The shift has taken the MLB by storm in recent years.  Broadcasters love to criticize the shift, despite its numerous advantages.  One potential problem that the shift may cause is an increase in fielding errors.  This may be a direct result of fielders playing out of their normal position.  Using the shift data provided to FanGraphs courtesy of Baseball Info Solutions, as well as batted ball data courtesy of Baseball Savant, I ran a logistic regression to find the likelihood of a batted ball resulting in a fielding error.

The approach I used to find the probability of a batted ball being a fielding error was to run a logistic regression.  The variables included in the regression were release speed, hitter-pitcher matchup (dummy variable with a value of 1 if the pitcher and hitter were both righties or lefties), runners on base dummy, launch speed (exit velocity), effective speed, launch angle, and dummy variables for both traditional and non-traditional shifts.  The model only included batted balls that were hit in the infield, as the majority of shifts occur in the infield.

Above are the results of the logistic regression used to determine the probability of a batted ball being an error.  The dependent variable is whether or not the error occurred.  Two results that logically make sense are Exit Velocity (Launch Speed) having a positive coefficient and Launch Angle having a negative coefficient.  Both of these variables are significant on the 1% level.  Exit Velocity having a positive coefficient shows that the harder the ball is hit, the harder the ball is to field.  Launch Angle has a negative coefficient, meaning that the lower the angle (meaning a ground ball over a fly ball) the more likely the fielder is to commit an error.  Both of these results are logical, and are consistent with research that has been conducted in the past. The most interesting results from the model are both traditional and non-traditional shifts leading to an increased likelihood of an error occurring.  Both variables were statistically significant on the 5% level, and prove that players struggle more in the field when playing out of their normal position.

While teams are unlikely to change their shifting patterns (more good comes out of the shift than bad), they must take into account which fielders are worse when playing out of position.

Despite the increased probability of an error occurring, I still believe that the positives out weigh the negatives when it comes to shifting.  In future research, it would be interesting to look at this data on a minor league level, as well as seeing if fielders who shifted more in the minors are more prepared to field out of position in the majors.

If you play in a traditional 12-team 5×5 roto auction league with 25-man rosters and a $200 FA budget per season, you might constantly feel like there is solid waiver-wire talent out there, but your roster is too stacked to cut anyone. So, you offer your league-mates a trade of two or three mediocre players for one of their better players, but they are facing a similar roster crunch and immediately see right through your pernicious plan. It can be tempting to cut the lowest-production, lowest-upside player on your roster, which in many cases is the $1 catcher you drafted. But is that catcher really providing value to your roster? Let’s break it down.

Let’s say you draft Realmuto this year for $10 and expect a line of 13 HR, 53 R, 58 RBI, 7 SB, .275 AVG (Steamer projected line, ~500 PA).  The other cost of drafting Realmuto is the opportunity cost of his roster spot. In a typical fantasy week, there are three or four days where your typical starting lineup is not intact. Whether it’s because a team is having an off-day or one of your regular starters is DTD with a bruised toe, holes in your lineup are bound to happen. A smart streamer can look for good matchups and plug those holes. If you have unlimited pickups allowed in your league, then there is no cost to picking up a player if you have an open roster spot. In my league, I can pick up players for $1 on free-agent days (M/W/F).

This begs the question: if you are streaming to fill in holes four times per week over 26 weeks of the regular season, and each game you plug in a streaming player you get 4 PA, then that is going to equal just over 200 PA and cost you around $78 FAAB (assuming three pickups per week * 26 weeks, and one of your streamed pickups fills holes twice in one week for a total of four fill-ins). What does a slash line of 200 PA for a waiver-wire bat look like?

Kevin Pillar screams waiver-wire bat. His Steamer projection reduced to 200 PA looks like: 5 HR, 25 R, 20 RBI, 5 SB, .270 AVG. That’s quite worse than Realmuto’s line in every way excepting AVG. It amounts to a little less than 50% of Realmuto’s line at the cost of $78 FAAB. Now you could argue that maybe amidst all your streaming you end up picking up a Jonathan Villar 2016 breakout type of bat and end up sticking with him and getting immense value, but that’s easier said than done. Maybe you are also going to research pitcher vs. batter matchups on a daily basis and you get an edge there, but that is also easier said than done.

How does the 200 PA of Kevin Pillar compare to a $1 draft day, bottom of the barrel catcher’s line? Even poor Jonathan Lucroy is projected by Steamer to beat this line: 10 HR, 44 R, 46 RBI, 2 SB, .268 AVG. Other such luminaries projected to outshine it include Tucker Barnhart, Christian Vazquez, and Tyler Flowers. Pretty much any catcher who is a starter and can bat .250+ for a season will put up much better counting stats than the Pillar line.

