Background

Back on 2016-Nov-11 I posted WAR and Eating Innings.

Basically, I was looking at reliever WAR and concluded that giving a lower replacement to relievers isn’t quite correct. Inning for inning, a replacement reliever needs to be better than a replacement starter, because eating innings has real value. But reliever/starter doesn’t actually capture the ability to eat innings, and I gave several examples where it fails historically.

I don’t have roster-usage numbers and don’t want to penalize a pitcher for sitting on the bench, but outs per appearance makes a nice proxy for the ability to eat innings; and in a linear formula that attempts to duplicate the current distribution of wins between relievers and starters, this gives roughly 0.367 win% as pitcher replacement level (as opposed to the current 0.38 for starters and 0.47 for relievers), and then penalized the pitcher roughly 1/100^th of a win per appearance.

The LOOGY needs to be pretty good against his one guy to make up for that penalty, but for a starter it will make almost no difference.

That’s pretty much the entire article summarized in three paragraphs. By design, this doesn’t change much about 2016 WAR — it will give long relievers a modest boost, and very short relievers (LOOGYs and the like) a very modest penalty, and have an even smaller effect on starters.

So why did I bother?

Well, first, there are historical cases where it does matter; but more to the point, I was thinking that relievers are being undervalued by current WAR, and to examine this I needed a method to evaluate a reliever’s value compared to a starter’s value, and different replacement levels complicate that.

Why Do I Think Relievers Are Undervalued?

You could just go to this and read it; it shows that MLB general managers thought relievers were undervalued as of a few years ago. But that’s not what convinced me. What convinces me is the 2016 Reds pitching staff. 32 men pitched at least once for the Cincinnati Reds in 2016. Their total net WAR was negative.

Given that the Reds did spend resources (money and draft picks) on pitching, if replacement level is freely available, then that net negative WAR is either spectacularly bad luck, or spectacularly bad talent evaluation.

32 Reds pitchers were used; sort by innings pitched, and the top seven are all positive WAR, accounting for 5.6 of the Reds’ total of 6.7 positive WAR. Of their other 25 pitchers, only three had positive WAR: Michael Lorenzen (reliever, 50 innings, part of the Reds’ closer plans for the coming year), Homer Bailey (starter, coming off Tommy John and then injured again, only six appearances), and Daniel Wright (traded away mid-season, after which he turned back into a pumpkin and accumulated negative WAR for the season).

It sure sounds like the Reds coaches knew who their best pitchers were and used them. Their talent evaluation was not spectacularly bad. But they had 17 relievers with fewer than 50 innings, and not one of them managed to accumulate positive WAR for the year.

Based on results, we can list the possible mistakes in who they gave innings to: Maybe they could have used Lorenzen a bit more. That’s it; otherwise it’s hard to improve on who they gave the innings to. They also usually gave the high-leverage innings to their best relievers.

So, if replacement level is freely available, why did the Reds coaches give a total of 574.2 innings to 22 pitchers who managed between them to accumulate no positive WAR and 7.1 negative WAR?

If that’s just bad luck, it is spectacularly bad luck; and spectacularly consistent, as the Reds seem to have known in advance exactly who was going to have all this bad luck.

I don’t really believe it is bad luck. Thus, I don’t really believe that the Reds pitchers were below replacement, and the alternative is that replacement (at least for relievers) is too high.

GMs Still Agree: Relievers Are Undervalued by WAR

The article I referenced above was from the 2011-2012 off season; maybe something has changed.

As I write this (2017-Feb-24), FanGraphs’ Free Agent Tracker shows 112 free agents signed over the 2016-2017 off-season. 10 got qualifying offers and thus aren’t truly representative of their free-market value. 22 have no 2017 projection listed, and most of those went for minor-league deals (Sean Rodriguez and Peter Bourjos are the exceptions, and they aren’t pitchers). I’m going to throw those 32 out.

That leaves a sample of 80 players, 28 of them relievers or SP/RP. A fairly simple minded chart is below:

(Hmm, no chart. There was supposed to be a chart. Don’t see an option that will change this. Relief pitcher Average $/Year=5.7105*projected 2017 WAR with an R² of 0.585; everyone else Average $/Year=4.6028+1.401*projected 2017 WAR with an R² of .5917. Note that the “everyone else” line, if you could see it, is below the relief pitcher line at 0 WAR, and then slopes up faster from there.)

R² values aren’t great, and overall values per WAR are low because most of the big paydays are on multiyear contracts where value can be assumed likely to collapse by the end of the contract (I’m not including any fall-off). But the trend continues — MLB general managers think relievers are worth more than FanGraphs thinks they are.

The formula I give above (replacement of 0.367 win% with a −0.01 wins/appearance) is based on trying to reproduce the FanGraphs results. But if the FanGraphs results are wrong, then so is my formula.

Why the Current Values Might Be Wrong

I’ve shown why I think the current values are wrong, but what could cause such an error?

Roster spots change in value over time. That’s all it takes; the reliever is held to a higher (per-inning) standard because historical analysis indicated that he should be. But if roster spots were free, then it would be absurd to evaluate starters and relievers at all differently. The difference in value depends on the value of a roster spot; or, if using my method, the “cost” imposed per appearance needs to be based on the value of a roster spot.

Prior to 1915, clubs had 21 players, and no DL at all. In 1941, the DL restrictions were substantially loosened, and a team could have two players on the DL at the same time (60-day DL only at that time). In 1984, they finally removed the limits to the number of players on a DL at a time; in 2011, a seven-day concussion DL was added, and a 26^th roster spot for doubleheader days; in 2017, the normal DL will be shortened to 10 days.

21 players and no DL makes roster spots golden. You simply could not have modern pitcher usage in such a period.

Not to mention the fact that, in 1913, you’d never have been able to get a competent replacement on short notice. Jets and minor-league development contracts both also dropped the value of a roster spot.

25-26 roster spots, September call-ups to 40, and starting this year you can DL as many players you want for periods short enough that it’s worth thinking about DLing your fifth starter any time you have an off day near one of his scheduled starts. Roster spots are worth a lot less today; it’s not surprising that reliever WAR seems off, when it was based on historical data, and the very basis for having a different reliever replacement level is based on the value of a roster spot.

Conclusion

When I started this, I was hoping to produce a brilliant result about what relief-pitcher replacement should be. I have failed to do so; there’s simply too little data, as shown by the low R² values on the chart I tried to include above, to make a serious try at figuring out what general managers are actually doing in terms of their concept of reliever replacement level.

But the formula I suggested back in November has an explicit term acting as a proxy for the value of a roster spot, and that term can be adjusted for era. If you drop the cost of an appearance from 0.01 WAR to some lower value, raising replacement a bit to compensate, you’ll represent the fact roster spots have changed in value over time.

Given any reasonable attempt to estimate the cost per appearance based on era, I don’t see how this could be worse than the current methods.

It’s no secret that Felix Hernandez struggled in 2016, looking little like the ace Mariners fans had come to expect from 2009-2014. After a good-but-not great 2015, there was some hope that Hernandez would fix what ailed him and come back as the fire-breathing ace he’s been for more than a half-decade.

Instead, he had the worst season of his career, striking out 7.2 per nine, walking 3.8 per nine, and allowing 1.1 home runs per nine. His sudden decline from ace to barely-passable fourth starter has baffled fans and media members alike. Many point to his declining velocity — his fastball averaged just 90.5 miles per hour in 2016, the lowest of his career.

Of course, the real answer has nothing to do with velocity. The answer is far simpler. The Muddy Mound Game Conspiracy has been hidden from the public’s memory for long enough, and it’s time to wake up, sheeple! Those close to me have called me a “muddy-mound truther,” as if that’s a negative thing. But, folks, don’t believe what they’re telling you. I’ve got the facts, and once you’ve taken in this mind-blowing information, you’re not likely to ever trust a grounds crew again.

The muddy-mound game is the day everything changed for Hernandez. I’m talking, of course, about June 1, 2015, when the Mariners faced the Yankees at home.

