Every athlete, professional or otherwise, talks about that feeling of being on a team. There’s something that happens when a team “clicks” – it’s a united feeling of team spirit that propels team members to compete, most often referred to as team chemistry. In the social sciences there’s no measure of team chemistry, but there is however Team Cohesion, which is defined as:

A dynamic process that is reflected in the tendency of a group to stick

together and remain untied in the pursuit of its instrumental objectives

and/or for the satisfaction of member affective needs [1].

Team cohesion has been shown to exist across multiple work group settings (organizational, military and sport) [2], as well as across multiple sports (basketball, golf [3], softball, and baseball [4]). Perhaps more interestingly, cohesion has also been bi-directionally linked to performance: when teams perform better, they are more cohesive; and when they are more cohesive, they perform better [2,5]. And while the research on this relationship is clear, it has mostly been conducted with non-professional teams. Indeed, team cohesion is one of many other “unobservable” properties that are untapped within profession sports.

How can we measure team cohesion in professional sports?

 As researchers, we would normally use a validated survey to measure team cohesion – a survey that I could rely on to accurately measure team cohesion. Unfortunately, when I don’t have access to a team, I’m forced to use alternative methods. The first step is to examine the literature; a few key findings are brought to light about indications of team cohesion:

• Team cohesion is related to the extent that members accept the roles on their team (captain, motivator, leader, follower, etc.) [6].
• Charismatic leaders will refer to their teams more often than referring to themselves [7].
• The higher the level of team cohesion, the better the team performance [2,5].

So, if I can somehow measure how often leaders refer to their teams (vs. themselves), then I can use this as an approximation of their leadership characteristics. And if leaders are acting like leaders, they may also be helping to solidify roles within their team. Therefore we might expect that:

Hypothesis 1: As leaders reference their team more, we should see increased team cohesion – and as team cohesion increases, we should see better performance.

A charismatic leader does not typically arise without a contextual or conditional trigger. Crisis often prompts the emergence of charismatic leadership – a setting that allows a charismatic leader to propose an ambitious goal [8]. Both the context and the charismatic leader influence one another, almost as if the leader requires crisis as an occasion to exemplify charismatic leadership [9]. Additionally, at the group level, team members have been shown to become more attached to the leader in times of crisis, prompting a greater presence of cohesion during times of crisis as followers rally around the charismatic leader [10].

In baseball, teams experience all types of crises throughout the long season, including injuries, losing streaks, playoff races, and team conflicts. Perhaps the most common and least contextual of these crisis is the race to the playoffs as the season comes to an end. With an understanding of how and when the playoff races begin to make an impression, I can expect to observe a temporal effect of charismatic leadership by using our previous indicator of team reference. That is, it may not only be that “there is a positive relationship between a leader’s team references and the amount of wins his team will have at the end of the regular season”, but also:

Hypothesis 2: The timing of when a team leader references his team can determine the effectiveness of his leadership.

Methods

As the first component of the measure, I needed to assess team leaders’ reference to themselves or their team, I used the most popular newspaper from that team’s city to extract quotations (e.g., San Francisco Chronicle for the Giants; the New York Times for the Yankees). A team leader was identified by teammates, coaches, or front offices as a “leader”, a “captain”, or having either of these qualities. If there was more than one identified team leader, I randomly chose between the two. I tracked the quotes from 8 randomly selected baseball team leaders from 8 randomly selected teams across an entire regular season (April 4^th, 2012 – October 3^rd, 2012). Statement settings included comments made in locker rooms after games, during the All-Star break, before a game started, or in any other setting. Any time the leader was documented as saying anything that appeared in the newspaper, that quote was documented for analysis. Leader quotes were qualitative coded independently between 3 different coders. Each quote was coded as containing “self-reference”, “team-reference”, and/or “other reference” (the 3 coders had 97% agreement on their final codes). I began this study in 2013 thus I used the 2012 season, which was the latest complete season at my disposal.