Long story short — even though your catcher’s line may look meek, and they don’t play every day, making your roster look thin, it will still likely be better than waiver-wire lineup hole streaming. Better to save your FAAB cash for other needs. If you play in an unlimited transaction league, you would still need about 500 PAs of Pillar to exceed the Realmuto line. That’s a lot of transactions, and you might not have time to get all the necessary PAs in. Punting C is like heeding the siren calls — it can be very tempting, but also a dangerous and costly exercise. Staying the course with the catcher you drafted is usually the best call in terms of value per FAAB dollar spent.

There is a segment of the population of the United States which meets the following criteria:  between the age of 18-21, devout FanGraphs reader, and was mesmerized by the movie “Moneyball.”  I have read the book and watched the movie a number of times, as well as dedicating time to understanding the guiding principles in the book and how they relate to professional baseball.  The relationship between on-base percentage and scoring runs in Major League Baseball is well established, but has anyone ever taken the time to examine the relationship at the collegiate level?

Collegiate baseball is volatile — roster makeups change dramatically each year, no player is around more than five years, not to mention there are hundreds of teams competing against one another. In terms of groundbreaking sabermetric principles, this study is not intended to turn over any new stones, but rather present information which may have been overlooked up to this point, which is the relationship between on-base percentage and runs scored in collegiate baseball.

To conduct this study, I compiled a list of Southeastern Conference team statistics from the 2014-2017 seasons (Runs Scored, On Base Percentage, Runs Against, and Opponents’ On Base Percentage).  I then performed linear regression on the distribution by implementing a line of best fit.  Some teams’ seasons were excluded due to inability to access that season’s data, and I felt like removing the 2014 Auburn season on the grounds that it was an outlier affecting the output (235 runs, 0.360 OBP).  Below is the resulting math:  the R², and the resulting predictive equation:

pic.twitter.com/4Fib3YNqhj

— T Hooper (@thooperfangraph) December 8, 2017

Runs Scored = ( 3,537. x OBP ) – 933.6791

R² = 0.722849

I am by no means a seasoned statistician, but in my interpretation of the R² value, the relationship between Runs Scored and OBP in this is moderately strong, with a team’s OBP accounting for roughly 72.3% of the variation in Runs Scored in a season.  Simply, OBP is statistically significant in determining the offensive potency of a team.

At the professional level, the R² is found to be around 0.90.  The competitive edge the Oakland A’s used in “Moneyball” was using this correlation to purchase the services of “undervalued” players.  But what about in college?  Colleges certainly cannot purchase their players, but the above information can be useful to college programs.

For example, the average Runs Scored per season of the sample I used was roughly 347.8.  If an SEC team wanted to set the goal of being “above average” offensively, they would be able to determine, roughly, what their target OBP should be by using the resulting predictive equation from the Linear Fit:

pic.twitter.com/icI3tbcX78

— T Hooper (@thooperfangraph) December 8, 2017

Does this mean if an SEC program produces an OBP of .362 they would score 348 runs precisely? Obviously not. Could they end up scoring exactly 348 runs? Yes, but variation exists, and statistics is the study of variation.  Here are a few seasons in which teams posted an OBP at or around 0.362, and the resulting run totals:

pic.twitter.com/XaR2Ed1s6P

— T Hooper (@thooperfangraph) December 8, 2017

The average of those six seasons’ run totals was 347.5, which is pretty darn close to 348, and even closer to the average of 347.8 runs derived from the sample.

Another use for this information is lineup construction and tactical strategy in-game.  The people in charge of baseball programs do not need instruction on how to construct their roster and manage their team, but who would disagree with a strategy of maximizing your team’s ability to get on base?

The purpose of this study was to examine the relationship between On Base Percentage and Runs Scored in college baseball, and how the relationship compares to its professional counterpart.  To conclude, the relationship between OBP and runs exists at the collegiate level, and carries considerable weight and value if teams are willing to get creative in utilizing its ability.

Disclaimer: I am a beginner-level statistician, and if you have any suggestions or critiques of this article, please feel free to share them with me.

Theodore Hooper is a Student Assistant, Player Video/Scouting, for the University of Tennessee baseball program.  He can be reached at thooper3@vols.utk.edu or on LinkedIn at https://www.linkedin.com/in/theodore-hooper/

Because I believed Jeff Sullivan that there was a 2% chance Ohtani would sign Friday, I wrote this article, that now reads a bit weird, but I’m not going to change it because I have to get back to the job that I do for money instead of for fun. Any complaints about said weirdness should be addressed to Jeff Sullivan.

The phrase “sure thing” is thrown around a lot in sports to describe things that are not actually sure things. Atlanta was going to win the Super Bowl. Up 25 points, it was a sure thing until it wasn’t. Shohei Ohtani is not a sure thing to be a superstar in MLB, or even an All-Star. He’s not even a sure thing to be an average big-league player. History is littered with players that were star players one day and also-rans the next. But what Ohtani is a sure thing to do is pay off his price tag. Barring a tragic accident or something else outside of the realm of baseball, the team that signs Ohtani will surely earn more than $20.5 million extra during the 2018 baseball season that they would not have earned without him.

