Beerrios! That’s a way better title, but we’ll stick with the original. So I’m spending my Saturday brewing a batch of beer and dealing with some pitchFx data. If everything goes well, you’re going to get some baseball info and some brewing highlights. But also Happy Opening Week! It’s the greatest time of the year.

All right, let’s deal with some baseball first. Jose Berrios had a pretty brutal 2016 with the big club — all in all, he started 14 games and rattled off a 3-7 record with an 8.02 ERA, an ugly 1.87 WHIP, and a not-top-of-the-rotation strikeout rate of 7.6 K/9. His FIP and xFIP were better but still not great at 6.20 & 5.64. His BABIP certainly didn’t help his numbers, sitting at 0.344, but that alone can’t explain how truly atrocious his numbers looked in his first taste of the big leagues. I’m going to use the pitchRx package to look at pitching data from 2016 and see if we can figure out what went wrong and how we can fix it.

All right, now on to the beer portion. Today I’m making my Deep Lake Dark Lager. Behind every great beer there is a great story. This story begins when I worked out at a remote research camp and fridge space was not reserved for amateur beer-making. A key process in lagering a beer is fermenting the beer at low temperatures, which is why I mentioned the fridge space. We got around lagering our beer in the fridge by putting the fermenting beer into a keg and dropping the keg into a lake to about 15 meters deep (~49 feet). At this depth the temperature was steady at about 5°C (41°F). A little tip for any newcomers to the brewing community: Your beer needs to maintain command, something Berrios couldn’t do. Zing!

If anyone wants to take a quick look at some gifs of Berrios’ sick curveball (and other pitches), check them out here: http://www.pitcherlist.com/Jose-Berrios/

I tried to find a comp for Berrios related to pitch velocity, and if we ignore his slider, Jacob deGrom comes out looking like a pretty good match. Here are how their pitch velocities line up using 2016 pitchFx data. I know it’s not a good idea to exclude one of deGrom’s best pitches, but I’m more interested in consistency between starts.

Just eye-balling, they look pretty good. Let’s take a look at pitch velocity by start.

Just looking by eye, it’s hard to tell if you could consider one guy more consistent than the other. But obviously we might be able to give deGrom the benefit of the doubt here, since he was pitching with scar tissue or bone spurs in his elbow. Either way, he was pitching in discomfort. There is one thing that catches my attention, though — it’s those last 11 starts by Berrios, and you can see his change-up velocities start to sneak up from ~83.5 to 86 MPH. The unfortunate thing is that there is no concurrent increase in four-seam (FF) or two-seam (FT) velocity. Near the end of the season Berrios was trying to complement his fastballs with a change-up that had a really poor velocity difference. Let’s check that out in a bit more detail.

Okay, you give that plot a bit more thought. My timer just went off and I’ve got to go sparge the grains. I converted a five-gallon water cooler into a mash tun for steeping my brews, which works awesome, because it’s insulated so it holds the heat really well. The aspect I really love about this beer is that is has a really light lager taste, but it has a nice dark colour, which makes it a great spring beer. And to get this effect in your beer is really simple. For the 45 minutes where you are steeping your grains, only add the light grains, then just before you sparge, throw on your dark grains (in my case carafa III). That way, as you sparge you get the colour from the dark grains and none of the taste. Yaaaay beer. Everything is all sparged and now I’ve got to bring the wort to a nice rolling boil.

All righty, let’s discuss that velocity difference. I’d say there is a similar trend from his early-season call-up and his late-season starts as well. He starts out with a pretty decent velocity difference, but with each start that difference gets smaller and smaller. Especially in the second half of the season — he started out with a fantastic velocity difference. That combination should have led to some really effective pitches, but as we move into September and October those pitches are starting to look more and more similar and their effectiveness all but disappears.

Back to brewing — boiling achieved! I’ve got to let the liquid boil down for a couple hours, so through the magic of the internet, let’s fast-foward to the next step. And what a fantastic surprise, the battery in my scale is dead and of course it’s some weird specialized kind that I don’t have on hand. Well luckily I wrote the weight on the bags when I packed the hops last fall so I’m going to eyeball it and hop(e) for the best. At least now I can honestly say I can never reproduce this batch, but that’s part of the fun. So I figure I added about an ounce of hops; we’ll really never know. I’ve got to let that boil for another 40 minutes then add the flavour hops and some irish moss.

I think we can agree that this was not a season marked by consistency for Jose Berrios. But I was curious as to how his release point affected the velocity of each pitch. For all of the data presented here, I used the pitchRx package to download and store the 2016 pitchFx data. In the pitchFx data, you can pull out the release point for each pitch recorded throughout the season. Using this data, I created a general additive model using the bam() function for the R peeps out there, and within the bam function I modeled pitch velocity and pitch break separately using a Gamma link. I like to use the Gamma link because, in a not very sciencey description, it’s very flexible and fits a wide range on models. So first, a couple of notes; 1) There are two plots coming up; the first predicts pitch velocity and the second predicts pitch break length (movement). 2) Pay attention to the prediction window, the coloured box, for each pitch. And 3) These models were only run on Berrios.

And pitch break (break_length):

You can tell that velocity and break length change with different release points. I mean, there is a pretty complicated relationship with how his release point affected both the pitch break and the velocity, and I’m not really sure what the sweet spot actually is. His change-up velocity plot has a really nice faded red area sort of right in the middle of the prediction grid. This area represents roughly an 84.5 MPH change-up which would complement his 93 MPH fastball quite nicely, but unfortunately his arm slot seems to be drifting along an axis which we will get to in a second. Did you happen to notice how the coloured boxes moved slightly among pitches?