Due to the disparity in responses, the sample was aggregated based on team leaders who played on teams that finished with a certain number of wins. Since 1996, no AL team has made the playoffs with less than 86 wins [11]. During the same time period, no NL team has made the playoffs with less than 82 wins [12]. For this study, leaders were categorized based on how their teams finished the regular season (86 or more wins for AL teams and 82 or more wins for NL teams). Those at or above the win mark were titled “high team leader” (HTL) and those below the win mark were titled “low team leader” (LTL). Four teams in the sample met the HTL criteria and their combined record was 368 – 280 (.568 wining percentage). Not all HTLs were on teams that made the playoffs in 2012, but each of the four teams were competing for a playoff spot in the months of August and September. Four teams in the sample met the LTL criteria and their combined record was 296 – 352 (.457 winning percentage).

     Table 1. Classification of high or low team leaders based on their team’s 2012 regular season record

Results

There was no significant correlation between the total number of team references and the total number of wins that a leader’s team had at the end of the regular season r = .237, p > .05). Nor was there an indication of a negative correlation between self-references and total number of team wins r = -.086, p > .05.

Leader responses were then aggregated between LTLs and HTLs. Of the 490 total responses, 252 responses were made after or in reference to a previous game. Quotes were then selected for these post-game interview responses after a leader’s team had won a game (162 total) or lost a game (90 total). After a loss, both HTLs and LTLs referred to their teams much more often than referring to themselves. LTLs were 7.20 times as likely to reference their team after a loss than reference themselves. When compared to LTLs, HTLs were less likely to refer to their team after loss (4.42:1). After a win, LTLs were 1.41 times as likely to reference their team than themselves. HTLs on the other hand were 2.32 times as likely to reference their team than themselves after a win (Table 1).

     Table 2. Ratios of team vs. self references for each type of leader

The monthly distribution of team reference for LTLs was relatively even across all months of the regular season. The highest percentage was July (19.9%) and the lowest was August (12%), a difference of 7.9% (Figure 1). The overall standard deviation for team references by month was σ = 2.88. In contrast, team reference for HTLs was much more dynamic. The highest percentage was September (39.6%) and the lowest was June (5.8%), a difference of 33.8%. September team references for HTLs were more than double any other month. The overall standard deviation was σ = 12.2, with the resulting distribution becoming much more parabolic (Figure 2). The quadric trend line that is used to represent the team reference distribution for HTLs showed a very good fit R² = .91.

Figure 1. Percentage of team reference by month LTLs

           Figure 2. Percentage of team reference by month HTLs with quadratic trend line

Discussion

The increased rate of team reference by HTLs as compared to LTLs may have helped to establish better role clarity – a characteristic of more cohesive teams. This was further marked by the fact that HTLs were on higher performing teams than LTLs. The direction of the team cohesion to performance relationship in this case is still unknown.

HTLs also referred to their teams most often during the end of the regular season. This relates to the theory that charismatic leaders will “activate” in times of crisis. In turn, this helps to create more team cohesion as members attach themselves to leaders in times of crisis.

[1] Carron, A.V., Colman, M.M., Wheeler, J., & Stevens D. (2002). Cohesion and Performance in Sport: A Meta Analysis. Journal of Sport & Exercise Psychology, 24, 168-188.

[2] Mullen, B. and Copper, C. (1994). The relation between group cohesiveness and performance: an integration. Psychological Bulletin.115, 210-227.

[3] Vincer, D., & Loughead, T.M. (2010). The Relationship Among Athlete Leadership Behaviors and Cohesion in Team Sports. The Sport Psychologist, 24, 448-467.

[4] Carron, A.V., Bray, S.R., & Eys, M.A. (2002). Team Cohesion and Team Success in Sport. Journal of Sports Sciences. 20(2). 119-126.

[5] Oliver, L.W., Harman, J., Hoover, E., Hayes, S.M., & Pandhi, N.A. (2003) A quantitative integration of the military cohesion literature. Military Psychology, 11, 57-83.

[6] Carron, A. V., & Eys, M. A. (2012). Group dynamics in sport (4th ed.). Morgantown, Fitness Information Technology.

[7] Shamir, B., Arthur, M.B., & House, R.J. (1994). The rhetoric or charismatic leadership: A theoretical extension, a case study, and implications for research. The Leadership Quarterly, 5(1), 25-42.

[8] Poon, J. & Fatt, T. (2000). Charismatic Leadership. Equal Opportunities International. 19(8), 24-28.

[9] Conger, J. A. (1999). Charismatic and transformational leadership in organizations: An insider’s perspective on these developing streams of research. The Leadership Quarterly, 10, 145-179.