To understand why this is a certainty, you can look at Stephen Strasburg in 2010. The Nationals were the worst team in baseball in 2009, finishing with 59 wins for the second consecutive season. They were not much better in 2010, adding 10 more wins to that total, but still finishing 5^th in the NL East. Their overall attendance for 2010 was bad, which is to be expected. 1,828,066 were said to have paid money to see the Nationals play that year, or about 22,500 per game. That was only about 10,000 higher, on the season, than they managed in 2009. Strasburg’s first game was electric (I was there). It was the kind of atmosphere that made no sense at all for a team that was mired in long-term terribleness. The game, played on a Tuesday, sold out with attendance only rivaled that season by opening day, up to that point.

But that only tells a small part of the story. The two Tuesday games the Nationals had played at home prior to this game averaged about 16,000 fans. It’s pretty safe to say that this game, against the Pirates, would have been in a similar range without Strasburg. But the Strasburg effect was much wider reaching. First, once it became known that Strasburg was pitching, the Nationals created a ticket package to sell many of the unsold tickets. The package included the Strasburg game, plus three additional games. For those that came to the stadium without a ticket, their choices were between that and the suddenly busy scalpers.

The weekend before Strasburg’s debut, the Nationals drew almost 91,000 fans against the Reds. That was about 6,000 more than they drew during their previous weekend series against the Orioles. But the Orioles are not really a fair comparison because they are Beltway rivals of the Nationals. If you go back the weekend series before that, when the Nationals were playing the Marlins, just over 63,000 came to the ballpark. Now, some of this might have been random or based on other factors, but fans were anticipating Strasburg’s debut and buying tickets in anticipation of it — fans including the humble author of this post. Some even speculated that the Nationals intentionally misled fans in order to juice the gate.

Strasburg’s second start was in Cleveland, who also seemed to have benefited from a large Strasburg-related spike in attendance for that game. His third game was a Friday and was sold out. Again, even weekend games prior to Strasburg were sparsely attended. The Saturday game after his start was nearly sold out, likely due to fans incorrectly believing it was going to be the day Strasburg pitched. His 3^rd home game was the first that did not sell out. But there is more to the story (again, I was there). This game was played during the week, during the day, and it was literally at or above 100 degrees that day. There were still almost 32,000 fans there. After pitching on the road, Strasburg again sold out the stadium for his 6^th start and had a large, but not sold-out game for his 7^th. His next home start, another Tuesday game, again sold out. I’ve probably gone on long enough, if not too long. If you didn’t know how much Strasburg boosted attendance, you do now.

And here is the question: As much hype as there was in D.C. during the summer of 2010, do we really think that Ohtani’s hype won’t meet or perhaps even far exceed it? I certainly do. Additionally, the team that signs Ohtani will have a much easier time plotting and planning exactly how they can wring the most dollars possible out of their fans. In 2010, the Nationals created a multigame package on the fly, but now teams are exploring more and more ways of earning extra dollars through dynamic pricing. If a team like Seattle were to get Ohtani and announces that he’ll be pitching the second game of the season, the added revenue they would be able to earn would be astounding. Last season, the Mariners’ attendance dropped from 44,856 on opening day to 18,527 the next day. With Ohtani, it’s safe to say they’d sell out their second game.

If you’ve stayed with me this long, you might be wondering “yeah, I knew all of this already, so what?” And yes, most FanGraphs readers probably already believed that Ohtani is going to really juice attendance wherever he ends up. But then, why did three teams not even bother to try to acquire him? There simply is no justification. If you are the Marlins, you can do both things. You can say you are cutting payroll by $50 million, but at the same time if Ohtani for some reason picks the Marlins (he wouldn’t), you find the $20 million to pay him. You will get it back and more. Take out a loan. Heck, take out a payday loan with onerous and unfair terms and you will still end up ahead. It simply makes no sense. He is, from a financial standpoint, literally a sure thing.

Earlier this season I set out to build a tool similar in nature to my dSCORE tool, except this one was meant to identify swing-change hitters. Along the course of its construction and early-alpha testing, it morphed into something different, and maybe something more useful. What I ended up with was a tool called cHit (“change Hit”, named for swing changers but really I was just too lazy to bother coming up with a more apt acronym for what the tool actually does). cHit, in its current beta form, aims to identify hitters that tend to profile for “impact production” — simply defined as hit balls hard, and hit them in the air. Other research has identified those as ideal for XBH, so I really didn’t need to reinvent the wheel. Although I’d really like to pull in Statcast data offerings in a more refined form of this tool, simple batted ball data offered here on FanGraphs does the trick nicely.

