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: 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).

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.

wRC is a very useful statistic.  On the team level, it can be used to predict runs scored fairly accurately (r^2 of over .9).  It can also be used to measure how much a specific player has contributed to his team’s offensive production by measuring how many runs he has provided on offense.  But it is rarely used for pitchers.

Pitching statistics are not so much based on linear weights and wOBA as they are on defense-independent stats.  I think defense-independent stats are fine things to look at when evaluating players, and they can provide lots of information about how a pitcher really performed.  But while pitcher WAR is based off of FIP (at least on FanGraphs), RA9-WAR is also sometimes looked at.  Now, if the whole point of using linear weights for batters is to eliminate context and the production of teammates, then why not do the same for pitchers?  True, pitchers, especially starters, usually get themselves into bad situations, unlike hitters, who can’t control how many outs there are or who’s on base when they come up.  But oftentimes pitchers aren’t better in certain situations, as evidence by the inconsistency of stats such as LOB%.  So why not eliminate context from pitcher evaluations and look at how many runs they should have given up based on the hits, walks, and hit batters they allowed?

To do this, I needed to go over to Baseball-Reference, as FanGraphs doesn’t have easy-to-manipulate wOBA figures for pitchers.  Baseball-Reference doesn’t have any sort of wOBA stats, but what they do have is the raw numbers needed to calculate wOBA.  So I put them into Excel, and, with 50 IP as my minimum threshold, I calculated the wOBA allowed – and then converted that into wRC – for the 330 pitchers this year with at least 50 innings.

Next, I calculated wRC/9 the same way you would calculate ERA (or RA/9).  This would scale it very closely to ERA and RA/9, and give us a good sense for what each number actually means.  (The average wRC/9 with the pitchers I used was 3.95; the average RA/9 for the pitchers I used was 3.96).  What I found was that the extremes on both sides were way more extreme (you’ll see what I mean soon), but overall it correlated to RA/9 fairly closely (the r^2 was .803).

Now, for the actual numbers:

The first thing that jumps out right away is that Koji Uehara had a wRC/9 of 0.08.  In other words, if that was his ERA, he would give up one earned run in about 12 complete game starts if he were a starter, which is ridiculous.  The second thing that jumps out is that most of the top performers are relievers – in fact, 12 out of the top 13 had fewer than 80 innings, with the only exception being Clayton Kershaw.  Also, the worst pitchers by wRC/9 had a wRC/9 much higher than their ERA or RA/9.  Pedro Hernandez, for example, had a wRC/9 of 7.68, and there were 6 pitchers over 7.00.  Kershaw actually has a wRC/9 that is lower than his insane RA/9, so maybe he’s even better than his fielding-dependent stats give him credit for.

But wait!  There’s more!  The reason we have xFIP is because HR/FB rates are very unstable.  So let’s incorporate that into our wRC/9 formula and see what happens (we’ll call this one xwRC/9):

Not a huge difference, although we do see Uehara’s number go down, which is incredible, and Tanner Roark’s – the second-best pitcher by wRC/9 – nearly double.  Also, Tyler Cloyd becomes much worse, and is now the worst pitcher by almost half a run per nine innings.  Kershaw’s wRC/9 goes up by a considerable amount, so much so that his xwRC/9 is now higher than his RA/9.  All in all, however, xwRC/9 actually has a smaller correlation with RA/9 (an r^2 of .638) than wRC/9 does, so it isn’t as useful. 

Now, logically, the people who outperformed their wRC/9 the most would have high strand (LOB) rates, and vice-versa.  So let’s look at the ten players who both outperformed and underperformed their wRC/9 the most.  The ones who underperformed:

We can see that everyone here – except for Koji Uehara, who had the fourth-highest LOB% out of all pitchers with 50 innings – is below the league average of 73.5%.  Only Uehara and Joel Peralta are above 70%.  Clearly, a low LOB% makes you allow many more runs than you should.  But what about Koji Uehara?  How did he allow all those runs (10, yeah, not a lot, but his wRC/9 was way lower than his RA/9) without allowing many baserunners to score and not allowing many damaging hits?  If you know, let me know in the comments, because I have no idea.

Now for the people who outperformed their wRC/9:

Just what you would expect:  high LOB%’s from all of them (each is above the league average).  Stephen Fife and Alex Sanabia are the only ones below 80%.

So what does this tell us?  I think it’s a better way to evaluate pitchers than runs or earned runs allowed since it eliminates context:  a pitcher who lets up a home run, then a single, then three outs is not necessarily better than one who lets up a single, home run, then three outs, but the statistics will tell you he is.  It might not be as good as an evaluator as FIP, xFIP, or SIERA, but for a fielding-dependent statistic, it might be as good as you can find.

Note:  I don’t know why the pitchers with asterisks next to there name have them; I copied and pasted the stats from Baseball-Reference and didn’t bother going through and removing the asterisks.

