Every year, at the conclusion of the Major League Baseball season, the MLB hands out awards to many of the games premier players. Every year, these awards are panned by critics and fans alike, usually wondering why their favorite players weren’t chosen.

Perhaps the most condemned award, especially by those of us who are more analytically inclined, is the Gold Glove Award.

After years of Derek Jeter winning Gold Gloves at shortstop, with some Rafael Palmeiros and Michael Youngs peppered in, the Gold Glove Awards pretty much became a joke among the MLB community.

The MLB seemed to catch on to that fact this season and implemented a “sabermetric component” in an attempt to help revitalize the legitimacy of the award.

This year’s Gold Glove finalists were recently announced and, to me, there appears to be progress being made. The inclusion of someone like Juan Uribe shows that the MLB is paying attention to the numbers, as Uribe is not someone who would typically pass the “eye test” that people have long based their defensive judgments on, but in reality was a pretty great defender and has been for the entirety of his 13-year career, especially at third base where he played 900 innings for the Dodgers this season.

However, this is not to say there weren’t still some odd picks in the list of finalists. The managers vote still constitutes a large portion of the selection process and these managers are still using the same “eye test” method, probably mixed in with some offensive contribution, that has controlled the fate of the award since its inception

To me, the eye test is a total cop-out, as no fan, let alone manager, can possibly watch every fielding attempt by every fielder throughout the course of a season through completely unbiased lenses as the advanced defensive metrics do. I will admit that the defensive metrics we currently have are far from perfect. But they at least account for every play on the same fair and unbiased scale for each player.

With that being said, here are what the finalists and winners of the Gold Glove Awards at each position might look like if voting were based strictly off advanced defensive metrics, free of human bias. So as not to overly complicate things, I used four defensive metrics to evaluate players. First, UZR and DRS made up the majority of the basis for my selections as they are the two most accepted and accurate defensive metrics. Though a little outdated, I still like to use RZR as sort of a tiebreaker for when UZR and DRS are too close to call. Then, just because, I included fielding percentage too. Though errors aren’t a good way to measure a defender’s ability or value, it’s safe to say that if a guy never makes an error of the course of a season he was probably pretty good, and if he made a ton of errors he probably struggled.

For catchers, the FanGraphs defense stat was used as a substitute for UZR, and rSB and RPP were used as substitutes for RZR and FP%. Pitchers aren’t included in the study.

Behold:

American League
Catcher – Salvador Perez

The MLB included Perez and Wieters, but also had a weird pick in Joe Mauer. Mauer won the Gold Glove at catcher from 2008-2010, despite never being great behind the dish. These likely came as a result of his offensive achievements. Perez gets the nod here for being the best all-around catcher. Wieters, despite being hated by DRS this year for some reason, was still the league’s best pitch-blocker and has a sound reputation for being a good defensive catcher and pitch-framer. Yan Gomes was the snub at his position, having the most valuable arm behind the plate in the American League.

First base – Mike Napoli

This was the weirdest one, on both ends of the spectrum. First, the MLB included Chris Davis – who is average at best in the field – and Eric Hosmer, who one might think would be good based on his athleticism but is actually quite terrible. Then, Mike Napoli came out on top on in the numbers. Napoli, a 31-year old lifetime catcher, played his first full season at first base this year. He also was diagnosed with a degenerative hip condition at the beginning of the year that voided his original contract with the Red Sox, and in reality he would have DH’d for almost any team in the AL that didn’t have David Ortiz. He basically had no reason to be good in the field. Yet, no matter what metrics you look at, Mike Napoli was the best defensive first basemen in the American League, and it really wasn’t close.

Second base – Dustin Pedroia

Pedroia – who already has two Gold Gloves under his belt – and Zobrist were head and shoulders above the rest of American League second basemen this year. Robinson Cano had a great year defensively in 2012 and rightfully won the Gold Glove. This season, it seems he was included by the MLB more for his reputation and offense, as he didn’t grade out much better than average by any defensive metric. Kinsler wasn’t loved by UZR, but he still had the second best DRS and RZR of any qualified second basemen, which is why he edged out Brian Dozier and Cano for my third finalist.

Third base – Manny Machado

This one was easy. It’s no secret that Manny Machado is incredible defensively, as his conversion from already Gold Glove-caliber shortstop to third base went even better than expected. Longoria and Donaldson were second and third, respectively, in each of the remaining categories, making them easy choices. Notably absent is Adrian Beltre, who has been an elite defensive third basemen his whole career and has won four of the last six Gold Gloves. However, at 34 years old, his age may be starting to wear on him as he posted his first negative defensive season since 2007.

Shortstop – Alcides Escobar

After the AL third base being the easiest choice, the AL shortstops were the hardest. The two Escobars had almost identical stats, and Yunel has been a better defender over his career, but Alcides had a miniscule edge in UZR and RZR. Florimon was also a sneaky choice to rival the two Escobars, as he led all qualified shortstops in both DRS and RZR. J.J. Hardy was a fine choice by the MLB, as he has been one of the premier defenders at shortstop for nearly a decade, but the defensive talent pool at shortstop is deep, as always, and Hardy just missed the cut this year.

Left field – Alex Gordon

Gordon has won the American League left field Gold Glove the last two seasons, and will likely win his third consecutive this season. He had the best ARM rating of any qualified outfielder in the American League with above-average range to go with it. The MLB’s selection of Andy Dirks was panned by some analysts, but I find it to be justified as he had the highest RZR of any left fielder with 500+ innings and was second in UZR.

Center field – Lorenzo Cain

Noticing a trend? This is now the third Kansas City Royal deserving of a Gold Glove and we still have one position to go. A hugely important, mostly unnoticed reason for the Royals success this year was that they were baseball’s best defensive team and it wasn’t even close. Their 79.9 team UZR dwarfed the second-place Diamondbacks (51.1) and third-place Orioles (39.9). Cain was one of the main contributors, playing elite defense at arguably the sport’s most difficult position. Ellsbury and Rasmus had great years as well – and were on the field more – but Cain was the best during his time in center, earning him the nod.

Right field – Shane Victorino

This offseason, the Red Sox took part in a current trend in the MLB by throwing away the idea of “corner outfielders” and simply trying to put the best possible athletes – usually natural center fielders – in the three outfield spots. Just a few examples being the Indians with Drew Stubbs (and Michael Brantley to an extent), the Pirates are with Starling Marte and now the Red Sox by signing Victorino to play right field. As you can see, it paid off, as Victorino had easily the best defensive season of any American League outfielder. Also, notice who snuck in at the third spot? David Lough, who racked up a full win’s worth of defensive value in just 577 innings for the, you guessed it, Kansas City Royals.

National League
Catcher – Russell Martin

I know, blasphemy, right? Yadier Molina has won five consecutive Gold Gloves and will probably make it six this year. He is incredible and one of the greatest defensive catchers of all-time. However, Russell Martin is pretty incredible himself and goes greatly unappreciated for his abilities behind the plate. He has a great catcher arm, in fact the most valuable in the MLB this season, and was the third-best pitch blocker in the MLB. While trying to concoct a way to cheat and give this award to Molina, I considered talking about pitch framing, the impact it has on a pitching staff and how that goes undetected in catcher’s defensive stats while Molina might be the best at it. But then I remembered that Martin is a pretty great pitch-framer, too which contributed a great deal to the success of Pirates pitching this year. Molina is a great catcher, but Martin was better this year and it would be pretty cool if he is rewarded for it.

First base – Anthony Rizzo

This was only one of two positions with the same three finalists as the three finalists chosen by the MLB. Good job MLB! Yonder Alonso and Brandon Belt are both pretty good with the glove for first basemen, but these three were clearly the best. Something tells me Gonzalez and his three Gold Gloves will end up winning another based on his reputation, but Rizzo was better across the board. Paul Goldschmidt also has a pretty nice showing, proving that he can do just about everything well and is already one of the league’s best players.

Second base – Darwin Barney

You can probably figure that Darwin Barney is a pretty great defender because otherwise why would he play every day for a Major League team. Part of that is probably because it’s the Cubs, but it’s mostly because Darwin Barney is a defensive wizard. You could probably say the same thing about DJ LeMahieu, too, though it doesn’t fully explain why Walt Weiss insisted on batting him second. There’s really not much else I can think to write about this one, besides maybe that the Cubs are kind of like the National League Royals in that we’ve had three positions and already three Cubs, except different in that it didn’t help lead them to any kind of success.

Third base – Juan Uribe

As I mentioned in the intro to this piece, Juan Uribe even being selected as a Gold Glove finalist shows a step in the right direction for the MLB and an even bigger one if he ends up winning it. By looking at him, you might not assess him as an elite defender on account of his, let’s say “shapely,” frame. However, he had a remarkable year at third base for the Dodgers, adding somewhere in the vicinity of two wins with his defense alone. This should not shock anyone, as he has a career UZR/150 of 19.7 at third base in a sample size of nearly 3,000 innings. In addition, he held his own at shortstop for nine years, logging close to 8,000 innings of above-average defense. Not to be lost in all of this is that Nolan Arendo appears to be exceptional at third base too, with a ridiculous 30 DRS in his rookie season that rivals Manny Machado. Also, hey, look. Another Cub!

Shortstop – Andrelton Simmons

It has been written on this site many times how ridiculous Andrelton Simmons is. He just had maybe the best defensive season ever. Basically, right now, he is to defense what Miguel Cabrera is to offense. He is going to win his first Gold Glove this year, which is a thing that, barring injury, will happen for many, many years to come. He has the potential to build a Hall of Fame career pretty much entirely with his glove, in the vein of guys like Ozzie Smith or Omar Vizquel. The Atlanta Braves are very lucky to have him, and you should watch him play shortstop with any chance you get. /gush

Left field – Starling Marte

As I wrote earlier, by playing Starling Marte in left field the Pirates are also taking part in the current trend of disregarding the preconceived notion of corner outfielders and just putting center fielders in the corners. Having two centerfielders in your outfield is very valuable defensively, and Marte is also an above-average hitter, making his role on the Pirates team a very valuable one. The MLB picked Eric Young Jr. over Carl Crawford, which isn’t a terrible selection as Young had the second highest RZR of any left fielder with 400+ innings and also edged Crawford out in DRS, 2-1. However, those two slight edges over Crawford didn’t make up for Crawford’s 8.6 – 3.9 edge in UZR.

Center field – Carlos Gomez

In addition to Carlos Gomez’s breakout year with the bat, he had an insane year with the glove in center field – one of the main reasons why, along with being one of the game’s elite baserunners, I picked him as my National League runner-up MVP on my Internet Baseball Awards ballot over on Baseball Propsectus. But I’d also really like to talk about that second name there. Some of you may have read Juan Lagares’ name and said, “Who?” My answer to “Who?” would be: “One of my favorite players in baseball after reading Jeff Sullivan’s piece on Lagares and his arm.” Uncovered in that piece, besides who is Juan Lagares, is that Lagares’ arm in center field this season was arguably the most effective arm since we began accumulating advanced fielding data in 2002. Dude has a great arm, but is even better at positioning and taking optimal routes to outfield ground balls by using his experience as an infielder. Lagares shows pretty great range in center, too, and the way he adds value with his arm makes him one of my biggest snubs in the MLB’s selections.

Right field – Gerardo Parra

Here’s the other position with the same three finalists as the three chosen by the MLB. Good job again MLB! Jason Heyward might have come out on top if he played a full season, but since he didn’t the award is probably Gerardo Parra’s to win. Parra has always been a phenomenal outfielder, but also has always been a part-time player due to his nasty platoon splits at the plate. This year, injuries forced him into the lineup on a nearly everyday basis and he was rewarded with recognition for his abilities in the field.