The inner workings of this tool takes six different data points (BB%, GB%, FB%, Hard%, Soft%, Spd), compares each individual player’s stat against a league midpoint for that stat, then buffs it using a multiplier that serves to normalize each stat based on its importance to ISO. I chose ISO as it’s a pretty clean catch-all for power output.

Now here’s the trick of this tool: it’s not going to identify “good” hitters from “bad” hitters. Quality sticks like Jean Segura, Dee Gordon, Cesar Hernandez, and others show up at the bottom of the results because their game doesn’t base itself on the long ball. They do just fine for themselves hitting softer liners or ground balls and using their legs for production. Frankly, chances are if a player at the bottom of the list has a high Speed component, they’ve got a decent chance of success despite a low cHit. Nuance needs to be accounted for by the user.

Here’s how I use it to identify swing-changers (and/or regression candidates): I pulled in data for previous years, back to 2014. I compared 2017 data to 2016 data (I’ll add in comparisons for previous years in later iterations) and simply checked to see who were cHit risers or fallers. The results were telling — players we have on record as swing changers show up with significant positive gains, and players that endured some significant regression fell.

There’s an unintended, possible third use for this tool: identifying injured hitters. Gregory Polanco, Freddie Freeman, and Matt Holliday all suffered/played through injury this year, and they all fell precipitously in the rankings. I’ll need a larger sample size to see whether injuries and a fall in cHit are related or if that’s just noise.

Data!

Okay, so here’s the breakdown. I pulled all 2017 hitters with 400 at-bats or more so I could capture some significant hitters that didn’t have qualifying numbers of ABs due to injury. Ball-bludgeon extraordinaire Joey Gallo is a pretty solid name to have heading up this list, as he’s pretty much the human definition of what this tool is trying to identify. JD Martinez, Aaron Judge, Cody Bellinger, Miguel Sano, Trevor Story, and Justin Turner all in the top 10 is pretty much all the proof-of-concept I needed.

Interesting notes:

Brandon Belt at 12 — Someone needs to tell the Giants to trade him to literally any other team, stat.

Giancarlo Stanton at 46 — Surprisingly, the MVP fell off from his stats in 2016. His grounders and soft contact rose by 3 or more percentage points, and shaved off the equivalent from hard and fly balls. His output was fueled by adding almost 200 ABs to his season — he could actually get better if he can stay healthy and add those hard flies back in!

Francisco Lindor at 58 — The interesting part of this is even though Lindor is still a decent way down the list, he actually was the biggest gainer from last season to this, adding 9.52 points to his cHit. We knew he was gunning for flies from the outset of the season, and it looks like his mission was accomplished.

Mike Moustakas at 87 — Frankly, being bookended by Jose Ramirez and Andrew Benintendi should, in a vacuum, should be great company. But this is a prime example of how cHit requires users to not take the numbers at face value. Ramirez and Benintendi aren’t slug-first hitters like Moose. They’ve got significantly better Speed scores, plus aren’t as prone to soft contact. I’d be very wary of Moose regressing, as he seems to rely on sneaking some less-than ideal homers over fences. If he goes to San Francisco I could see his value crater (see Belt, Brandon).

Eric Hosmer at 206 — Nope, negative, pass, I’m trying to sign quality hitters here <— Suggested responses for GMs when approached this offseason by Scott Boras on behalf of Hosmer.

Final Notes:

•  Batted-ball distribution data is noticeably absent. In one of my iterations I added in those stats, and found that they actually regressed the accuracy of the formula. It doesn’t matter where you hit the ball, as long as you hit it hard.
• Medium% and LD% are noisy stats. They also regressed the formula.
• I may look to replace BB% in future iterations. For now though, it does a decent job of capturing plate discipline and selectivity.
• K% doesn’t seem to have much of an impact on cHit (see Gallo, Joey).
• R-squared numbers over the last four years of data hold pretty steady between .65 and .75, which is really encouraging. Also, the bigger the pool of data per year (number of batters analyzed), the higher R-squared goes; which is ultimately the most encouraging result of this whole endeavor.

Input is greatly appreciated! I’m not a mathematician in any stretch of the imagination, so if there’s a better way of going about this I’d love to hear it. I’ll do a writeup about my swing-change findings at a later date.

We all know that Aaron Judge hit for more power this year than Jose Altuve. But, whose power was more impressive? Aaron Judge, who is 6’7 and 282 pounds, has a considerable size advantage over Jose Altuve, at 5’6 and 164 pounds. Perhaps Altuve is actually a better power hitter for his size than is Judge. Let’s expand this idea to the entire league: who is the pound-for-pound top power hitter?

Role of Height and Weight in Batter Power

Using simultaneous linear regression, I estimated the effects of two physical characteristics — height and weight — on batter power. Measures of batter height and weight were taken from MLB.com. For batter power, I used Isolated Power.

As shown in the figures below, weight and height have positive relationships with power.