In fantasy, the 5 categories are meant to evaluate the overall value of a pitcher, and players that are best able to predict future value can win serious jelly beans. A pitcher accumulates Ks by defeating individual batters, while a low WHIP indicates that he can avoid putting opposing players on base. ERA evaluates a pitcher’s run prevention skill. Saves and wins are meant to measure a pitcher’s ability to dominate opposing teams, whether for an inning or an entire game. However, wins compare poorly with quality starts and W+QS when correlated with commonly used pitching statistics.

The chart below shows the correlation between wins, quality starts, and the combination of the two with other commonly used pitcher evaluation metrics. By calculating the correlation between these 3 categories and other pitcher metrics such as FIP, OPS allowed, batting average against, homeruns allowed per 9 innings, and runs above average by the 24 base/out states (RE24), we can measure not only the relationship between the variables, but also how much they differ from each other.

None of these statistics correlate as well with wins as they do with quality starts and W+QS. In fact, the difference between QS and W+QS is negligible in every case. This result makes sense—since QS make up the majority of the W+QS total, the two are almost identical in the chart. The actual values of each correlation are less important that the overwhelming conclusion that wins do not have much to do with pitcher skill, while the difference between QS and W+QS is negligible.

 Why, then, might it be useful to use W+QS? These results show that it may not be very different from using quality starts, but is far more reliable way to judge a pitcher’s performance than wins alone. W+QS double count the games when a pitcher goes somewhat deep into a game, pitches fairly well (3 ER or less), and exits the game while leading his opponent. This scenario might not be much different than the QS by itself, but it does retain an element of “winning the ballgame for your team”, which is what the win category somewhat accurately captures. A winning pitcher is generally on a winning team, although that statement may not mean much.

W+QS may be an unnecessarily complicated way to repeat the same evaluation standards as quality starts, but some players may prefer it simply because it retains the W while relegating it to a position of less importance. Maybe owning a great pitcher like James Shields doesn’t have to be so frustrating after all.

Even as a fan of a different AL East team, seeing Manny Machado go down with a knee injury this Monday saddened me. Fortunately, reports indicate the injury is not as serious as originally feared, and Machado could return for spring training. Machado is part of a class of young stars that have simultaneously taken baseball by storm and wrecked the grading curve for everyone to come after them. People are already giving up on Jurickson Profar because he isn’t a star at an age when most players are in Low-A ball. Bryce Harper ranks in the top 20 in the MLB in wRC+ at the age of 20, and hardly anybody notices.  Anyways, I digress. So where does Machado’s age-20 season rank?

Machado compiled 6.2 WAR in 2013, good for 10th in the MLB. In the last 55 years, only Alex Rodriguez in 1996 and Mike Trout in 2012 have posted a higher WAR in their age-20 season. Of course, there were some better seasons before then, but Machado probably wouldn’t have been allowed to play in those days.

Unlike Rodriguez and Trout, Machado’s offensive numbers, while impressive for a 20 year-old are league average overall. A-rod had a 159 wRC+ in ’96, and Trout had a 166 wRC+ last year. Machado managed a 101 wRC+, providing most of his value with the glove. UZR credited him with 31 runs saved, best in the majors. After a very hot start that was fueled by an inflated BABIP, Machado slowed down.

So what can Orioles fans expect from Machado going forward?

Machado is an aggressive contact hitter. His walk rate of 4.1% is one of the lowest in the MLB, and his strikeout rate of 15.9% is well below the MLB average. While Machado will never be Joey Votto, the walk rate will improve as he matures. His minor league walk rate was above 10%. Additionally, Machado should hit for more power. I could just say that he hit 51 doubles and those will turn into home runs. But, that would be lazy, and doubles don’t always turn into home runs as a player develops. Sometimes they turn into singles. Just ask Nick Markakis.

However, there are other reasons to believe Machado will hit for power. First of all, he has excellent bat speed, and there’s no lack of raw power. Some of the home runs he has hit are very impressive. Of the 14, ESPN Home Run Tracker classifies 10 of them as either No Doubters or Plenty.  The average speed off the bat was just a shade behind Robinson Cano. Furthermore, despite playing in one of the best home run ballparks in the league, and having an average fly ball distance on par with Nick Swisher, Machado’s HR/FB ratio of 7.9% is in the bottom third of the MLB. Bet on this ratio improving. While he does have a very high rate of infield flies (9th in MLB), he should be able to bring that down with improved discipline.

Hopefully for Orioles fans and baseball fans, Machado will have a complete recovery from his knee injury. It might be hard to live up to expectations after producing a 6.2 WAR season at age 20, but with improved offense Machado could be up to the task. Expect the plate discipline and power to improve, as the defense inevitably regresses from a season that stretched the upper bounds of UZR. It’s a very small group he’s in, but star players at age 20 tend to be stars at 25.

