Coming into the year, the Boston Red Sox were riding high after the 2013 title in which they’d gone from worst to first. Just about everyone with a worthwhile opinion thought that’d they at least be in contention for the playoffs again this year, and it wasn’t uncommon to see people picking them to repeat in 2014.

One of the few questions people did have about the team was how would they integrate their two young players, Jackie Bradley, Jr. and Xander Bogaerts, in their first full seasons as starters. Of these two players, Bradley was the one that people seemed most concerned about. This made sense, since he was less regarded as a prospect than Bogaerts (number 2 overall on most prospect top 100 lists). But while Bradley has been a complete zero with the stick (57 wRC+), his defense has carried him to 1.5 fWAR so far this season. Bogaerts, on the other hand, has a wRC+ of 82, which combined with mediocre defense has left him hovering around replacement level.

Now, there’s no doubt that people are disappointed by Bogaerts’ season, and they have every right to be. Bogaerts was hyped as the rare prospect with superior skills and a significant amount of polish, and he showed why when he played like a veteran down the stretch in last year’s playoffs. Nobody was expecting him to be replicate Mike Trout’s rookie season, but a league average regular was probably a reasonable expectation. Obviously Bogaerts has underperformed relative to that standard.

Guys like Trout, Yasiel Puig and Manny Machado have essentially ruined the kind of expectations we now put on guys going through their first full seasons. Do you know how many batting-title-qualified rookies have had an OPS lower than Bogaerts’ current .650? 311! And of that 311, 283 of them were older than Bogaerts’ current 21 years of age. Bogaerts is struggling, but that’s what rookies do. There’s no greater jump in professional baseball than the one to the majors.

Bogaerts is actually hitting pretty well against fastballs and changeups. The crux of his issues this year have been against breaking balls. And there’s really no way to sugarcoat it. He’s been terrible against any and all spin, hitting just .143 and slugging .167. Unfortunately, opposing pitchers have noticed, and Bogaerts has only seen more breaking balls as the season has progressed.

As the rate of breaking balls has gone up against Bogaerts, his numbers have gone down. The Red Sox shortstop was actually a well above average hitter heading into June (119 wRC+ in March/April, 149 wRC+ in May), but then everything fell apart. Bogaerts posted an almost unthinkable .426 OPS in June, a number less than half (.897) of what he posted the month before. He followed that up with a much improved, but still terrible July (.595 OPS) and continued to struggle in August.

Bogaerts’ struggles with breaking balls coincide with the part of his game that has perhaps regressed the most as his season has progressed: his plate discipline. After working 25 walks through the end of May, Bogaerts has been told to take his base just seven times since. A large part of that has been the decline of his ability to discriminate between a breaking ball thrown for a strike, and one thrown for a ball.

As you can see in the graph above, Bogaerts has stayed fairly steady against fastballs and changeups, but his ability to recognize breaking balls has completely melted away. As for why this has happened, that’s difficult to say. Maybe Bogaerts has always struggled against breaking pitches. But the most likely answer is that he’s a rookie struggling to adjust against pitchers capable of taking advantage of his weaknesses. Nevertheless, it’s at least been a prolonged slump, and one that Red Sox fans have to hope isn’t a glimpse into continual struggles for their youngest player.

Then, putting aside things that we can actually measure, there’s the possibility that Bogaerts is simply in his own head right now. As a ballplayer, he’d probably tell you he’s trying to do too much. There’s certainly something to that side of the argument. It can’t be easy to fail so spectacularly after being hyped as the next face of one of the most prestigious franchises in the game.

There’s also an argument to be made that some responsibility for Bogaerts’ struggles can be set at the feet of his manager, John Ferrell. There have been rumors that Ferrell was the person in the organization pushing the hardest for the Red Sox to resign Drew, which they ultimately did in late May. Drew, who had never played any position but shortstop in his big league career at that time, would be forcing Bogaerts over to third base, the position he played down the stretch of the 2013 title run. Bogaerts expressed some disappointment at time as a result, and an argument can be made that the team’s decision to resign Drew shook his confidence. Before Drew joined the lineup on June 2nd, Bogaerts was batting .296/.389/.427. Since then he’s hit .169/.201/.279. You might say that those dates are arbitrary and coincidental, and you can make of them as you wish. I will say that confidence is a huge part of succeeding in this game, and it should not be overlooked.

Overall, Bogaerts probably won’t look like he belongs back in AA forever, though we may have to wait until 2015 to see the player we were all hoping for. We got that player in the first couple months of this season, but pitchers’ adjustments, along with Bogaerts lack of adjustment to those adjustments, have torpedoed what was initially a very promising rookie year. That said, young players with Bogaerts pedigree and polish often turn into solid players at the very least, and I’m still as excited as ever about his career going forward. He’ll figure it out.

Does Troy Tulowitzki suffer without Carlos Gonzalez in the lineup?

Several weeks ago, in the same way my last article on rookie first and second half splits was inspired, my attention was alerted when a podcast personality contrived that Troy Tulowitzki, before his most recent bout with the injury bug, had performed poorly because Carlos Gonzalez had been out of the lineup.

The pundit grabbed the lowest handing fruit he could find in an effort to create a narrative, and a dogmatic one at that, as to why the Colorado Rockies slugger had not lived up to his pre All-Star break numbers.

******* *******’s (I’d prefer the article to be more about the subject of Tulowitzki and Gonzalez than the podcast member) argument was that without Carlos Gonzalez in the lineup, pitchers could approach Tulowitzki without fear, give him less strikes, and that is why his hitting has declined.

While this pundit surmised that Troy Tulowitzki’s performance declines when Carlos Gonzalez is out of the lineup, the numbers tell a much different story.

While we will look at the more direct numbers in a moment, the idea that Tulowitzki plays worse without Gonzalez is essentially the idea of lineup protection at a micro level. There have been countless instances that have debunked the idea of lineup protection, and, to my knowledge, none that have proved its existence.

The research looked at all games from 2010—Carlos Gonzalez’ first complete season—to today.

The results paint a much lighter picture than the Guernica that ******* ******* painted.

In games where Tulo has played without Cargo, he has had a higher AVG, OBP, OPS, and BB%. One might think that Tulowitzki would continue his normal performance without Carlos Gonzalez in the lineup, but, as this information suggests, it is hard to imagine that Tulo plays better because Carlos Gonzalez is not in the lineup, which leads me to believe what one would normally think about out of the ordinary performances in a small amount of at bats.

The utility of these results should be used for descriptive, and not predictive, purposes. Troy Tulowitzki has only had 479 plate appearances without Carlos Gonzalez, and that is far from a large enough sample size to be deemed reliable.

But because of the recent remarks made by Tulowitzki, it seems like it will be more likely than not that sooner rather than later we will see a large enough of a sample size of Tulo in another uniform to see if this trend continues.

While Tulo has played worse and is hurt as of late, we might expect that it is because he was unlikely to live up to the performance he had in the first half, and not because of Cargo’s presence or lack thereof in the lineup. Over the course of the first half of the season, Tulowitzki’s posted the 15^th best OPS in a half of a season since 2010.

Tulo’s latest play suggests a regression to the mean, and while we are powerless to know exactly why regression happens, some pundits proclaim to know the reason (i.e. Tulo plays worse without Carlos Gonzalez), when really their specious statement is noise with a coat of eloquent words painted upon it.

When the next “expert” tells you that Tulo has preformed poorly, because “ he wants out of Colorado” or  “he wants to be traded”, you’ll know to be more skeptical and not passively agree.

If he gets healthy at some point this season, we should expect Tulowitzki to perform close to his projections in all areas for the rest of the year, and it will be with or without Carlos Gonzalez, not because of him.