Because of a malfunction with the Safeco Field roof, rain covered the mound, making it muddy and slippery. Hernandez visibly had trouble with his stride leg in his delivery, and was seen at times scraping the dirt out from between his cleats.

Through the first three innings, Hernandez was perfect, striking out three and inducing five ground-ball outs. And then, in the top of the fourth inning, as the rain came down harder and covered the mound, Hernandez appeared to land awkwardly on his first pitch to the inning’s second batter, Chase Headley.

At that point, it was clear something wasn’t right. Hernandez would walk five batters in the next inning-and-two-thirds (after having walked just 15 in 70.2 total innings up until that point in 2015) and give up seven runs before being removed.

This is the point, almost exactly, where Hernandez’s command abandoned him. From this game forward, Hernandez has had 46 starts, and has walked 3.4 per nine. In the 46 starts leading up to this game, he was averaging just 1.9 walks per nine. It seems unlikely that an ace pitcher would lose his command entirely in the span of two innings, but the numbers say that’s exactly what has happened.

Mariners fans may recall that in 2009, Hernandez began to add a Luis Tiant/Fernando Valenzuela-esque twist to his windup. Hernandez himself said that he had picked it up from watching teammate Erik Bedard. It should be noted that Hernandez made the jump from “promising young pitcher” to “perennial Cy Young contender” in 2009. The twist in his windup may not be directly responsible for Hernandez’s ascension to the throne, but it certainly played a large role.

In the chart below, you’ll see four sets of data. The first column is from when Hernandez debuted through the 2008 season. Row two spans 2009 until June 1, 2015 — from when he first started adding the twist, until the muddy-mound game. Row three is the 46 starts before June 1, 2015, and row four shows us the 46 games including, and since, the muddy-mound game.

So, not only has Hernandez declined dramatically since the fourth inning of that game, but it’s actually been the worst stretch he’s had in his entire career. Oddly enough, this stretch has come right after the best stretch of his career.

But there’s more! It’s not just boring data that shows dramatic decline. There’s been a visible change in Hernandez windup over the last year and a half since this game. I’m going to play right into my enemies’ hands here — as they would say, I’m putting on my tinfoil hat. But, the joke is on them, because now they can’t hear my thoughts.

Three things stand out — Hernandez has reduced the torque of his twist, he’s lowered his hands, and the position of his stride leg is inconsistent. I took a series of images of Hernandez at the top of his windup, detailing the changes. To the undeniable proof!

First, we have an image from Hernandez’s perfect game against Tampa Bay on August 19, 2012:

The twist is as prominent as ever in this game; the front of Hernandez’s shoulder is basically facing the viewer. His hands are close to his neck, and his arms are raised high enough for us to read the jersey script. Hernandez’s drive leg is bent at a slight angle. Considering he threw a perfect game with 12 strikeouts with these mechanics, it would seem that these represent a good version of his windup.

Let’s jump ahead. This one comes from April 18, 2015 — Hernandez’s second home start of the year.

For the most part, things look similar here. He’s turning slightly less, but we can still read the jersey script, and see most of the front of his left shoulder. Moving on!

Nothing appeared too different in his next few starts, though he didn’t look exactly the same as the previous image. This image is from the first inning of the infamous muddy mound game itself:

Some small tweaks, but for the most part, things appear the same. Considering Hernandez was dominating during this stretch, it’s hard to argue with the results.

Here’s an image from Hernandez’s first slip off the mound in the fourth inning:

Unfortunately, Hernandez spent most of the rest of his outing after slipping pitching from the stretch, so it’s hard to find an example of his windup immediately after the injury. It’s hard to tell from this image, but this came on the first pitch of the second at-bat of the fourth inning. Hernandez falls off the mound, looks a little ginger on his left foot, but shakes it off and returns to the mound. The story is the same for the very next pitch. Hernandez appears to be visibly uncomfortable, on his way to walking five batters and throwing a wild pitch.

Small changes to his motion became evident throughout the rest of 2015, and the best example of these changes came on September 10 against the Rangers:

It’s clear that his hands have lowered, though his front shoulder still seems pretty well twisted to face us, the viewer. It’s also notable that Hernandez’s stride leg is now wrapped more around him at an angle, whereas before it was closer to perpendicular with the ground. Hernandez didn’t give up a run in this game, but did walk four batters.

In Hernandez’s second home start of 2016, April 29 against the Royals, we see not much has changed:

His hands have raised slightly, but still cover the jersey script more than before. Where his shoulder once squarely faced the camera, it appears almost to be pointing straight at the batter in this picture. His stride leg still appears to be almost wrapped around his drive leg — consistent with the last image, but more dramatic than at any point before that. It’s worth noting that Hernandez walked 18 batters in just 32.2 April innings in 2016.

Skipping ahead to Hernandez’s return from the disabled list, things appear to be more problematic:

Hernandez’s hands are now at an all-time low, almost entirely covering the jersey script. The front shoulder still faces the batter more than it used to, and the angle of his stride leg seems as wrapped over the drive leg’s knee as ever.

The last exhibit from the 2016 season comes on September 5 against Texas:

Hernandez’s hands appear to have lowered even a little further. His stride leg is angled so much that it’s almost passing over his drive leg’s knee from our point of view. While his front shoulder once looked square and broad to the viewer, we now essentially just see the side of Hernandez’s arm, and little of the shoulder itself. At this point, he’s twisting less than ever, his hands are at their low point, and his stride leg is the most out-of-whack it’s ever been.

The final piece of evidence — and I apologize for the quality, but winter-league baseball isn’t streamed at the quality of MLB games — is from Winter Ball. Observe:

The camera angle here isn’t exactly the same as Safeco Field, but as the most recent piece of evidence of what Felix is doing, it should be included. First, some good news: Hernandez’s stride leg is more perpendicular with the ground than it has been since the first three innings of the muddy-mound game itself. His hands have been raised up above the jersey script partially, though not quite as high as before the injury occurred.

The bad news, though, is the worst news. Hernandez has less of a torso-twist in his windup than ever. In fact, we can’t even see his shoulder at the top of his windup — the only image where this is true.

Watching the video, the twist seems less dramatic than at any point. It should be mentioned that in the video this was lifted from, Hernandez’s line is: 1 IP, 2 H, 2R, 2BB, 1 K. He also threw a wild pitch with no one aboard, and threw the ball into center field for an error when the runner on first took off early.

So why did the King stop twisting so much? It’s hard to say. Hernandez has been known throughout his career as a guy that doesn’t watch much film of himself. He didn’t even start throwing bullpens in between starts until late in 2016. I exchanged messages with 710 ESPN Mariners Insider, Shannon Drayer, to confirm that both of those statements are true.

My hypothesis? He subtly changed his motion to not feel pain in his ankle after slipping on the muddy mound. Less twist means less torque, which means less force landing on the ankle, and that his legs will land just a bit sooner. This has caused his legs to be “ahead” of the motion of his upper body, and with that he’s lost his feel for his command.

As someone who doesn’t watch film, it seems entirely believable that once Hernandez got healthy, he didn’t realize he was doing anything wrong, and the bad habits he picked up to compensate for his injury became his new normal.

Velocity would be nice, but Hernandez, more than anything, needs to rediscover his command. He pitched at an ace level in 2013 with a 91.3 MPH average fastball. Velocity doesn’t usually return with age, but command can.

The path toward re-discovering his command appears clear. Hernandez needs to return to his older wind-up, when he twisted so much that the batters could read his name and number on his jersey. He became an ace when he began twisting, and began falling apart when he stopped twisting.

It appears that he made progress in winter ball with his hands and his stride leg. Though I remain skeptical that his performance is going to rebound in any significant way until he makes like Chubby Checker and starts doing the twist again.

Brett Miller does the agate page for the print edition of the Seattle Times. He is also a proud Washington State University alum, and good at drinking beer and taking criticism. Complain about this article directly to him at bmiller@seattletimes.com.