Weight has a stronger relationship with power than height, though it is difficult to see in the figures alone. (It’s also not intuitively clear exactly how height affects power.) In subsequent analyses, I consider both weight and height.

Who are the top pound-for-pound power hitters?

Using the model, one can predict a batter’s expected power (based on height and weight) and compare it to their actual power.

Who are the top pound-for-pound power hitters? See below for the results.

Khris Davis, formerly the #9 top power hitter, emerges as the #1 pound-for-pound power hitter in baseball. In 2017, Davis, who is three inches and over 30 pounds below average for a Major League hitter, hit a remarkable 43 home runs in 2017, with an ISO of .281. Nolan Arenado and Josh Donaldson made similar jumps in the rankings, from #7 to #2, and #10 to #3, respectively.

Notable power hitters have fallen slightly on this list, though remain in the top 10. For example, Aaron Judge fell from the top spot to #8, while Giancarlo Stanton dropped three spots (#2 to #5). It is important to note here that these power hitters are still impressive – continuing to hold spots in the top 10, regardless of their size.

Biggest improvements in rankings

Which players showed the most improvement in the list? Below are results from the top 50 players on the list.

Andrew Benintendi showed the largest increase in rankings (from 184 to 43). Jose Altuve nearly broke into the top 10, jumping from 132 to 12. Lastly, Eddie Rosario improved 68 spots (100 to 32). Altuve, in particular, has recently shown increases in power (from .146 to .194 to .202 in 2015-2017); as a result, his pound-for-pound status may continually increase in upcoming years.

Who was more impressive?

To reference the initial question in this article: was Jose Altuve’s or Aaron Judge’s power more impressive? Results from the above analyses were compiled from 2015 to 2017 seasons. To compare Altuve and Judge’s recent season, take a look below.

Aaron Judge tops Jose Altuve in the pound-for-pound hitter rankings – by a very thin margin – in 2017. Judge’s power performance exceeded expectations (as predicted by his height and weight) to a slightly higher degree than Altuve.

Full Rankings

If you want to see the full list of hitters for this dataset, including the worst pound-for-pound power hitters (poor Jason Heyward!), click here.

Analysis

Read the rest of this entry »

Baseball season is coming to a close and the Baseball Writers’ Association of America (BBWAA) will soon unveil its votes for AL and NL MVP. The much-anticipated vote is consistently under the public microscope, and in recent years has drawn criticism for neglecting a clear winner *cough* Mike Trout *cough*. This being one of the closest all-around races in years, voters certainly have some tough decisions to make. This might be the first year since 2012 where it’s not wrong to pick someone other than Mike Trout for AL MVP.

Of course, wrong is subjective. The whole MVP vote is subjective. Voter guidelines are vague and leave much room for interpretation. The rules on the BBWAA website read:

There is no clear-cut definition of what Most Valuable means. It is up to the individual voter to decide who was the Most Valuable Player in each league to his team. The MVP need not come from a division winner or other playoff qualifier. The rules of the voting remain the same as they were written on the first ballot in 1931:

1.  Actual value of a player to his team, that is, strength of offense and defense.

2.  Number of games played.

3.  General character, disposition, loyalty and effort.

4.  Former winners are eligible.

5.  Members of the committee may vote for more than one member of a team.

It won’t do any good for me to saturate the web with another opinion piece on who deserves to win. It won’t change the vote, and I don’t think I could choose. My goal is rather to illustrate how BBWAA voters have interpreted these rules over time. Have modern sabermetrics driven any shifts in voter consideration? Do voters actually consider team success? Do voters unconsciously vote for players with a better second half?

I thought the best (and most entertaining) way to answer these questions would be to create a model that would act as an MVP voter bot. Lets call the voter bot Jarvis. Jarvis is a follower.

1. Jarvis votes with all the other voters.
2. It detects when the other voters start changing their voting behavior.
3. It evaluates how fast the voters are changing behavior and at what speed it should start considering specific factors more heavily.
4. It learns by predicting the vote in subsequent years.

I created two different sides to Jarvis. One that is skilled at predicting the winners, and one that is skilled at ordering the players in the top 3 and top 5 of total votes. The name Jarvis just gives some personality to the model in the background: a combination of the fused lasso and linear programming. And it also saves me some key strokes. If you are interested in the specifics, skip to the end, but for those of you who’ve already had enough math, I will spare you the lecture.

Jarvis needs historical data from which to learn. I concentrated on the past couple decades of MVP votes spanning 1974 to 2016 (1974 was the first year FanGraphs provided specific data splits I needed). I considered both performance stats and figures that served as a proxy for anecdotal reasons voters may value specific players (e.g., played on a playoff-bound team). For all performance-based stats, I adjusted each relative to league average — if it wasn’t already — to enable comparison across years (skip to adjustments here).  Below are some stats that appeared in the final model.