When Spring Training rolled around the Yankees had one the better rotations in baseball on paper. CC Sabathia lost weight, Huroki Kuroda was back for another season, Ivan Nova was poised for a breakout and they had two new big additions to the staff. Masahiro Tanaka was fresh off setting records in Japan and signing a massive contract and Michael Pineda was healthy and finally ready to contribute. However, at this point in the season Kuroda is the only one who remains from that highly touted staff. Nova and Sabathia have suffered season ending injuries with Tanaka out since the All-Star break and his rest of season and possibly even 2015 season in question. Pineda is currently on a rehab stint and could rejoin the rotation as soon as Wednesday after missing most of the season to this point with a multitude of injuries.

However, despite all of these injuries Brian Cashman has made a few minor moves and some strategic callups to help build what has become a very successful rotation. Kuroda has still remained part of the rotation with Cashman adding Brandon McCarthy and Chris Capuano and calling up pitchers like Shane Greene and Chase Whitley. David Phelps had also joined the rotation replacing the injured starters yet he himself has also gotten injured and found himself on the disabled list. They also added Esmil Rodgers who in a spot start on Friday pitched well earning himself a win and potentially another start until Pineda returns.

The question remains though although this rotation has been extremely successful to this point can they maintain the success enough to carry the Bronx Bombers to the playoffs? The Yankees currently sit six games out of first in the division while also trailing in the race for the second wild card spot by 1.5 games need to the rotation to pitch well in order to make a run at October.

As of right now the four guys poised to remain in the rotation for the foreseeable future are Kuroda, McCarthy, Capuano, and Greene with the fifth spot likely being Pineda’s when he returns, likely in the next two weeks.

Kuroda has pitched much like the Yankees had expected of him throwing to a 3.97 ERA, which is slightly above his 3.46 career ERA, but it is an anticipated regression for a pitcher in his age 39 season. For his career Kuroda although he has thrown less innings had been a better second half pitcher (3.52 ERA vs 3.39) and this season the trend has continued with Kuroda throwing to a 4.10 ERA in the first half and he has a 3.42 ERA so far in the second half. The Yankees have tried to limit the aging Kuroda’s pitch count and innings so far this season wanted to ensure the right hander was stronger down the stretch run as Kuroda faded in 2013 late in the season. If Kuroda figures to maintain his career splits and pitch better in the second half he should be able to maintain his success to this point in the season and be the pitcher he was expected to be early on in the season.

The two minor trades that Cashman made before the trade deadline are also going to factor into the Yankees postseason chances. Thus far McCarthy and Capuano have been huge for the Yankees pitching to a 2.21 and 2.84 ERA respectably over 9 starts combined and have a combined 5-1 record in those 9 starts. So far over his 36 innings as a Yankee McCarthy is pitching much better than his career averages in K/9, BB/9, and HR/9. He has faced 155 batters as a Yankee meaning only his K rate has stabilized (70 BF). Thus the other two statistics especially his HR rate which is currently at .74 is much improved compared to his career 1.03. The improved HR rate is likely what has caused his vast success to this point, and pitching down the stretch in the power-hitting AL East and in Yankee Stadium, chances are this will regress back to his career averages and McCarthy will once again be a back-of-the-rotation starter, as opposed to the ace he has been for the Yankees so far since the trade.

Although Capuano’s sample size has been smaller than McCarthy’s his success has been similar. According to career averages Capuano is striking out around a half batter more per nine and walking about a half batter less. Those don’t account for the increase in success he’s had. So far in 19 innings in New York Capuano has yet to allow a home run. However, looking back at his time earlier this season with the Red Sox his season HR/9 is at .53 significantly lower than his career 1.20. Unless at the age of 35 and in his 10^th season Capuano has magically figured out the secret to keeping the ball in the ballpark he will likely regress back and beginning pitching more like he has in the past with his ERA moving back into the range of his xFIP which currently sits at 3.35 as a Yankee and 4.07 for his career.

Lastly, that leaves the rookie revelation that has been Shane Greene. As Eno Sarris points out, looking at Greene’s pitch mix gives him a few good comps of successful major-league starting pitchers. However, Greene’s minor league track record did not signal anything similar to this type of success he’s had since being called up. However, there is room for excitement as Greene has posted the lowest K/9 rate since his call up than he did at any point in his minor league career meaning that rate could see an increase. Also, his walk rate seems to be on par with his minor-league record, especially when looking at his numbers over 2013 and the first half of 2014.

Where Greene has succeeded in the big leagues has been with his ability to limit BABIP (.268) and his low HR/9 numbers. Throughout his minor-league career the highest HR/9 Greene posted at any stop was in rookie ball when he posted a .79 rate over 23 innings. Thus far in 37 big league innings Green’s HR/9 has been .72. He has a track record of being very successful at keeping the ball in the ballpark. However, what remains to be seen is if his BABIP comes back down to Earth and his K rate remains low. If he doesn’t retain the ability to strike batters out like he did in the minors and regresses to his minor-league BABIP numbers — only one stop lower than .330 — Greene figures to regress to the below-average pitcher he was in the minors

Over the last month the Yankees’ makeshift rotation has been keeping them alive in the playoff race. However, looking at each member of their rotation, there is reason believe that significant regression is coming with Kuroda being the only one performing near his career averages. Unless each of these arms continues this unprecedented success or Pineda and potentially although unlikely Tanaka return and pick up right where they left off it doesn’t seem like this current Yankee rotation has what it takes to reach the playoffs.

Big-league teams today employ a myriad of data-driven strategies to eek every last drop of value from the players on their rosters. Many of these strategies consist of matching up hitters and pitchers based on their handedness. Between lineup platoons and highly-specialized bullpens, managers today go to great lengths to ensure they’re putting their players in the best possible situation to succeed.

It’s easy to see why. With very few exceptions, Major League hitters hit much better against opposite-handed pitching. In terms of wOBA (vs. opposite-handed – vs. same-handed), lefties perform about .031 better against righties, while righties hit .043 better against lefties. Yet not all platoon splits are created equal. Players like Shin-Soo Choo, David Wright, and Jonny Gomes are notorious for their drastic splits, while others put up comparable numbers no matter who’s on the mound. Ichiro Suzuki and Alex Rodriguez are a couple of the no-platoon-split poster boys.

Ok, so some batters have bigger platoon splits than others, but is there any particular reason for this? Take Choo for example. Is there something inherent to his skill set or approach that causes him to struggle against lefties?

Hoping to find an answer, I ran some regressions in search of attributes that might make a player more likely to have an exaggerated platoon split. I tested all sorts of things out there — from walk rate and swing% to a player’s height and throwing arm — but didn’t come away with much. Aside from a hitter’s handedness, attributes that proved statistically significant included: a hitter’s overall wOBA, his line drive rate, his strikeout rate, and his contact rate on pitches out of the zone, but even those relationships are extremely weak. It takes .100 points on a batter’s wOBA, or a 10% increase in K% or LD%, to move a batter’s platoon split by just .010 points. This tells us something, but not a ton, and at the end of the day, these variables account for a nearly negligible 4% of the variation in hitters’ platoon splits. Here’s the resulting R output. My sample included all batter seasons from 2007-2013 with at least 100 plate appearances against both lefties and righties, excluding switch hitters:

Good hitters or guys who strike out frequently might be a little more prone to having large platoon splits. But for all practical purposes, a player’s ability to hit one type of pitching better than the other seems to be a skill that’s independent of all others. Aside from going by a player’s platoon stats, which can take years to become reliable, there’s little we can do to anticipate which hitters might fare particularly bad against same-handed pitching. And with the exception of players with long track records of unusual platoon splits — like Choo and Ichiro — it’s generally safe to assume that any given hitter’s true-talent platoon split is within shouting distance of the average: .043 for lefties and .031 for righties.