For a few years, it’s struck me as unusual that pitching and hitting metrics are asymmetric.  If the metrics we use to evaluate one group (FIP or wRC+) are so good, why don’t we use them for the other?

One issue is that we’re not used to evaluating pitchers on an OPS-type basis, and similarly we’re not used to evaluating hitters on an ERA basis.  Fine.  But there’s a bigger issue: Why do pitching metrics put so much more emphasis on the removal of luck?

While most sabermetricians are aware of BABIP, and recognize the pervasive impacts it can have on a batting line, attempts to (precisely) adjust hitter stats for BABIP are surprisingly uncommon.  While there do exist a few xBABIP calculators, these haven’t yet caught on en masse like FIP.  And xBABIP doesn’t appear on player pages in either FanGraphs or Baseball Prospectus.

xBABIP itself isn’t even the end goal.  What you probably really want is xAVG/xOBP/xSLG, etc.  Obtaining these is a bit cumbersome when you need to do the conversions yourself.

Moreover, it strikes me that xBABIP cannot be converted to xSLG without some ad hoc assumptions.  Let’s say you conclude a player would have gained or lost 4 hits under neutral BABIP luck.  What type of hits are those?  All singles?  2 singles and 2 doubles?  1 single, 2 doubles, 1 triple?  The exact composition of hits gained/lost affects SLG.  Or maybe you assume ISO is unaffected by BABIP, but this too is ad hoc.

At least to me, whenever a hitter performs better/worse than expected, we really care to know two things:

1. Is it driven by BABIP?
2. If so, what is the luck-neutral level of performance?

As I’ve attempted to illustrate, answering #2 is not so easy under existing methods.  (Nor do people always even attempt to answer it, really.)  Even answering #1 correctly takes a little bit of effort.  (“True talent” BABIP changes with hitting style, so it isn’t always enough just to compare current vs. career BABIP.  And then there are players with insufficient track record for career BABIP to be taken at face value.)

Compare this to pitchers.  When a pitcher posts a surprisingly good/bad ERA, we readily consult FIP/xFIP/SIERA.  Specific values, readily provided on the site.  So why not for hitters?

Here I attempt to help fill this gap.  The approach is to map a hitter’s peripheral performance to an entire distribution of hit outcomes.  These “expected” values of singles, doubles, triples, home runs, and outs, can then be used to computed “expected” versions of AVG, OBP, SLG, OPS, wOBA, etc.

Recovering xAVG and xOBP isn’t that different from current xBABIP-based approaches.  The main extension is that, unlike xBABIP, this provides an empirical basis to recover xSLG, and also xWOBA.

Steps:

1. Calculate players’ rates of singles, doubles, triples, home runs, and outs among balls in play.  (Unlike some other BABIP settings, I count home runs as “balls in play” to estimate an expected number.)
2. Regress each rate separately on a common set of peripherals.  You’ll now have predicted rates of each for each player.   (Keeping the explanatory variables common throughout ensures the rates sum to 100%.)
3. Multiply by the number of balls in play (again counting home runs) to get expected counts of singles, doubles, triples, home runs, and outs.
4. Use these to compute expected versions of your preferred statistics.

What explanatory peripherals are appropriate?  Initially I’ve used:

• Line drive rate, ground ball rate, flyball rate, popup rate
• Speed score
• Flyball distance (from BaseballHeatMaps.com), to approximate power
• Speed * ground ball rate
• Flyball distance * flyball rate

These explanatory variables differ somewhat from those in the xBABIP formula linked earlier.  The main distinctions are adding flyball distance (think Miguel Cabrera vs. Ben Revere) and using Speed score instead of IFH%.  (IFH% already embeds whether the ball went for a hit.  Certainly in-sample this will improve model fit, but it might not be good for out-of-sample use.)

Regression results:

Technical notes:

• These are rates among balls in play (including home runs)
• Each observation is a player-year (e.g. 2012 Mike Trout)
• I’ve used 2010-2012 data for these regressions
• Currently I’ve only grabbed flyball distance for players on the leaderboard at BaseballHeatMaps.  This is usually about 300 players per year, or most of the “everyday regulars.”  (Fear not, Ben Revere/Juan Pierre/etc. are included.)  The remaining cases get an indicator for ‘FB Dist missing.’
• LD%, GB%, FB%, and IFFB% are coded so that 50% = 50, not 0.50.
• Pitcher proxy = 1 if LD% + GB% + FB% = 0.  Initially I haven’t thrown out cases of pitcher hitting, nor other instances of limited PA.
• Notice the interaction terms.  The full impact of GB% depends both on GB% and Speed; the full impact of FB% depends on both FB% and FB distance; etc.  So don’t just look at Speed, GB%, FB%, or FB Distance in isolation.
• Don’t worry that the coefficients on pitcher proxy “look” a bit funny for HR rate and Outs rate.  (Remember that these cases also have LD%=0, GB%=0, and FB%=0.)  In total the average predicted HR rate for pitchers is 0.01% and their predicted outs rate is 94%.
• Strictly speaking, these are backwards-looking estimators (as are FIP and its variants), but they might well prove useful in forecasting.

I next calculate xAVG, xOBP, xSLG, xOPS, and xWOBA.  For now, I’ve simply taken BB and K rates as given.  (xBABIP-based approaches seem to do the same, often.)

Early results are promising, as “expected” versions of AVG, OBP, SLG, OPS, and wOBA all outperform their unadjusted versions in predicting next-year performance.  (At least for the years currently covered.)

Which players deviated most from their xWOBA?  Here are the leaders/laggards for 2012, along with their 2013 performance:

Is performance perfect?  Obviously not.  The model does quite well for some, medium-well for others, and not-so-well for some.  Obviously this is not the end-all solution for xHitting.

Some future work that I have in mind:

• A still more complete set of hitting peripherals.  I’m thinking of park factors, batted ball direction, and possibly others.
• Testing partial-season performance
• Comparing results against projection systems like ZiPS and Steamer

Otherwise, my main hope from this piece is to stimulate greater discussion of evaluating hitters on a luck-neutral basis.  Simply identifying certain players’ stats as being driven by BABIP is not enough; we really should give precise estimates of the underlying level of performance based on peripherals.  We do this for pitchers, after all, with good success.

Above I’ve contributed my two cents for a concrete method to do this.  A major extension to xBABIP-based approaches is that this offers an empirical basis to recover xSLG and xWOBA.  While the model is far from perfect, even in its current form it generates “expected” versions of AVG, OBP, SLG, OPS, and wOBA that outperform their unadjusted versions in predicting subsequent-year performance.  (Not just for leaders/laggards.)

Comments and suggestions are obviously welcome!

(Note: “Patience” here is really shorthand for “ability to get on base,” whether that’s via hits or walks. But it’s pithier and generally gets the point across as to what I’m trying to look at.)

In one of the Thursday chats on FanGraphs with Eno Sarris, I posed the following question, which he posted and the chatters answered collaboratively: Name the three players (minimum 3000 plate appearances) in the expansion era (since 1961) with a career on-base percentage above .400 and an isolated power number below .200. (Answers at the end of this post.)

In the entirety of baseball history, 36 players with 3000 plate appearances have achieved such numbers, and 24 since the beginning of the 20th century, but there are only three such players in the past 50 years. This is not particularly surprising; you won’t see many career lines such as Ty Cobb’s .366/.433/.512 anymore, or even Paul Waner’s .333/.404/.473.

But just how has the relationship between hitting for power and getting on base changed through the years?

Since we started at the individual level, let’s continue there. Let’s start with the last 20 years, from 1994-2013. Excluding pitchers, the league-wide on-base percentage was .338 and the league-wide ISO was .159. Over that time period, 761 players have had 1500+ plate appearances. How they break down on OBP and ISO lines:

Now, 1901-1920, during which time only 377 players had 1500+ plate appearances and the league averages were a .326 OBP and .082 ISO:

In either era, a substantial majority of players had either both an above average OBP and ISO, or both were below average. However, that majority is 59% in the last 20 years and was 68% in the deadball era. So one conclusion we can draw is that fewer players now sacrifice power to reach base or vice versa than they did in the olden days. (Whether they did so consciously or not.)

However, this breaks down if we go to extremes.*

From 1994-2013, 13 players had an OBP 10% above average and ISO 10% below average, while there were 15 players with an ISO 10% above average and OBP 10% below average. Overall, 3.7% of all players with 1500 PA are here.

From 1901-1920, 8 players had an OBP 10% above average and ISO 10% below average and 5 players had an ISO 10% above average and OBP 10% below average. Overall, 3.4% of the players with 1500 PA.

Players who get on base without power or hit for power without getting on base are basically as common now as they were in the dead ball era. But it’s also less common now for a player to sacrifice one or the other to any degree.

What about this power-patience relationship league-wide?

First, below are some league-wide stats over various time frames (excluding pitchers):

Time Frame	OBP	ISO	BB%	HR%
1901-present	.333	.130	8.7%	2.0%
1901-1920	.326	.082	7.6%	0.4%
1994-present	.338	.159	8.8%	2.8%
1901-1960	.341	.111	8.5%	1.2%
1961-present	.332	.142	8.8%	2.4%

The comparison between 1901-1920 and 1994-2013 really isn’t surprising. Most fans know that the dead ball era was not a time to hit for power, while the most recent times have generally been more offense-happy, especially the late 90s/early 00s.

In that chart we also see all of post-1900 baseball divided into two eras, divided along the Baseball Reference-identified beginning of the expansion era. OBP was actually higher before the Sixties while power was lower.

For now, I want to conclude with the year-by-year ratio of extra bases (2B+2*3B+3*HR) to bases reached (H+BB+HBP), graphically. I realize this might have some flaws similar to those of OPS, but a simple ISO/OBP ratio be even worse in that regard. I wanted to strip out total plate appearances or at-bats, and just look at the average number of extra bases that were earned each time a player reached base, which the selected method essentially does. The difference between ISO/OBP and the ratio selected is, on average, about 4%. At any rate this should do for a quick comparison:

A lot of famous seasons like 1930, 1968, and 1987 are identifiable on the chart. (The lowest ratio of the expansion era actually occurred in 1976, not 1968, however.) Also, it wouldn’t greatly surprise me if Babe Ruth is single-handedly responsible for the sharp increase from 1918 to 1921. (He got on base a lot, of course, but his power was the thing.) Most importantly, however, it’s clear that over time the ability of Major League player to hit for power has gone up relative to their ability to get on base. This too is not surprising to those familiar with baseball history.

And so all of this really only gives us a limited idea of the relationship between reaching base and hitting for power over time. Over the next few weeks, we’ll go further into things, both on the individual level and league level. Working backwards, next week will focus on the data underlying the above line chart.

Answers to the initial question:

Joe Mauer (.405 OBP, .145 ISO)
Rickey Henderson (.401 OBP, .140 ISO)
Wade Boggs (.415 OBP, .115 ISO)

*It’s not a Rickroll, it’s a Joelroll, which is even better because it rhymes.

Adam Wainwright has a great curveball. It’s probably the best curveball in baseball. Look at the curveball leaderboard, and you’ll find that he’s on top by a wide margin. Of course, if you’ve seen Wainwright, even in GIF form, you don’t need those numbers to tell you that. You know it’s a nasty pitch.