I chose to stick with hitters in this article, because pitching prospects are extremely difficult to predict, and I think the pitchers who do get the hype are typically deserving. However, I do see a trend of some unnoticed hitting prospects turning out great careers in the majors. Let’s get right to it.

1. Travis Demeritte – 2B – ATL

In 2016, Demeritte went from the Rangers’ to the Braves’ system and spent the entire year in high-A ball, where he dominated at the plate. A 2B with power like Cano, good speed and the ability to get on base is such a rarity.

In my opinion, Demeritte has the highest chance of being a perennial All-Star out of these five prospects. The middle infield in Atlanta has an extremely bright future. I’m predicting that Demeritte will make his splash in 2018, and make his first ASG appearance by 2020 (age 25). Let’s look at his numbers from a season ago:

Let’s compare these to the four All-Star 2B in 2016 and Brian Dozier.

Some things to keep in mind as we compare these players: Demeritte was playing in A+ ball, but he did play an average of 12 less games than these major-leaguers. As you can see, it’s basically a two-man race (other than Dozier’s 42 HRs) between Altuve and Demeritte here. While we cannot expect these A+ ball numbers to translate directly against ML pitching, Demeritte definitely deserves more attention in top-prospect lists. While he’s not quite as speedy as Altuve, he has more power, and he walks at a far higher rate. The one glaring weakness is the K numbers for Demeritte. However, some of the top players in the league K at very high rates. As long as the OPS stays high, it doesn’t really matter how a guy makes outs anymore.

I should note that 2016 was a breakout year for Demeritte; in years past he didn’t quite live up to his potential, and also served an 80-game PED suspension. These could be the main reasons why he hasn’t garnered much attention yet. He still has to prove himself to most. However, I’m sold. I’d pencil him in for the majority of the 2020s’ ASGs right now.

2. Ramon Laureano – OF – HOU

Laureano has all the tools: he can play any OF spot well, he has speed and pop, and he gets on base. Houston’s farm has taken a bit of a hit due to some trades in the last two years, but that’s because they knew they had guys like Laureano who don’t have super high trade value, but have a chance to be great ML players like the guys they traded. Let’s look at Laureano’s 2016 numbers.

The numbers speak for themselves. This is the making of a star; where is the hype? I know it’s not a huge sample size, and we don’t have much to go off from the previous year either, but in A+ and AA last year he put up those phenomenal numbers you see above.

If those aren’t All-Star numbers, then I don’t know what are. Laureano’s ability to play all three OF spots will keep him in the lineup everyday and help his chances of making it to the ASG. When he does get the call-up, if his numbers stay relatively close to this, there’s no way he doesn’t make three to four All-Star Games. As of now, he’s more of a speed threat, but as he develops, the speed/power combo will even out and he will be an Andrew McCutchen-type player. Keep tabs on this guy.

3. Christin Stewart – OF – DET

While researching Stewart, I couldn’t find an article more recent than September of 2015. There’s no one talking about him…why? As we know, Detroit is aging and looking to deal top players. So, I’m assuming we will be seeing a lot of opportunities for young guys to step up and prove themselves. Detroit’s system isn’t super deep, but that could change anytime if they do decide to move some key pieces. Regardless, I see Stewart as the prospect to watch moving forward; he has the tools to be an All-Star. Let’s check out his numbers from 2016.

The power is impressive, and by this chart he looks even a bit better than the two previous guys I mentioned. However, with the K numbers pretty high up there, and not a whole lot of speed, Stewart is a player that could fall into slumps. Often times, adjusting to the majors can be challenging, and some top prospects never quite figure it out. While Stewart’s MiLB numbers are pretty insane, his slump potential makes him a pretty risky pick here. However, I do believe that if he does indeed figure it out, he will make it to a few ASG and serve as an everyday player in this league for a decade. HRs and BBs get it done. Keep an eye on Stewart.

4. Jason Martin – OF – HOU

Another Houston OF prospect…another future All-Star? I think so. The future is certainly bright over at Minute Maid Park: Altuve is a cornerstone, Correa is a centerpiece, Springer is a baller, and they have prospects for days. If they can just figure out how to pitch, they could be a WS contender for the next eight years.

Why Martin, though? Let’s check out his 2016 numbers from high-A ball.

Impressive, to say the least. At just 20 years old, he pumped out 23 homers in 121 games. He walks every eight at-bats, and he also grabbed 22 bags on the season. The ability to walk and run (lol) will typically keep guys out of major slumps. While Martin is not a highly-touted prospect at this point, I think he will be a household name by 2022. I expect him to get the call-up in 2019 and play a significant role during a pennant race that year. In 2020, he will burst onto the scene and prove his worth to this franchise.

With Houston’s current build, this might be a guy we see dealt if they are trying to add talent at the deadline this year. That doesn’t change my prediction, however. I see Martin suiting up for the ASG a few times throughout his career. Stay posted.

5. Tom Murphy – C – COL

You can’t keep putting Yadier Molina in there every year. And with Buster Posey most likely making that change to 1B full-time within three years, Jonathan Lucroy getting dealt to the AL, Kyle Schwarber playing OF, etc, pathways for guys like Tommy Murphy open up. Making the All-Star Game as a C is not saying as much as other positions, in my opinion. A decent hot streak in the first half will inflate your hitting numbers. For example, Derek Norris in 2014. It may seem like he was the best catcher in the league at the halfway point, but, as usual, it evened out by season’s end.

With that being said, Murphy has proven he has pop, and playing in Colorado is a huge advantage for him. While I don’t think he will be a Hall-of-Fame catcher, I do think he’s flying under the radar right now and will probably open some eyes in 2017. I’d say he makes two appearances in the ASG before 2022. However, once he gets up near 30 and he’s no longer playing in Colorado, I think he will have trouble keeping a job.

I have him on the list, first of all, because he meets the criteria, and also because I think people should pay attention to him, and lastly because he’s ML-ready, unlike the rest of these guys. Trevor Story didn’t have a whole lot of hype; most people didn’t expect him to make the team out of spring, but with the Jose Reyes situation, the kid got a shot and as we all know, he ran with it. I’m not saying Murphy will make a cannonball-esque splash like Story, but I think he will turn some heads and maybe even get some ASG votes this year. Anything can happen, especially in Colorado. Keep tabs on him.

Honorable Mentions

Dylan Cozens – OF – PHI

There’s not a lot of buzz surrounding Cozens, which is surprising to me, because usually when we see 40 HR in 134 games, we really perk up. In his age-22 season, he played all 134 games at the AA level for the Phillies affiliate, Reading Fightin’ Phils, a place where most Phillies prospects prosper. The reason why Cozens doesn’t quite make the cut here is because of the words, “future All-Star.” He is one of those lefties that mash in the right ballpark and against RHP, but usually career platoon hitters, even if they are highly effective, don’t make the ASG.

Rhys Hoskins – 1B – PHI

Hoskins is another AA player in the Phillies system. He probably has a little bit more of a well-rounded hitting ability than does Cozens, but he’s a 1B, and that’s an overloaded position. You have to be incredible to crack that ASG squad, and I just don’t think Hoskins will ever be quite at that level. I do believe he will pan out to be an everyday guy for a good amount of time in this league. He has really good power and he gets on base, two things that will keep you in the lineup more often than not.

Bobby Bradley – 1B – CLE

Bradley is another guy I would keep an eye on; I’m just not sold on him yet. He has a a lot of raw power, but a really high K rate in the low levels of the minors. Also, he’s a 1B, so once again, really hard to make the ASG at that position.

Mariners starter James Paxton is going to win the 2017 American League Cy Young award. You heard it here first.

In baseball, there is no better time of year to have bold, lofty, and irrational expectations than in spring training. But there are numbers to back up this claim, even though he is a 28-year-old who has never made more than 20 starts in a major-league season.

Here is why this is going to happen.

Paxton has always pitched at the level of a top-of-the-rotation starter

There has never been a question about his talent. Paxton debuted in September of 2013, and took the league by storm immediately, posting a 1.50 ERA over 24 innings in four starts. In 2014, his ERA was 3.04 in 74 innings. His worst season, 2015, still featured a decent 3.90 ERA in 13 starts. Not ace-like numbers, but numbers that would put him in the top two or three of most rotations in baseball.