So remember how Berrios was apparently tipping his pitches this past year? Well, if not, check this out. So the way he was delivering the ball basically gave the batters a full view of what was coming. I mean, I know I don’t possess the ability to spot small things in deliveries and assess pitches. I watched gifs of Berrios throwing all of his pitches over and over many times and I can’t pick anything up. But I am sure that there are players out there who can pick up those minor details. So I’m thinking there may be more to this than just how he started his wind-up, and where he was releasing the ball was also giving batters a clue as to what was coming. Check out this plot showing how Berrios and deGrom released their pitches.

So you’re probably wondering what’s going on there. Each ellipsoid represents a different pitch, curveballs in blue, 2-seamers in orange or orange-red etc. Each ellipsoid contains 95% of the pitches thrown for each pitch type. Generally deGrom releases the ball about a foot over in comparison to Berrios, but that’s not what it important. What’s important is how each pitcher’s change-up overlaps with their respective fastballs. deGrom has remarkable consistency to throw both types of fastballs and his change-up, and the ellipsoids are basically completely overlapping. Right away we can see that something is going on with how Berrios is releasing his change-up. It only overlaps with about half of his fastball release points, but his arm angle also seems to be drifting, and you can see the ellipsoid is stretched one direction. So I’m guessing he’s not only tipping his pitches in his wind-up, but there is also some release-point trouble happening here that no doubt some hitters are able to pick up on.

Final update on the beer: I added in the flavour hops and irish with about five minutes left and took everything off the heat. Luckily, it’s still a bit cold here so I left the beer outside to cool for a couple hours to get it down to room temperature so I could pitch the yeast. And fast-forward a couple of days…I let the yeast start the fermentation process at room temperature for a couple of days, then moved it into a fridge. I’ll leave it there for about three weeks, transfer the beer to a keg, and then it’s basically ready to drink!

Thanks for sticking it out to the end; I hope you enjoyed “Beerrios.” This ended up having a lot more deGrom in it than initially planned, but I think it was a good comparison to include. I think we were able to successfully identify a couple serious flaws from Jose Berrios’ debut season, and hopefully he’ll be able to shake that off, work on fixing his mechanics, and take another shot at the majors in 2017. I have a feeling we are going to see him mid-April or early May, and I really hope we get to see what he can do over an entire season. If he can transfer just a fraction of his minor-league success to the majors, we will get to see a pretty dynamic young pitcher, and the Twins have been waiting a long time to get a pitcher of this caliber back into their rotation.

So I got a little carried away with the new splits leaderboard when I was looking up some wRC+ data. I was curious about which players performed the best/worst in high-leverage situations and one thing led to another and it led me to looking at top performers across the three leverage situations (low, medium, and high). If you want to know more about how leverage is calculated there is an old article in The Hardball Times here.

I used the splits leaderboards to gather 2016 hitter data by leverage situation and I only included players who had a minimum of 20 PA per split. Once I gathered all the data I converted each player’s wRC+ by leverage situation to a percentile and calculated each player’s mean percentile rank along with the variation around the mean using standard deviation to produce the following plot.

The blue line is just a LOESS line showing the general trend of the data. What the line is telling us is that players on the extreme end of the percentile ranks also seem to have the lowest variation or, more simply put, good players seem to be consistently good and bad players seem to perform poorly across all leverage situations. Using that plot as my baseline, I started exploring the data to answer some question about player performances in 2016. I included the top 10 players in ordered tables going from from least interesting to most interesting, at least in my opinion. First, let’s look at the top performers from this year.

Boring, Mike Trout leads the way as the top performer. Apparently it doesn’t matter when he comes up to the plate; he is going to smash the ball. But I’m not going to focus on Trout, as I’m not qualified to write about him and he’s above my pay grade, so let’s leave him to the professionals. Like I said before, least interesting first and hopefully it’ll get more exciting as we go. Here’s a fun fact to keep you going: In high-leverage situations among players with a minimum of 20 PA, Ryan Howard led the league in ISO with a 0.640 mark. Ryan Schimpf was second with an ISO of 0.542. And Howard did that with a 0.118 BABIP, too.

Second, let’s take a look at the worst performers of the season.

After a pretty impressive career, although it also came with its fair share controversy, we see A-Rod make this list. And it doesn’t look like he is going to be playing again this year, which casts some doubt on whether he is going to make it to 700 career home runs (he’s currently at 696).  But more importantly, our poorest performer of 2016 looks to be Yan Gomes. I was inclined to say A.J. Pierzynski should actually be considered the poorest performer of the year since his standard deviation was about half of Gomes’, but then I noticed that Yan Gomes was in the 0th percentile in high-leverage situations — literally the worst. Not all-time worst, but still pretty bad! And I guess if you want to argue that the worst percentile should actually be 1, as in the 1st percentile, then you could make that argument, but the value was rounded to 0 when Yan Gomes registered a whopping -72 wRC+ in high-leverage situations. The second-worst was Gerardo Parra at a -59 wRC+; that’s a pretty significant gap between first and second. Fun-fact time: In high-leverage situations, Mike Zunino ran a 30.8% walk rate, although he also struck out 30.8% of the time too. Yasmani Grandal had a 30.4% walk rate to go with a much smaller 13% K%.