[10] Kets de Vries, F. R. (1988). Prisoners of leadership. Human Relations, 41, 261-280.

[11] Gaines, C. (2011, April 21). Chart of the Day: What it takes to make the playoffs in Baseball. Business Insider. Retrieved from http://www.businessinsider.com/chart-of-the-day- what-it-takes-to-make-the-playoffs-in-baseball-2011-4

[12] Bloom, B.M. (2005). Padres Try to Recover from 82-80 Record. San Diego Padres. Retrieved from http://m.padres.mlb.com/news/article/1236830/

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

Expanding on my research for the book, the following series of articles will reveal the finest single-season rosters for every Major League organization based on overall rankings in OWAR and OWS along with the general managers and scouting directors that constructed the teams. “Hardball Retrospective” is available in digital format on Amazon, Barnes and Noble, GooglePlay, iTunes and KoboBooks. The paperback edition is available on Amazon, Barnes and Noble and CreateSpace. Supplemental Statistics, Charts and Graphs along with a discussion forum are offered at TuataraSoftware.com.

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

Terminology

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

OWS – Win Shares for players on “original” teams

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

Assessment

The 1931 Philadelphia Athletics    OWAR: 53.6     OWS: 347     OPW%: .524

Connie Mack acquired all of the ballplayers on the 1931 Athletics roster. Based on the revised standings the “Original” 1931 A’s finished in second place, two games behind the Yankees. Philadelphia paced the Junior Circuit in OWS and led the League in OWAR for the fourth straight season (1928-1931).

“Bucketfoot” Al Simmons (.390/22/128) collected his second successive batting title and placed third in the American League MVP balloting. Mickey Cochrane drilled 31 doubles and delivered a .349 BA. Max “Camera Eye” Bishop amassed over 100 bases on balls in eight consecutive seasons (1926-1933). Jimmie Foxx belted 30 round-trippers and drove in 120 baserunners. Charlie Grimm aka “Jolly Cholly” contributed a .331 BA with 33 doubles and 11 triples.

Jimmie Foxx ranks second to Lou Gehrig among first basemen while Lefty Grove places runner-up to Walter Johnson according to Bill James in “The New Bill James Historical Baseball Abstract.” Teammates cataloged in the “NBJHBA” top 100 rankings include Cochrane (4th-C), Simmons (7th-LF), Wally Schang (20th-C), Bishop (43rd-2B), Jimmie Dykes (52nd-3B), Grimm (85th-1B), Joe Dugan (88th-3B) and Doc Cramer (91st-CF).

Lefty Grove claimed the 1931 American League MVP award with a dominant performance including League-bests in victories (31), ERA (2.06), WHIP (1.077) and complete games (27). He also struck out the most batsmen in the circuit for the seventh year in a row. George “Moose” Earnshaw topped the 20-win plateau for the third straight season. Herb Pennock and Tom Zachary furnished 11 victories apiece.

The “Original” 1931 Philadelphia Athletics roster

Honorable Mention

The “Original” 1911 Athletics            OWAR: 46.1     OWS: 303     OPW%: .597

Philadelphia coasted to the pennant by a nine-game margin over Boston. “Shoeless” Joe Jackson posted a .408 BA in his first full season. He collected 233 safeties, scored 126 runs and led the Junior Circuit with a .468 OBP. Eddie Collins swiped 38 bags while batting at a .365 clip. “Home Run” Baker (.334/11/115) topped the American League in circuit clouts for the first of four consecutive campaigns. Matty McIntyre totaled 102 runs and produced a .323 BA. “Gettysburg” Eddie Plank delivered a 23-8 record with a 2.10 ERA including six shutouts. Jack Coombs led the League with 28 victories despite allowing 360 hits in 336.2 innings pitched. Bris Lord aka the “Human Eyeball” supplied a .310 BA and accrued 92 tallies.

The “Original” 2002 Athletics            OWAR: 45.8     OWS: 304     OPW%: .578

Jason Giambi (.314/41/122) coaxed 109 bases on balls and tallied 120 runs as the ’02 squad finished five games ahead of the Angels for the American League pennant. Miguel Tejada (.308/34/131) achieved MVP honors and made his first All-Star appearance while registering 108 aces and 204 base knocks. Barry Zito claimed the Cy Young Award with a record of 23-5 and an ERA of 2.75. Tim Hudson contributed 15 victories and a 2.98 ERA while portsider Mark Mulder accrued 19 wins. Eric Chavez launched 34 long balls, drove in 109 baserunners and earned the second of six consecutive Gold Glove Awards.

