespedes post, they have a ton of cash to spend but only if they’re willing to spend it. They love guys who hit home runs. That’s basically their back end of the lineup (Carter, Valbuena, Rasmus). Their 1B Chris Carter ($4.5m) is a mini Chris Davis (low avg/high power) and he will be headed to arbitration. But in the offseason I think they will look to upgrade. They’ll obviously want to replace him with someone more improved. But Davis will cost them a lot; as a more analytics front office I’m not sure if they would see the value in paying up for him. Then again, pairing Davis, who hits lefty, with Correa/Altuve would really help them score runs along with mixing and matching their lineup.

Honorable Mentions: 
The last two teams I looked into with 1B trouble were the Cardinals and Pirates. St. Louis has Matt Adams coming off the DL and we’re not sure if he’s 100% just yet. We know Brandon Moss is not a long-term solution. The Pirates’ Pedro Alvarez has been super inconsistent with Pittsburgh. I think they’ll look to upgrade or float around some other names during the offseason. To be honest, I think Adam Lind would be a great addition to the Cardinals or Pirates instead of Davis. Adam Lind has a club option for $8m this offseason; he hits lefty and has had a solid year for Milwaukee. Overall, I don’t think these two teams will end up throwing money at Chris Davis but they may need 1B help next season. Its baseball, anything can happen.

In the end, I believe Davis enjoys playing in Baltimore. Due to his success there, the favorable ballpark and the DH factor I think he should stay. For his long-term career he should seriously consider staying in the AL with the DH factor. But I think another club will come in and make a play to acquire Davis. Power/RBIs come at a premium these days. Dan Duquette, GM of the Orioles, has experience and knows what he’s doing. If the price tag became too high I think he will definitely consider looking elsewhere on the market. Possibly an Adam Lind or Mark Trumbo.

Similar players such as Nelson Cruz signed a 4yr/57m (14m AVV) at age 34 and Albert Pujols signed a 10y/240m (24mAAV) in 2011. This sets a decent basis for Davis. In terms of his contract, I think Davis could get a 5-year deal worth about $18-21 million a year. His WAR for this season is 4.2 which puts him in the ballpark for this. So, it’s near our estimation. Personally, I would not give Davis $20m for 5 years. I think that’s going overboard but some teams are more into his skill than others. Power really comes at a premium in today’s game and Davis has a ton of it. I wouldn’t be surprised if it went to 6 years, but I just don’t see as many teams bidding on Davis right now. Scott Boras is his agent which will probably drive up the asking price. That may turn off the Orioles which could lead to another club coming in and swooping up Crash Davis. I think it’s favored to be the Orioles or Mariners come signing day.

Projection: 5 years, $100 million

The timeless struggle between pitcher and batter is one of dominance — who holds it and how. Both players use a repertoire of techniques to adapt to each other’s strategies in order to gain advantage, thereby winning the at-bat and, ultimately, the game.

These strategies can rely on everything from experience to data. In fact, baseball players rely heavily on data analytics in order to tell them how they’re swinging their bats, how well they’ll do in college, how they’ll perform at Wrigley versus Miller.

Big data has been used in baseball for decades — as early as the 60s. Bill James, however, was the first prominent sabermetrician, writing about the field in his Bill James Baseball Abstracts during the 80s. Sabermetrics are used to measure in-game performance and are often used by teams to prospect players.

Baseball fans familiar with sabermetrics, the A’s, and Brad Pitt have likely seen Moneyball, the Hollywood adaptation of Michael Lewis’ book. The book told the story of As manager Billy Beane’s use of sabermetrics to amass a winning team.

Sabermetrics is one way baseball teams use big data to leverage game theory in baseball — on a team-wide scale. However, by leveraging their data through the concepts of game theory on a smaller scale, baseball teams can help their men on mound out-duel those at the plate.

Game theory studies strategic decision making, not just in sports or games, but in any situation in which a decision must be made against another decision maker. In other words, it is the study of conflict.

Game theory uses mathematical models to analyze decisions. Most sports are zero-sum games, in which the decisions of one player (or team) will have a direct effect on the opposing player (or team). This creates an equilibrium which is known as the Nash equilibrium, named for the mathematician John Forbes Nash. What this means is that if a team scores a run, it is usually at the expense of the opposing team — likely based on an error by a fielder or a hit off a pitcher.

In the case of pitching, game theory — especially the use of the Nash equilibrium — can be used to predict pitch optimization for strategic purposes. Neil Paine of FiveThirtyEight advocates using big data and sabermetrics to analyze each pitch in a hurler’s armory, then cultivating the pitcher’s equilibrium — the perfect blend of pitches that will result in the highest number of strikeouts, etc.