But, the curveball has always been a great pitch for Wainwright. While Wainwright has posted a career-best 2.55 FIP and 2.80 xFIP in 2013, his curveball has a slightly lower swinging strike rate than it did in 2012. Also, the curve hasn’t produced as many groundballs. Wainwright was solid, but not spectacular in 2013.

So, how has Wainwright been so much more successful in 2013 than in 2012?

Perhaps the biggest factor is that Wainwright has utilized his four-seam fastball much more frequently in 2013, throwing it on over 20 percent of his pitches. Before 2012, Wainwright didn’t feature a four-seam fastball. Even in 2012, he threw the pitch very sparingly.

The four-seamer has been a very effective pitch for Wainwright in 2013. He’s throwing the pitch for a strike 71% of the time, a higher rate than the two-seamer or sinker, whose usage has been curtailed. This helped Wainwright get ahead, and according to StatCorner he threw more pitches ahead in the count than ever before. As a consequence, Wainwright had a career-best 3.7% walk rate in 2013. Entering 2013, his walk rate sat at 6.7%.

Furthermore, the four-seamer produced swings and misses. The pitch had a 7.6% whiff rate. The sinker’s best rate was 4.2%. By run value, Wainwright’s four-seamer was the 8th best in baseball in 2013. I know, pitches exist in the context of repertoires, but consider that Wainwright’s two-seamer had a run value on par with the two-seamer of Jeremy Bonderman. That should tell you that it wasn’t his most effective pitch.

Even with the increased usage of the four-seam fastball, Wainwright has not sacrificed his groundball rate. At 49.1%, it is nearly equal to his career rate of 49.4%.

He’s throwing the pitch harder than ever. Maybe it took Wainwright more than a year to fully recover from the Tommy John injury he suffered before the 2011 season. When he threw the four-seamer in 2012, it averaged less than 90 miles per hour.

During the playoffs, the four-seamer has averaged nearly 94 miles per hour. Maybe the guns are juiced up, or maybe adrenaline is kicking in, but the pitch is up almost two miles from the regular season. Whatever the case, Wainwright is relying on his four-seamer even more during the playoffs. He’s thrown 23 innings, and surrendered only four runs, with 20 strikeouts and just a lone walk.

At age 32, and after throwing more than 240 innings during the regular season, Wainwright is looking stronger than ever. The addition of his four-seam fastball is proof that you can teach an old dog new tricks. Kudos to Cardinals pitching coach Derek Lilliquist and Wainwright for making the adjustment.

Note: I have no idea if I’m the first to do this, but quite frankly I don’t care.

There’s always been something strangely romantic to me about being the absolute worst at something. And when I say worst, I don’t just mean one of the worst–I’m talking about being the absolute worst period whatever period ever period. I can’t explain why it is–perhaps it’s because I’ve been last at virtually everything throughout my life, or perhaps it’s because I’m a fan of the Orioles–but for some reason, I’m transfixed by the idea of being the floor, the ultimate, the person or entity that everyone else looks down upon.

Now, what do my strange, borderline masochistic feelings towards the awful have to do with three of the better all-time players, two of whom are enshrined in Cooperstown and one of whom probably should be? Well, they all have one thing in common, which no one has seemed to realize: At one point or another, they were all the worst qualifying position player in the majors.

How, you ask? When? Why? I’ll answer your questions, but first I’d like to share with you some of the other big names that fit this criteria. Since the season ended on the 29th of September¹, there are now 143 seasons, meaning 143 worst players (or LVPs, for the sake of this exercise). I gathered up each of them, and saw that of the 143 atrocious seasons, many of them involved players that had good–or in some cases, great–careers. I then proceeded to order each player season by career WAR, to present you, the unedumacated reader, with…The Best Of The Worst.

By that, I mean: the following post consists of the top-10 careers (as measured by career WAR) for position players that were the worst in the major leagues for a particular season. I classified the general area of their career that the LVP season happened in: start-of-career bump, middle-of-career fluke, or end-of-career decline; I also put in my attempt at an explanation as to why the bad season happened. Oh, and I also divided them into groups (as they were somewhat similar), à la Bill Simmons’ NBA Trade Value Rankings.

Off we go!

GROUP I: AGING IN THE OUTFIELD²

10. Marquis Grissom

Career WAR: 26.9

LVP year/WAR: 2000/-1.8

Classification: End-of-career decline

Grissom had a solid career for the most part–he won a World Series, with a club that doesn’t tend to do well in the postseason; he won four consecutive Gold Gloves (from 1993 to 1996); at the time of his retirement, he was one of only seven players all-time with 200 home runs, 400 stolen bases, and 2000 hits (a club later joined by Johnny Damon); and he is now, to paraphrase Drake, 46 sittin’ on 51 mil ($51,946,500, to be exact). Also, as you can see above, he compiled a decent career WAR total, including two 5-win seasons in 1992 and 1993 for the Expos. However, you sure as hell wouldn’t have known that from watching his horrid 2000 season.

Traded to the Brewers in 1998 after the Indians resigned Kenny Lofton, Grissom was never able to recapture the magic from his early days north of the border, or at the very least, his sufficing days in Atlanta or Cleveland. At this point, his fielding in center (which peaked at 20.7 Def³ in 1994) was in decline, but his glove work in 2000, while unsatisfactory (-3.8 Def), wasn’t particularly bad for him, as he’d proceed to have Defs lower than that in four of his next (and last) five seasons. His baserunning was also trending downward; his BsR (which peaked at 10.5 in 1992, when he stole 78 bases) had plummeted all the way to -0.5, as he swiped a mere 20 bags. Again, though, this is a relatively minute contribution.

His batting was the major reason for his hideousness in 2000: He put up a Starlinesque triple-slash of .244/.288/.351, in a season when 16 players hit 40 home runs, 15 batted at least .330, and the major league-average triple-slash was .270/.345/.437. This all added up to an Ichiroesque wOBA of .282 and an Hechavarriaesque wRC+ of 59, which, combined with the aforementioned poor baserunning and defense, was enough to give him -1.8 WAR and edge him past Mike Lansing (-1.7) for the LVP.

This disappointing offensive season, while not all that unusual, was certainly a fluke to some degree. In terms of plate discipline, he was basically the same in 2000 (6.1% BB, 15.5% K) as he was for his career (6.2% BB, 13.8% K); it was when he put the ball in play that he got in trouble. His ISO of .108 was his lowest since 1991 (his first full season), and it convalesced the next year to a much healthier .183 (albeit in 172 fewer plate appearances); in addition, his BABIP was at .270, the second-lowest of his career to that point, although it dropped even further, to .242, the next year. It wasn’t like he had a huge rebound in 2001, either; however, the increase in ISO (and not qualifying for the batting title) was enough for a lofty -0.9 WAR in 468 trips to the plate the next year.

9. Carlos Lee

 Career WAR: 28.2

LVP year/WAR: 2010/-1.5

Classification: End-of-career decline

El Caballo clearly had some late-career struggles (as Richard Justice sure liked to point out); the huge (for the time) $100 million dollar deal that Houston signed him to certainly didn’t help the fans’ image of him. The contract notwithstanding, Lee had a decent career–two Silver Sluggers (2005, 2007), a five-win season in 2004 with the White Sox, and the career WAR that precedes this section. He also had the rare (for this era) distinction of never striking out 100 times in a season, and to top it all off, he was a player who acknowledged, and embraced, his critics. Plus, you can’t blame him for signing the contract–blame that dipshit of a GM, Ed Wa-wait, what’s that you say? Lee wasn’t signed to the ridiculous contract by Wade, but by…Tim Purpura? The guy with one reference on his Wikipedia page? Who the hell is he? Oh, whatever. Where was I?

Ah, yes. Lee’s final years. It should be noted that Mr. Lee’s abominable antepenultimate⁴ season was bookended by respectable seasons in 2009 and 2011, when he put up a combined 3.9 WAR–not exactly Mike Trout, but also not Delmon Young. With aaaaaalll of that said, though, the fact of the matter is: Carlos Lee was really goddamn awful in 2010. He provided typical Carlos Lee defense (-23.2 Def, edging his -22.3 Def from 2006 for the worst of his career) and baserunning (-3.6 BsR…pretty much in line with his career numbers), which commiserated with a .246/.291/.417 triple-slash (.310 wOBA, 89 wRC+) to give him a WAR of -1.5.

I brought up earlier that his 2010 season was, to some extent, a fluke. The main reason for his poor offensive showing in 2010 was twofold: a low BABIP (.238, 21 points lower than his previous career low of .259) motivated by a 15.6% line-drive rate, well below his career average of 20%; and a decrease in free passes (5.7% BB, much lower than his career rate of 7.5%). Both of these measure bounced back the following season, to .279 and 9%, respectively.

And lest we forget, 2010 was a year with a looooot of bad players–Melky Cabrera (-1.4 WAR) getting run out of Atlanta, Adam Lind (-1.0) and Jason Kubel (-0.4) coming crashing down to Earth after breakout seasons, Jonny Gomes (-0.4) and Carlos Quentin (-0.3) showing off their fielding prowess, Cesar Izturis (-0.4) being Cesar Izturis…But I digress. The main takeaway: 2010 Carlos Lee=horrible. Basically all other years Carlos Lee=not (to varying degrees).

GROUP II: THEY DON’T RACKA THE DISCIPRINE

8. Ray Durham

Career WAR: 30.3

LVP year/WAR: 1995/-1.4

Classification: Start-of-career bump

The Sugarman’s career met a premature end, but he was a trusty player for most of it. He was never a star player–his career-high single-season WAR was 3.9 in 2001, in his last full year with the White Sox–but he was always a contributor, putting up at least a two-win season for nine of the eleven seasons from 1996 to 2006. He made two All-Star teams (in 1998 and 2000), scored 100 runs in every year from 1997 to 2002 (if you care about such things), and stole at least 23 bases a season over that span (plus 30 in 1996). When his career started, though, he was just a fifth-round draft pick by the White Sox in 1990, who worked his way up through the farm system and won the starting second baseman job in 1995 spring training. How did that first season go?

Well, let’s start by saying he was never a very good defender. His career high Def was 8.1 in 2001, and he followed that up with -11.9 in 2002; for his career, his Def was -62.5, 2nd-worst among second basemen over that time. In the year in question, though, he took his defense to a new level. He put up…a -20.7 Def. Now, that doesn’t sound particularly (or at least historically) shitty, at least at first glance; after all, three players had worse figures this year alone⁵. However, one must consider the position that Mr. Durham manned was (and is) one of the premier defensive positions on the field, such that there have only been two–count ’em, two–players ever with a Def lower than that at second: Todd Walker (-21.5) in 1998, and Tony Womack (-24.2) in 1997. What’s more, Durham achieved that in only 1049.2 innings (in 122 games played); supposing he played 20% more innings (~1250, a standard 7 of the 19 qualified second basemen reached in 2013), he could have easily had a -25 Def, a depth the likes of which no second baseman has sunk to.

As dreadful as he was with the glove, he was still pretty reprehensible with the bat. In 517 plate appearances, he posted a .257/.309/.384 triple-slash and a .306 wOBA. In this day and age, those numbers are all right; in 2013, Brandon Phillips was able to put up a 91 wRC+ with similar lines. During the height of the PAWSTMOMNEP⁶ Era, in the Cell? Those numbers are unacceptable, and this was reflected in Durham’s 82 wRC+ and -10.9 Off. His awfulness in these two areas was not offset by his relatively solid baserunning (1.3 BsR), and he finished the season with a WAR of -1.4, which tied him with Kevin Stocker for the honor of ultimate player.