Paxton’s ERA was similar in 2016 (3.79) to his 2015 number, but he made dramatic improvements.

Utilizing a new arm slot taught to him by Tacoma pitching coach Lance Painter, his average fastball velocity rose from 94.2 in 2015 to 96.8 in 2016 — an almost unprecedented gain for a starter. Paxton gained newfound command with his new arm slot, walking just 1.8 batters per nine innings, one walk fewer than his already-good career mark of 2.8.

Digging a little deeper into advanced stats, Paxton’s numbers are similar to the game’s elite. Looking at the FIP of pitchers who threw at least 250 innings from 2013-2016 (the four seasons Paxton has spent time in the majors), Paxton’s 3.32 is 25^th in the league. Teammate Felix Hernandez No. 22 with a 3.27 FIP. The chart below shows where Paxton stands among other left-handed starters.

Paxton’s FIP over the past four seasons is eighth-best among major-league left-handers, and third-best among just the southpaws currently in the American League. That’s consistency.

Looking at 2016, Paxton’s 2.80 FIP ranked fourth-lowest in all of baseball among pitchers with at least 120 innings, and first in the American League. The next-closest American League pitcher, Corey Kluber, had a 3.26 FIP.

When Paxton is on the hill, he’s as good as just about anyone in the league. And his best numbers have come in his most recent season.

At 28, Paxton might still have room to improve. Paxton improved dramatically in 2016 in three major areas that he was already good at — strikeouts, limiting walks, and preventing home runs. In any case, Paxton’s ability to be a top-tier starter is obvious.

About that injured elephant in the room

It’s hard not to notice that Paxton has by far the fewest innings pitched among elite left-handers. It’s true, Paxton hasn’t been able to stay on the field. But his injury history doesn’t reveal the types of injuries one would expect to be recurring or career-derailing.

Paxton has been on the disabled list three times in his career, for a strained left oblique and shoulder inflammation in 2014, a strained tendon in his left middle finger in 2015, and for a sore pitching elbow after getting hit with a line drive in 2016. He also had start pushed back a day due to a torn fingernail.

This paints a picture of bad luck as much as being chronically injury-prone. Paxton has had trouble staying on the field, but it hasn’t been one faulty limb or ligament that just won’t get right. Perhaps he’ll suffer another major injury in 2017, but his injury history alone doesn’t include enough evidence to see it as an inevitability.

The 2017 AL Cy Young field isn’t that intimidating

Clayton Kershaw doesn’t pitch in the American League, so why can’t Paxton reach the summit of the junior circuit? The competition all have their own flaws.

2016 Cy Young winner, Boston’s Rick Porcello, is coming off the best season of his career by far. Not to mention, his teammates and fellow Cy Young contenders David Price and Chris Sale will take turns stealing the spotlight from one another.

It also remains to be seen how Sale adjusts to the right-handed-hitting haven of Fenway Park; teammate David Price saw his surface numbers suffer moving into the hitters’ paradise that is Fenway Park — his ERA ballooned to 3.99.

Among other contenders, Detroit’s Justin Verlander will be turning 34 and is coming off of his best season since 2013. It’s probably more likely that his current ability falls somewhere in between his very good 2014-15 and his Cy Young-caliber 2016.

The most credible threat to Paxton is Cleveland’s Corey Kluber, and he’s now on the wrong side of 30. Kluber also benefited from an above-average defense in 2016, while Paxton had one of the league’s worst defensive teams playing behind him.

As it stands, a thin field, as well as three top contenders’ home ballparks playing against them, gives a healthy Paxton as good of a chance as anyone.

Don’t forget the new outfield defense

Despite his outstanding FIP, Paxton’s ERA was a good-not-great 3.79, and his record was just 6-7. Certainly not Cy Young numbers.

But with a much-improved defense behind him, shaving a run off of his ERA isn’t unrealistic, and would likely increase his win and innings totals.

In 2016, the Mariners outfield defense was atrocious. Nori Aoki took the scenic route to every fly ball. Seth Smith and Nelson Cruz turned in defensive efforts that would be hard to call average in a slow-pitch softball league.

In The Fielding Bible’s defensive runs saved (DRS) stat, the Mariners 2016 outfield had a -27 DRS, making them better than just the Twins, Tigers, and Orioles.

Jarrod Dyson (+19 DRS), Mitch Haniger (+1) and a healthy Leonys Martin (-2) could help turn one of the worst outfields in baseball in 2016 into one of the very best. Paxton will certainly be one of many pitchers benefiting from a greater number of fly balls being turned into outs.

It’s also worth noting that the infield’s three worst gloves — Adam Lind (-2), Dae-Ho Lee (-3) and Ketel Marte (-2) — will be wearing different uniforms in 2017.

With the Mariners upgrading so many spots on defense, Paxton’s ERA should drop significantly. The difference between a 3.80 ERA and 2.80 ERA over 200 innings is 22 runs. If the defense saves him anywhere close that many runs, the additional wins would certainly follow.

Okay, so how does this make him a Cy Young contender?

Everything is in place for Paxton to take his rightful place in the upper echelon of major-league starters. He has the talent, and now a defense behind him that will help him cash in on his nearly limitless potential.

What he needs more than anything is a little good luck with the injury bug. Considering his luck over the past few years, he seems due for that. If that happens, American League hitters will certainly notice.

Paxton is one of the league’s five or 10 best pitchers. Pairing his ability with what should be one of the league’s best defenses should reduce his record and ERA to put him in a peer group with elite guys like Chris Sale, Corey Kluber, and Madison Bumgarner.

(I didn’t mention Clayton Kershaw because he is, of course, peerless.)

James Paxton will be your 2017 American League Cy Young award winner. See you at the award ceremony — or the loony bin.

Brett Miller does the agate page for the print edition of the Seattle Times. He is also a proud Washington State University alum, and good at drinking beer and taking criticism. Complain about this article directly to him at bmiller@seattletimes.com.

Back in December, I introduced “xFantasy” through a series of entries here at the FanGraphs Community blog. At its inception, xFantasy was a system based on xStats that integrated hitters’ xAVG, xOBP, and xISO in order to predict expected fantasy production (HR, R, RBI, SB, AVG). The underlying models are put together into an embedded “Triple Slash Converter” in Part 2. Part 3 compares the predictive value of xFantasy (and therefore xStats) vs. Steamer and historic stats, ultimately finding that for players under 26, xStats are indeed MORE predictive than Steamer!

To quote myself from the first piece, Andrew Perpetua over at the main blog has developed a great set of data using his binning strategy, which has been explained and updated this offseason, including some additional work since then to include park factors and weather factors. He produces xBABIP, xBACON, and xOBA numbers based on Statcast’s exit velocity/launch angle data, along with the resulting ‘expected’ versions of the typical slash-line stats, xAVG/xOBP/xSLG. Recently, Andrew has published a set of “2017 estimates” that takes the past two years of Statcast data and weights them appropriately to come up with the best estimate for a player’s xStats moving forward. After a bit of back and forth on Twitter with Andrew discussing how exactly these numbers get weighted, I think they are looking really good. I’m now adopting these numbers as the basis for xFantasy from this point on.

There are a few key takeaways from xFantasy so far that will tell us where to go next:

1. xFantasy is not *truly* a projection. We don’t have minor-league data. We don’t have data from before 2015. At this point, xFantasy for 2017 is a weighted average of player performance from 2015-2016, so keep in mind that things like injuries or down years might have tanked a player’s xStats.
2. More data is always better than less data. Steamer projections do a better job with established players than xFantasy does, likely due to having more info about past performance.
3. Players under 26 have short track records, and xFantasy beats Steamer in projecting them going forward! For young players, or players that have undergone some significant, recent transformation at the MLB level, xFantasy could give us better info than traditional projections.