In the off season I wrote about how Manny Machado’s 2013 second-half struggles lied in his inability to select pitches he could hit. Essentially, his innate ability to get bat to ball combined with a poor understanding of knowing which pitches he could drive led to him swinging and making contact on pitches he could not barrel up. This led to an increase in fly balls – especially infield fly balls – which indicate poor contact is being made. Machado was swinging at junk and this caused his batting average and extra base hit production to plummet in the second half of 2013.

Fast forward to now, and Machado has been hitting .301/.340/.494 for the last two months after a cold start coming off of knee surgery. He has a .193 ISO during that time period as well as a 24.3% line drive rate. He certainly has been barreling up the ball for the last two months and has been one of the only Orioles hitters  doing so since the All Star break. Therefore, I wanted to see if Machado has changed his approach in any meaningful way and has learned to be selectively aggressive. Meaning, while he still is never going to be an on base machine, he can still be patient enough to wait on pitches he knows he can hit and hit well rather than making contact on pitches he cannot hit well.

Looking into his basic 2014 plate discipline numbers, interestingly, reveals little to no positive change from 2013. He is swinging more at pitches in the zone and out of the zone. He has an O-Swing% of 32.8%, a Z-Swing% of 68.6% and an overall swing% of 49.9% all of which are two to three percentage points higher than last year. Furthermore, he is making less contact on pitches in and out of the zone. His O-Contact% is 63.5% and his Z-Contact% is 85.4% alongside an overall contact% of 77.9% all of which are three to four points lower than last season. If Manny was swinging and barreling up better pitches to hit his swing rate may be the same, but he should not be swinging at pitches out of the zone more often. Furthermore, his contact rate would be higher especially on pitches in the zone, which it is not. Also, his swinging strike rate is up and his pitches seen in the zone are down. So, if those numbers are not showing why Manny is being more successful to date this year, then either there is another reason or it has simply been luck so far.

A quick look at some other figures tells a slightly different story.  His walk rate is nearly two points higher to date this season and his pitches per plate appearance is up from 3.53 P/PA to 3.68 P/PA. While that may not seem like an astronomical increase, it is significant. Manny had 710 plate appearances last season, if he had this season’s rate of P/PA he would have seen 106.5 more pitches last year. Therefore, his increasing strikeout rate is not surprising simply because he is seeing more pitches. He also is not striking out at an absurdly high rate to begin with, only slightly above 2014 league average. Basically, Machado is seeing more pitches this year than last, and this has led to a higher walk rate and a higher strike out rate.  This, however, does not quite prove the theory of selective aggression that I am purporting.

Using heat maps, this theory can truly be put to the test. Manny may be swinging slightly more and making a little less contact, but what matters here is whether or not he is swinging at good pitches for him to hit, which his recent numbers and line drive rate would suggest he is doing. Below are two heat maps. One is of Manny’s 2013 season swing rates by pitch location, the whole season, and the second one is his 2014 season swing rates by pitch location to date.

Of note, Manny Machado thus far in 2014 has swung significantly less at pitches out of the zone that are down and away, down and in, and up and in.  Also, he has focused on swinging at pitches that are middle in, middle, down, middle up, and even up and away. This allows him to extend his arms and drive the ball, especially the other way. In 2013, Manny focused much more on pitches in the middle of the plate and up and in. The swings at pitches that are up and in especially, and the other problem areas as well, zapped his ability to make solid contact and nosedived his 2013 offensive production.

Next up in this what is turning more and more into a slideshow are contact rate heat maps for 2013 (first picture) and to date in 2014 (second picture).

Manny seemed to make much more contact on pitches inside and outside the strike zone in 2013.  In particular, he made contact at a much higher rate on pitches up and in, down and in, and up and away. These are pitches that Manny simply cannot drive well, which means that if he is making contact with these pitches they are most likely to be outs, which in turn led to his struggles in the second half of 2013.  In 2014 his contact rates are much more concentrated within the strike zone and specifically middle in, down, and up. He is still making lots of contact on pitches too far up and away and down and away, but much lower than he was in 2014. This minimizes the bad contact and allows him to see more pitches that he can make hard contact on.

To bring it all home, below are two more heat maps. These heat maps are Manny’s batting average by pitch location again for the entirety of the 2013 season and the 2014 season to date. Again, the first one will be 2013 and the second one will be 2014.

These heat maps reveal more about how Manny’s approach at the plate has transformed. In 2013, the averages were decently high all around the plate and even out of the zone. However, this is not necessarily a great thing. Manny was swinging at pitches wherever they may be and his average was not great in many of those pitch locations. Fast forward to 2014, and the hitting zones are much more concentrated and with higher batting averages. The section that is middle in Manny is hitting .242 on pitches thrown to that location and is swinging 82% of the time at pitches in that location, tied for highest of any spot on his 2014 swing map.  He is swinging and driving pitches that are middle in, up, and down. He can drive the ball by extending his arms on up and away pitches and he can pull his arms tight to either pull the middle pitches or inside out them to center field or right field. These are the pitch locations that Manny can hit and hit hard and he is swinging more at those pitches than he was in 2013.

The adjustments made to Machado’s plate discipline provide a selective aggression that make him a better batter. As stated before, he is unlikely to become an on base machine. But, Manny has shown that he can hit doubles and home runs. If he maintains a higher average and his selectively aggressive eye at the plate he can continue to be an all star level player for the Orioles. Time will tell how pitchers adjust and how he adjusts, but the developments this year over last provide a great picture into Machado’s ability to adapt and thrive.

This post was originally posted to www.Orioles-Nation.com on 8/8/2014

Many are questioning the thought process behind Ruben Amaro Jr. standing pat at the non-waiver trade deadline.  The Phillies have a lot of veterans under fairly large contracts.  According to Philly.com, when asked about why he didn’t move some of his veterans, Amaro stated

“In this day and age, I think one of the most over-coveted elements of baseball are prospects,” Amaro said. “I don’t know how many prospects that have been dealt over the last several years have really come to bite people in the a**. I think what’s happened is, I think teams are really kind of overvaluing in some regards.”

I thought it would be fun to actually go back and see how many prospects or minor league players who were traded at the deadline panned out.  I went back to 2005 and used every single transaction that involved both an MLB player and a prospect (I considered a prospect a guy who had never been in the MLB, or a guy who had been in the MLB but had yet to achieve rookie status).  I also strictly used trades that were done on July 31, in each year from 2005-2011.  I skipped 2012 and 2013 because it’s harder to get a gauge on whether or not prospects traded will make it or have any success.  Also, from 2011 until now, prospects have had about three years to get to the big leagues and I felt that was a good place to end. 

There were 53 transactions in that time, some very minor, some very major, and some in between. I took each transaction and compiled each player’s WAR after the trade (WARAT).  I still applied this criteria if there was a player who was traded on two different July 31s.  For example, Jake Peavy was traded twice, so his WARAT will be different from one trade to the next.  Some players appear as prospects and MLB guys as well, like Jarrod Saltalamacchia, who was traded as a prospect, and later on once he was not considered a rookie anymore.

I will look at the percentage of prospects that never made it, the percentage that made it but provided negative WAR, and the percentage that made it and provided positive WAR.  I will then look at the MLB guys who were traded and the percentage of guys who provided positive and negative WAR for the remainder of their careers.

The data I found was very interesting.  There were 85 “prospects” traded and 66 MLB guys traded. Below is a table with each trade.  In parenthesis, I noted whether each player was a prospect (P) or an MLB guy at the time.  I will then have their WARAT, or WAR after trade.  If a prospect never made it to the show, I use the abbreviation “NMI.”