Position player specific stats: AVG, OBP, HR, R, RBI

Starting pitcher (SP) specific stats: ERA, K, WHIP, Wins (W)

Relief pitcher (RP) specific stats: ERA, K, WHIP, Saves (SV)

Other statistics for both position players and pitchers:

Wins Above Replacement (WAR) – Average of FanGraphs and Baseball Reference WAR

Clutch – FanGraphs’ measure of how well a player performs in high-leverage situations

2nd Half Production – Percent of positive FanGraphs WAR in 2nd half of season

Team Win % – Player’s team winning percentage

Playoff Berth – Player’s team reaches the postseason

Visualizing the way Jarvis considers different factors (i.e. how the model’s weights change) over time for position players reveals trends in voter behavior.

Immediately obvious is the recent dominance of WAR. As WAR becomes socialized and accepted, it seems voters are increasingly factoring WAR into their voting decisions. What I’ll call the WAR era started in 2013 with Andrew McCutchen leading the Pirates to their first winning season since the early 90s. He dominated Paul Goldschmidt in the NL race despite having 15 fewer bombs, 41 fewer RBI, and a lower SLG and OPS. While Trout got snubbed once or twice since 2013, depending on how you see it, his monstrous WAR totals in ’14 and ’16 were not overlooked.

As voters have recognized the value of WAR, they have slowly discounted R and RBI, acknowledging the somewhat circumstantial nature of the two stats. The “No Context” era from ’74 to ’88 can be characterized perfectly by the 1985 AL MVP vote. George Brett (8.3 WAR), Rickey Henderson (9.8), and Wade Boggs (9.0) were all beaten out by Don Mattingly (6.3), likely because of his gaudy 145 RBI total.

Per the voting rules, winners don’t need to come from playoff-bound teams, yet this topic always surfaces during the MVP discussion. Postseason certainly factored in when Miggy beat out Mike Trout two years in a row, starting in 2012. See that playoff-berth bump in 2012 on the graph below? Yeah, that’s Mike Trout. What the model doesn’t consider, however, are the storylines, the character, pre-season expectations: all the details that are difficult for a bot to quantify. For example, I’ve seen a couple of arguments for Paul Goldschmidt as the front-runner to win NL MVP after leading a Diamondbacks team with low expectations to the playoffs. I’ll admit, sometimes the storylines matter, and in a year with such a close NL MVP race, it could push any one player to the top.

What can I say about AVG and HR? AVG is a useless stat by itself when it comes to assessing player value, but it’s ingrained in everyone’s mind. It’s the one stat everyone knows. Hasn’t everyone used the analogy about batting .300 at least once? Home runs…they are sexy. Let’s leave it at that.  Seems like these are always on the minds of MVP voters and that is not likely to change any time soon.

I’m sure some of you are already thinking, “What about pitchers!?” Don’t worry, I haven’t forgotten — although it seems MVP voters have. Only three SP and three RP have won the MVP award since 1974, and pitchers account for only about 7.5% of all top-5 finishers. As you can see in the factor-weight graph below, their sparsity in the historical data results in little influence on the model; voter opinions don’t change often, and their raw weights tend to be lower than position players. Overall, it seems as though wins continue to dominate the SP discussion, along with ERA and team success. While I would expect saves to have some influence, voters tend to be swayed by recency bias and clutch performance along with WHIP and WAR.

What would an MVP article be without a prediction? Using the model geared to predict the winners, here are your 2017 MLB MVPs:

AL MVP: Jose Altuve    Runner Up: Aaron Judge

NL MVP: Joey Votto   Runner Up: Charlie Blackmon

Here are the results from the model tuned to return the best top-3 and top-5 finisher order:

It’s apparent that I adjusted rate and counting stats for league and not park effects given both Rockies place in the top 2. Certainly, if voters are sensitive to park effects, Stanton and Turner get big bumps, and Rockies players likely don’t have a chance. Larry Walker was the only Colorado player to win the MVP since their inception in 1993, but in a close 2017 race it might make the difference.

Continue reading below for the complete methodology and checkout the code on github.

A previous version of this article was published at sharpestats.com.

Statistical Adjustments

Note: lgStat = league (AL/NL) average for that stat, qStat = league average for qualified players, none of the adjusted stats are park adjusted

There were two different adjustments needed for position player rate stats and count stats.

Rate stat adjustment:  AVG+ =  AVG/lgAVG  

Count stats: HR, R, RBI

Count stat adjustment:  HR Above Average =  PA*(HR/PA – lgHR/PA)

There were three different adjustments needed for starting pitcher (SP) and relief pitcher (RP) rate stats and count stats.