Durham’s defense never became great, but his offense rebounded after this fluke rookie season. His 6% walk rate as a rookie was much lower than his career average of 9.7%, and was by far the lowest of his career; his .127 ISO as a rookie was also considerably lower than his career ISO of .158, and was the third-lowest of his career. He was inconsistent for a few years after 1995, alternating between solid (2.0 WAR in 1996, 3.2 in 1998) and not so solid (0.3 in 1997, 1.2 in 1999), before accruing 2.7 WAR in 2000, the start of a seven-year run of at least two wins. But, despite what this article might lead you to believe, he was not, in fact, a good rookie.

7. Ron Fairly

Career WAR: 35.3

LVP year/WAR: 1967/-0.8

Classification: Middle-of-career fluke

In terms of hitting, Fairly is akin to the players that precedes him (and the player that he precedes): They all have so-so averages and power numbers, in addition to undesirable defense, but have fairly good plate discipline, which allowed them to enjoy fruitful careers. Hence, the cheesy and racist title for this section⁷.

Anyway…Fairly was another player like Durham–never elite, but always productive. He had two 4-win seasons (1970 and 1973), made the All-Star team in 1973 and 1977, and owned a career .360 OBP in an era where there was a dearth of offense. He also won three World Series, in 1959, 1963, and 1965–all with the Dodgers, with whom he spent the first 11.5 years of his 21 years in the majors. He was adequate throughout most of his tenure in Los Angeles; after his first three seasons (1958-60) when he didn’t start, he put up at least 1.9 WAR in each of the next six seasons (1961-66).

And then along came his putrid 1967. “How putrid?” you inquire. Very putrid, I reply. His defense (-15.7 Def in 1167.1 innings) and baserunning (-1.5 BsR) were as weak as they’d ever been , but this year was all about the offense. As a well-conducted player at the plate, Fairly took the base on balls quite a bit in his career–about once in every eight trips to the plate (12.5%). While his BB% of 9.7% was down from that average, and the lowest of his career to that point, it was basically in line with the MLB average of 9.8%; in addition, his strikeout rate of 9.2% (compared to 10.4% for his career) was well below the MLB average of 15.8%.

Like with Grissom, Fairly’s issues were chiefly with balls in play. He didn’t have a whole lot in the way of power, as his .101 ISO was a good deal below the major league-average of .148, and below his respectable career ISO of .142. The luck dragons were also not particularly fond of him that year; his BABIP freefell to a hapless .224. Even in the year prior to The Year Of The Pitcher, the major leagues still managed to hit .255/.302/.404, with a .280 BABIP and a .148 ISO; Mr. Fairly “hit” .220/.295/.321, which gave him a .277 wOBA and an 82 wRC+ (as opposed to .329 and 113 for MLB). In the end, he had -0.8 WAR for the year, which tied him with Zoilo Versalles for the LVP title⁸.

In summary, ISO and BABIP were the main reasons for Fairly’s nauseating 1967; each was down from .177 and .288 figures the year before, and after another down year in 1968 (.066 and .259)⁹, they would rebound to .202 and .270 in 1969, and would remain high as Fairly enjoyed the best years of his career in Montreal¹º.

6. Eddie Yost

 Career WAR: 37

LVP year/WAR: 1947/-0.8

Classification: Start-of-career bump

As Matt Klaassen wrote last year, one can only express sorrow when looking back at the career of Mr. Yost, who played 60 years too early. For his career, the third baseman had a modest .254 batting average and .371 slugging percentage, but a phenomenal .394 on-base percentage, due to a 17.6% career walk rate that, as the article points out, is second only to Barry Bonds since 1940. However, this was in the pre-pre-pre-Moneyball days, before many people knew about any stats, much less “advanced” stats like OBP. So, sadly, Yost is doomed to walk the earth as a forgotten man. Well, not really–he died last year–but you get what I’m saying.

In 1947, however? Eddie Yost wasn’t underappreciated, as anyone who knew anything about baseball could see that he was awful. After logging 47 combined plate appearances in 1944 and 1946 (and joining the navy in 1945, just in time for the end of the war), Yost finally got a chance to start in 1947, getting 485 plate appearances for the Washington Senators. How did he do with those plate appearances? Well…

He accrued free passes, or so it would appear at first glance; his walk rate of 9.3% would be sterling in this era, what with our major league walk rate of 7.9%. Back then, however, the major league walk rate was 9.7%, so he was actually below average; moreover, the major league strikeout rate was 9.6%, meaning his 11.8% strikeout rate was worse that average. His defense–which would never be that good, as his -91.7 career Def shows–was also rather lousy, to the tune of -6 Def, as was his baserunning (-1.5 BsR). However, it’s possible to play at an elite level with poor plate discipline (as Carlos Gomez sure has shown) and with poor fielding (as Miguel Cabrera sure has shown); what, then, made him so dissatisfactory?

Well, as that annoying bundle of sticks that the women love might say, it was all about (hashtag) that power. He had a .054 ISO; even in a year where the average ISO was .117, that’s not exactly Miggy levels. His BABIP was right around average (.275, to .277 for the majors), but this Pierre-like power, coupled with the aforementioned above-average strikeout rate, gave him a batting average of .238 and a slugging percentage of .292. His on-base percentage was a solid .312; however, the major league-average OBP was .336, along with a .261 AVG and .378 SLG. All of this commiserated to give him a .277 wOBA, 84 wRC+, and -17.1 Off; when Green Day was awakened, Fairly had -0.8 WAR, which beat out Jerry Priddy (-0.6) for the LVP title.

From there, Yost only got better. Yeah, there wasn’t much worse he could get, but his WAR still improved in each of the next four seasons, and he was a two-win player for seven straight years (1950-56). He pinnacled with 6.2 WAR in 1959, when he even hit for decent power, socking 21 dingers (with a .157 ISO) in his first year after leaving The Black Hole Known As Griffith Stadium¹¹. It’s a shame he had to start out as shittily as it did.

GROUP III: A ROCK AND GUITAR PLACE¹² (OR, AGING IN THE OUTFIELD, PART II)

5. Dave Parker

Career WAR: 41.1

LVP year/WAR: 1987/-0.6

Classification: End-of-career decline

Paul Swydan reminisced on the career of Parker earlier this year after it was announced that he (i.e. Parker) had Parkinson’s disease. I’ll briefly rehash Swydan’s reporting here.

Parker’s job when called up was to replace the player who is #1 on this list, and obviously, those were some big shoes to fill. Parker did not shrink from the spotlight, however, as he produced 30.3 WAR over his first five full seasons (1975-79), which tied him with The Despised One for fourth-most in the majors over that span. He attained quite a bit of hardware over this time as well–the NL MVP trophy in 1978 and Gilded Gloves¹³ in 1977-79–and won batting titles in 1977 and 1978.

These five years were the best of his career, and after the fourth year (1978) he was rewarded with a five-year, $5 million-dollar contract–the largest in MLB history at the time. However, much like a certain power-hitting Pennsylvanian today, he would struggle to live up to this contract; after the first year (1979), when he put up 5.7 WAR and was instrumental in helping the Pirates win the Fall Classic, he would only log 1660 plate appearances over the final four years of the deal (and only contribute 1.6 WAR in those years). This was due to several factors, namely his affinity for a certain white substance that is, generally speaking, frowned upon in our society; his continued usage of said substance earned him a full-year suspension for the 1986 season, which he was able to circumvent via community service, donations of his salary, and submission to random drug tests.

After his contract expired in 1983, he signed with the Reds, and his production was essentially the same as in the last few years in Shitts¹⁴ Pittsburgh (save for his fluky, 5.4-WAR 1985 season) and as it would be for the rest of his career. There was one year in particular, though, where he really hit rock bottom: the year that followed the suspension year.

In the year in question–his last in Cincy–Parker was, shall we say, no muy bueno. A career .290/.339/.471 hitter, Parker hit .253/.311/.433 in 1987. While one might attribute this to his 16.1% strikeout rate and 6.8% walk rate (compared to 15.5% and 8.9%, respectively, for the majors), these numbers are actually pretty analogous to his career numbers (15.1% and 6.1%, respectively). His power was also comparable to his career figures (.180 ISO in 1987, .181 for his career).

For Mr. Parker (like for so many of the others on this list) the issues arose from two areas: when the other team fielded the balls he hit, and when he fielded the balls the other team hit. Parker’s .265 BABIP was the lowest of his career for a full season, not to mention being 49 points below his career BABIP of .314 and 24 points below the major league-average BABIP of .289. His glovework also left something to be desired¹⁵–he posted a -17.8 Def, which was second-worst in the majors.

Overall, his hitting wasn’t too dreadful–his triple-slash was good enough for a .316 wOBA and 87 wRC+. He wasn’t even that bad, period–his WAR was -0.6, a relatively good figure. Out of the 143 seasons, only 5 players were LVPs with a higher WAR; Parker was just unfortunate enough to have a down season in a year where the only serious competition for the LVP was Cory Snyder (-0.5).

One last thing on Parker: As painful as his 1987 season was, his last season (1991) was even worse–he had -1.2 WAR in only 541 plate appearances for the Angels and Blue Jays. Unfortunately, he was robbed of the LVP crown by some scrub named Alvin Davis. Hah! What a loser! It’s not like any site editor has ever vehemently defended Davis and would cancel my account if I was to insult Mr. Mariner!

(Your move, Cameron.)

4. Bernie Williams

Career WAR: 44.3

LVP year/WAR: 2005/-2.3

Classification: End-of-career decline

Williams’ case for Cooperstown has generated quite a bit of controversy, over everything from the impact and weighting of postseason play to the cost of defense to True Yankeedom. That point, however, is now moot, as Williams is now off the ballot; whether or not he deserves to be is a can of shit I’d rather not open right now.

With Williams, the superlatives are certainly present–five All-Star appearances (1997-2001), four Gilded Gloves¹⁵ (1997-2000), four World Series rings (1996, 1998-2000), a Silver Slugger (2002), and the ALCS MVP in 2002. He also had seven 4-WAR seasons over an eight-year period (1995-2002), and was the 12th-most valuable position player in baseball over that time. Plus, he was, y’know, a True Yankee.

It’s the years to which this period came prior that I am focusing on. After that eight-year run of dominance, Williams fell off a cliff (as Paul Swydan explained earlier this year), putting up…wait for it…-3.3 WAR over the next four seasons, dead last in the majors in that span. Most of that negative WAR came from one year: 2005, the second-to-last of Mr. Williams’ career.

In said year, Williams (he of the career .297/.381/.477 triple-slash) batted a mere .249/.321/.367. The PAWSTMOMNEP Era was beginning to transition into the Era of the Pitcher, but offenses were still favored–the major league triple-slash was .264/.330/.419–and Williams’ batting (and -1.4-run baserunning) was enough to give him a .305 wOBA, 85 wRC+, and -11.2 Off. His strikeout rate in 2005 (13.7%) mirrored his career rate (13.4%) and was much better than the MLB rate (16.4%), and while his walk rate of 9.7% was low by his standards (career walk rate of 11.8%), it was still considerably better than the MLB average of 8.2%; his batted-ball rates were also all right (19% LD/43.5% GB/37.5% FB). It was a poor BABIP (.270, as opposed to .318 for his career and .295 for MLB) and a poorer ISO (.118, as opposed to .180 for his career and .154 for MLB) that did him in.

But Williams’ offensive struggles pale in comparison to his defensive ineptitude. Never the greatest with the glove, Williams hit a new low in 2005¹⁶, as he had a -30.2 Def in 862.2 innings. In terms of UZR, he was 29.2 runs below average, and because he didn’t play that much, his performance extrapolates to 42.5 runs below average per 150 games. As a point of reference, Adam Dunn’s worst career UZR/150 as a outfielder was -39.2 in 2009. So, yeah.