Paine has gone so far as to create his own formula, the Nash Score, to predict which pitcher should throw which pitches in order to outwit batters.

In perfect game theory, the Nash equilibrium states that each game player uses a mix of strategies that is so effective, neither has incentive to change strategies. For pitchers, Paine’s Nash Score uses their data to find the optimal combination of pitches to combat batters, including frequency.

Paine does point out that creating this kind of equilibrium in baseball can be detrimental to a pitcher. He is, after all, playing against another human being who is just as capable of using game theory to adapt strategies to upset the equilibrium.

If a pitcher’s fastball is his best, and his Nash Score shows that he should be using it more often, savvy hitters are going to notice. “ . . . In time, the fastball will lose its effectiveness if it’s not balanced against, say, a change-up — even if the fastball is a far better pitch on paper,” writes Paine.

In this case, a mixed strategy is the best — in game theory, mixed strategies are best used when a player intends to keep his opponent guessing. Though pitch optimization using Paine’s Nash Score could lead to efficiency, allowing pitchers to throw fewer pitches for more innings, it could also lead to batters adapting much quicker to patterns, thus negating all the work.

In his first year of being eligible for arbitration, Matt Harvey will be able to substantially increase his salary for the 2016 season. Since beginning his career with the New York Mets in 2012, he has taken off to become an All-Star pitcher and fan favorite. His agent, Scott Boras, and the front office of the Mets will negotiate a one year salary based off his success in 2015. We’ll cut right to the chase and get into the hard numbers which will help us identify a rough projection of what we would expect Matt Harvey to receive this coming winter.

For more background on arbitration cases, read my previous article which discusses what is allowed/not allowed.

Overall performance:
Since 2012, Matt Harvey at age 26 has a career 2.59 ERA with 24-17 win/loss record. During his 2013 season Harvey was on a tear with a 2.27 ERA and became one of the leading NL Cy Young candidates before his injury. He also started the 2013 All-Star game which happened to be in Citi Field that year. After tearing his UCL and missing the entire 2014 season, Harvey came back strong this year and has pitched in 26 games thus far with a 2.88 ERA through 171 innings (11th best in league). He has a 12-7 win record and gives up less than a hit per inning (which ranks 9th in all of MLB). His WHIP is also one of the top 10 leagues best at 1.03 so he rarely allows runners on base and is averaging 8.6 strikeouts per game.

His W/L record this season does not show his true value, as the Mets started the first half of the season with one of the worst offenses in the league. After acquiring premier Major League hitters such as Yoenis Cespedes and Juan Uribe, the Mets have led the league in runs scored giving Mets starters big run support. Since those acquisitions, Harvey has pitched in 7 games winning 3 and losing 0. But the Mets’ bullpen blew Harvey’s lead in 3 other games in which he had outperformed the other team. Had it not been for a mediocre bullpen, Harvey could have been 6-0 in 7 games since August 1st. Clearly, Harvey is an ace to this team and is the backbone of a staff that has propelled the Mets to first place. He is a consistent pitcher and does not show signs of letting up even after having TJ surgery. Without Harvey, the Mets would lose a dominant, consistent ace which is obviously hard to come by.

Leadership/Public appeal:
As one of the older members on the New York Mets’ young pitching staff, Harvey is one the leaders on this team. After fighting his way back from injury rehab, he has become a consistent stronghold to the Mets’ rotation. Although Dr. Andrews, who performed Tommy John surgery on Harvey, has stated he should not exceed 180 innings due to his injury, Harvey is continuing to pitch on an innings watch to help the Mets win, especially through the postseason. Even if it hurts his chances at re-injuring himself, he is going out there to pitch.

As a leader, you need to show guts and heart; Harvey has definitely displayed that, battling out there everyday. Matt Harvey also is a fan favorite.  He ranks 9th in all of Major League Baseball and 1st with the Mets in 2015 top jersey sales. Many fans across the country are purchasing his jersey, thus showing how popular he is with people. When he returned to the mound this season to pitch, his first game back drew the biggest crowd (39,000 fans) for the second home game of the season since Citi Field opened in 2009.  That was 10,000 more fans in attendance than last year and 20,000 more than two years ago. During the 2013 All-Star game at Citi Field, which Harvey started, the Mets drew their most fans in history at 45,000. When he’s the night’s starting pitcher, fans flock to the ballpark to see Matt Harvey. At the same time he’s able to strikeout hitters, captivate a crowd and draw extra revenue in from ticket sales than if he wouldn’t be pitching. The Mets fans also have a popular nickname for Harvey: The Dark Knight. Symbolizing his leadership skills and journey back from Tommy John surgery, Harvey symbolizes the 2015 Mets team and has dramatically changed the mood of the fan base since his arrival/return. There’s no denying this.