Rate stats: ERA, WHIP

Rate stat adjustment:  ERA+ =  ERA/lgERA  

Count stats I: K

Count stat I adjustment:  K Above Average =  IP*(K/IP – lgK/IP)

Count stats II: Wins (W), Saves (SV)

Count stat II adjustment:  Wins Above Average = GS*(W/GS – qW/GS)

Fused Lasso Linear Program

I combined two different approaches to create a model I thought would work best for the purpose of predicting winners and illustrating change in voter opinions over time. Stephen Ockerman and Matthew Nabity’s approach to predicting Cy Young winners was the inspiration for my framework for scoring and ordering players. A players score is the dot product of the weights (consideration by the voters) and the player’s stats.

The constraints in the optimization require the scores of the first place player to be higher than the second place, and so on and so on. This approach, however, doesn’t allow for violation of constraints. I add an error term for violation of these constraints, and minimize the amount by which they are violated.

Instead of constraining the weights to sum to 1, I applied concepts from Robert Tibshirani’s fused lasso which simultaneously apply shrinkage penalties to the absolute value of weights themselves as well as the difference between weights for the same stat in consecutive years. This accomplishes two things: 1) it helps perform variable selection on statistics within years helping combat collinearity between some performance statistics, and 2) it ensures that weights don’t change too quickly overreacting to a single vote in one year.

However, this approach and formulation cannot be solved by traditional linear optimization methods since absolute value functions are non-linear. The optimization can be reformulated as follows:

To select the lambda parameters, I trained the model using the first 10 seasons of scaled data increasing the training set by 1 season each time and tested with the subsequent year’s vote.After in season statistical adjustments, I scaled the stats by mean and standard deviation of training data to enable comparison across coefficients. All position player stats were replaced with 0 for pitchers and vice versa.

References:

1. Ockerman, Stephen and Nabity, Matthew (2014) “Predicting the Cy Young Award Winner,” PURE Insights: Vol. 3, Article 9.

2. R. Tibshirani, M. Saunders, S. Rosset, J. Zhu, and K. Knight. Sparsity and smoothness via the fused lasso. Journal of the Royal Statistical Society Series B, 67(1):91–108, 2005.

We saw the Yankees basically bullpen the AL wild-card game. Sure, it was on accident, but their bullpen pitched 8.2 innings. And they did it well. This made me think about whether a team could put together a pitching staff that is almost completely used for bullpenning for the entire season.

To see if this would be possible, we will look at the Yankees since they are the team most closely equipped for it already. In the wild-card game, they essentially used four relief pitchers (let’s not count the one out Luis Severino had). Chad Green, David Robertson, Tommy Kahnle, and Aroldis Chapman combined for 8.2 innings and one earned run. Clearly, if a team could do this all the time, they would. In that game they did not use other relievers Dellin Betances and Adam Warren, as well as regular starting pitchers Jordan Montgomery and Jaime Garcia, who would have been available that night.

Since we now know what happened in that bullpen game, can we find out if it is possible to do it over a full season? First off, and MLB roster is comprised of 25 men for any given game and an additional 15 that can be called up if needed. An AL team can get by with 12 position players: one for every starting position (including DH) plus a fourth outfielder, utility infielder, and backup catcher.  Let’s say a team’s backups can field multiple positions, like many can. We can get rid of the everyday DH and use one of the backups or starters in that role for a needed day off. That leaves us with 11 position players and room for 14 pitchers.

Many of the Yankees’ own relievers can go multiple innings. Among those pitchers are Chad Green, David Robertson, Tommy Kahnle, Adam Warren, and occasionally Aroldis Chapman and Dellin Betances. Each are effective in their own right. The problem we have to face is the amount of rest needed for these pitchers. The four from the wild-card game each pitched with two days of rest, so we’ll set that as a bench mark. I also don’t want to assume a team needs five pitchers each game like they did in the wild card.

I don’t want to completely get rid of the starting pitcher. It would be dumb to just throw away what Luis Severino and other starters bring to that team. Instead, I want to put a hard limit on how much they pitch each game and how often they pitch. Theoretically, a team could go with a three-game cycle of pitchers. Games are played almost every day during the season, so the two days of rest benchmark will be used here. If we are using four pitchers per game every three games, we need 12 pitchers.

I didn’t make this with any set reason, just the best options the Yankees would have in my view. There are many other options available for them and some may be even better. But, if this is the set of pitchers being used, that leaves two extra spots for our 14 available pitchers. Those two extra spots can be utilized for guys needed for extra innings that can pitch multiple innings, or a guy needed for an inning or two in case one of the above gets into trouble.

If a team were to go by this set of pitchers, the regular starting pitchers would be throwing 162 innings over a season. That would be seen as pretty normal for a starting pitcher over the course of a season and in some cases much less. Severino pitched 193 innings himself. The relievers, however, would see a pretty big bump in action. They would pitch 108 innings in a season, more than any of the pitchers above did last year. However, some of those pitchers were starters to begin their careers. Green, Warren, Betances, and Holder have each pitched more than 108 innings in a season. Now, that could be a reason for their increased effectiveness as relievers, but they would still only be pitching two innings in a game, not five or six.