The disconcerting work in the field by Williams, coupled with ineffectiveness at the plate, gave him a -2.3 WAR for the year; this put him in a class of his own, as the next-worst player was Scott Hatteberg, whose -0.7 WAR was a full 1.6 behind him. Maybe, if his production hadn’t completely deteriorated at the tail end of his career, Williams would be in the Hall right now, and the point would still be moot, but for a better reason.

GROUP IV: CENTRAL COMPETITORS

3. Ted Simmons

Career WAR: 54.2

LVP year/WAR: 1984/-2.4

Classification: End-of-career decline

Look, I’m not saying Ted Simmons should go to the Hall of Fame. What I will say is this:

Simmons is player A. Ichiro Suzuki is player B. Just sayin’.

Anyway, regardless of one’s opinion on Mr. Simmons, one cannot deny that he was an excellent all-around player for most of his career. People of his day certainly didn’t, as he was named to eight All-Star teams (1972-74, 1977-79, 1981, 1983) and won a Silver Slugger (1980). He was generally regarded as the second-best hitting catcher of his era, behind Johnny Bench, and while catchers are held to a lower offensive standard than most other players, he was no slouch with the bat–his career wRC+ was 116, better than Adrian Beltre and Andruw Jones. His defense was mediocre (53rd out of 113 catchers in Def over the course of his career), but he was still outstanding, as the above comparison should show.

Like all mortal men, though, Simmons’ production decayed as he aged; after contributing at least three wins in 12 of 13 seasons from 1971 to 1983, he was at or below replacement level in four of his last five years. In the first of those five years, he was a special kind of awful.

In 1983 (the last year of the 13-year period), Simmons was actually quite valuable, to the tune of 3.7 WAR for the Brewers. The next year…well, everything fell apart. His triple-slash collapsed from a healthy .308/.351/.448 to a sickly .221/.269/.300, which took his wOBA from .352 to .259, his wRC+ from 122 to 60, and his Off from 16.6 to -24.6. His plate discipline was fairly similar in both years (6.3% BB%, 7.8% K% in 1983; 5.6% and 7.5% in 1984), although his walk rate in both years was a good deal below his career average of 8.8%. This meltdown was primarily caused by a David Murphy-like¹⁷ dropoff in BABIP, from .317 to .233, and a near-halving of ISO, from .140 to .078; both of these numbers were a good deal below Simmons’ career numbers (.284 and .152, respectively). What’s more, he spent most of his time at DH, meaning he was held to a higher offensive standard; thus, these already bad numbers were reduced even further.

When Simmons did play in the field (at first and third, not catcher), his defense was somewhat rotten, as he posted -4 TZ in 457.1 combined innings. With the subtracted defensive runs for not fielding at all, his Def dropped from -3 in 1983 to -14.5 Def (12th-worst in the majors) in 1984.

When the dust had settled, Simmons was left with -2.4 WAR, which gave him a comfortable lead over Curtis Wilkerson (-1.1) for the LVP honor. Simmons never really got much better than this–he gave the Brew crew 1 WAR in 1985, before costing the Braves a combined 1 win as a utility man over the next three years. Retiring at age 39, Simmons might’ve been enshrined if he had kept up his consistency into his late 30s.

While Simmons was arguably Hall-worthy, there’s no arguing over these next two. Well, there actually is a fair amount of arguing over this next guy, but…never mind.

2. Pete Rose

Career WAR: 80.3

LVP year/WAR: 1983/-1.9

Classification: End-of-career decline

Yes, the LVP in back-to-back years was a very valuable player overall. Surprised? Well, that’s allowable–when you started reading this, you probably had no idea what you were reading in the first place, much less if it would involve two exceptional players performing uncharacteristically poorly in two consecutive years.

Moving on…Rose hardly needs an introduction, but I’ll give him one anyway. Seventeen All-Star nods (1965, 1967-71, 1973-82, 1985); a three-time batting champion (1968-69, 1973) and three-time World Series champion (1975-76, 1980); two Gilded Gloves (1969-70); a Silver Slugger in 1981; the NL ROTY¹⁸ and MVP in 1963 and 1973, respectively; and one of the better (and most deserved)¹⁹ nicknames in baseball. Plus, there was that whole 4,256 hits thing, but nobody cares about that.

Rose spent most of his career with the Reds, winning two of his three championships with them. The third? That was won with the Phillies, with whom he spent five mostly forgettable years at the end of his career. After averaging 4.7 WAR over his first sixteen seasons with the Reds (and being the fourth-most valuable player in baseball over that span), Rose only earned 3.8 WAR in the next five years combined. To be fair, he was at least middling for the first four years, finishing above replacement level in each. In the last year (1983), however, he was anything but middling–and not in a good way.

1983 wasn’t a particularly great year for hitters–the aggregate MLB triple-slash was .261/.325/.389; nonetheless, Rose was still considerably below thoe numbers. Never one to hit for power (his best ISO was .164 in 1969), he sunk to new lows in 1983, pulling a Ben Revere;²º his ISO at season’s end was a repulsive .041, considerably lower than the major league ISO of .128. BABIP also wasn’t too kind to him, as he posted a .256 mark in that department, a good deal below the major league BABIP of .285. His plate discipline was superb (9.4% and 5% walk and strikeout rates, compared to 8.4% and 13.5%, respectively, for the majors), but this could not compensate for his failings in the other areas, and he ended up with a .245/.316/.286 triple-slash, with a .277 wOBA, 68 wRC+, and -21.6 Off.

He didn’t do himself any favors on the basepaths (-1.5 BsR) or in the field (-8 TZ, -14.7 Def in 1034 innings between first and the oufield), but he was never the greatest in those categories. In this one year, he was an all-bat guy with no bat²¹, and that usually doesn’t have good results.

When all was said and done, Rose’s WAR was -1.9, a figure that easily bested Dave Stapleton (-0.7) for the LVP title. One last note on Rose: Unlike the #1 player on this list, people seem to be cognizant of Rose’s awfulness in his LVP year–probably because Rose’s year occured near the end of his career, and he never received a chance to outshine it. This next guy, though? Well…

1. Roberto Clemente 

Career WAR: 80.5

LVP year/WAR: 1955/-0.9

Classification: Start-of-career bump

Yeah, I’d say he made up for one bad season. Either that, or fifteen All-Star games (1960-67, 1969-72)²², twelve consecutive Gold Gloves²³ (1961-72), four batting crowns (1961, 1964-65, 1967), the NL MVP (1966), the WS MVP (1971), and 80.1 career WAR were all for naught.

Despite all of the undeniable awesomeness of Clemente’s career as a whole, there is still that one blemish on his record: his less-than-perfect rookie year. After being drafted by the Pirates in 1954, Clemente was given the opportunity to start immediately, and the outcome wasn’t very good.

Clemente was never a particularly patient hitter, with a career BB% of 6.1%; in 1955, however, he was especially anxious, with a 3.6% BB% that was a good deal below the major league-average of 9.5%, and was the second-worst individual figure in the majors²⁴. He didn’t strike out that much, as his 12% K% wasn’t too much worse than the major league-average of 11.4%, and was identical to his career rate.

Always a high-BABIP guy (with a career number of .343), Clemente’s balls were unable to find holes in 1955, as he had a BABIP of .282 that, while being higher than the major league BABIP of .272, was still the second-lowest of Clemente’s career. His power also hadn’t developed yet²⁵, as his .127 ISO (which was also similar to the major league ISO of .136) was much lower than his career ISO of .158. Overall, Clemente batted .255/.284/.382, with a .294 wOBA, 73 wRC+, and -18.5 Off. His baserunning wasn’t much of a factor (-1.3 runs, compared to 2.1 total for his career), but on defense, he was substandard, putting up a -4.6 Def that was 21st out of 31 outfielders²⁶.

This all coalesced into a WAR of -0.9, which allowed Clemente to beat Don Mueller (-0.7) for the LVP title by a narrow margin. It would take Clemente a few years to really get going; from 1956 to 1959, he was worth a modest 8.9 WAR²⁷ (44th in the majors) as he struggled through various injuries. By 1960, though, he was healthy, and would contribute 72.7 WAR (fourth in the majors) from then until…well, you know.

***

What does all of this mean? Well, the average major league player is worth 2.97 wins over the course of their career; the average player that won an LVP is worth 6.04 wins over the course of their career. Impacted by outliers, you say? Even when the ten players listed here are taken out, the average career WAR of the remaining 133 is 3.05–slightly better than for every player. Looking a little deeper, we can see that of the 16,292 players with a plate appearance, 852 (or 5.2%) are worth 20 or more wins over the course of their careers. For LVPs? 15 out of 143, or 10.5%²⁸.

Is this good news for Eric Hosmer and Adeiny Hechavarria? Possibly. Would assuming this is good news for Hosmer and Hechavarria be drawing a causation from a correlation? Probably. I don’t know. What do I know? I know that if you read this all of the way through, I just wasted a sizable chunk of your time. And in my book, that is a job well done.

——————————————————————————————————-

¹Or the 30th, technically. Whatever.

²As far as I can tell, that’s an original joke. Feel free to chastise me if I’m wrong.

³How exactly do I cite the Def stat? Is it a plural type of thing, like “Player X had 5 Defs last year”, or a singular, like…well, like I wrote in the post?

⁴Spellcheck, you have crossed a line.

⁵The worst fielder in the majors, according to Def? Carlos Beltran and his -21.4. Yes, the three-time Gold Glove-winning, two-time Fielding Bible-winning Carlos Beltran. Yes, I’m also unsure how to react.

Why has no one else realized this, though? Cameron? Sullivan? God forbid, Cistulli? I’m looking at you all! Write something about this, or else I’ll be forced to!

⁶You know, the Possibly Affiliated With Substances That May Or May Not Enhance Performance Era.

⁷Hey, it’s South Park’s words, not mine.

⁸Versalles’ career was also rather notable–and not just for his abnormal appellation.

⁹To be fair, every hitter had a down year in 1968.

¹ºOne doesn’t receive too many opportunities to type this (much to the chagrin of Mr. Keri).

¹¹According to the B-R bullpen, there were only two–count ’em, two–fair balls ever hit out of Griffith. TWO! In 51 motherfucking seasons! So Safeco ain’t so bad, I guess.

¹²Get it? ‘Cuz Parker did…and Williams did…oh, never mind.

¹³Not a typo (read on).

¹⁴Sorry, force of habit (I’m a Ravens fan).

¹⁵In a manner not dissimilar to a controversial shortstop of our era (or to the next player on the list), Parker was always one whose reputation overshadowed his production in the field, as neither basic statistics (.965 career fielding percentage, 137th out of 167 players over the course of his career) nor advanced statistics (-127.5 career Def, 688th out of 704 players over the course of his career) were particularly fond of his work with the glove.

¹⁶Actually, every Yankees defender hit a new low in 2005, as their team defense was the lowest of any team in the UZR era (-141.7 runs); this was due in no small part to the horrifying outfield of Williams, Gary Sheffield (-26 UZR), and Hideki Matsui (-15.2 UZR).

¹⁷I’ll have more on that in the coming weeks.

¹⁸How does one abbreivate Rookie of the Year? ROTY, RotY, or some combination of the two?

¹⁹Deserved on more than one level.

²ºI shouldn’t need to explain what I mean by that. Also, Rose pulled a Ben Revere in 1984 and 1986, albeit in non-qualifying seasons.