On Deck

The “Original” 1907 Phillies

References and Resources

Baseball America – Executive Database

Baseball-Reference

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

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

Retrosheet – Transactions Database

Seamheads – Baseball Gauge

Sean Lahman Baseball Archive

It is well established that having more rise on your four-seam fastball is a good thing. The question then becomes, can we identify the optimal amount of rise as compared to the league-average fastball. For the purposes of this analysis, we will look at swinging-strike rate, from all four-seam fastballs thrown since the dawn of the PITCHf/x era, in regular-season action.

We in the sabermetrically-inclined community tend to pooh-pooh popular baseball concepts, particularly ones where the science, on the surface, doesn’t appear to jive with the age-old baseball wisdom. Don’t worry, this is not a DIPS discussion, nor a discussion on a pitcher’s ability to manage contact. I bring up this concept in relation to the term “late life” as in movement later in the pitches trajectory. Physics tell us that the ball will have a very predictable trajectory from the moment the ball leaves the pitchers hand, until it reaches the front of the plate. That, however, is merely half the story. There are two important points I want to bring up:

1. Batters cannot compute vertical trajectory explicitly; they essentially tap into a huge vault of experience telling them how far a pitch will drop based on their experience with pitches of similar velocity.
2. A hitter’s swing is largely ballistic (very difficult to change mid-swing) and takes about 0.18 seconds to execute. That means that a hitter has roughly 0.2 seconds post-release of the ball to gather information and form an educated guess as to where the ball will end up.

Based on these assumptions, I computed late movement, in both the vertical direction and horizontal direction. I then compared this to the expected vertical movement based on the velocity (more velocity, less drop obviously). This to me is the optimal way to look at movement, since presumably they cannot gather any more information. A great hitter may be able to factor in their knowledge of the pitcher’s ability to rise the fastball, but they are fighting their memories of all the other fastballs they’ve seen, so more difficult than you would think.

Which brings us to a very interesting graph: The height and colours in the histogram reflect the magnitude of the swinging-strike rates, shown in sequential order of velocity. If you scroll all the way to the bottom, you’ll see that the center of the histogram is somewhere around -.6, or 0.6 feet more rise than the average four-seam fastball when looking at the pitch 0.2 seconds after release until it crosses home plate.

We see a very clear normal curve, with more “normal” at higher n. Thus we can now compute the value of rise in a four-seam fastball, as distributed by a normal curve centered around 0.6 feet above the mean drop. Not really a stats guy, so not sure how to do that exactly. What I find interesting is that the 7 inches or so of rise is pretty consistent across the velocity spectrum. I’m not sure why it peaks at this point, though I would surmise that it’s probably the sweet spot where the hitter feels like they can make contact, but can’t, as opposed to extreme rise which would freeze the hitter.

This leads us to our last graph (warning: this one scrolls for a while). You’ll see the same graph as above, but you’ll see Whiff%, GB% and HR% stacked one on top of the other.

This actually paints a very intuitive picture. If there is more rise than average, you’ll get swinging strikes. If it drops more than average, you’ll get groundballs and if it drops about what you’d expect, you’ll get some groundballs, but also homers. Ignore the SSS noise with homers at the higher velocities. Again what is interesting with the GB% and Whiff% histograms are how consistent they are irrespective of velocity. So… if velocity doesn’t impact this analysis, let’s collapse it all into one final graph:

Paints a very clear picture: if your four-seam fastball isn’t getting at least 5 inches of late rise, you are going to be giving up a lot of homers. Note that swing% (swings/total pitches) is normally distributed around a mean of .2 feet of rise and appears to track pretty closely to HR%, implying that hard contact is not affected within 1 standard deviation.

Looking forward to the feedback.