So what’s it mean? At this time, I will echo Andrew’s repeated recommendations that you should *not* use xFantasy as your projection system of choice in 2017. On average, Steamer will do better (at least for now…I think 2017 could be the year where we finally have enough Statcast data to put up a challenge). But xFantasy could be very useful in helping you to identify players (on a case-by-case basis) with short track records that might deserve a bump up or down from the projections spit out by the traditional systems.

For now, I’ve identified 10 (five up, five down) hitters aged 26 and under heading into 2017 that might deserve a second look based on xFantasy. Included below is each player’s xFantasy line and Steamer-projected 2017 line, both scaled to 600 PA, along with the 5×5 $ values, and at the far right, the difference between the two.

While the Billy Butler/Danny Valencia debacle was definitely the most interesting thing going on with the A’s late in 2016, Ryon Healy was a pretty good story himself. He came seemingly out of nowhere to hit over .300 with 13 HR in 283 second-half PAs, playing his way into a spot as the everyday 3B and likely No. 3 hitter for the 2017 A’s. xStats says you should believe it, with a .324 xAVG and 30 xHR. Steamer hasn’t bought into the average/power yet, but the relatively low ~20% K rate looks real.

Trevor Story was the best player in baseball for a couple of weeks this past year, and it seems to me that the late-season injury has made people forget that. xFantasy didn’t forget, though, and even with the huge K-rate, is seeing a .281 xAVG with 39 HR and 12 SB. Based on this line, I’m slotting Story comfortably into the same tier of SS’s as Correa, Seager, and Lindor for 2017. Downgrade in weekly H2H leagues where the away games can kill him a bit.

Gary Sanchez and Trea Turner have been well covered by Andrew here and here. I’ll just add that even though both are expected to regress from their lofty 2016 performances, xFantasy backs up the idea that they’ll both still be among the best players in baseball. Steamer is missing the boat on both guys.

I personally had a love/hate relationship with Tyler Naquin in 2016, who bounced on and off my roster in the “Beat Paul Sporer” NFBC league and always seemed to hit well when he was on the wire, and never when he was on my team. He’s been a trendy topic this offseason among people still using “Sabermetrics 1.0” to point at his BABIP and say he’ll be terrible in ’17. Statcast says he actually hit well enough to earn a .370 BABIP! Combine that with what seems to be a developing power profile and something like 15 SBs and you’ll have a nice little player for your fantasy squad. Just hope Cleveland plays him!

On the downside, we have quite a few players that have been trendy ‘sleeper’ picks in the lead-up to 2017 drafts so far. Javier Baez, even if he manages to find playing time in a crowded Cubs infield, just hasn’t hit the ball well enough to overcome the poor plate discipline. Mitch Haniger hit .229 in limited time (123 PA) but Statcast says he hit even worse than that — let’s hope it’s just a sample-size thing, because a .213 xAVG won’t cut it if you’re only getting 20 HR from him.

Yasiel Puig has been in the major leagues longer than many of these guys, so at this point maybe we should just believe Steamer, but I figured it would be worth including him here because it’s an interesting case to study. He hit .255 and .263 in 2015 and 2016 respectively, and that wasn’t bad luck according to Statcast, with a .249 xAVG in that time. Steamer still buys a bounceback to his pre-2015 ways with a .284 projection. I’m actually leaning toward Steamer here, because I believe that Puig’s stats have been heavily influenced by his various leg injuries over the past two years. Maybe I should see repeated injuries and use that to project future injuries, but in this case I’m going to give a 26-year-old the benefit of the doubt and say that a healthy Puig should match this Steamer projection in 2017.

Two more 24-year-olds close us out:  Max Kepler was very, very good in July and very, very bad after that, en route to an xFantasy line that doesn’t believe in the power, and *does* believe in the very poor BABIP and AVG. Staying away from that garbage pile, and moving on to another…A.J. Reed! He was supposed to be the chosen one last year, and instead he gave us his best 2014 Melvin Upton impression…without the speed. His playing-time picture is even more unclear than Baez’s, and even if he plays, Statcast tells me he has some work to do.

And finally, for an honorable mention of a player that’s new on the scene, but too old to qualify, I have to bring up Ryan Schimpf:

Woah.

Next time…

I closed out Part 3 by promising xFantasy for pitchers was coming, and it is! Using a model based on scFIP, xOBA, and xBACON, xFantasy for pitchers v1.0 now exists. There’s still work to be done in order to determine how useful it actually is, though!

As I said last time, it’s been fun doing this exploration of rudimentary projections using xFantasy and xStats. Hopefully others find it interesting; hit me up in the comments and let me know anything you might have noticed, or if you have any suggestions.

Baseball is great! We all love baseball. That’s why we’re here. We love everything about it, but we especially love the players who stick out. You know, the ones who’ve done something we’ve never seen before, or the ones that make us think, “Wow, I didn’t know that could happen.” It’s fun to look at players who are especially good — or, let’s face it, especially bad — at some aspect of this game. They’re the most interesting part of this game we love.

But not everyone can be interesting. Some players are just plain uninteresting! Like this guy.
http://gfycat.com/TinyWeakBonobo
OMG taking a pitch? That’s boring. You’re boring everybody. Quit boring everyone!

https://gfycat.com/GargantuanCreamyAmberpenshell
You caught a routine fly ball? YAWN! Wake me when something interesting happens.

But it’s hopeless; nothing interesting will ever happen with Stephen Piscotty. I’m sure the two GIFs above have convinced you that he was the least interesting player in baseball last year. But, on the off-chance that you have some lingering doubts, we can quantify it. I’ve made a custom leaderboard of various statistics for all qualified batters in 2016. For each of these statistics, I computed the z-score and the square of the z-score. In this way, we can boil down how interesting each player was to one number — the sum of the squared z-scores. The idea is that if a player was interesting in even one of these statistics, they’d have a high number there. Here are the results:

Click through for an interactive version

I don’t need to tell you who the guy on the far right is. On the flip side, though, there are two data points on the left that stick out. The slightly higher of the two is Marcell Ozuna, with an interest score of 1.627. The one on the very far left is Stephen Piscotty, with an interest score of 0.997. That’s right — if you sum the squares of his z-scores, you don’t even get to 1! This is as boring and average as baseball players get.

Where the real fun begins, though, is when you start making scatter plots of these statistics against each other. I’ve made an interactive version where you can play around with making these yourself, but here are a few highlights:

AVG vs. SLG

IFFB% vs. OPS

ISO vs. wRC+

Pretty boring, right? But wait, there’s more! Let’s investigate a little further what went into his interest score. Remember how we summed his squared z-scores and got a value below 1? Well, let’s look at the individual components that went into that sum.

Yes, you’re reading that right — where he stood out the most was in games played and plate appearances. Yay, we got to see that much more boring! Also, I think it is especially apt that his AVG was EXACTLY league average.

All right, time to step back and be serious for a second. As Brian Kenny is always reminding us, there is great value in being a league-average hitter. Piscotty was worth 2.8 WAR last year, just his second year in the league. He’s already a very valuable contributor to a very good team. Maybe it’s time we started noticing guys who do everything just as well as everyone else, and value their contributions too?

(Nah, I’m going to go back and pore over Barry Bonds’s early-2000s stats for the next few hours.)

All the code used to generate the data and visualizations for this post can be found on my GitHub.

Following up on excellent recent pieces by Travis Sawchik and Jeff Sullivan, I had a hypothesis: If there is truly a swing-path revolution underway in MLB, perhaps the best hitters by wOBA and wRC+ showed more marked FB+LD%’s (Air%) tendencies in 2015-2016 than in years past? If not them, then perhaps there is a trend among the middle and/or lower classes of hitters?

The hypothesis was wrong, but the investigation still gave some interesting context to the 2016 power spike and the profiles of recent successful/unsuccessful MLB hitters in general.