Everyone always seems to be looking for players who are on the extreme ends of the leaderboards, but let’s give some love to the unsung heroes of the world, the completely average performers! I wasn’t sure if I simply wanted to use mean percentile rank as a measure for averageness, so I decided to go with what I called Deviation in the table. Deviation is calculated by adding the standard deviations (SD) of a players percentile ranks to the Δ50 column. The Δ50 column is calculated as the absolute value of a players mean rank minus 50.

And Scooter Gennett comes away as the most average performer of the season! He also ran a 0.149 ISO on the season and I think 0.150 is usually considered average. Look how wonderfully average these guys were; we should all take a minute to enjoy the little things in life. I realize this may not be the sexiest table, but it’s still interesting. You might not be getting a whole lot out of these guys over an entire season, but they are going to go up there and do average things whether you like it or not.

Two tables left — hopefully you’re still with me here. Let’s look at consistency. People always say consistency is key. I guess that’s good advice except when you’re on the terrible end on the spectrum.

Ramon Flores and Ivan De Jesus both had extremely consistent seasons; it’s just too bad they are on the wrong end of the spectrum. But I have to say Ramon Flores beats out Ivan De Jesus as he registered on average 12 percentile ranks poorer. In third we see Mike Trout showing incredible consistency while being the top performer in the league, followed closely by Paul Goldschmidt. It’s interesting see the top four players on this list from opposite ends of the spectrum, but the rest of this list bounces back and forth as well.

And here we are, the last one or as the title says “the Funky”. I found that volatility was the most interesting question, or which players showed the most boom or bust in 2016. Most of the players in this list performed best in low- and medium-leverage situations, often above the 90th percentiles.

After perusing though the list, one of the most interesting names that jumps out should be Jarrod Saltalamacchia and his 97th percentile rank in high-leverage situations last year. And here’s another twist, would it surprise you to hear that in 2016 Miguel Cabrera was the least-clutch hitter among all Tigers qualified hitters? Check out the Tigers leaderboard here. But the 2016 volatility award goes to Sandy Leon, who absolutely mashed balls in low-leverage situations, was no slouch in medium-leverage spots, but dropped off the map in high-leverage situations. I have no idea how BABIP relates to wRC+, but with Sandy Leon it looks like his BABIP reflects what was happening in the different situations (0.434, 0.393 and 0.190). There is probably some combinations of descriptive stats that would explain some of the variance, and BABIP may very well be included, but I’m not going to go into that here.

Hope you enjoyed this. If anyone wants a copy of the R code I used to make the graph and tables, leave a comment below and I’ll pass it along. I ended up finding a pretty cool library to create html tables in R so you don’t have to mess around with formatting and manual inputs. As long as you’re willing to put a little work into understanding css you can basically customize the look of your tables.

Going back to January 2016, Dave Cameron wrote an article detailing the breakdown of money owed to Chris Davis over the life of the deal he signed last year. For myself, this provided insight into how teams value long-term contracts, but more importantly it led me to more questions about how money depreciates over time. Fast-forward to the present and we start to see some articles and comments with people speculating about how much money teams are going to throw at Bryce Harper when he reaches free agency in a few years. The numbers have been pretty incredible; $400 million? $500 million? Even $600 million? Then someone threw out an even larger number: $750 million.

The best thing to do is ignore these numbers because we are still a couple of years away from free agency and he just had a down year where he was “only” worth 3.5 WAR, which gave the team a value of $27.8 million. At some point the numbers don’t even make sense because the contract values are getting so inflated. But at the same time, good for him, maybe he’ll buy a baseball team once he retires, or a mega-yacht. But unfortunately we will need to wait until after the 2018 season before we find out the value of this contract. In the meantime, speculation will run rampant and the media will throw out inflated numbers for the amusement of the masses.

Now, the purpose of this article is not to predict the value of Bryce Harper’s future contract, but to examine a few scenarios as to the actual value in present-day dollars. To do this I will use the concept of Net Present Value (NPV) from Dave Cameron’s Chris Davis article and then use some of the numbers from his article predicting a contract for Bryce Harper. Let’s set a couple rules; (1) Match the length of contract given to Stanton — 13 years, (2) use nice round numbers and get as close to the total values as possible, (3) use a discount rate of 4%, (4) this is an exercise in futility and not to be taken too seriously and finally (5) to estimate NPV for a massive contract.

Here are the scenarios for a 13-year contract totaling in excess of $400M, $500M and $600M.

Over the life of this contract, the value of each in NPV is significantly less than the actual amount signed. That’s because $5 today won’t buy you as much five years down the road. To get a little more numerical, 13 years from now currency will lose ~40% of its value. Quoting the Chris Davis article again, the league and the MLBPA have agreed to use a 4% discount rate to calculate present-day values of long-term contracts. Since important people within the industry take this into account, that’s likely why we don’t see too many contracts with a significant amount of deferred money.

Since players are taking — and I use this term very lightly — a “hit” when they sign a long-term deal, I wondered what kind of contract structure would benefit a player the most. Again, I wanted to use nice round numbers, so I settled on a 10-year, $100M contract, looking at an equal payment structure, a front-loaded contract, and a back-loaded contract. Here’s what I came up with:

There’s not a huge difference, but a player would gain just over $5M by signing a front-loaded contract as compared to a back-loaded contract. It seems as though the agents and the MLBPA are more concerned about total dollars rather than NPV since they probably want to drive up total contracts.