 As you can see, some trades worked out better than others.  Of the 85 prospects, 72.9% of them (62) made it to the big leagues.  So, that means 23 prospects, or 27.1% of those traded, never stepped on a big league field.  Of the 62 that made it, 32 were good for positive WAR after the trade, 21 were worth negative WAR, and 9 were at 0 WAR. The WAR of all the prospects that made it adds up to 97.8.  That’s an average of about 1.2 WAR per prospect. 

Now we can analyze the MLB guys. There is a wide variety of age in the group of 66 MLB players.  Some were traded fairly early in their MLB careers; some were traded as their career was winding down.  I found that 69.6% of these players (46) were good for positive WAR after they were traded.  19 players (28.7%) were worth negative WAR, and 1 player was worth zero WAR after the trade. When you add their WAR together, you get 178.8, averaging 2.7 WAR per MLB player traded.

So, on average, teams were trading an MLB guy that would be worth 2.7 WAR for the rest of their career, for a prospect that would turn out to be worth 1.2 WAR in that same time period.

In addition, if you add up the total WARAT for each individual trade, the MLB player’s WARAT was higher than the prospect’s WARAT in 32 of the 53 trades (60.3%).  The prospect’s WARAT was higher in 17 of 53 trades (32%).  Finally, there were three trades that cancelled each other out, and were neutral.

There are many ways to look at this and some things to keep in mind.  It may seem like trading an established big leaguer is not smart from these numbers.  However, it depends on the situation a team is in.  Also, most of these “prospects” have yet to finish their MLB careers, so they are still in the process of racking up WAR. Good examples include Kluber, Masterson, Moss, Murphy, Andrus, Davis, and Feliz. On the other hand, some of the MLB guys were traded when they were still pretty young.  Saltalamacchia, Martinez, Teixeira and Encarnacion are examples, but they are still older than most right now.  These guys are providing most of the WARAT for the MLB guys. Also, some of the MLB guys were so old that they only lasted another couple years in the MLB. 

You have to take money into account as well.  For some trades, teams are not only getting prospects in return, but they’re dumping salary and now have money they could spend elsewhere in the off-season. One example of a trade that worked out really well for one team and not so well for another was the huge Braves-Rangers trade.  The Braves received Mark Teixeira, and traded four prospects that have all turned out well.  Teixeira was great for Atlanta, but was only there for half of 2007 and half of 2008, with the Braves not even advancing to the postseason with him.  The Rangers however, got guys who helped the Rangers reach the World Series in 2010 and 2011.  Be careful with the prospects you trade away.

Since I am relating this article to Ruben Amaro Jr., I will connect this data to the Phillies’ current situation.  The evidence shows it probably would have been smart for them to move their older, more expensive players for prospects, even if they aren’t considered top prospects.  Amaro stated that he doesn’t know how many prospects in past years have come back to bite teams.  Yes, not every prospect is going to pan out.  And yes, some of them could come back to bite.  However, as mentioned before, over 70% of prospects dealt at the deadline from 2005-2011 at least made it to the major leagues.  There is also a good chance that most prospects that make it will contribute positive WAR.  That’s a pretty good turnout. Hamels, Utley, Rollins, Papelbon, Howard, Burnett, and Byrd will all be north of 30 years old next year, with some over 35.  So, they do not have young guys who are already established, like Martinez, Encarnacion, and Teixeira like I talked about earlier.  They are old.  The current Phillies team has proven it’s not going to win, so why wouldn’t they trade off some of their assets, and take a chance on some prospects panning out, while at the same time free up money for future off-seasons? They are not going to win in 2015 or 2016 most likely, so even if their current players still provide positive WAR in the next two years, what’s the point in keeping them around?  Go out and completely reload and blow the roster up.  With the amount of guys they could trade, or could have traded, you’re bound to have some of the prospects you get in return pan out, as the data above suggests.  Stock up the minor league system, and take the hit at the major league level for a couple years.  Add that to the money they will be saving, and they will be well-equipped to contend in three years.

Prospects are not “over-coveted” in baseball.  The problem for Amaro and the Phillies is that they do not have the right people in charge of evaluating and developing prospects.  They have traded for prospects in the past, such as the Pence and Victorino trades in 2012 (not included above) and have not gotten good returns.  So, maybe Ruben Amaro Jr. just isn’t very good at what he does, and wants to believe that giving up major-league veterans for prospects when your team is completely out of it is not a good idea.

Over the last few weeks, I have written a series of posts looking into how a player’s stats, age, and prospect status can be used to predict whether he’ll ever play in the majors. I analyzed hitters in Rookie leagues, Short-Season A, Low-A, High-A, Double-A, and Triple-A using a methodology that I named KATOH (after Yankees prospect Gosuke Katoh), which consists of running a probit regression analysis. In a nutshell, a probit regression tells us how a variety of inputs can predict the probability of an event that has two possible outcomes — such as whether or not a player will make it to the majors. While KATOH technically predicts the likelihood that a player will reach the majors, I’d argue it can also serve as a decent proxy for major league success. If something makes a player more likely to make the majors, there’s a good chance it also makes him more likely to succeed there.

After receiving a few requests, I decided to apply the model to players of years past. In what follows, I dive into what KATOH would have said about recent top prospects, look at the highest KATOH scores of the last 20 years, and highlight some instances where KATOH missed the boat on a prospect. If you’re feeling really ambitious, here’s a giant google doc of KATOH scores for all 40,051 player seasons since 1995 ( minimum 100 plate appearances in a short-season league or 200 in full-season ball).

Before I delve into the parade of lists, I want to point out one disclaimer to what I’m doing here. KATOH was derived from the performances of historical players, so applying the model to those same players might make it look a little better than it is. Take a player like Jason Stokes for example. Although he was a very well-regarded prospect in the early 2000’s (#15 and #51 per Baseball America in 2003 and 2004), KATOH consistently gave him probabilities in the 70’s and 80’s. But part of that is likely because Stokes’ data points were incorporated into the model. If I had created KATOH in 2005, Stokes’ MLB% may have been a few percentage points higher. Even so, a few data points generally aren’t enough to substantially change a model that incorporates thousands. In other words, it’s probably safe to assume that a player’s MLB% using today’s KATOH is roughly in line with what he would have received at the time.

Now, onto the results. Here’s what KATOH thought about some of the most recent top 100 prospects:

2013 Top 100 Prospects

2012 Top 100 Prospects

2011 Top 100 Prospects

Next, lets take a look at some of the highest KATOH scores of all time, namely those who received a score of at least 99.9%. There aren’t any complete busts among these players, as virtually all of them went on to play in the majors.

All-Time Top KATOH Scores

All of the players who registered a KATOH score of at least 99.9% did so while playing in either Double- or Triple-A. This isn’t all that surprising since these are the levels closest to the big leagues. But what about the lower levels? Like we saw in Double- and Triple-A, there weren’t any complete busts among the highest ranking hitters from full-season A-ball. For both full-season leagues, each of the 20 top ranked players has either made it to the majors, or in the case of Carlos Correa, is young enough to still has an excellent chance to do so. But on the bottom two rungs on the minor league ladder, we come across a few instances where KATOH whiffed, most notably in Garrett Guzman (74%), Richard Stuart (72%), and Pat Manning (72%).

Top KATOH Scores for Seasons in High-A

Top KATOH Scores for Seasons in Low-A

Top KATOH Scores for Seasons in Short-Season A

Top KATOH Scores for Seasons in Rookie ball

Now for KATOH’s biggest whiffs. Looking at seasons prior to 2011, the following players had very high KATOH ratings, but never made it to baseball’s highest level. The biggest miss was Cesar King, a defensive-minded catcher from the Rangers organization. Though to KATOH’s credit, King did spend five days on the Kansas City Royals’ roster in 2001 without getting into a game. Following King are a couple of busted Yankees prospects in Jackson Melian and Eric Duncan. Not to make excuses for KATOH, but these guys’ high scores may have had something to do with the way the Yankees over-hyped their prospects back then. If those two weren’t on Baseball America’s top 100 list, KATOH would have pegged them in the 70’s, rather than in the high-90’s.