Injury history:
As stated earlier, Matt Harvey missed all of 2014 season undergoing Tommy John surgery to repair his torn UCL. His recovery has been a success thus far but is always a case for concern in the future. But arbitration cases do not quite debate the future; only his previous success. He has shown no discomfort and has spent 0 days on the disabled list this year. To combat future problems the Mets’ pitching staff went to a 6-man rotation, which has caused Harvey (and other Mets pitchers) to skip a couple starts. Harvey has constantly said he feels good and does not show any signs of slowing down unless the Mets management shut him down.

Performance of club:
The Mets are currently in first place by 6 games and it looks like it will stay that way come October. Largely in part due to Harvey’s success on the mound, the Mets would not be in the same situation without him or his 12 wins this season. When the playoff schedule arrives, Harvey will easily be the game 1 or game 2 starter depending on how he finishes the season.

Record of the players past compensation: 
Harvey made MLB’s minimum salary in 2013 at $498,000 and this year at around $510,000. This will be his first eligible year of Arbitration 1. His value to the team over the last couple years has been sky-high but he’s been grossly underpaid.

Comparative salaries:
Tyson Ross was arbitration 1 last year for the San Diego Padres. In his 2014 campaign he pitched to a 2.81 ERA / 1.211 WHIP with 13 wins in 191 innings pitched. He also struck out 9 hitters per inning and was named an All-Star that same season. But Ross pitches in a heavily favored pitcher’s ballpark. His stats at home included a 1.88 ERA with an 8-5 record but his away stats included a 3.79 ERA with a 5-9 record. Clearly, Ross does not pitch better on the road and his starts could have been affected by where he pitched. Compared to Harvey’s career numbers, he pitches more consistently than Ross at home (12-7, 2.15 ERA) and away (12-10, 3.14 ERA). From our previous numbers we know that Harvey has been a better pitcher overall this season in ERA, WHIP, wins and many other pitching statistics than Ross had in his 2014 season. Following Ross’ 2014 year, he was able to negotiate a 1yr/$5.25m deal in January. Ross is not as consistent and skilled as Matt Harvey. Since Harvey surpasses Ross in success we can see he is due much more in salary as well.

Chris Tillman is the next player we can compare to. Although a little less successful, Tillman was able to get a 1yr/$4.3m deal. The season prior to his arbitration, Tillman had a 13-6 record with a 3.34 ERA and struck out only 6.5 K/9 in 207 innings. Tillman is on the lower end of the comparison as he agreed to almost a million dollars less than Tyson Ross.

Summary:
These players give us the best guideline and recent examples in terms of numbers/dollars that can help us estimate what Harvey should be owed for the 2016 season. Harvey is definitely much better than Ross and Tillman. He brings more to the table than just numbers as he is a figurehead in New York, one of the largest markets in baseball. The first-place Mets could not be where they are if it was not for Harvey. His health was a concern earlier this year but he hasn’t had any setbacks this entire season except for skipping a start here or there. We can expect Harvey to easily surpass Tyson Ross and his $5.25m deal.

Due to the pizzazz of the Dark Knight, the revenues generated from his starts/jersey sales and the recent success of the team, Harvey should be able to negotiate himself around a 1yr/$6.3m deal. If we talk about fairness in terms of his contract, I think this is “fair” to both parties. We have to take into account everything that Harvey brings to the table and I think he’s more valuable than Ross and most previous pitchers who went to arbitration 1 and did not sign a multi-year deal. The one factor that could haunt Harvey’s dollar amount is his elbow due to TJ surgery. If that happens to wear out during the last couple of weeks in September and postseason, we can easily make a case that he should be owed less. But as for now he’s been Harvey-esque and back to where he was before the surgery. Next year his innings limit should be lifted or increased dramatically so there won’t be too much of a cause for concern compared to if he spent time on the DL this season. Obviously, he isn’t a sure bet that he will remain healthy but arbitration does not greatly take into consideration future success/problems, only previous. That is why we project him to get approximately $6.3m.

Overall, both sides will negotiate and the Mets will offer less than what I project. I could definitely see the Mets’ offering $5.5 to $6m. But Scott Boras will clearly try to get more for Harvey — I think around $7m. Both arguments will be justified. In the end, I think an arbitrator would agree that 1yr/$6.3m is common ground, a good midpoint and fit for an agreement by both parties. Stay tuned for more…

Projection: 1yr/$6.3m

…because he’s the hero Queens deserves…