And in case you’re wondering what those annual salaries would look like in NPV from the table above, I’ve created another table to show what those salaries actually look like in NPV over the life of our hypothetical 10-year contract.

What I was hoping to show you next was a cool interactive plot similar to the table above, but instead of showing you the annual salaries it will show cumulative earnings as the life of our 10-year/$100M contract as time progresses. Well unfortunately I am unable to get this plot to show up on this webpage; it has something to do with WordPress being unable to use Javascript. If you’ll bear with me, you can click the link below (it just opens a new window and shows the plot).

https://docs.google.com/spreadsheets/d/19qGcrwGmdZemmYG_LaP_Ay6_5g6hL3VKT8z-Q3-PWXI/pubchart?oid=422413074&format=interactive
Front-loaded contracts seem to have the most benefit to the players themselves since they actually get more value out of any long-term contracts they might sign. For a player to maximize their career earnings it looks like it would be way more beneficial to sign shorter-length contracts with higher AAV than those long-term contracts. Maybe that is why we are beginning to see more deals with opt-out clauses in them.

This week the strike zone has been getting a lot of attention. If you’ve been paying any attention to baseball (and I’m sure you have since fantasy baseball leagues are starting to open up) there have been a few articles/releases suggesting that MLB may be considering raising the strike zone from the hollow beneath the kneecap to the top of the kneecap. It seems like a good idea since strikeout rates are on the rise, but was this a result of (1) pitchers getting better or (2) hitters getting worse or (3) have strikes been getting called differently? I’ll give you a hint; it’s neither of the first two suggestions, at least not directly. No, instead let’s focus on the strike zone and more specifically two things: (1) visualizing the strike zone from 2008 to 2015 and (2) using a standardized set of pitches look at how those pitches have been called over time.

Let’s go through the methods I used before we get to the plots. I used the pitchRx package in R to gather and store the data and used many of the functions included in the package. Next I went through the data and subset the PITCHf/x data by year since I was interested in looking at annual changes. Now due to a combination of time restraints and lack of computing power I didn’t run all of the pitches thrown in each year so I did some subsetting instead. I downloaded a CSV from the FanGraphs leaderboards of all qualified pitchers from 2008 to 2015. In each year I randomly selected 20 pitchers from the list of qualified starters to represent how the strike zone was called for that given year. Finally I ran the data through a general additive model (seen here) which was used to create the “heat maps” for the probability of called strikes in the plots below. I also tested the probability of five standard pitches being called strikes, but that is addressed a bit more later one so I won’t bore you with the details twice. Added note: if anyone actually wants a copy of the R code leave a comment below and I’ll get in contact with you.

Below I’ve included a GIF of the strike zone from 2008 to 2015 . If you watch it a few times you’ll begin to notice the gradual changes to the bottom of the strike zone, plus when it flips from 2015 to 2008 you can really notice the difference. It’s not surprising that there are inter-annual differences between the zones since I’m sure MLB makes a few minor tweaks every off-season and maybe there is a changing of the guard over time for the umps. I also need to apologize about the 2010 plot, the left (L) and right (R) are reversed and I can’t seem to switch them. We will just have to deal with that one plot being different. In all plots the label “L” refers to left-handed batters and “R” to right handed batters.

Now I wanted to find a way to quantify changes to how pitches were being called and I decided on using a set of standardized pitches. Below is a plot showing the locations I chose for my test pitches. I went with five different locations. The pitch right down the middle was my control of sorts, just to make sure things were getting called consistently over time. The remaining locations were the ones I was really interested about; three of those pitches were all located on the lower edge of the strike zone and the final pitch was located 0.2 feet or 2.4″ (the metric system would be more useful here, just sayin’) below the bottom edge of the strike zone. When I initially began this simulation I expected that the lowest pitch would be a second control pitch that would consistently be called a ball, but the results were pretty surprising. Also, I’d like to include that the strike zone to lefties is slightly shifted so that more outside pitches are called strikes.

OK so we are almost at the exciting conclusion. Using those standardized pitches from the plot above I used the general additive model to predict the probability of that pitch being called a strike in a given year. The results are summarized in the plot below. We can see that the pitch being thrown at coordinates 0, 2.5 (the one down the middle) the probability of being called a strike is basically 100% every year. Well that’s a good thing at least that call is consistent. The low pitch thrown down the middle on the bottom edge of the strike zone, coordinates 0, 1.7 (green line), has increasingly been called strike since 2008 to both right- and left-handed batters. Pitches down and in to righties increased pretty significantly this past season where the probability crept above 50%; to lefties that pitch is down and away and it’s been called pretty consistently since 2011 (red lines). Pitches thrown down and away to righties or down and in to lefties (coordinates 1, 1.7 — purple lines) haven’t changed all that much over the time period.

Now we get to what I think is the most interesting pitch. The low fastball down the middle (coordinates 0, 1.5) the one that should be out of the strike zone. This pitch is represented by the gold/yellow lines on the plots. In 2008 these pitches had a chance of being called a strike ~10% of the time to both righties and lefties. Over the last eight seasons that number has trended upwards and in the 2015 season settles in somewhere around 36-40%, which is not an insignificant proportion.

Based on this data it certainly appears as though MLB is justified into looking at raising the strike zone. Pitchers that live down in the zone have been given an increasing advantage in a relatively short amount of time. Hopefully this sheds some light onto the debate on whether or not to raise the strike zone in the coming seasons or maybe the umps will be able to make some adjustments for the upcoming season.