KATOH’s Biggest Misses

And here are the major leaguers who KATOH deemed least likely to make it when they were in the minors. Its worth noting that a couple of them — Jorge Sosa and Jason Roach — made it as pitchers.

Worst KATOH Scores Who Made it to the Majors

KATOH’s far from perfect, but overall, I think it does a pretty decent job of forecasting which players will make it to the majors. That being said, it’s still a work in progress, and I have a few ideas rolling around in my head to improve on the model. Furthermore, I’m working to develop something that will forecast how a minor leaguer will perform upon reaching the majors, to complement his MLB%. I’ll be dropping these new and improved KATOH projections (for both hitters and pitchers) after this year’s World Series, when we’ll all be desperate for something baseball-related to get us through the winter.

Statistics courtesy of FanGraphs, Baseball-Reference, and The Baseball Cube; Pre-season prospect lists courtesy of Baseball America.

Bryce Harper has been disappointing so far in 2014, both before and after he launched three home runs in one AA rehab game.  The highly touted left-hand hitting outfielder has been pretty bad for a guy with a .346 BABIP.

As of August 7, 2014, he’s still been walking a lot (11.2%), but he’s striking out far too often (27.4%).  His ISO is just .121, which is lower than Dustin Ackley, Alexei Ramirez, and Billy Hamilton.  He’s also slugging just .374.

Yes, it’s only 215 PA so far.  That’s about a third of a season however, so I’m going to dig into to something that may contribute to why he’s struggling and hitting for next to no power.

First I will look into the types of pitches he’s getting.  Harper is seeing significantly more fastballs in 2014, and a lot less curve balls.  He is seeing 56.2% fastballs in 2014, compared to 45.9% in 2012 and 49.9% in 2013.  He is seeing 9.1% curve balls in 2014, compared to 13.1% in 2012 and 12.4% in 2013.

Now that we know that, let’s look at what Harper has actually produced with these pitches.  His HR/FB is less than half of what his career mark is.  This year, his HR/FB rate is 7.1%, down from his career mark of 15.6%.  This is interesting because he is hitting more fly balls than he ever has, at 34.4%, which is about 1% above his career average.  The final difference in his fly ball rates are infield flies.  He’s hitting infield popups 9.5% of the time, up from his career percentage of 7.6%.

So what does all this mean?

Harper has gone through a lot in 2014.  He’s changed his stance a couple times and he’s missed time with a thumb injury.  These two factors, especially the thumb issue, could be causing Harper to be late on fastballs.  There’s evidence that shows he is late on some pitches as well.  His ISO is just .071 when he hits the ball to center field and .118 when he goes to the opposite field.  For his entire career, his ISO is .209 to center and .188 to the opposite field.  That’s a pretty significant difference.  Most of his fly balls are going to center and left as well, as you can see here, which suggests he’s not driving the ball the other way with as much authority as he usually does.  His contact has clearly been weaker when taking the ball up the middle and the other way.

Let’s all remember he’s still a 21 year old kid.  He’s learning. He will be fine.  This is just a blip on the road and an area in which he’s struggled with this season.

The fact that Harper is getting pitched differently means he will need to make an adjustment, just as pitchers have clearly made an adjustment to him.  With his talent, he will certainly make that adjustment.  Once his thumb is fully healed, he will be able to drive the ball better as well.  These are also still short samples too, so if you’re a Nationals fan, there’s no reason to think Harper’s non-existent power will continue.

It’s no secret that a vast majority of Mets fans want Wilmer Flores to be playing shortstop every day. It’s also no secret that manager Terry Collins has some strange infatuation with Ruben Tejada, opting again and again to give him starts at shortstop.

Although Collins hasn’t given the media any clear reasoning as to why this is, there are a few reasons we can speculate. The biggest one is defense — Ruben Tejada has made major strides at shortstop this season, posting the highest DRS of his career. Flores, on the other hand, is a second baseman, and even his defense at second is questionable — he really profiles more as a corner infielder. However, with the other three infield positions being blocked by Daniel Murphy, David Wright, and the new-and-improved Lucas Duda, Ruben Tejada is the odd man out.

The other side of the coin is the one I’m going to be focusing on: offense. When Tejada started getting regular playing time as a 21-year-old in 2011, he showed some legitimate offensive potential, hitting line drives at an extremely impressive 28.1% rate (would have ranked 2nd among qualified batters,) good for .287/.345/.345 in 877 PAs between 2011 and 2012. Then, in 2013, he came to spring training out of shape, hit .202, got sent down, got hurt a couple times, and basically threw yet another monkey wrench into the Mets’ rebuild. The job became his to lose in 2014, and he’s hit a measly .228/.348/.280, the OBP even being inflated by the amount of intentional walks he received in the 8 hole. His 0.4 fWAR this season cancels out his -0.4 last season, making him a perfect replacement-level player.

Meanwhile, Wilmer Flores has been a top offensive prospect in the Mets system since he was signed out of Venezuela as a 16-year-old in 2007.  His numbers finally started to reflect his talent in 2012, when he hit .300/.349/.479 between high A and AA. In 2013, he exploded in AAA, and the past two seasons has hit .321/.360/.543 with 28 home runs and 47 doubles in exactly 162 games. Sure, he plays in Vegas, one of the most hitter friendly parks in AAA, but these are still numbers that demand attention — attention that he hasn’t yet seemed to receive from Terry Collins. Despite Tejada’s offensive struggles, he has still started 86 games at short this season, as opposed to Flores’ 20. One of the reasons a few Mets fans have been pointing to is the fact that Flores has yet to actually produce at the major league level, hitting only .220/.254/.304 in his 201 big league plate appearances. But is that slash-line an accurate reflection of his talent? And, for that matter, is Tejada’s?

For this mini-evaluation, we’ll use slash12’s xBABIP formula. It’s never a perfect system, but it will give us a good estimation of what these players slash-lines should look like (or at least their average and OBP.)

After inserting Ruben Tejada’s batted ball profile, we get that his xBABIP for 2014 is .329 — much higher than his actual BABIP of .288. We can then plug that backwards into the BABIP formula to determine how many hits he theoretically should have. Since the formula is (H-HR)/(AB-HR-K+SF), we can plug in everything except for hits to get (H-2)/(289-2-65+0)=.329, simplify that to (H-2)/(222)=.329, multiply both sides by 222 to get H-2=73, and we can come to the conclusion that Ruben Tejada should have 73 hits on the year, instead of the 66 he has. This would make his batting average .253 and his OBP .364 (although, keep in mind that that’s being inflated by the 10 intentional walks he’s had while hitting 8th in the order. If we decided to remove those, his OBP would drop to .345).

Now, doing the same to Wilmer Flores is slightly tricky, as we don’t have nearly as large a sample size worth of batted ball data to use. In the interest of accuracy, we’ll use his career profile, so we can at least get a sample of 201 PAs instead of his 100 this year. Plugging his batted ball profile into the xBABIP calculator, we get a result of .333, compared to his actual career BABIP of .268. Doing the same backwards math we did with Tejada, this brings his expected career batting average up to .272, and his career OBP up to .304.