²¹I know I’ve heard that expression before–I think it was used to describe Jesus Montero–but I can’t seem to find where it was used.

²²No, I didn’t do my math wrong–from 1959 to 1962, MLB had two All-Star games.

²³I was going back and forth about whether to call this one gilded; over the indicated time span, Clemente was eighth among outfielders in Def–quite good, but not the best (as winning a Gold Glove in each year would imply).

²⁴It was not, however, the worst mark of his career, as he would post walk rates of 2.3% and 3.3% in 1956 and 1959, respectively.

²⁵In terms of power, Clemente was a late peaker, with five of his six highest ISOs coming during or after his age-31 season (1966). I’d be interested in knowing how common that is.

²⁶For whatever reason, defensive records for each individual outfield position only go back to 1956–any time before that, it’s all just lumped into “Outfield”. Also, for that matter, innings played on defense only go back to that date as well, which doesn’t seem to make sense, given that play-by-play data is available back then.

²⁷Interestingly enough, Clemente’s greatest defensive seasons were during this period. He had 20.7 Def in 1958, and 19.3 in 1957; his next-best season with the glove was in 1968 (16.8).

²⁸The other five (besides the ten listed here): Milt Stock (22.3 career WAR, -2.7 in 1924); Alvin Davis (21.1 career WAR, -1.6 in 1991); Raul Ibanez (20.5 career WAR, -1.7 in 2011); Jason Bay (20.3 career WAR, -1.1 in 2007); and Buck Weaver (20.3 career WAR, -1.1 in 1912).

Happy 21st birthday, Bryce Harper!

In two seasons to date, Harper has posted a 128 wRC+ while hitting .272/.353/.481 in 1094 plate appearances.

Steamer projections have Harper projected to hit .266/.347/.464 as a 21-year old, which would make for a 125 wRC+. But if Harper posts a lower batting average, OBP, and slugging than he did in either of his first two years, I imagine that would be a major disappointment, not just for fans of the Washington Nationals, but for fans of the sport of baseball. And also, perhaps mostly, for the player himself. (But at least the projections have him down for a career-high 23 home runs.)

Changing gears for a moment, how about that Mike Trout. You may have heard, but some people thought he was the American League’s most valuable player after he hit .326/.399/.564 in 639 plate appearances in 2012. Then he somehow got even better as a hitter in 2013, posting a .323/.432/.557 line in 716 PA.

But when Trout was 19, he hit .220/.281/.390 in a 40-game, 135-PA cameo in 2011. Harper would crush that line as a 19-year old rookie in 2012. Then, of course, Trout’s age-20 season set an impossible standard that Harper had about a 3.4×10^9 percent chance of surpassing, if we’re being optimistic.

Because of the one-year age difference, had Trout just ended up reasonably good rather than ridiculously great, he might have served as a decent guide for how Harper could develop. Sort of a one-year advance copy. But Trout’s 2013 season confirmed that he is ridiculously great, so that idea is out the window for now.

What about other players who got their starts as teenagers? According to the Baseball-Reference.com similarity scores, Harper through his age 20 season has posted numbers most similar to Tony Conigliaro (956), Ken Griffey (954) and Mickey Mantle (954). All three of these players debuted in their age 19 seasons.

Mantle was already a great hitter when he was 20, posting a .311/.394/.530 line in 626 PA (158 wRC+), but the other two players set more worldly, but still great-for-20, lines: Griffey a .300/.366/.481 (666 PA, 132 wRC+) and Conigliaro a .269/.338/.512 (586 PA, 131 wRC+).

Harper’s wRC+ in 2013 was 137, slightly better than either Griffey or Conigliaro, but he only put in 497 plate appearances. Still, the three players had awfully similar age-20 seasons.

When he turned 21, Conigliaro’s effectiveness decreased to a 123 wRC+ and .265/.330/.487, before a recovery when he turned 22 (144 wRC+, .287/.341/.519, 389 PA) prior to the disaster that occurred on August 18, 1967, when he was hit in the face by a pitch.

Griffey’s improvement was steadier, as he posted a .327/.399/.527 line when he was 21 and a .308/.361/.535 one at 22 years old, with wRC+ marks of 148 and 145, before experiencing his first two 160 wRC+ seasons the next two years.

One more player I want to talk about in this context is Giancarlo Stanton. He fiddled around in A+ and AA when he was 19, because the universe doesn’t just up and grant every great talent the ability to hit Major League pitching as a teenager. Stanton instead debuted in his age 20 season and hit .259/.326/.507 (118 wRC+ in 396 PA) before hitting 34 home runs in his age 21 season with a 141 wRC+ and a .262/.356/.537 line in 601 PA.

So where the heck are we now? I just shared a lot of names and players and numbers and slashes, but none belong to Bryce Harper. He’ll have a heck of a lot more to do with his development than Mickey Mantle’s ghost.

I think the record shows, however, that players who hit well when they are 19 and 20 generally don’t stagnate at 21. The projected line from the beginning of this post still seems low.

To conclude, here is a possible range of outcomes for Bryce Harper in 2014:

Worst-case: His health remains an issue. His stats end up about as projected…or worse.

Mid-case #1: He actually gets healthy but still faces a Conigliaro-like decline between his age 20 and age 21 seasons. (Although, Conigliaro’s decline still left him hitting at a darned good level.)

The Steamer projection is somewhere between this and the prior case.

Mid-case #2: Ken Griffey. Don’t let the version of Ken Griffey from his mid-20s in the mid-90s, the version who hit 56 home runs in consecutive seasons, interfere with the classification of this as a “mid-case.” A 10-20 point jump in Harper’s wRC+, as Griffey experienced when he turned 21, would be a welcome development and continue Harper on his perennial all-star path.

Best-case: Mike Trout. I might have skipped a couple mid-cases, but let’s get back to Trout. It’s going to always get back to Trout, I think, for years when we have conversations like this. But if Trout could struggle when he was 19–unlike Harper, Mantle, Conigliaro, Griffey (sorry Stanton)–and then explode when he turned 20, why can’t the other once-in-a-generation talent of this generation experience a similar jump? (Please allow me a “why can’t” when talking about best-case scenarios.) It wouldn’t be a change from bad to great, but good to unfathomable, and it would come a year later, but maybe instead of having Griffey’s age-20 season and Griffey’s age-21 season, Harper can skip right to Trout or Mantle’s age-21 season.

The “Griffey-Griffey” path is still a more realistic hope for those looking for Harper to exceed the computed expectations set by Steamer. I don’t think a 150 wRC+ is out of reach, but even a 140 or 145 wRC+ or so would be a nice continuation for Harper’s career.

Adam Wainwright pitched a decent game Monday night in Game 3 of the NLCS, throwing 7 innings and giving up 6 hits, no walks and striking out 5. He had a game score of 62, usually a sign of a well-pitched game, and he ended up with the loss because the Cardinals offense chose to take the night off. Brian Kenny (@MrBrianKenny) of the MLB Network started a movement called KillTheWin, his quixotic effort to have the win eliminated as a baseball statistic. I wrote a couple posts at my blog Beyond The Scorecard because I thought it was an interesting idea and seemed like a fun issue to research and will include the links at the end of this post, but Wainwright’s game got me thinking–how often in the postseason is a pitcher not justly rewarded for a good effort?

As the use of starting pitchers has changed over time, the win has become a far less effective metric in judging pitcher effectiveness. I don’t remember how I stumbled across using a game score of 60 as my marker of effectiveness (probably at Kenny’s suggestion) and like any other single number it’s not the entire story of a pitching performance, but it grants the opportunity to separate pitching effectiveness from a lack of offensive production or bad defense. Including Monday’s game there have been 1,393 postseason games played since 1903, meaning there have been 2,786 starts in postseason history–this chart shows the breakdown of wins, losses and no-decisions for those starters in that time frame:

In the postseason, starting pitchers won almost 36% of their starts. This covers the entire spectrum of postseason play, from the games in the early 1900s when a pitcher typically finished what he started all the way to examples like Saturday where Anibal Sanchez was removed after 6 innings (and 116 pitches)…and throwing a no-hitter. Different times, to be sure. With this context, this chart shows how often a pitcher who had a game score of 60 or greater was credited with the win:

Definitely an improvement over the general trend, but still, a pitcher who pitches well enough to attain a game score of 60 or greater has done all he can–he’s given up few hits and walks and struck out a decent number of hitters. In short, he’s kept base runners off base, the primary job of a pitcher and almost 35% of the time has nothing to show for it, or even worse, is tagged with a loss. This chart shows these numbers since the playoffs were expanded in 1969:

The introduction of relievers definitely hurt the cause of these starting pitchers, with almost 40% of pitchers who threw very good games not receiving a win. On the flip side, it is gratifying to see that only around 9% of wins go to pitchers who were the beneficiaries of being on the right side of 13-12 scores or games along those lines–justice exists somewhere. This last chart shows the record by game score stratification:

Who was that unlucky pitcher with a game score greater than 90 who received the loss? Nolan Ryan in Game 5 of the 1986 NLCS.

The 10-15 regular readers of my blog hopefully are aware that I typically write with my tongue firmly lodged in my cheek, and the win is so entrenched in baseball lore that removing it as a point of discussion simply won’t happen, but it doesn’t mean that it has to receive the emphasis it does. When we have the wealth of data that sites like FanGraphs places at our fingertips, we don’t have to rely on a metric that was formed at the inception of organized baseball that is a relic today, particularly one that doesn’t give an accurate portrayal of pitching performance around 35% of the time. Kill The Win–maybe not, but we can certainly de-emphasize it.

#KillTheWin blog posts:

The first one, which lays out definitions and rationale

The second one, which expands it

A final one, an exercise in absurdity

Talcott v. National Exhibition Co., 144 A.D. 337, 128 N.Y.S. 1059 (2 Dept., 1911)

What was Merkle’s Boner?

On September 23, 1908 the Chicago Cubs played the New York Giants at the famed Polo Grounds.  Al Bridwell came to bat with two outs and the game tied 1-1 in the bottom of the ninth.  He laced a single to the outfield and the runner on third trotted home, thinking he had just scored the winning run.  The Cubs second baseman Johnny Evers, of the famed “Tinkers to Evers to Chance” double play combination and future Hall of Fame inductee, however, called for the ball from the outfield because Fred Merkle, the Giants runner on first, had not touched second base.  Although there is controversy regarding whether Evers got the actual ball back, the umpire ruled Merkle out at second and due to the force, the apparent winning run was erased.

As was common at the time, the fans at the Polo Grounds would walk across the field after the game to exit the ballpark.  By the time the play was decided and the winning run nullified, however, the fans believing the Giants had won were already streaming across the field and it was impossible to resume the game before the game was called on account of darkness.

On October 6, 1908, the National League Board of Directors made its final ruling that because Merkle had failed to reach second, the force rule was applied correctly and the game was a tie.  At the end of the season, the Cubs and Giants were tied for first place and a makeup game was needed to determine which team would play in the World Series.  This game was played on October 8, 1908 at the Polo Grounds and reportedly drew 40,000 people, the largest crowd ever to have attended a single baseball game at the time.

The Cubs won this game over the Giants and went on to beat the Tigers 4-1 in the World Series, their last World Series victory.

The play that forced the makeup game was dubbed “Merkle’s Boner” and Fred Merkle was tagged with the nickname “Bonehead.”  Years later, Merkle admitted that he never touched second base but claimed he had been assured by umpire Bob Emslie that the Giants had won.  Despite a solid 16-year Major League career, including four seasons with the Cubs, Merkle was never able to shake the stigma of the play.