Some know him as “The Freak”, while others like myself know him as “Big Time Timmy Jim“. Tim Lincecum is planning on showing if he’s got anything left in the tank sometime next month. This year he had some problems with his hip and ended up getting surgery in mid-September. Here’s a link to a some info about hip labrum surgery for those who are interested. Early in his career he was one of the most dominant starters out there and you could make an argument that for a short period he was the most dominant pitcher in baseball. Over the last four years he’s become a dependable 4th or 5th starter, but the 2015 season was one of the worst of his career.

Age has seemingly caught up with another pitcher. Lincecum is yet another example of a pitcher whose velocity peaked early in his career and has been on a decline ever since. We don’t have PITCHf/x data for his rookie 2007 season, but we have the data for the rest of his career. Besides the 2011 season where he regained some form, he’s shown a pretty consistent decline in velocity over time.

To me, the obvious outlier is the most recent season where he saw his average fastball velocity dip below 88 MPH and about 2 MPH slower than the 2014 season. This is where we can see how his hip issues affected his velocity on the mound. Below is table with his peripheral stats (excluding his rookie season). To give a quick overview, K/9 has been trending downward, possibly relating to his diminished velocity. It doesn’t look like his BB/9 or HR/9 has any significant trend, but FIP has almost always been more generous than ERA.

As I said before, Lincecum recently had hip surgery and I assume he is nearing the end of his rehab since he’s planning a February showcase to try and secure another contract. Given his uncertain injury status, and his performance over the last four years, he’s likely only going to be able to secure a 1-year contract possibly with some performance bonuses. Teams are definitely taking a risk if they decide to sign him, since over the last two years he has been just slightly above replacement level, accumulating o.1 WAR in 2014 and 0.3 WAR in 2015. I’ll also mention that as a starter in 2014 he was worth 0.3 WAR, and he was worth -0.2 WAR as a reliever.

He’s certainly not the most imposing pitcher to ever set foot on the mound, standing 5′ 11″ and weighing in at 170 lbs (maybe with a wet towel wrapped around his waist); he’s one of those pitchers who needs to use his whole body to gain the necessary momentum to get those 90+ MPH fastballs. If you go back and look at the fastball velocity chart above it’s pretty clear that there was a significant drop in velocity this previous season. I think it’s pretty fair to think that his hip issues had something to do with that phenomenon. Here’s a link to an article from MLB Trade Rumors with some info about his surgery. I remember reading a more in-depth article earlier in the off-season saying that his hip issues were screwing with his mechanics, but I’ve been unable to find a link to that story. But the takeaway should be that he wasn’t healthy. He wasn’t able to generate the necessary power due to his hip issues and his velocity suffered as a result.

So the question becomes, if the surgery was a success and his rehab goes well, what can we reasonably expect from him for the upcoming season? Well that is definitely a tricky question since he’s almost 32, he’s two years removed from throwing in the 90s, and there’s the possibility that he won’t be back with the team that drafted him. I think in the best-case scenario we could see him start hitting his 2012-2013 velocity (~90.3 MPH) and if that’s the case we could start to see his K/9 creep up to around the 9.0 mark again. But that’s just my opinion and my opinion means basically nothing, so I’ll include a comparison.

I was only able to find one example of a pitchers who’d undergone the same type of surgery as Lincecum and that was Charlie Morton. In October 2011 he also underwent the hip surgery. You can check out his velocity chart below. He also had Tommy John the following June so if you’ll humour me and ignore the elbow issues you’ll see that his velocity over the 2011 season dropped from 94 to just under 92, only to return to 95+ after recovery from TJ.

Over the last two years Lincecum has amassed 0.4 WAR and made $35 million. There is no doubt that the Giants overpaid for his service over the last couple of years and I can’t see him getting anywhere near that annual salary. If we go by the market rate of ~$8 million/WAR, on a bounceback contract where a team expects a 0.5 WAR season we could see a contract in the ballpark of $4 million. Even that seems high to me; if I were to venture a guess I would put it around the $2-million mark with incentives. I’m definitely not saying he’s going to be the pitcher from five years ago, but a dependable 4th or 5th starter with the potential to strike out almost 200 batters sounds pretty awesome to me. You’ve always got to wonder if he’s got any magic left in him. Baseball is better with The Freak in it and hopefully he gets back on the mound soon.

Only a few of the major free-agent names remain available as we approach the new year. One of the most intriguing is Alex Gordon. He’s not only been an excellent fielder over the course of his career, but he’s also been an above-average hitter. His age-25 and 26 seasons were cut short by injury and I think we can give some leeway to a 23-year-old rookie for not having an above-average bat, but otherwise he’s had an excellent career. Here’s are his stats throughout his career:

There’s no doubt that he’s a great baseball player. He’s also accumulated 3 seasons with 6+ WAR since his rookie season. But there’s always the question as to whether a player has peaked or not, especially when their age starts creeping into the 30s. To try and answer this I look at the OPS values he’s put up over the years and extrapolated those numbers into his age-40 season. Below, in black, are the seasons that he’s already played. I’ve also included a line-of-best-fit through the data with the black portion representing past seasons and the red portion representing his future offensive output. Based on the seasons he’s put together, the model predicts that he will peak at about 34 years of age. Most players peak in their late 20s, but it’s not unheard of for players to peak later. Projections should always be taken with a grain of salt, but whichever team decides to take a shot on Gordon could expect his offensive production to remain relatively constant over the next few years.