I read a great book by Mike Stadler called the Psychology of Baseball. In it he referenced that it is far more difficult for humans to control where a ball ends up vertically (due to the need for advanced spatial reasoning) compared to horizontally. You can find his discussion starting on page 86. Amazon Link

I’m going to show you three pictures which will illustrate this quite well. Data is inclusive of all pitches thrown in regular season games since 2010. The first is a heat map of sorts which maps vertical distance from the center of the zone (from PITCHf/x data sz_top and sz_bottom) on the y axis and velocity on the x axis. What we see quite clearly is that it is *much* better to throw a four-seam fastball up in the zone than down in the zone, almost irrespective of velocity. In fact, a 92 MPH four-seam fastball thrown 0.8 feet above the center of the zone will get about 13% swings and misses; a 98 mph four-seam fastball thrown below the center of the zone will get 12% swings and misses. Behold the graph, from a fan:

The question then becomes, if a pitcher throws the ball up in the zone, how will the probability of a HR change? This brings us to picture #2, where we have the same x and y axes (apparently that’s the plural of axis, thanks google), but instead we have HR% (# of HRs/Total Pitches). I’ve removed 99+ MPHs from the graph as they were displaying SSS noise.

So interestingly, if you look at the totals on the right, it paints a visual that HRs are NOT hit on high fastballs, but rather on fastballs closer to the heart of the zone (vertically). In fact (and a story for another day) there is a 97% R-squared correlation between distance from the center of the zone and HR%. On an aside, this also reproduces other research which indicate that faster fastballs yield fewer home runs. The trend is also quite linear (don’t have a computed R2 for that, but that’s old news anyway).

Now, if you are far more likely to get a swinging strike and you aren’t putting yourself at risk for a home run by throwing up in the zone, if we looked at a distribution of four-seam fastballs, we should see a higher proportion of four-seamers up in the zone, ideally right at the top 0.8 to 1.0 feet above the zone, where whiffs are plentiful and HRs are scarce. Beware SSS in some of the higher velocities, but note that a 95 MPH fastball only .4 feet above the center of the zone will yield more HRs than an 88 MPH fastball thrown at the top of the zone (the 95 MPH fastball will still yield more whiffs, but just goes to show how important command is). This is what we actually see:

A nearly uniform distribution across all velocities, slightly skewed to below the center of the zone. I’m not ready to conclude that pitchers are not capable of pitching up in the zone with four-seam fastballs, it may just be old school “pitch down in the zone” thinking. I still find it astonishing how consistent the data is across the velocity spectrum. It almost appears to me that if a pitcher can simply pitch higher in the zone with a four-seam fastball, they can make their stuff play up a lot, sort of like MadBum:

Still not pitching at the top end of the zone, but definitely skewed higher, with his distribution centered around .3 feet above the heart of the zone.

Red = High GB% rate (ground balls / total pitches)
Yellow = Medium ; Green = Low

The size of the circle also represents the magnitude.

Numbers are in Feet, with -X being inside (handedness neutral) and Z being height in feet above the center of the strike zone (as per PITCHf/x strike zone top and bottom). The X is flipped for left handed batters. After I’ve published a few of these, I’ll work on publishing a version to Tableau Public, though not sure how it will perform given the huge underlying data set.

Some observations:

1) The cutter, which appeared to have two hot zones for swings and misses, appears to have only one hot zone for groundballs, of about .5 feet to 1 foot below the center of the zone and between .4 feet away and .4 feet in from the center of the plate. In the previous post we saw that as you went farther away from the plate horizontally and about .5 foot lower, you get swinging strikes.

2) Changeups down and away get groundballs. They also get swings and misses. Groundbreaking stuff here…

3) Two-seamers and sinkers have a very large area that get groundballs (another shocker), though what surprises me is how high it starts (almost at the center of the plate). It makes me wonder if I need to double-check my methodology. As you get lower in the zone, you get fewer swings and more takes, so the GB% goes down dramatically.

4) Curveballs only get groundballs if they are in the strike zone when crossing the plate (down and away). If you bury it, you basically trade the GB for a swing and a miss. I’m thinking I need to rebuild this chart with fewer grids, but a bunch of pie charts, to somehow visualize how results morph based on location.

Finally figured out how to get PITCHf/x data into Tableau (used Alteryx to scrape MLB) — having lots of fun and appreciate the feedback!