Now, these are only two stats, and they only tell us so much — Flores seems to be a better hitter, but his career 4.5% BB rate is clearly overmatched by Tejada. There isn’t a formula out there for expected slugging percentage — at least, as far as I know — so we can’t really determine what that would be (and subsequently, what their OPS would be). We could assume the same ISO, which would not be entirely accurate, but it would give us a .305/.669 for Tejada and a .355/.659 for Flores. Still, I think it’s clear, both from my biased perspective as a Mets fan and my objective perspective as a baseball fan, that Flores has the brighter future offensively — but it’s up to the Mets to decide how to capitalize on it.

Examining the foundations of batting analysis began in Part 1 with an historical examination of the earliest statistics designed to examine the performance of batters. In Part 2, I presented a new method for calculating basic averages reflecting the “real and indisputable” rate at which batters reached base. In Part 3, I examined the development of run estimation techniques over the last century, culminating with the linear weights system. I will employ that system now as I reconstruct run estimation from the bottom up.

We use statistics in baseball to tell stories. Statistics describe the action of the game or the performance of players over a period of time. Statistics inform us of how much value a player provided or how much skill a player showed in comparison to other players. To tell such stories successfully, we must understand how the statistics we use are constructed and what they actually represent.

A single, for instance, seems simple enough at first glance. However, there are details in its definition that we sometimes gloss over. In general, a single is any event in which the batter puts the ball into play without causing an out, while showing an accepted form of batting effectiveness (reaching on a hit), and ultimately advancing to first base due to the primary action of the event (before any secondary fielding errors or advancement on throws to other bases). Though this is specific in many regards, it is still quite a broad definition for a batting event. The event could occur in any inning, following any number of outs, and with any number of runners on the bases. The ball could be hit in any direction, with any speed and trajectory, and result in any number of baserunners advancing any number of bases.

These kinds of details form the contextual backdrop that characterizes all batting events. When we construct a statistic to evaluate these events, we choose what level of contextual detail we want to consider. These choices define our analysis and are critical in developing the story we want to tell. For instance, most statistics built to measure batting effectiveness—from the simple counting statistics like hits and walks, to advanced run estimators like Batter Runs or weighted On Base Average (wOBA)—are constructed to be independent of the “situational context” in which the events occur. That is, it doesn’t matter when during the game a hit is made or if there are any outs or any runners on the bases at the time it happens. As George Lindsey noted in 1963, “the measure of the batting effectiveness of an individual should not depend on the situations that faced him when he came to the plate.”

Situational context is the most commonly cited form of contextual detail. When a statistic is described as “context neutral,” the context being removed is very often the one describing the out/base state before and after the event and the inning in which it occurred. However, there are other contextual details that characterize the circumstances and conditions in which batting events occur that also tend to be removed from consideration when analyzing their value. Historically, where the ball was hit, as well as the speed and trajectory which it took to reach that location, have also not been considered when judging the effectiveness of batters. This has partly been due to the complexity of tracking such things, especially in the century of baseball recordkeeping before the advent of computers. Also, most historical batting analyses focus exclusively on the outcome for the batter, independent of the effect on other baserunners. If the batter hits the ball four feet or 400 feet but still only reaches first base, there is no difference in the personal outcome that he achieved.

If the value of a hit was limited to only how far the batter advances, then there would be no need to consider the “batted-ball context,” but as F.C. Lane observed in 1916, part of the value of making a hit is in the effect on the “runner who may already be upon the bases.” By removing the batted-ball context when considering types of events in which the ball is put into play, we’re assuming that a four-foot single and 400-foot single have the same general effect on other baserunners. For some analyses, this level of contextual detail describing an event may be irrelevant or insignificant, but for others—particularly when estimating run production—such a level of detail is paramount.

Let’s employ the linear weights method for estimating run production, but allow the estimation to vary from one completely independent of any contextual detail to one as detailed as we can make it. In this way, we’ll be able to observe how various details impact our valuation of events. Also, in situations where we are only given a limited amount of information about batting events, it will allow us to make cursory estimations of how much they caused their team’s run expectancy to change.

To begin, let’s define the run-scoring environment for 2013.[i] While we have focused on context concerning how events transpired on the field, the run scoring environment is another kind of contextual detail that characterizes how we evaluate those events. The exact same event in 2013 may not have caused the same change in run expectancy as it would have in 2000 when runs were scored at a different rate. We will define the run scoring environment for 2013 as the average number of runs that scored in an inning following a plate appearance in each of the 24 out/base states – a 2013-specific form of George Lindsey’s run expectancy matrix:

While we will focus on examining various levels of contextual detail concerning the events themselves, the run-scoring environment can also be varied based on contextual details concerning the scoring of runs. The matrix we will employ, as defined by Lindsey, reflects the average number of runs scored across the entire league. If we wanted, we could differentiate environments by league or park, among other things, to try and reflect a more specific estimate of the number of runs produced. As the work I’m going to present is meant to provide a general framework for run estimation, and these adjustments are not trivial, I’m going to stick with the basic model provided by Lindsey.

With Lindsey’s tool, we can define a pair of statistics for general analysis of run production. Expected Runs (xR) reflect the estimated change in a team’s run expectancy caused by a batter’s plate appearances independent of the situational context in which they occur. A batter’s expected Run Average (xRA) is the rate per plate appearance at which he produces xR.

xRA = Expected Runs / Plate Appearances = xR / PA

xR and xRA create a framework for estimating situation-neutral run production. Based on the contextual specificity that is used to describe the action of a plate appearance, xR and xRA will yield various estimations. The base case for calculating expected runs, xR₀, is calculated independently of any contextual detail, considering only that a plate appearance occurred. By definition, an average plate appearance will cause no change in a team’s run expectancy. Consequently, no matter a player’s total number of plate appearances, his xR₀ and, by extension, his xRA₀, will be 0.0.

This is completely uninformative of course, as base cases often are. So let’s add our first layer of contextual specificity by noting whether an out occurred due to the action of the plate appearance. This is the most significant contextual detail that we consider when evaluating batting events – it is the only factor that determines whether a plate appearance increases or decreases a team’s run expectancy. In 2013, 67.5 percent of all plate appearances resulted in at least one out occurring. On average, those events caused a team’s run expectancy to decrease by .252 runs. The 32.5 percent of plate appearances in which an out did not occur caused a team’s run expectancy to increase by .524 runs on average. We’ll define xR₁ as the estimated change in run expectancy based exclusively on whether the batter reached base without causing an out; xRA₁ is the rate at which a batter produced xR₁ per plate appearance.

You’ll notice that the components that construct xRA₁ can only take on two values—.524 and -.252—in the same way that the components that construct effective On Base Average (eOBA) (as defined in Part 2) can only take on two values—1 and 0. These statistics—xRA₁ and eOBA—have a direct linear correlation:

In effect, xRA₁ is a weighted version of eOBA, incorporating the same contextual details but on a different scale. This estimation provides us with an association between reaching base safely and producing runs. However, the lack of detail would suggest that all players that reach base at the same rate produce the same value, which is over simplified. It’s why you wouldn’t just use eOBA, or eBA, or any other basic statistic that reflects the rate which a batter reaches base, when judging the performance of a batter. Let’s add another layer of contextual detail to account for the different kinds of value a batter provides when he reaches base.

xR₂ will represent the estimated change in run expectancy based on whether the batter safely reached base and the number of bases to which he advanced due to the action of the plate appearance; xRA₂ will be the rate at which a batter produces xR₂ per plate appearance. While xR₁ and xRA₁ were built with just two components to estimate run production, xR₂ and xRA₂ require five components: one to define the value of an out, and four to define the value of safely reaching each base.