So what does this graph tell us? Well basically nothing! It’s not very good practice to extrapolate past the range of your data, but it is interesting nonetheless. Also, considering Gordon has been so good for so long it’s tough to assume that he hasn’t peaked yet. That’s not to say he can’t continue to improve or even perform at a high level, but since it’s getting later in the offseason and so much money has been thrown at pitchers let’s assume he signs for 4 years. Below are his projected OPS values and as you can see from the graph above that Gordon may not even be in his offensive prime.

So far I’ve shown you data for Gordon’s career and also used that data to project his performance over the next 4 years. Assuming he signs a 4-year contract this off-season I wanted to find his closest comparables from his career so far and see how those players performed through their age-35 season. In order to compare players I used the Mahalanobis distance for all players that fell into the following criteria; (1) played in every season from their age 29 to 31 seasons, (2) at least 1200 ABs over that time and (3) played every season in their age 32-35 seasons. The Mahalanobis distance was calculated using common offensive statistics standardized by the number of at-bats. Here is a table with the lowest Mahalanobis Distance’s to Alex Gordon through his career thus far as well as their cumulative WAR for their age 32-35 seasons.

Last year Dave Cameron broke down the cost for WAR here and found the number to be somewhere around $7 million. Tim Dierkes projected a 5-year, $105-million contract or roughly $21 million per year. In order to live up to that annual salary, he would have to produce about 3 WAR per season which is 12 WAR for a 4-year contract and 15 WAR for a 5-year contract. Melvin Mora, Jim Edmonds, Ken Caminiti and Lou Whitaker each exceeded that 3-WAR threshold.

As this offseason progresses, offers will undoubtedly be presented to his agent so now it’s only a matter of when he signs. Based on the players that he was compared to, Alex Gordon definitely has the potential, not to mention the ability to exceed the standards of the contract he inevitably signs.

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

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

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

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

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

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

Innings pitched (IP) seems to be the standard for judging a player’s workload. Sure it will tell you how deep into a game a pitcher went and it’s often used as a measure of pitcher durability, but it tells you nothing about a pitcher’s effectiveness. A far more useful stat is the pitch count during each particular outing, or even better pitches per innings pitched (P/IP). I think we can all agree that all innings are made differently. A pitcher can throw three pitches or it can take 61 pitches as evidenced by Steve Trachsel (1997 – Chicago Cubs) and still get credit for 1 IP. Actually I think it’s possible to throw zero pitches and get 3 outs, but I don’t have the motivation to look up the rule at this particular moment.

Here are some stats for three players in the 2015 season.

All the players in the table above have very similar peripheral statistics, aside from an IP difference of 12 between players 1 and 2. From looking at these stats it’s a toss-up as to who has had the most successful season — do you choose player 2 since he has the most IP or player 3 since he’s made the most starts? In the table above Chris Heston is player 1, Matt Harvey is player 2 and Yovani Gallardo is player 3. What really separates the players is the pitch counts and P/IP.

Chris Heston – 2461 Pitches and 15.4 P/IP

Matt Harvey – 2533 Pitches and 14.8 P/IP

Yovani Gallardo – 2959 Pitches and 17.5 P/IP

Chris Heston has 12 IP less than Harvey but has thrown 72 fewer pitches this season. Harvey and Gallardo have thrown about the same amount of innings, but Gallardo has thrown 426 more pitches this season. The reason I chose Harvey as one of the pitchers for this comparison is due to the very public feud between the Mets, Boras and Harvey. In case you missed it, there was a disagreement with the innings limit imposed on Harvey in his first season after Tommy John surgery. Boras wants the Mets to stick to 180 IP while the Mets thought it was more of a soft cap. I wanted to look at the relationship between the IP in a season and the total number of pitches thrown. Luckily this data was readily available for download via FanGraphs, but only pitch counts back to 2002 were available. Below is a plot showing all pitchers who threw more than 100 innings in a season compared to their pitch counts. The data has a linear relationship, with the red line showing the mean and the outside black lines are the prediction intervals where we would expect 95% of the observations to fall within.

Now based on the 180 IP limit imposed on Matt Harvey, a linear model predicts that a pitcher would throw 2867 pitches in a season with an upper limit of 3158 and a lower limit of 2576. Now this means that at 180 IP we can reasonably expect a pitcher to throw between 2576 and 3158 pitches. Now for a guy coming off a major surgery, doesn’t a range of 582 pitches seem a bit extreme? It basically amounts to a difference of 5 complete games’ worth of pitches. In the plot below I also highlighted an innings range based on the range of innings where a pitcher throws 2867 pitches in a season. Now most importantly this range extends from 160 to 200 innings.

The medical team could just have easily set a limit anywhere between 160 and 200 IP. This is why an innings limit doesn’t work well in this situation; there is just too much variability in the data. In the future it will probably be a better idea for team officials and the medical staff to discuss a pitch limit over a season instead of an innings cap. Since the main goal of limiting a pitcher’s workload is to reduce stress on his arm I think the plot above does a good job showing that innings limits will have very little effect on actually managing a pitch count. Harvey is obviously thinking about the long term here because I know he doesn’t want to go through another surgery. After a second Tommy John the chances of a pitcher returning to the majors drops to somewhere around 30%, not to mention the drop in potential future earnings.