Here’s a plot of the average FB%+LD% (Air%) for each year, 2009-2016, for all qualifying MLB hitters per FanGraphs leaderboards, divided into three roughly even buckets of 40-50 players by wRC+ (<100wRC+ left, 100-120wRC+ center, >120 wRC+ right):

Here’s a plot of the average FB%+LD% (Air%) for each year, 2009-2016, for all qualifying MLB hitters per FanGraphs leaderboards, divided into three roughly even buckets of 40-50 players by wOBA ( <.320 left, .320-.350 center, >.350 right):

The consistency of these numbers is remarkable. The writing has been on the wall for some time with regards to the benefits of hitting it in the air.

Perhaps plenty of hitters are (and always have been) trying to hit it in the air more often and are either failing to make the change stick, or not finding success quickly enough to stick with the change / stay in the league?

We aren’t seeing across-the-board nor player-class-specific changes that stand out beyond random variation by this method (yet).

There could be an equilibrium point here where given the best pools of pitching and hitting talent available (regardless of how they arrived at said status), the outcomes will be pretty similar at a macro level, save for major fundamental changes to how the game is played.

This does not mean that individual players cannot aspire to find more optimal approaches. Surely there have always been hitters finding success via these means, and only recently have we been focusing on batted-ball data and focusing on these traits of the transformations.

Preach on, Josh Donaldson: Ground balls? They call those outs up here.

In “Hardball Retrospective: Evaluating Scouting and Development Outcomes for the Modern-Era Franchises”, I placed every ballplayer in the modern era (from 1901-present) on their original team. I calculated revised standings for every season based entirely on the performance of each team’s “original” players. I discuss every team’s “original” players and seasons at length along with organizational performance with respect to the Amateur Draft (or First-Year Player Draft), amateur free agent signings and other methods of player acquisition.  Season standings, WAR and Win Shares totals for the “original” teams are compared against the “actual” team results to assess each franchise’s scouting, development and general management skills.

Expanding on my research for the book, the following series of articles will reveal the teams with the biggest single-season difference in the WAR and Win Shares for the “Original” vs. “Actual” rosters for every Major League organization. “Hardball Retrospective” is available in digital format on Amazon, Barnes and Noble, GooglePlay, iTunes and KoboBooks. The paperback edition is available on Amazon, Barnes and Noble and CreateSpace. Supplemental Statistics, Charts and Graphs along with a discussion forum are offered at TuataraSoftware.com.

Don Daglow (Intellivision World Series Major League Baseball, Earl Weaver Baseball, Tony LaRussa Baseball) contributed the foreword for Hardball Retrospective. The foreword and preview of my book are accessible here.

Terminology

OWAR – Wins Above Replacement for players on “original” teams

OWS – Win Shares for players on “original” teams

OPW% – Pythagorean Won-Loss record for the “original” teams

AWAR – Wins Above Replacement for players on “actual” teams

AWS – Win Shares for players on “actual” teams

APW% – Pythagorean Won-Loss record for the “actual” teams

Assessment

The 1993 California Angels 

OWAR: 39.3     OWS: 277     OPW%: .533     (86-76)

AWAR: 27.8      AWS: 212     APW%: .438     (71-91)

WARdiff: 11.5                        WSdiff: 65  

The “Original” 1993 Angels placed runner-up to the Rangers for the division title, yet the ball club held a fifteen-game advantage over the “Actual” Halos. Tim Salmon garnered 1993 AL Rookie of the Year honors with a .283 BA, 31 dingers, 95 ribbies and 93 runs. Devon White collected his fifth Gold Glove Award and posted career-bests with 42 doubles and 116 runs scored. “Devo” successfully swiped 34 bags in 38 attempts. Dante Bichette provided a .310 BA while clubbing 43 two-base hits and launching 21 moon-shots. Wally Joyner aka “Wally World” contributed 36 doubles along with a .292 BA. Chad Curtis tallied 94 runs and pilfered 48 bases in his sophomore season. Brian Harper (.304/12/73), Mark T. McLemore (.284/4/72) and Paul Sorrento (.257/18/65) augmented the Angels’ attack.

Wally Joyner ranked thirty-seventh among first basemen according to “The New Bill James Historical Baseball Abstract” top 100 player rankings. “Original” Angels registered in the “NBJHBA” top 100 ratings include Dickie Thon (57^th-SS), Tim Salmon (72^nd-RF), Devon White (81^st-CF), Tom Brunansky (85^th-RF), Dante Bichette (90^th-RF) and Brian Harper (99^th-C). Furthermore, the list includes Gary Gaetti (34^th-3B) and Chili Davis (64^th-RF) from the “Actual” Angels ’93 roster.

Original 1993 Angels                                      Actual 1993 Angels

Chuck Finley (16-14, 3.15) whiffed 187 batsmen and paced the Junior Circuit in complete games with 13. The Halos compensated for a pedestrian rotation with a stellar bullpen consisting of Bryan Harvey (1.70, 45 SV), Roberto Hernandez (2.29, 38 SV) and Alan Mills (5-4, 3.23). Mark Langston (16-11, 3.20) topped the “Actuals” in strikeouts (196) and innings pitched (256.1) while earning his fourth All-Star invitation.

  Original 1993 Angels                              Actual 1993 Angels 

Notable Transactions

Devon White 

December 2, 1990: Traded by the California Angels with Willie Fraser and Marcus Moore to the Toronto Blue Jays for a player to be named later, Junior Felix and Luis Sojo. The Toronto Blue Jays sent Ken Rivers (minors) (December 4, 1990) to the California Angels to complete the trade. 

Dante Bichette

March 14, 1991: Traded by the California Angels to the Milwaukee Brewers for Dave Parker.

November 17, 1992: Traded by the Milwaukee Brewers to the Colorado Rockies for Kevin Reimer.

Wally Joyner

October 28, 1991: Granted Free Agency.

December 9, 1991: Signed as a Free Agent with the Kansas City Royals. 

Bryan Harvey

November 17, 1992: Drafted by the Florida Marlins from the California Angels as the 20th pick in the 1992 expansion draft.

Brian Harper 

December 11, 1981: Traded by the California Angels to the Pittsburgh Pirates for Tim Foli.

December 12, 1984: Traded by the Pittsburgh Pirates with John Tudor to the St. Louis Cardinals for Steve Barnard (minors) and George Hendrick.

April 1, 1986: Released by the St. Louis Cardinals.

April 25, 1986: Signed as a Free Agent with the Detroit Tigers.

March 23, 1987: Released by the Detroit Tigers.

May 12, 1987: Purchased by the Oakland Athletics from San Jose (California).

October 12, 1987: Released by the Oakland Athletics.

January 4, 1988: Signed as a Free Agent with the Minnesota Twins.

November 4, 1991: Granted Free Agency.

December 19, 1991: Signed as a Free Agent with the Minnesota Twins. 

Mark T. McLemore 

August 17, 1990: the California Angels sent Mark McLemore to the Cleveland Indians to complete an earlier deal made on September 6, 1989. September 6, 1989: The California Angels sent a player to be named later to the Cleveland Indians for Ron Tingley.

December 13, 1990: Released by the Cleveland Indians.

March 6, 1991: Signed as a Free Agent with the Houston Astros.

June 25, 1991: Released by the Houston Astros.

July 5, 1991: Signed as a Free Agent with the Baltimore Orioles.

October 15, 1991: Granted Free Agency.

February 5, 1992: Signed as a Free Agent with the Baltimore Orioles.

December 19, 1992: Released by the Baltimore Orioles.

January 6, 1993: Signed as a Free Agent with the Baltimore Orioles.

Honorable Mention

The 2001 Anaheim Angels 

OWAR: 37.4     OWS: 267     OPW%: .467     (76-86)

AWAR: 31.1      AWS: 225     APW%: .463     (75-87)

WARdiff: 6.3                        WSdiff: 42  

The “Original” and “Actual” 2001 Angels finished in the American League West basement. Perennial Gold Glove center fielder Jim Edmonds socked 38 doubles and 30 long balls. “Jimmy Baseball” supplied a .304 BA with 95 runs scored and 110 ribbies. Mark T. McLemore batted .286 and nabbed 39 bags in 46 attempts. Troy Glaus crushed 41 circuit clouts and 38 two-baggers as he topped the century mark in runs and RBI. Garret Anderson rapped 194 base knocks including 39 doubles and 28 round-trippers while establishing a personal-best with 123 RBI.  Jarrod Washburn delivered 11 victories with an ERA of 3.77. Troy Percival (1.65, 39 SV) made his fourth appearance in the Mid-Summer Classic and furnished a 0.988 WHIP with more than 11 strikeouts per 9 innings pitched. Glaus, Anderson, Washburn and Percival appear on the “Original” and “Actual” Angels rosters in 2001.