In 2013, a batter safely reaching first base during a plate appearance caused an average increase of .389 runs to his team’s run expectancy. Reaching second base was worth .748 runs, third base was worth 1.026 runs, and reaching home was worth 1.377 runs on average. Where xRA₁ provided a run estimation analog to eOBA, xRA₂ is built with very similar components to effective Total Bases Average (eTBA), though it’s not quite a direct linear correlation:

The reason xRA₂ and eTBA do not correlate with each other perfectly, like xRA₁ and eOBA, is because the way in which a batter advances bases is significant in determining how valuable his plate appearances were. Consider two players that each had two plate appearances: Player A hit a home run and made an out, Player B reached second base twice. Their eTBA would be identical—2.000—as they each reached four bases in two plate appearances. However, from the run values associated with reaching those bases, Player A would record 1.125 xR₂ from his home run and out, while Player B would record 1.496 xR₂ from the two plate appearances leaving him on second base. Consequently, Player A would have produced a lower xRA₂ (.5625) than Player B (.7480), despite their having the same eTBA. These effects tend to average out over a large enough sample of plate appearances, but they will still cause variations in xRA₂ among players with the same eTBA.

As stated in Part 2, the two main objectives of batters are to not cause an out and to advance as many bases as possible. If the only value that batters produced came from accomplishing these objectives, then we would be done – xR₂ and xRA₂ would reflect the perfect estimations of situation-neutral run production. As I hope is clear, though, the value of a batting event is dependent not only on the outcome for the batter but on the impact the event had on all other runners on base at the time it occurred. Different types of events that result in the batter reaching the same base can have different average effects on other baserunners. For instance, a single and a walk both leave the batter on first base, but the former creates the opportunity for baserunners to advance further on average than the latter. To address this, the next layer of contextual detail will bring the official scorer into the fray. xR₃ will represent the estimated change in run expectancy produced during a batter’s plate appearance based on:

(1)    whether the batter safely reached base,

(2)    the number of bases, if any, to which the batter advanced due to the action of the plate appearance, and

(3)    the type of event, as defined by the official scorer, that caused him to reach base or cause an out.

xRA₃ will, as always, be the rate at which a batter produces xR₃ per plate appearance.

Each of the run estimators that were examined in Part 3, from F.C. Lane’s methods through wOBA, are subsets of this level of xR. Expected runs incorporate estimations of the value produced during every event in which the batter was involved, including those which may be considered “unskilled.” The run estimators examined in Part 3 consider only those events that reflected a batter’s “effectiveness,” and either disregard the “ineffective” events or treat them as failures. xR₃ provides the total value produced by a batter, independent of the effectiveness he showed while producing it, based solely on how the official scorer defines the events. Consequently, some events, like strikeouts, sacrifice bunts, reaches on catcher’s interference, and failed fielder’s choices, among other more obscure occurrences, are examined independently in xR₃. From the two components of xR₂ and the five of xR₃, we build xR₄ with 18 components: five types of outs and 13 types of reaches.

To help illustrate how xR has progressed from level to level, here is a chart reflecting the run values for 2013 as estimated by xR based on the contextual detail provided thus far.

xR Progression

Beyond any consideration of skilled or unskilled production, xR₃ is the level at which most run estimators are constructed. It incorporates events that are well defined in the Official Rules of the game, and have been for at least the last few decades, and in some cases for over a century. While we still define most of a batter’s production by his accomplishing these events, we live in an era where we can differentiate between events on the field in more specific ways. Not all singles are identical events. We weaken our estimation of run production if we don’t account for the different kinds of singles, among other events, that can occur. xR₃ brought the official scorer into action; xR₄ will do the same with the stat stringer.

While the scorer is concerned with the result of an event, a stringer pays attention to the action in between the results. They chart the type, speed, and location of every pitch, and note the batted ball type (bunt, groundball, line drive, flyball, pop up) [ii] and the location to which the ball travels when put into play.While we don’t have this data as far back in time as we have result data, we do have decades worth of information concerning these details. By differentiating events based on these details, we will begin to unravel the “batted-ball context.” Ideally, we would know every detail of the flight of the ball, and use this to group together the most similar possible type of events for comparison.[iii] At present, we’re limited to what the scorers and stringers provide, but that’s still quite a lot of information.

xR₄ will represent the estimated change in run expectancy produced during a batter’s plate appearance based on:

(1)    whether the batter safely reached base,

(2)    the number of bases, if any, to which the batter advanced due to the action of the plate appearance,

(3)    the type of event, as defined by the official scorer, that caused him to reach base or make an out,

(4)    the type of batted ball, if there was one, as defined by the stat stringer, that resulted from the plate appearance,

(5)    the direction in which the ball travelled, and

(6)    whether the ball was fielded in the infield or outfield.

xRA₄ will be the rate at which a batter produces xR₄ per plate appearance.

There are 18 components in xR₃ which describe the assorted types of general events a batter can create.  When you add in these details concerning the batted-ball context, the number of components increases to 145 for xR₄. With such specific details being considered, we can no longer rely on a single season of data to accurately inform us on the average situation in which each type of event occurs; the sample sizes for some events are just too small. To address this, there are two steps required in evaluating events for xR₄. The first is to build a large sample of each event to build an accurate picture of their relative frequency in each out/base state. I’ve done this by using a sample covering the previous ten seasons to the one in which the estimations are being made. Once this step is completed, the run-scoring environment in the season being analyzed is applied to these frequencies, in the same way it is when looking at single season frequencies for basic events.

For instance, the single, which is traditionally treated as just one type of event, is broken into 24 parts based on the contextual details listed above. By observing the rate at which each of these 24 variations of singles occurred in each out/base state from 2004 through 2013, and applying the 2013 run-scoring environment, we get the following breakdown for the estimated value of singles in 2013:

This process is repeated for every type of batting event in which the ball is put into play. One of the ways we can use this information is to consider the run value based not on the result of the event, but on the batted-ball context that describes the event. Here are those values in the 2013 run-scoring environment:

Similarly, we can break down each player’s xR₄ by the value produced on each type of batted ball. Here are graphs for xR₄ produced on each of the four types of batted balls resulting from a swing, with respect to the number of batted balls of that type hit by the player. For simplicity, from this point on, when I drop the subscript when describing a batter’s expected run total, I’m referring to xR₄.

Line drives are the most optimal result for a batter. The first objective of batters is to reach base safely, and they did that on 67.0 percent of line drives last season. No batter who hit at least eight line drives in 2013 caused a net decrease in his team’s run expectancy during those events. For most batters, hitting the ball into the outfield in the air is the ideal way to produce value, as fly ball production tends to create a positive change in a team’s run expectancy. However, fly balls have the most variance of any of the batted ball types, and there are certainly batters who hurt their teams more when hitting the ball at a high launch angle than a low one. Here are the players to produce the lowest xRA on fly balls last season (minimum 50 fly balls):

For each of these batters, hitting the ball on the ground or on a line drive were far better results on average.