So I’ve shown you why I don’t think IP is a good indicator and now I’m going to show you why I think pitch counts and P/IP should be more important statistics.  Based on the linear model shown in plot 1 the formula to predict pitches in a season is as follows: Pitches = IP*14.5 + 256.9. Now the intercept for this model is 256.9 which suggests that if you don’t throw a single inning in a season you would still be expected to have thrown 257 pitches. Obviously there is something going on at the lower inning totals, but we are going to ignore that for the purpose of this article. As an added note, the lower prediction interval from plot 1 has an intercept of -33.975, so we are very within range of showing 0 pitches for 0 IP from this model.

Heston and Harvey both rank very high in P/IP among qualified starters while Gallardo is dead last among qualified starters. Efficiency is key here. Should Harvey be directly compared to Gallardo based on IP? No, absolutely not, Harvey is among the most efficient pitchers in the game this year. He has been able to get through innings while keeping his pitch count down and most importantly reducing stress on his arm. An inverse prediction based off pitch counts was used to predict the IP in the table above. Based on their pitch totals from this season Harvey and Heston have “thrown” less than their IP totals suggest and Gallardo has actually thrown quite a bit more. This has a big effect on that innings cap imposed on Harvey for this season. His stats show that he’s thrown 171.2 IP, but based on the number of actual pitches he’s thrown in game situations his number may be closer to 157 IP. Does that mean he should have the equivalent of 23 IP left in the tank for this season? Well that’s not up to me, but IP should less important than total pitches.

One thing I didn’t look at this article was the proportion of pitches thrown throughout the 2015 season. It’s been in the back of my mind, but I don’t have a reference for what the most stressful pitches are on a pitchers arm. I think it’s safe to assume that all pitches are not equal. Let’s think a Dickey knuckleball vs. Chapman fastball. The amount of effort needed for each pitch type is likely highly dependent on the pitch speed and type, but to simplify things here I’ve just assumed that all pitches are equal. We also need to realize that all pitchers are not equal, whether it be mechanics or individual variation in abilities. I was curious to see where Mark Buehrle’s pitch count (leaderboard here) lined up with all other pitcher since 2002 and lo and behold he’s thrown the most pitches since records became available. Obviously he doesn’t throw as hard as many of the other guys in the league, but that hasn’t stopped him from being a workhorse and one of the most effective pitchers over the last decade.

In the past few years a number of high profile pitchers have gone under the knife for Tommy John surgery (TJS). This surgery involves reconstructing the ulnar collateral ligament (UCL) in the throwing arm to re-stabilize a players elbow. I’ve heard a few stories about TJS — firstly, pitchers who get the surgery are able to throw harder after the procedure and another where college pitchers were voluntarily undergoing the procedure and sacrificing a year of pitching due to the belief that they would be able to throw harder or have more stamina. Whether either of these are actually true I have no idea, and I didn’t do any digging to find the answer. Instead I wanted to take a closer look at some pitchers who’ve undergone the procedure in the last couple of years and compare their performances before and after the surgery. In the table below I’ve included 4 players who missed the entire 2014 season or a significant portion of it. Matt Harvey underwent the procedure in October of 2013 while the other pitchers had the surgery sometime in 2014.

In 2013 all of the pitchers had pretty good years. They all made at least 26 starts and threw at least 150 innings. Fernandez and Harvey were both striking out more than one batter per inning, while Moore and Corbin still posted very respectable numbers. Now Harvey and Corbin didn’t pitch at all in 2014 and the other two suffered their injuries early in the 2014 season. Matt Moore only pitched 10 innings so it is tough to draw any conclusions due to small sample size, while Jose Fernandez threw 51.2 innings before he was shut down. His 2014 season was looking very promising posting very high K/9 numbers with a low ERA and his FIP and xFIP were even more favourable.

Now lets jump ahead to 2015. If you want to check over their 2015 stats they are in the table above. I’m not going to regurgitate them for you, but I will give a quick synopsis of each player. Harvey is having an excellent first year in his recovery, and in limited sample Corbin and Fernandez are also throwing really well. Matt Moore has had a season to forget so far, but he is just about return from a stint in AAA where he posted pretty strong numbers so the jury is still out.

Any time a player is coming off a major injury it is entirely within reason that psychological issues, fitness/conditioning or lack of practice has an effect on their performance. Without any first-hand knowledge of their unique situations fans always want a pitcher to just step right back in and perform at previous levels without any decline in performance. It’s tough to only compare stats from a before and after season and say with confidence whether a pitcher has lost any ability. So I wanted to go a step further and look at some PITCHf/x data and take a look at how their fastball, breaking ball and change-up velocities have changed, as well as any changes in the movement of their breaking balls.

Let’s start off with fastball velocities. As you can see from the table above Matt Moore has data going all the way back to 2011. His fastball velocities have decreased each year which should be a cause for some concern. The remaining 3 pitchers have all shown increased fastball velocities since their rookie years. Whether this is proof that TJS has an effect on increasing pitch speed I’m not sure and I’m not going to speculate, but I would welcome any comments from people who may have some theories. I’ll let you read through the rest of the table, but in general, Moore is showing decreased speed for all of his pitches this year and everybody else is throwing their stuff just a little bit harder.

OK now that’s enough looking at tables, let’s move on to some pretty graphs. Who doesn’t like a nice graph? So the first one from the set of pitch trajectories that I’m going to show you are the mean fastball trajectories from each pitcher with different colours showing a trajectory from different years. Now I’ll admit that I don’t know much about trajectories and how to analyze them, but the interesting part that I found from these was the release point. Matt Harvey has been remarkably consistent with his fastball release point; Fernandez and Corbin haven’t changed all that much either. But look at how Moore’s arm slot has dropped in the last three years. Now again I’m certainly no expert in pitching mechanics but something seems to be going on there that might be related to the drop in velocity that we saw above.