It is possible to ask these relievers to stretch their arms out to be able to throw that many innings in a season. Relievers do transition to starting and this wouldn’t be quite the workload necessary. If a pitcher needs a break during a cycle through this set of pitchers, that could be what the additional two pitchers on the roster are for, or some of the 40-man pitchers could be called up to give a guy a break. They could also call up an actual starter from the minors to take over for four or five innings after the three-inning “starter” in this example. My point here is that if the relievers get tired over the course of a season, there are ways to give them breaks. Plus, the Yankees have so many resources and available pitchers that they have that capability to give breaks.

If the Yankees wanted to, they could keep Severino, Tanaka, Gray, Green, Warren, Robertson, Kahnle, Betances, and Chapman all on the roster for the whole season. That makes up 3/4 of the necessary pitchers. Shreve, Holder, and Gallegos could each be cycled up and down from AAA with other pitchers like Ben Heller, Domingo German, etc. in order to give breaks to the core nine pitchers. Another solution is to go out and get more relievers who can pitch multiple innings on a regular basis. They certainly have the prospects to do that. Pitchers like Brad Hand, Yusmeiro Petit, and Mike Minor each pitched over 77 innings and were very effective doing so.

Clearly there is much more that would be needed to make this a reality, and I don’t have the resources to know if it is even possible. Maybe these guys simply couldn’t pitch that many innings over a full season or they would lose too much velocity of break on their pitches from fatigue. But I saw David Robertson pitch 3.1 masterful innings in the wild-card game and pitch another 1.2 innings three days later. Obviously that is only two outings, but he was nevertheless effective in doing it, and I believe if any team could make this happen, it would be the Yankees.

A few days ago, I read an article on FanGraphs that flew in the face of everything I wanted to believe. This article told me that Aaron Judge — the man who holds the record for the most home runs hit in a season as a rookie — was not clutch. As a lifelong Yankee fan, I immediately got defensive. It didn’t matter that I wasn’t really sure that I even believed that “clutch” existed. Or, at the very least, I wasn’t sure we were measuring it correctly.

I decided to go a different route. I decided to go back in time, and replace Aaron Judge with a completely league average player…in every situation he was in. I took every plate appearance, from every base-out situation from 2014 through 2017, and averaged some random samples to find out exactly how many runs a hitter was expected to generate (xRBI). How many more runs did Aaron Judge force across the plate than the average player (RBI – xRBI)? So I calculated some xRBIs…because I like to pluralize RBI. My distribution of dRBI was a bit skewed — so I adjusted for HRs (high HR rates would inflate your RBI over your xRBI…but solo shots are still valuable things), and SOs (because strikeouts provide essentially no opportunity to bring in a run). Now, my distribution looked more normal.

And here we have it! Aaron Judge’s 2017 ranks….879th out of 954 hitter-seasons with 350+ PAs?! Dammit. Apparently Aaron Judge, based on the base-out opportunities he’s been provided, drove in 10 fewer runs than we should have expected. Womp womp.

What does this tell us? You know…I’m not really sure. Here’s the top 15 player-seasons:

         name      Season  PA   OBP HR  K.rt RBI   xRBI  dRBI
1  Miguel Cabrera    2014 685 0.371 25 17.08 109  83.03 25.97
2  Nolan Arenado     2015 665 0.323 42 16.54 130 106.55 23.45
3  Mike Trout        2014 705 0.377 36 26.10 111  88.87 22.13
4  Robinson Cano     2014 665 0.382 14 10.23  82  61.04 20.96
5  Michael Taylor    2015 511 0.282 14 30.92  63  43.13 19.87
6  Devin Mesoraco    2014 440 0.359 25 23.41  80  60.15 19.85
7  Nolan Arenado     2017 654 0.369 35 15.90 126 107.23 18.77
8  Giancarlo Stanton 2014 638 0.395 37 26.65 105  86.28 18.72
9  Ryan Braun        2014 580 0.324 19 19.48  81  62.53 18.47
10 Justin Morneau    2014 550 0.364 17 10.91  82  64.13 17.87
11 Matt Kemp         2015 648 0.312 23 22.69 100  82.15 17.85
12 Paul Goldschmidt  2014 479 0.392 19 22.96  69  51.28 17.72
13 David Ortiz       2014 602 0.355 35 15.78 104  86.35 17.65
14 Yoenis Cespedes   2014 645 0.301 22 19.84 100  82.69 17.31
15 David Ortiz       2016 626 0.401 38 13.74 127 109.82 17.18

They’re all pretty good. Were these the most clutch guys? I’m not really sure where I’m going with this. I’m not even sure if I’m going anywhere with it. I guess it’s just a different way to think about clutch. My process doesn’t take the game score into consideration. It doesn’t take into consideration whether or not a player is playing at home, or any other context for that matter. But in trying to quantify a relatively subjective stat…should any of that matter?