While groundballs may be a preferable result for some batters when compared to fly balls, they are still effectively batting failures for the team. There were 840 batters in 2013 to hit at least one groundball and only 44 produced a net positive change in their team’s run expectancy. Of those 44 players, only 11 hit more than 10 groundballs, and only two (Mike Trout and Juan Francisco) hit at least 100 groundballs. Here are the players with the highest xRA on groundballs in 2013 who hit at least 100 groundballs:

xR₄ allows us to tell the most detailed story concerning the type of value a batter produced, independent of the situational context at the time the plate appearance occurred. Because we gradually added layers of detail to our estimation, we can compare how each level of expected runs correlates to this most detailed level. In this way, we can judge how much information each level provides with respect to our most detailed estimation. Here is a graph that charts a batter’s xR₄ with respect to his xR₁, xR₂, and xR₃ estimations:

The line that cuts through the data reflects the xR₄ values charted against themselves. For each xR_n, we can calculate how well it correlates with xR₄ and, consequently, how much of xR₄ it can explain. Remember that we have already shown that xR₁ has a direct linear correlation with eOBA and xR₂ has a very high, though not quite direct, correlation with eTBA. For the xR₁ values, we observe a correlation, r, with xR₄ of .912, and an r² of .832, meaning that knowing the rate at which a batter reaches base explains over four-fifths of our estimation of xR₄. For the xR₂ values, r² increases to .986; for the xR₃ values, r² increases slightly higher to .990.[iv]

The takeaway from this is that when considering the whole population of players, there is little difference in a run estimator that considers the batted-ball context and one that does not; you can still explain 99 percent of the value estimated by xR₄ by stopping at xR₃. In fact, if all you know is the rate at which a batter accomplishes his two main objectives—reaching base and advancing as far as possible—you can explain well over 90 percent of the value estimated by xR₄. However, on an individual level, there is enough variation that observing the batted-ball context can be beneficial. Here are the five players with the largest positive and negative differences between their xR₃ and xR₄ estimations:

These changes are not massive, and these are the extreme cases for 2013, but they are certainly large enough that ignoring them will weaken specific analyses of batting production. Incorporating batted ball details into our analysis adds a significant layer of complexity to our calculation, but it must be considered if we want to tell the most accurate story of the value a batter produced.

If this work seems at all familiar, you may have read this article that I wrote last year on a statistic that I called Offensive Value Added (OVA). For all intents and purposes, OVA and xR are identical. I decided that the name change to xR would help me differentiate estimations more simply, as I could avoid naming four separate statistics for each level of contextual detail, but there was also a secondary reason for changing the presentation of the data. OVAr was the rate statistic associated with OVA, and it was scaled to look like a batting average, much in the same way that wOBA is scaled to look like an on base average. At the time, I choose to do this to make it easier to appreciate how a batter performed, since many baseball enthusiasts are comfortable interpreting the relative significant of a batting average.

After thinking on the subject, though, I came to decide that I prefer statistics that actually “mean” something to those that give a general, unit-less rating. For instance, try to explain what wOBA actually reflects. It starts as a run estimator, but then it’s transformed into a number that looks like a statistic with specific units (OBA), while not actually using those units. Once that transformation occurs, it no longer reflects anything specific and only serves as a way to rate batters. The same principle applies to other statistics as well, most notably OPS, which is arguably the most meaningless of all baseball statistics, perhaps all statistics ever (don’t get me started).

xR and xRA estimate the change in a team’s run expectancy caused by a batter’s plate appearances. They are measured in runs and runs per plate appearance, respectively. xRA may not look like a number you’ve seen before, and generally needs to be written out to four decimal places instead of three, unlike basic averages, but it’s linguistically very simple to use and understand. I’d rather sacrifice the comfort of having a statistic merely look familiar and instead have it actually reflect something tangible. This doesn’t take away from the value of a statistic like wOBA, which is a great run estimator no matter what scale it is on; a lack of meaning certainly does not imply a lack of value. Introducing an unscaled run average, xRA, will hopefully create a different perspective on how to talk about batting production.

There is one final expected run estimation that I want to consider that could easily cover an entire new part on its own, but I’ll limit myself to just a few paragraphs. The xR estimations we have built have been constructed independent of the situational context at the time of the batter’s plate appearance. Since we want to cover the entire spectrum of context-neutral run estimation to context-specific run estimation, we will conclude by considering xR_s, which is an estimate of the change in a team’s run expectancy based on the out/base state before and after the action of the plate appearance. This is very nearly the same thing as RE24 but it only considers runs produced due to the primary action of plate appearances and not baserunning events.

In many respects, xR_s is the simplest run estimator to construct of all that we have built thus far. There are only three pieces of information you need to know in a given plate appearance to construct xR_s: the run-scoring environment, the out/base state at the start of the action of the plate appearance, and the out/base state at the end of the action of the plate appearance. Next time you go to a baseball game, bring along a copy of a run expectancy matrix, like the one provided earlier. On a scorecard, at the start of every plate appearance, take note of the value assigned to the out/base state, making adjustments if any runners move while the batter is still in the batter’s box. Once the plate appearance is over, note the value of the new out/base state, separating out any advancement on secondary fielding errors or throws to other bases. Subtract the first value from the second value, and add in any RBIs on the play, and write the number in the box associated with the batter’s plate appearance; you just calculated xR_s. Do this for a whole game, and you will have a picture of the total value produced by every batter based on the out/base state context in which they performed.

The effective averages and expected run estimations provide a foundation on which batting analysis can be performed. They combine both “real and indisputable facts” with detailed estimations of the run produced in every event in which a batter participates. Any story that aims to describe the value that a batter provides to his team must consider these statistics, as they are the only ones which account for all value produced. 147 years ago, Henry Chadwick suggested that batters should be judged on whether they passed a “test of skill.” I think they should be judged on whether they passed a “test of value.”

Thanks to Benjamin H Byron for editorial assistance, as well as the staff at the Library of Congress for assistance in locating original copies of the 19^th century newspaper articles included in Part 1.

Here is data on eOBA, eTBA, and each level of xR and xRA estimation, for each batter in 2013.

Bibliography

[i] I’ll be focusing on 2013 because the full season is complete. All the work described here could easily be applied to 2014, or any other season, I just don’t want to use incomplete information.

[ii] While these terms are used a lot, there aren’t any specific definitions commonly accepted that differentiate each type of batted ball. For terms used so commonly, it doesn’t make much sense to me that they are not well defined. It won’t apply to the data used in this research, but here is my attempt at defining them.

A bunt is a batted ball not swung at but intentionally met with the bat. A groundball is a batted ball swung at that lands anywhere between home plate and the outer edge of the infield dirt and would be classified as a line drive if it made contact with a fielder in the air. A line drive is a batted ball swung at that leaves the bat at an angle of at most 20° above parallel to the ground (the launch angle), and either lands in the outfield or makes contact with any fielder before landing (generally through a catch, but sometimes a deflection). A fly ball is a batted ball swung at, with a launch angle between 20° and 60° above parallel (not inclusive), that either lands in the outfield or is caught in the air by a player in the outfield. A popup is a batted ball swung at that either (a) leaves the bat at an angle of 60° or greater above parallel and lands or is caught in the air in the outfield, or (b) leaves the bat at an angle greater than 30° and lands or is caught in the air in the  infield.

This would result in some balls being classified differently than they currently are, and not just because differentiating between a line drive and a fly ball is somewhat difficult with just a pair of eyes. If the defense were to play an infield shift, and the batter were to hit a line drive into the outfield grass into that shift, subsequently being thrown out at first base, it would likely be called a groundout by current standards. Batted balls should not be defined based on defensive success or failure, but by the general path which they take when leaving the bat. It may be unusual to credit a batter with making a line out despite the ball hitting the ground, but it more accurately reflects the type of ball put into play by the batter.

I don’t know that these are the “correct” ways to group together these events, but as we now are using technology that tracks the flight of the baseball from the moment it is released by the pitcher through the end of the play, we should probably have better definitions for types of batted balls than those currently provided by MLB. I don’t expect a human stringer to be able to differentiate between a ball hit with a 15° launch angle or a 25° launch angle, but that doesn’t mean we shouldn’t have some standard definition for which they should aim.

[iii] In theory, xR₅ would attempt to consider details that are even more specific, perhaps the initial velocity of the ball off the bat, the launch angle, and whatever other information can be gleaned from technology like HIT F/X. The xR framework leaves room to consider any further amount of detail that a researcher wants to consider.

[iv] Though not charted here, the r² value based on the correlation between wRAA, the “counting” version of wOBA, and xR₄ is .984. As wRAA is nearly identical to xR₃ but excludes a few of the more rare events from its calculation, it’s not surprising that the r² value between wRAA and xR₄ is just slightly smaller than the r² between xR₃ and xR₄.