On to the curveballs! There doesn’t seem to be too much going on with arm slot changes here. Fernandez looks like he changed up his arm slot from the 2013 season and his release point has been almost identical in 2014 and 2015. Harvey on the other hand has slightly dropped his arm, but from my standpoint it doesn’t seem too significant.

Lastly we come to the sliders. Look at Harvey and Corbin! If the pitches weren’t different colours it would be very difficult to tell them apart based on the release point. Moore seems to have dropped his arm slot from the 2013 season, but his release point has remained the same the last 2 years. Corbin is definitely targeting the bottom corner of the strike zone with his slider; it looks like he may be trying to get hitters to chase. Moore and Harvey look like they are also doing a good job of keeping those pitches down in the zone.

For those of you who are not too familiar with stats, I’m going to give you a quick lesson about confidence intervals. In the plots below I’ve included the 95% confidence intervals. Basically if the ends don’t overlap from the coloured bars you can consider the differences from year to year to be significantly different statistically (boring!). On to the fun stuff — the year after Fernandez and Harvey had TJS, the spin rates on their curveballs are considerably lower. I know it’s a little tough to tell if the bars are overlapping on Harvey’s curveball, but trust me, the lines aren’t overlapping. Maybe both pitchers are a little worried about their elbows or maybe it’s just advice from the doctor, trainers, coaches, their parents, who knows. Harvey is also showing a decreased spin rate on his slider from 2 years ago. If we ignore 2013 for Moore, then Moore and Corbin have maintained consistent spin rate from their last season.

And finally we get to our last plot; hopefully I’ve kept you all interested up to this point. This is looking at the pitch movement (in inches). The decreased spin rate illustrated above for Fernandez and Harvey’s curveball has also led to less movement. Fernandez has lost just a little over a 1/2 inch from his curveball since last year, but about 1.5 inches from his 2013 curve. That seems like an awful lot, but I don’t know if there has been any change in the effectiveness of his curveball in that time. Oddly enough after TJS the sliders are showing more movement. Maybe that elbow is a little more stabilized, or maybe it has something to do with increases in velocity, but unexpected on my end to see that.

From what I can tell Harvey, Corbin and Fernandez haven’t lost a step. Moore is somewhat of a mystery though. It’s tough to tell if anything has changed, but he only threw 10 innings last year so any direct comparison to last year would be useless. I’m a little alarmed at Moore’s decreasing fastball velocity since 2011. He’s going to need to start relying on his secondary pitches if he’s going to be successful going forward. But the basic conclusion that I’m going to draw from this analysis is that players are able to come back from Tommy John and still be effective. I’m sure there are articles that argue in favour and against my conclusion, but by showing you some information about pitch speed, release point and spin rate you can go ahead and make you own conclusions.

It’s been just over a month since Ian Desmond’s mid-season outlook. Things were not going well for Ian Desmond, playing in his contract year in 2015 he was hoping to set himself up for a massive pay day. After turning down a reported $107 million dollar extension, Desmond was hoping for a productive 2015 season. Things could not have gone much worse in the first half of the season.

Desmond’s monthly splits reveal a roller coaster season for the soon-to-be free agent. March and April started out slowly, his play picked up in May, and then June came. The month of June was simply abysmal, so of course let’s take a more in-depth look at his numbers that month. His performance that month compared to his career averages were all much worse. He walked only 3% of the time while striking out 33.3% of the time (just over 10% higher than his career average). Any time you combine a low walk rate and a high strikeout rate you can expect a really poor OBP. In the month of June his OBP (note: NOT HIS BATTING AVERAGE!) was below the Mendoza line and his wRC+ was 22. That means in the month of June Ian Desmond created 78% less runs than league average. For a player in his walk year and especially someone who turned down over $100 million, it should be concerning to say the least.

Then something strange happened: Ian Desmond started turning his season around after the All-Star break. His stats in the second half have been a complete turnaround. He’s walking more, striking out less but still more than his career average, and generally just performing better. His August BABIP is well above his career average suggesting that we can expect some regression at some point.

While only 35 games into the second half, his performance compared to the first half is night and day. He has already hit more home runs and stolen more bases in less than half the games, and his RBI total is inching closer to his first half mark. Most importantly, in the second half of the season he has been worth 1.1 WAR (Bryce Harper for comparison has been worth 1.5 WAR in the second half). Not only is this good news for Desmond’s free-agent stock, but the Nationals will need all the help they can get while they try to chase down the teams in front of them for a playoff berth. As of right now, the Nationals are 5.5 games back of the Mets for the division lead and 10.0 games back of the Cubs for that second wildcard.

As an added bonus, I thought it might be useful here to show a plot of Ian Desmond’s career trajectory as predicted by his seasonal OPS. This model was created using the methods presented in the book “Analyzing Baseball Data with R” by Max Marchi and Jim Albert, and I’ve excluded Desmond’s age-23 season where he only played 21 games.

Based on the age trajectory graph it looks like Desmond may have already peaked in his career. What this means for his potential earnings this upcoming offseason remains to be seen. Any GM looking to add a top-tier hitting shortstop for the next few seasons will inevitable come calling his agent, but the data tells us that his best days may be behind him.