What does Merkle’s Boner have to do with this case?

As a result of the play and the October 6^th mandate for the makeup game, the Polo Grounds played host to the makeup game on October 8, 1908.  This game was “of very great importance to those interested in such games, and a vast outpouring of people were attracted to it.”  On the morning of the game, the ticket booths at the Polo Grounds were inundated with people trying to secure reserved seats for that afternoon’s game.

Plaintiff Fredrick Talcott, Jr. went to the ballpark intending to buy tickets for the game and entered an “inclosure” where the ticket booths were located.  After finding that the tickets were sold out, he tried to leave the inclosure along with a great number of people also trying to exit at the same time.  As he attempted to leave, however, ballpark attendants prevented his exit and he was “detained in the inclosure for an hour or more, much to his annoyance and personal inconvenience.”  Mr. Talcott brought this lawsuit seeking damages for false imprisonment.  He further claimed to have been pushed by the defendant’s “special policemen.”

The Giants countered that plaintiff simply could have used one of the other exits available.  Mr. Talcott alleged, however, that he was not aware of any other exits to the inclosure and none were pointed out to him.

Who won?

The case went to a jury trial and Mr. Talcott was awarded $500 in damages (approximately $12,000 today) with judgment entered on May 19, 1910.

The Giants appealed but the appellate court affirmed the judgment in favor of Mr. Talcott.

Why?

The jury found that that plaintiff’s detention was unwarranted.  The appellate court agreed with this finding, ruled that the award was not excessive and found no reason to interfere with the jury’s verdict.

Additionally, the court found that Mr. Talcott was not required to demonstrate that he incurred any special or actual damages as a result of the detention.

Pitch sequencing is a complicated topic of study. Given the previous pitch(es) to a batter, the next pitch may depend on factors such as the game-based information (e.g., count, number of outs, runners on base); the previous pitch(es), including their location, type, and batter’s response to them; and the scouting report against the batter as well as the repertoire of the pitcher. In order to approach pitch sequencing from an analytical prospective, we need to first simplify the problem. This may involve making several assumptions or just choosing a single dimension of the problem to work from. We will do the latter and focus only on the location of pitches at the front of the strike zone. Since we are interested in pitch sequencing, we will consider at-bats where at least two pitches were thrown to a given batter. The idea is to use this information to generate a simple model to indicate, given the previous pitch, where the next pitch might be located.

We can start with examining the distance between pitches, regardless of the location of the initial pitch. If this data, for a given pitcher, is plotted in a histogram, the spread of the data appears similar to a gamma distribution. Such a distribution can be characterized many ways, but for our purposes, we will use the version which utilizes parameters k and theta, where k is the shape parameter and theta is the scale parameter. With a collection of distances between pitches in hand, we can fit the data to a gamma distribution and estimate the values of k and theta. As an example, we have the histogram of C.J. Wilson’s distances between pitches within an at-bat from 2012 overlaid with the gamma distribution where the values of k and theta are chosen via maximum likelihood estimation.

Author’s note: I started working on this quite a few weeks ago and so, at the time, the last complete set of data available was 2012. So rather than redo all of the calculations and adjust the text, I decided to keep it as-is since the specific data set is not of great importance in explaining the method. I will include the 2013 data in certain areas, denoted by italics.

While this works for the data set as a whole, this distribution will not be too useful for estimating the location of a subsequent pitch, given an initial pitch. One might expect that for pitches in the middle of the strike zone, the distribution would be different than for pitches outside the strike zone. To take this into account, we can move from a one-dimensional model to a two-dimensional one. Also, instead of using pitch distance, we are going to use average pitch location, since this will include directional information as well. To start, we will divide the area at the front of the strike zone into a grid of three-inch by three-inch squares. We choose this discretization because the diameter of a baseball is approximately three inches and therefore seems to be a reasonable reference length. The domain we consider will be from the ground (zero feet) to six feet high, and three feet to the left and right of the center of home plate (from the catcher’s perspective).

We will refer to pairs of sequential pitches as the “first pitch” and the “second pitch”. The first pitch is one which has a pitch following it in a single at-bat. This serves as a reference point for the subsequent pitch, labeled as the “second pitch”. Adopting this terminology, we find all first pitches and assign them to the three-inch by three-inch square which they fall in on the grid. Then for each square, we take its first pitches and find the vector between them and their associated second pitches (each vector points from the first pitch to the second pitch). We then average the components of the vectors in each square to provide a general idea of where the next pitch in headed for the first pitches in that square.

In areas where the magnitude of the average vector is small, the location of the next pitch can be called isotropic, meaning there is no preferred direction. This is because average vectors of small magnitude are likely going to be the result of the cancellation of vectors of similar magnitude in all directions (from the histogram, the average distance between pitches was approximately 1.5 feet with most lying between 0.5 and 2.5 feet apart). One can create contrived examples where, say, all pitches are oriented either left or right and so there would be two preferred directions rather than isotropy, but these cases are unlikely to show up at locations with a reasonable amount of data, such as in the strike zone. In areas where the average vector has a large magnitude, the location of the next pitch can be called anisotropic, indicating there is some preferred direction(s). Here, the large magnitude of the average vector is due to the lack of cancellation in some direction. For illustrative purposes, we can look at one example of an isotropic location and one of an anisotropic location. First, for the isotropic case:

In this plot, the green outline indicates the square containing the first pitches and the red arrows are the vectors between the first and second pitches. The blue arrow in the center of the green square is the average vector. For the grid square centered at (-0.375,2.125), we have a fairly balanced, in terms of direction and distance, distribution of pitches. Therefore the average vector is small in magnitude. In other cases, we will have the pitches more heavily distributed in one direction, leading to an anisotropic location:

As opposed to the previous case, there is a distinct pattern of pitches up from the position (-0.125,1.625), which is shown by the average vector having a substantially larger magnitude. This is due to most of the vectors having a large positive vertical component. Running over the entire grid where at least one pitch had a pitch following it, we can generate a series of these average vectors, which make up a vector field. In order to make the vector field plot more legible, we remove the component of magnitude from the vector, normalizing them all to a standard length, and instead assign the length of the vector to a heat map which covers each grid square.

For the 2013 data set:

By computing these vectors over the domain, we are able to produce a vector field, albeit incomplete. Computing this vector field based on empirical data also lends itself to outliers influencing the average vectors as well as problems with small sample size. We can attempt to handle these issues and gain further insight by finding a continuous vector field to approximate it. To do this, we will begin with a function of two variables, to which we can apply the gradient operator to produce a gradient field. We can zoom in near the strike zone to get a better idea of what the data looks like in this area:

Note that as we move inward, toward the middle of the strike zone, the magnitude of the average vector shrinks. In addition, the direction of all vectors seems to be toward a central point in the strike zone. Based on these observations, we choose a function of the form

P(x,z) = (1/2)c_x(x – x_0)^2 + (1/2)c_z(z – z_0)^2.

The x-variable is the horizontal location, in feet, and z the vertical location. This choice of function has the property that there is a critical point for P and when the gradient field is calculated, all vectors will radially point toward or away from this critical point. The constants in the equation of this paraboloid are (x_0,z_0), the critical point (in our case, it will be a maximum), and (c_x,c_z) are, for our purposes, scaling constants (this will be clear once we take the gradient). The gradient of function P is

grad(P) = [c_x(x – x_0), c_z(z – z_0)].

Then c_x and c_z are constants that scale the distances from the x- and z-locations to the critical point to determine the vector associated with point (x,z). Note that grad(P)(x_0,z_0) = [0,0]. In fact, we will give this point a special name for future reference: the pitching sink. For vector fields, a non-mathematical description of a sink is a point where, locally, all vectors point toward (if one imagines these vectors to be velocities, then the sink would be the point where everything would flow into, hence the name). This point is, presumably, the location where we have the least information about the direction of the next pitch, since there is no preferred direction. Again using Wilson’s data as an example:

For the 2013 data set:

The gradient field is fit to the average vectors using linear least squares minimization for the x- and z-components. This produces estimates for c_x, c_z, x_0, and z_0. For the original vector field, if we are interested in the location where the average vector is smallest in magnitude (or the location where there is the least bias in terms of direction of the next pitch), we are limited by the fact that we are using a discretized domain and therefore can only have a minimum location at a small, finite number of points.

One advantage to this method is that it produces a minimum that comes from a continuous domain and so we will be able to get unique minimums for different pitchers. Another piece of information that can be gleaned from this approximation is the constants, c_x and c_z. If c_x is large in magnitude, there may be a large east-west dynamic to the pitcher’s subsequent pitch locations. For example, if a first pitch is in the left half of the strike zone, the next pitch may have a proclivity to be in the right half and vice versa. A similar statement can be made about c_z and north-south dynamics. Alternatively, if c_x is small in magnitude, then less information is available about the direction the next pitch will be headed. For Wilson, the constants obtained from the best fit approximation are a pitching sink of (-0.163,2.243) and scaling constants (-0.925,-1.055).

For C.J. Wilson’s 2013 season, we have the sink at (-0.109,2.307) and scaling constants (-0.902,-0.961), so the values are relatively close between these two seasons.

We can now obtain this set of parameters for a large collection of pitchers. For each pitcher, we can find the vector field based on the data and then find the associated gradient field approximation. We can then extract the scaling constants and the pitching sink. We can run this on the most recent complete season (2012, at the start of this research) for the 200 pitchers who threw the most pitches that year and look at the distribution of these parameters.

The sinks cluster in a region roughly between 1.75 and 2.75 feet vertically and -0.5 and 0.5 feet horizontally. This seems reasonable, since we would not expect this location to be near the edge or outside of the strike zone. Similarly, we can plot the scaling constants:

The scaling constants are distributed around a region of -1 to -0.8 vertically and -0.7 and -0.9 horizontally.

One problem that arises from this method is that since we are averaging the data, we are simplifying the analysis at the cost of losing information about the distribution of second pitches. Therefore, we can take a different approach to try to preserve that information. To do so, at a grid location, we can calculate several average vectors in different directions, instead of one, which will keep more of the original information from the data. This can be accomplished by dividing the area around a given square radially into eight slices and calculating the average in each octant.

However, since each nonempty square may contain anywhere from one to upwards of thirty plus pitches, using octants spreads the data too thin. To better populate the octants, we can find pitchers with similar data and add that to the sample. To do this, we will go back to the aforementioned average vectors and use them as a means of comparison. At a given square, with a pitcher in mind whose data we wish to add to, we can compute the average vector for a large collection of other pitchers, compare average vectors, and add the data from those pitchers whose vector is most similar to the pitcher of reference. In order to do this, we first need a metric. Luckily, we can borrow and adapt one available for comparing vector fields:

M(u,v) = w exp(-| ||u||-||v|| |) + (1-w) exp(-(1 – <u,v>/||u|| ||v||))

Here, u and v are vectors, and w is a weight for setting the importance of matching the vector magnitudes (left) and the vector directions (right). For the calculations to follow, we take w = 0.5. The term multiplied to w on the left is an exponential function where the argument is the negative of the absolute value of the difference in the vector magnitudes. Note that when ||u|| = ||v||, the term on the left reduces to w. As the magnitudes diverge, the term tends toward zero. The term multiplied to (1-w) is an exponential function with argument negative quantity 1 minus the dot product between u and v, divided by their magnitudes. When u and v have the same direction, <u,v>/||u|| ||v|| = 1, and the exponent as a whole is zero. When u and v are anti-parallel, <u,v>/||u|| ||v|| = -1 and the exponent is -2 so the term on (1-w) is exp(-2) which is approximately 0.135, which is close to zero. So when u = v, M(u,v) = 1 and when u and v are dissimilar in magnitude and/or direction, M(u,v) is closer to zero.