On Deck

What Might Have Been – The “Original” 1999 White Sox

References and Resources

Baseball America – Executive Database

Baseball-Reference

James, Bill. The New Bill James Historical Baseball Abstract. New York, NY.: The Free Press, 2001. Print.

James, Bill, with Jim Henzler. Win Shares. Morton Grove, Ill.: STATS, 2002. Print.

Retrosheet – Transactions Database

The information used here was obtained free of charge from and is copyrighted by Retrosheet. Interested parties may contact Retrosheet at “www.retrosheet.org”.

Seamheads – Baseball Gauge

Sean Lahman Baseball Archive

Author’s Note: This is the second of a two-part article, both of which are intended to stand on their own. The first introduces terminology and a mathematical framework used to derive statistics; the second uses these new ideas to draw conclusions which are hopefully intriguing to the reader. If you need it as a reference, you can refer back to the first article (here).

Below, I’ll use some metrics – average and weighted-average Euclidian distance between relievers – to look at the 2016 season. Ideally, we’d like to be able to associate a covariate with these metrics. That is, we’d like to be able to say “bullpens with lower weighted-average distances are (blank),” where we fill in the blank with some common-sense concept or truism about the way we know the game to work. Short of that though, maybe we can just get an understanding of why the bullpens at either extreme have found themselves there.

So, without further ado, here are the bullpens of all 30 teams as sorted by weighted average Euclidian distance in 2016.

How can we interpret this? There’s no real obvious trend here: there are “good” and “bad” bullpens on both ends of the table, along with “good” and “bad” teams. At the extremes are good case studies, though: A subpar Phillies bullpen on a subpar Phillies team, a solid Orioles bullpen on a solid Orioles team, and of course, the Cubs. What can we learn from looking at them in more detail?

The 2016 Phillies Bullpen: An Ode to Brett Oberholtzer

Most people reading this know how the Phillies season went last year. They were supposed to be bad. Then, briefly, they appeared to be good. People did what they could to explain why the Phillies appeared to be good, including looking at their overachieving bullpen. As it turns out, the Phillies were bad after all. Baseball is fun.

The Phillies being bad explains part of what you see above. They tended to employ a lot of guys in the middle innings when they were already behind in the game. That’s a product of circumstance, and not an indictment of those guys. Elvis Araujo, Severino Gonzalez and Colton Murray weren’t great pitchers, and it’s sort of odd to have three of those guys rotating into your bullpen at various points in the season. Then again, the Phillies were bad, and those three guys were young, and they could afford to give young guys longer runs than a competing team could have.

There are those three guys, and then there’s Brett Oberholtzer, a slightly older, more experienced pitcher, whose MLB time before 2016 was mostly as a starter. He can be considered the quintessential mop-up guy in 2016. He’s way over there to the left – in fact, he had the lowest average score differential when entering the game out of any relief pitcher in 2016. Here’s what his inning-score matrix looked like:

This doesn’t even do Brett Oberholtzer justice, though. Here’s a histogram of score differential by appearance that puts it into context.

Oberholtzer made 26 appearances for the Phillies in 2016, and most of them were in garbage time. Then, there was the one appearance where the Phillies actually led when he came into the game. It was the 10th inning, and most of the Phillies bullpen had already been spent. Pete Mackanin had little choice but to bring Oberholtzer in to protect a one-run lead in the 10th. Which he did, earning a save. Brett Oberholtzer has no “regular” mode, no “normal” days. Baseball is wonderful. Baseball is weird.

Getting back to the Phillies bullpen as a whole: It’s not so atypical outside of Oberholtzer and an abundance of negative-score pitchers. Jeanmar Gomez was used in a fairly typical “closer” role, with Hector Neris and Edubray Ramos in higher-leverage setup roles. This all seems to comport with how we think of modern bullpens.

The 2016 Orioles: A Well-Oiled Machine

The Orioles had a very effective bullpen by most measures in 2016. Certainly, it helps to have Zach Britton churning out ground ball after ground ball, but overall the group was very effective, registering a league-leading 10.22 WPA for the season (with second place not being particularly close). Their 53 “meltdowns” were also fewest in the league. This was a playoff team, largely because of their bullpen. That is to say, this is a very different team than the 2016 Phillies.

That said, there are some similarities here.

The general shape is the same, although the Orioles were giving their bullpen a lead more often than the Phillies. One striking similarity is the presence of a “mop-up” guy, in this case, Vance Worley. Worley logged an impressive 64.2 innings in just 31 relief appearances. He was also never given the ball with a lead of less than six (!).

Worley soaked up a lot of innings for the O’s, and he did so in a rather effective way, ending with an ERA of 3.53 – a number which, while partially luck-driven, probably doesn’t suffer from quite as much inherited-runner variance as the average reliever. He created his own messes, and was allowed to clean them up, because Buck Showalter mostly thought the game was over anyway. The overall structure of a bullpen may be related, by necessity, to the depth that the starting rotation can get on a regular basis.

One item of interest here: The unweighted average distance is actually higher in the O’s bullpen than in the Phillies bullpen. When weighting by inverse variance, the Phillies show an even larger average distance, while the average distance narrows for the Orioles. This speaks to more rigid roles, particularly for the setup guys. Darren O’Day was very seldom called upon when the team was behind (four out of 34 appearances, none when trailing by more than three runs), whereas Hector Neris was used a bit more fluidly (18 out of 79 appearances, five appearances when trailing by five or more runs). There may again be a team effect at work here: Maybe the Phillies found themselves needing to get Neris work more often during long losing streaks, and were set on throwing him on a certain day regardless of score.

The 2016 Cubs: An Embarrassment of Riches

If you’ve been under a rock or are currently time traveling, this may shock you: The Cubs were really good last year. They even won the World Series! The Cubs!

OK, with that out of the way, this graph is going to look quite different than the previous two.

Did the Cubs ever not have a lead going into the seventh inning? Well, yes, I assure you that they did. Multiple times, in fact! However, they didn’t do it often enough to give anyone in their bullpen a “mop-up” role, or anything that resembles one. Look at that graph! The Cubs had Aroldis Chapman and Hector Rondon, and then they had seven other guys hanging out in the O’Day / Neris / Brad Brach neighborhood of the graph. What’s going on here?

There’s another thing that’s different about the Cubs which can help explain this. A lot of members of their bullpen have very high variances by score. Whereas O’Day, Neris and Brach have score variances in the single digits, many of the Cubs relievers have score variances north of 10. Take another look at the score variances in the Phillies and Orioles bullpen. Double-digit numbers are typically reserved for long men, mop-up guys, and lower-leverage relievers. Here’s Justin Grimm, who represents this pretty well:

Maybe this was a conscious decision by Joe Maddon, matching up in high-leverage situations with different arms. Maybe this was simply a necessary decision to keep everyone fresh in the face of repeated high-leverage situations: If you have late-game leads for five or six consecutive games, the same three arms can’t be used in all of them. It’s not as if Justin Grimm was used a lot in these situations, and no one would refer to him as a “high-leverage reliever.” He did have a dozen or so appearances in the high-leverage areas of the graph, though, and that’s not nothing.

You can chalk this up to the Cubs being really, really good in 2016, and likely, there’s some merit to that. But it also probably doesn’t tell the whole story. Out of 279 relievers with 20 or more appearances in 2016, only 18 of them had an average inning of 7 or later, an average score differential of 1 or more, and a score variance of 10 or more. Five of those 18 were on the Cubs. The Nationals, Rangers, Red Sox and Dodgers – all good teams in their own right, if not quite as dominant as the Cubs – had one such player each. The Indians had none.