Throughout the pre-sabermetric revolution days of baseball, the statistics that determine fielding ability (namely errors and fielding percentage) had generated much criticism of fielding stats and undeserving gold glove award winners (Derek Jeter et al), and had kept fielding ability a mystery. However, this mystery in part led to the sabermetric revolution in baseball statistics. In the current day and age, with improved measures of performance available publicly, measuring fielding ability is somewhat less of an enigma, but still far from perfect.

One of the most often used fielding metrics in this day and age is UZR or Ultimate Zone Rating (click the link for an excellent FanGraphs explanation). Instead of counting perceived plays and errors, UZR records every batted ball hit to each of the numerous zones on the baseball field at each trajectory and the runs lost/saved as the fielder gets to the ball or falls short. This is found by matching the average result of the play with the Run Expectancy Matrix. Therefore, UZR provides a very accurate measure of how valuable that fielder was in terms of runs saved/lost over the course of the season.

However, there are major problems with UZR. Sample size issues cause large fluctuations from month to month and even year to year. Moreover, it does not provide a stable basis of fielding ability. Even when all players’ impacts are averaged to a constant, UZR/150, averaged to runs saved/lost per 150 defensive games, the metric is very volatile.

The reasons behind this might actually be easier to identify and correct than you might think. Let’s face it: not all fielders get the same amount of balls hit to them in the same place at the same trajectory within the same number of outs or innings. Infielders with a good knuckleballer on the mound and a slap hitter at the plate are going to get more grounders to each zone than infielders whose teams have fly ball pitchers on the mound and face lots of power hitters at the plate.

However, while the actual amounts may fluctuate from pitcher to pitcher and hitter to hitter, many fielders get a decent sample size of each batted ball to each zone over the course of multiple seasons. Even with a staff of fly ball pitchers, infielders will still handle their fair share of ground balls to each zone over the course of a season. So if there was a way to average all the pitchers and hitters together and measure the value and frequency of making a play in each zone based on the entire AL, NL, or MLB* average batted ball chart, then we could create a similar metric that would be more predictive, rather than purely descriptive.

*The purpose of separating the leagues is the discrepancy of hitting ability with the DH in the AL and the increased frequency of bunts (from pitchers) in the NL.

If we take the average percentage of batted balls to each zone with each trajectory for the AL, NL, or MLB and multiply that by the average runs saved/lost for plays made or missed in that zone, we can find a universal batted ball sample from which to apply the fielders’ impact. While this would not be directly proportional to the runs saved/lost for the fielder during that season for that pitching staff and the batters faced, it would be a metric independent of the impact that the pitcher and hitter has on the fielders. It would measure pure fielding ability over multiple seasons in the form of runs saved, but unbiased by the specific ratio of batted balls per zone and trajectory hit to the fielder over the seasons.

Predictive UZR will have sample size issues but when taken over multiple seasons, a starting fielder should get his fair share of batted balls hit to each zone with each trajectory. The percentages for his success rates at each zone and trajectory can then be applied not to the actual ratio of batted balls per zone hit his way (from his team’s pitching staff and hitters faced) but rather the average ratio of batted balls per zone hit in the entire AL, NL, or MLB.

Both UZR and Predictive UZR are very valuable for different things. UZR is a good reflection of the fielder’s direct impact on defense for the season. However, this might not accurately reflect the fielder’s true talent level because of the assortment of batted balls hit his way. Predictive UZR, while not a concrete reflection of the past runs saved, is a more pure measure of fielding ability. It can provide a number that, when compared to UZR, tells which fielder got lucky and which fielder did not, based on his pitching staff and the hitters faced. Another interesting twist the concept of Predictive UZR brings is that it can be based on the average batted ball chart of teams, divisions, and differing pitching staffs in addition to the AL, NL, or MLB. So a fielder’s projected direct impact, or UZR, can be transferred more easily as he moves from team to team, forming the basis of more accurate fielding projections.

Predictive UZR is not by any means a substitute to UZR, but rather complements it and works with it in intriguing ways. It is a concept worth looking into that has the potential to leave fans, media and front office personnel better informed about the game of baseball.

Nik Oza
Georgetown Class of 2016
Follow GSABR on twitter: @GtownSports

This is part two of a three-part series detailing a method of judging pitch framing based on the prior probability of the pitch being called a strike.  In part 1, we motivated the method.  Here in part 2, we will formalize it.

The formula we’ll use for judging catcher framing is pretty simple on its face. For each pitch delivered, we calculate a value

IsCalledStrike + prob(CalledStrike)

Here, IsCalledStrike is simply 1 if the pitch is called a strike, and 0 otherwise.  The second term is the probability that the pitch would have been called a strike, absent any information about the catcher’s involvement. We add up these values for every called ball or strike that a catcher receives, and report the resulting number.  Since this method is essentially identical to defensive plus/minus, I’ve taken to calling it Catcher Plus/Minus (CPM), although someone reading this can probably come up with something better.  I should mention the following: it has been brought to my attention that this method has been developed before.  However, I can’t find it written up anywhere on the web.  So you are welcome to consider this the documentation of an existing method, if you’d like.

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