We now have a means of comparing the data from different pitchers to better populate our sample. To demonstrate this, we will again use C.J. Wilson’s data. First, we will run this method at a point near his sink: (-0.125,2.125). Since we will have up to eight vectors, we can fit an interpolating polynomial in between their heads to get an idea of what is happening for the full 360 degrees around the square. The choice of interpolating polynomial in this case will be a cubic spline function. This will give a smooth curve through the data without large oscillations. Working with only Wilson’s data, which is made up of 30 pitches, this looks like:

The vectors are spread out in terms of direction, but one vector which extends outside the lower-left quadrant of the plot leads to the cubic spline (light blue curve) bulging to the lower left of the strike zone. Otherwise, the cubic spline has some ebb and flow, but is of similar average distance all around.

When we remove the vectors and replace them with the average vector of each octant (red vectors), we have a better idea of where the next pitch might be headed. We also color-code the spline to keep the data about the frequency of the pitches in each octant. Red indicates areas where the most pitches were subsequently thrown and blue the least. We see that the vectors are longer to the left and, based on the heat map on the spline, more frequent. However, a few short or long vectors in areas that are otherwise data-deficient will greatly impact the results. Therefore, we will add to our sample by finding pitchers with similar data in the square. We will compute the value of M between Wilson at that square and the top 200 pitchers in terms of most pitches thrown for the same season.

For Wilson, the top five comparable pitchers in the square (-0.125,2.125), with the value of M in parentheses, are Liam Hendriks (0.995), Chris Young (0.986), A.J. Griffin (0.947), Kyle Kendrick (0.943), and Jonathan Sanchez (0.923). Recall that this considers both average vector length and direction. Adding this data to the sample increases its size to 94 pitches.

For this plot, the average vector (the blue vector in the center of the cell) is similar to that of Wilson’s solo data. However, since the number of pitches has essentially tripled, the plot has become hard to read. To get a better idea of what is going on, we can switch to the average vector per octant plot:

Examining this plot, most of the average vectors are in the range of 1-1.5 feet. The shape of the interpolation is square-like and seems to align near the edge of the strike zone, extending outside the zone, down and to the left.

We can also run this at points nearer to the edge of the strike zone. On the left side of the strike zone, we can work off of the square centered at (-0.875,2.375) (note that we drop the plots of the original data in lieu of the plots for the octants).

For the original sample, the dominant direction (where most of the vectors are pointed, indicated by the red part of the spline) is to the right, with an average distance of one to two feet in all directions. Now we will add in data based on the average vectors, increasing our sample from 15 to 97 pitches.

For the larger sample, the spline, which is almost circular, has average vectors approximately 1 to 1.5 feet in length. The preferred directions are to the right (into the strike zone) and downward (below the left edge of the strike zone). Also note that comparing the two plots, the vectors in the areas where there are the most pitches in the original sample (between three and six o’clock) have average vectors that retain a similar length and direction.

Switching sides of the strike zone, we can examine the data related the square centered at (0.875,2.375). For the original sample, the dominant direction is to the left with little to no data oriented to the right. Since there are octants that contain no data, we get a pinched area of the cubic spline. This is due to the choice of how to handle the empty octants. We choose to set the average distance to zero and the direction to the mean direction of the octant. This choice leads to pinching of the curve or cusps in these areas. Another choice would be to remove this octant from the sample and do the interpolation with the remaining nonempty octants.

Adding data to this sample increases it from 9 pitches to 67, and the average vector and spline jut out on the right side due to a handful of pitches oriented further in this direction (this is evident from the blue color of the spline). In the areas where most of the subsequent pitches are located, the spline sits near the left edge of the strike zone. Again, the average vectors in the red area of the spline maintain a similar length and direction.

Moving to the top of the strike zone, we choose the square centered at (0.125,3.375). The original plot for a square along the top contains 11 pitches and no second pitches are oriented upward. There are only have four non-zero vectors for the spline and the dominant direction is down and to the left.

In this square, the sample changes from 11 to 72 pitches by adding similar data. Note the cusp that occurs at the top since we are missing an average vector there. Unsurprisingly, at the top of the strike zone, the preferred direction for the subsequent pitch is downward, and as we rotate away from this direction, the number of pitches in each octant drops.

Finally, along the bottom of the strike zone, we choose (0.125,1.625). Starting with 27 pitches produces five average vectors, with the dominant direction being up and to the left.

With the additional data from other pitchers, the number of pitches moves up to 87. The direction with the most subsequent pitches is up and to the left. In areas where we have the most data in the original sample (the red spline areas), the average vectors and splines are most alike.

There are several obvious drawbacks to this method. For the model fitting, we have some points in the strike zone with 30+ pitches and as we move away from the strike zone, we have less and less data for computing the averages. However, as we move away, the general behavior becomes more predictable: the next pitch will likely be closer to the strike zone. So the small sample should have less of a negative effect for points far away. This is also a potential problem since we use these, in some cases, small samples to calculate the average vector in each square, which is used as a reference point for adding data to the sample. It may be better to use the vector from the gradient field for comparison since it relies on all of the available data to compute the average vector (provided the gradient field approach is a decent model).

Another problem is that in computing the average vector, we are not taking into account the distribution of the vectors. The same average vector can be formed from many different combination of vectors. However, based on the limited data presented above, adding to the sample, using M and the average vectors, does not seem to have a large effect on octants where there is the most data in the original sample. These regions, even with more data, tend to retain their shape. These are also the areas that are going to contribute most to the average vector that is used for comparison, so this seems like a reasonable result.

A smaller problem that shows up near the edge of the zone is that we still occasionally, even after adding more data, get directions with only one or two pieces of data and this causes some of the aberrant behavior seen in some of the plots, characterized by bulges in blue areas of the spline. One solution to this would be to only compute the average vector in that octant if there were more than some fixed number of pitches in that direction. Otherwise, we could set the average vector to zero and the direction to the mean direction in that octant.

Obviously, an analysis of one pitcher over a small collection of squares in the grid does not a theory make. It is possible to examine more pitchers, but because the analysis must be done visually, it will be slow and imprecise. Based on these limited results, there may be potential if the process can be condensed. The pitching sink approach gives an idea of where the next pitch may be headed. As we move toward the sink, we have less information on where the next pitch is headed since near this point, the directions will be somewhat evenly distributed. As we move toward the edge of the strike zone, we get a clearer picture of where the next pitch is headed if only for the reason that it seems unlikely that the next pitch will be even further away.

While this model seems reasonable in this case, there may be cases where a more general model is needed to fit with the behavior of the data. To recover more accurate information on the location of the next pitch, we can switch to the octant method. Since some areas with this method will have very small samples, we can pad out the data via comparison of the average vectors. This seems to do well at filling out the depleted octants and retains many of the features of the average vectors in the most populated octants of the original samples. At this point, both these models exist as novelties, but hopefully with a little more work and analysis, they can be improved and simplified.

The loss to the Pirates, the recent removal of Dusty Baker, and the upcoming free agency of Shin-Soo Choo has overshadowed Bronson Arroyo and his status with the Reds. It seems that if there is one player who never receives enough attention, it is him. But while the baseball world may not seem to realize that he is a free agent, there is no doubt that Walt Jocketty and his staff are very much aware of the 36 year-old starter’s expired contract.

Bronson Arroyo, with the exception of 2011, has been not only one of the Reds best starters, but one of the most consistent pitchers in baseball. He has not been a Cy Young candidate and he is not the ace of the Reds by any means. But the one thing that cannot be denied is his innings pitched per year. Since joining the Reds, he has thrown over 1600 innings and has averaged about 211.1 innings pitched per year. They have started to dip recently but throwing 202 innings each year of the past two seasons shows that despite the age, he still has his durability. He has managed to avoid the DL in his career which is something to be marveled at. Every year that he has pitched with the Reds, he has started at least 32 games and averaged 6-7 innings per start. This kind of reliability is something to be desired out of a starter in this day and age where there is at least one Tommy John surgery or one pitcher who is on a strict innings limit.

One of the things that allow Arroyo to be so durable is the fact that he does not waste his time out of the zone with his pitches. His goal is to go right at the hitters. This season, he was fifth in the majors in walks per nine with 1.51. During his tenure with the Reds (2006-2013), he has averaged 2.31 BB/9 which is good for 14th among pitchers who have thrown at least 1000 IP during that time frame. He seems to be trying to improve those numbers as his BB/9 has been 1.54 over the past two seasons. He indicates that he refuses to beat himself by giving up the free pass (which can help him out seeing as how does not strike out a lot of batters and he does tend to give up home runs).

Bronson Arroyo has made himself a very good pitcher due to great durability and his ability to change speeds when he pitches. Last season his fastball averaged 87 mph and his curveball averaged about 70 mph. The change of speeds helps him to keep most batters off balance because they have no idea what kind of speed is going to be released from his arm or what kind of arm slot the baseball is going to be thrown at. While watching a Reds game, one of the guests in the booth said that he would rather face a pitcher like Aroldis Chapman because he knows what speed and arm slot to expect most of the time. Chapman will throw his fastball about 85.4% of the time and his off-speed pitch (slider) about 14.6% of the time. Once the batter stands in the batter’s box, he can expect to see that heater for the majority of the time. Bronson Arroyo throws his fastball (or sinker) last season for 44.1% of the time. That is 55.9% of the time that he throws one of his 3 other off speed pitches that ranges anywhere from 70 mph to 77.6 mph.

Despite the fact that Arroyo is such a good pitcher, it is unlikely that he will return to the Reds. The Reds, I’m sure, would like nothing more than to have Bronson Arroyo return to their team. The problem is that the Reds are going to have a full rotation and none of the other pitchers are going to the bullpen any time soon. Tony Cingrani has emerged as a phenomenal young left-handed starter that has earned a starting spot. Homer Bailey and Mat Latos have proven to be durable aces that on their best day can match up with anyone and shut down the best of offenses even in Great American Ballpark. Mike Leake probably would have been sent to the bullpen to make room for Arroyo but because of the great bounce-back season that he had, he has re-solidified his spot in the rotation as well. Cueto could be an option to be sent to the bullpen because of his long list of injuries but it is true that when healthy, he is one of the best pitchers in the game. The Reds also have several very talented pitching prospects in the minors in Robert Stephenson, Daniel Corcino, and Nicholas Travieso who are just waiting for an excuse to be called up to the majors. And because of Arroyo’s proven track record it is almost a solid guarantee that he will not be sent to the bullpen.

If you take away anything from these past few paragraphs, it should be that Arroyo is a solid and dependable starter. Maybe on certain teams (I’m looking at you, Houston) he could be an ace but on most teams he will be a solid mid-bottom of the rotation starter for any team. His tendency to give up home runs could be cured in a more pitcher-friendly ballpark but it is unlikely that the problem will go away all together. He is a good pitcher who might get his 3 years, and 30+ million dollars somewhere but he will not find it in Cincinnati. Cincinnati is a mid-market team who is going to have to worry about signing up Homer Bailey, Mat Latos, and Tony Cingrani in the future and they have already spent a lot of money to keep Jay Bruce and Joey Votto locked up for the long haul. Their depth in pitchers allows them to look elsewhere for places on where to spend all of the money that they would have to spend in order to resign Arroyo. Perhaps they could use it to get La Russa out of retirement . . .