It’s safe to say that Joe Maddon managed his bullpen differently than any of these teams in 2016. It’s also hard to argue with the results.

Author’s Note: This is the first of a two-part article, both parts of which are intended to stand on their own. The first introduces terminology and a mathematical framework used to derive statistics; the second uses these new ideas to draw conclusions which are hopefully intriguing to the reader. If you’re not into math, you can skip to the second article (here) and refer back to this one as needed.

Recently, I wrote about the inning-score matrix, and how we could refine the concept to put a finer point on when and how certain relief pitchers are used. Statistical oddities and outliers are always fun topics of conversation, and certainly, appearance data can give us that.

But can it give us more than that? I don’t care so much that Will Smith was used differently after he was traded or that Brett Oberholtzer was the closest thing to a true mop-up man in the game last year – OK, actually, those things are really interesting too – so much as I care to define how managers are employing bullpens. This may not even give rise to why managers are doing what they’re doing; it’s difficult to attribute intent when looking at numbers abstracted away from the human elements of the game. However, the decision to bring a specific relief pitcher into the game is a conscious one by the manager, largely influenced by game situation. To that end, appearance data can also be aggregated by team — and, if what we care about is the managerial decisions that give rise to bullpen roles, we should really be focused at the team level.

To gain insight into, and ultimately quantify, how bullpens are constructed, we need to define a few concepts. As we go through, I’ll do my best to explain the concept that we’re trying to quantify in baseball terms, before diving into the nuts and bolts of how I’m quantifying them.

Concept 1: Center of gravity

Your personal center of gravity is probably around your belly button – it’s the point at which half of your mass is above, half is below, half is left, half is right.

In addition to their physical centers of gravity (which they work so hard on, Bartolo Colon notwithstanding), relief pitchers have another “center of gravity”: the one at the center of their inning-score matrix. The inning-score matrix has two dimensions (score differential on the X-axis, inning on the Y-axis), and each appearance can be plotted in these two dimensions.

If we treat all appearances equally, a reliever’s center of gravity can be defined as the average inning and score when entering the game. This tells us a great deal about how the pitcher is being used on its own. For example, without looking at the names, you can probably guess which of these guys was a high-leverage reliever in 2016 and which was a mop-up guy.

Player A: Vance Worley; Player B: Zach Britton

The center of gravity is a snapshot of a player’s role. It doesn’t tell you everything – you can’t pick out a lefty specialist, for example, or a guy whose game situations changed drastically over the course of a season. In fact, in the latter case, a player’s center of gravity for an entire season may actually be misleading. Still, it’s the most information you can get about the player’s usage in a couple numbers. We’ll think of it as where the player “lives” in the inning-score matrix.

Concept 2: Euclidian distance

If you’re not a math person, ignore the word “Euclidian.” This is just “distance” in the way you think about it in everyday life. If I have two points in space, a straight line between them has a distance, and in layman’s terms, we’d say that the size of that distance constitutes “how close” or “how far apart” the two points are. Mathematically, for two points with coordinates (x_i, y_i) and (x_j, y_j), the Euclidian distance between them can be calculated as:

A bullpen lives in the two-dimensional space that we used to define center of gravity: For every appearance a member of the bullpen makes, there is an inning (y), and there is a score (x). In this space, each member of the bullpen has a center of gravity. As such, we can say the two pitchers in our earlier example were far apart, but that these two are close together:

Player A: Shane Greene; Player B: Justin Wilson

In fact, you can start to look at entire bullpens graphically, in order to form an image of how the bullpen is constructed. Our “twins” from above are easy to pick out when we do this:

Nice to look at, and the trend makes intuitive sense: guys who pitch later in games are generally also trusted with leads. But how can we use it to compare bullpens? We need metrics to quantify what we’re seeing above, to describe how similar or dissimilar the roles are in a bullpen. Then we can compare that to other bullpens and give context to how a team is managing their pen relative to the rest of the league.

Concept 3: Average Euclidian distance

The simplest thing one could do would be to sum the distances of the lines connecting each player’s center of gravity. This has the disadvantage of being biased: Bullpens which have more qualifying players will have more dots to connect and, therefore, more total distance.

Naturally, we can calculate an average of these distances instead. This requires us to know how many unique distances there are between distinct pairs of relievers. We can deduce this logically: From the first of n relievers, there are (n – 1) lines, connecting that reliever to all the others. From the second reliever, we’ve already drawn the line to the first reliever, so we can draw (n – 2) more lines, connecting him to the remaining relievers … and so forth. Thus, for n relievers in a bullpen, there are (n – 1) + (n – 2) + … + 2 + 1 distances between them, and we can calculate the average Euclidian distance as:

This looks intimidating, but the numerator is really just the sum of all the distances of all the lines that we drew. The denominator is the number of lines that we drew. Voila: an average!

Concept 4: Weighted-average Euclidian distance

You may be tiring of all this talk about Euclidian distance. It’s important, though, to take this one step further. To use the average distance between all members of the bullpen as a basis of comparison is to make the assumption that all relievers are created equal – that, if you’re a fan of the Indians, you care about the distance between Kyle Crockett and Dan Otero as much as you do about the distance between Bryan Shaw and Cody Allen. You probably don’t, and that makes sense – the former duo isn’t nearly as important to the makeup of the Indians’ bullpen as the latter. We should, therefore, be emphasizing certain relievers and the distances associated with them.

How do we characterize certain members of a bullpen as important, numerically? We could weight them by, say, the average Leverage Index at the time they entered the game; players who are trusted in critical situations are surely more important, right? The issue with this idea is that leverage is highly correlated with the inning and score – in fact, it’s derived from them. Weighting by Leverage Index would tell us that players in a certain area of the graph are more important to team success. This is intuitive and not very interesting.

What do we want to measure? It might be interesting to know how rigid or fluid a team’s bullpen is; that is, do they have a “seventh-inning guy” or a “mop-up guy” who is consistently called on in certain situations? In this case, we want to give more weight to relievers who have lower variance by game situation when entering the game. If the manager gives someone a highly-specific role by inning and score, that reliever is important insofar as the structure of the bullpen is concerned. That may not translate to how important they are with respect to the outcome of games, but presumably, that reliever has a fixed role because they have a skillset that in some way lends itself to his residence in a certain part of the graph.

Fortunately, the concept of inverse-variance weighting is an established mathematical concept. The idea is that players with lower variance by inning and score should be weighted more heavily. In short, this works in three steps:

1. For each pair of players, divide the Euclidian distance between them by the sum of score and inning variances associated with their centers of gravity;
2. For each pair of players, divide 1 by that very same sum of score and inning variances;
3. Divide the sum of results of (1) by the sum of results of (2).

Mathematically, this looks like this:

Portrait of a Modern Bullpen

If you’re still with me, you may be wondering what the use of all this is. Let’s summarize what we’ve done so far:

• The average Euclidian distance between members of the bullpen tells us how clustered or spread out that bullpen is as a whole.
• Using a weighted average refines that metric in order to emphasize members of the bullpen that have well-defined, rigid roles – usually a closer and a setup man or two, but sometimes a surprise as well.

We can summarize a bullpen with these metrics and a plot of all members of a bullpen (as represented by their centers of gravity). Here’s how the 2016 Marlins bullpen looks in a snapshot. The 2016 Marlins have been chosen because they were a very average bullpen in terms of performance as well as structure, on a very average team overall. I couldn’t find anything at all that stood out about them.

We can use this framework to compare bullpens going forward: Which teams have very large distances between relievers? Which are more clustered? Which are oriented differently? We can not only compare bullpens within a single season, but also how bullpen structures have changed over time across the league. We can explore whether the structure of a bullpen is consistent from year to year on a single team, or if certain managers have ways of managing their bullpens which consistently show up in the data associated with their teams. There are a lot of exciting possible applications.

And of course, we can point out statistical oddities along the way. Why wouldn’t we?