I love bat flips. I would have no problem if bat flips became a more theatrical experience. By the power of inference, or by simply reading the first sentence, I’m certain you can accurately predict how I feel about Jose Bautista’s bat flip.  While anyone with an incorruptible soul has been nobly spewing self-righteous significations about how disrespectful Bautista’s bat flip was, I’ve been primarily concerned with one thing: the trajectory of that bat flip. It was a huge exclamation point on a huge moment and it was a pretty significant departure from more “conventional” bat flips.

Most bat flips do not exceed shoulder height. Think about the bat flips that you have mimicked the most in your life.  For me it’s been Griffey Jr,  Sosa, McGwire, Ortiz, and McGriff. One could argue that what those players possessed were, by definition, closer to bat drops rather than flips, but you’ll still find these players featured in various “best of bat flips” videos on YouTube. Bautista’s bat flip diverges from the norm immediately upon release, in that it actually started at his shoulders. While this is awesome, it didn’t break new ground. Yasiel Puig flips his bat from above his head on fly outs and triples. Yoenis Cespedes had a triumphant bat flip of his own on Monday night, but for a superabundance of reasons that you already know, Bautista’s bat flip has hogged the limelight. In lieu of this, we’ll focus on breaking down Bautista’s bat flip into some tangible numbers and simply apply that same method to Cespedes’ for a comparison.

MLB debuted Statcast this year, and among its nifty features was the home run tracker. The home run tracker allowed viewers at home to process new data on home runs — specifically, exit velocity, the angle of the home run, and distance. The data I’m about to bring to you is based on this exact premise, but it studies the bat flip.  BatCast: The Bat Flip Tracker™.

Disclaimers:

1. There is no ™ on BatCast, I just thought it was funny and hope that it’s not illegal to falsely claim a copyright.
2. I am not an engineer, mathematician, or a numerically-inclined vampire. The last math class I took was trigonometry during my junior year of high school 13 years ago.
3. I’m about to present some very inexact numbers based on frozen images I’ve gathered from the internet to bring you the BatCast data on Jose Bautista’s bat flip.

Without further ado:

JOSE BAUTISTA

7^th Inning – ALDS Game 5

Rangers @ Blue Jays

Score: 3 – 3

Here is the freeze frame of the moment in time that somehow is already emblazoned across purchasable T-shirts. Following the majestic shot will be the explanation of the method I used to come up with the rough, ROUGH BatCast numbers (also featured in metric to honor the Blue Jays and the soil, or turf, of Canada where it all went down).

You didn’t think I’d forget the GIF(s), did you? (GIF sources: FS1 + mlb.com)                

The numbers:

Launch Height: 5′-2″ (1.57m)

Jose Bautista stands exactly 6′-0″ tall (1.83m). In the image I printed out and measured hastily, he is about 3.33″ tall. If you’re disappointed in my measurements already, I did warn you that it would be rough, and you have every right to stop reading. If we measure up to his shoulder/trap area, where he released the bat, we get 2.87″. After we apply some simple algebra: 3.33/2.87  =  72/x we come up with 62″ or 5′-2″ (1.57m) for the launch height. This also works with the idea that the head and neck comprise 10.75% of our total height.

Horizontal Distance: 6′-6″ (1.98m)

Bautista hurls the bat across his body with his left hand from his right shoulder, which at point of launch, was pretty much on the inside corner of home plate for a right-handed hitter. The bat lands just outside the left-handed batter’s box which we know is 4’ wide. Given that the plate is 17” wide and there is a 6” cushion between the batter’s box and the plate, we can estimate the horizontal distance that the bat traveled to be right around 6.5’ (1.98m).

Hang Time: 1.52 seconds

I derived this number from watching the video and using my phone as a stop watch.  After 10 runs, I had an average time of 1.52 seconds. There is no metric conversion for time (winky face).

Parabolic Trajectory Calculator

This online calculator was paramount to finding the rest of the data provided. Once I had the initial height, the hang time, and the horizontal distance, I tinkered with numbers for the initial velocity and trajectory angle until everything jived with the rough numbers I had figured.

Jose launches this bat pretty tight to his body, as evidenced by where the bat lands (at the outside edge of the left-handed batter’s box).  A rough/convenient measurement of the launch angle gives us 76 degrees. But after manipulating the numbers in the calculator, we have a more accurate launch angle of 76.8 Degrees.

Launch velocity: 14.63 mph (23.54 kmh) and Apex: 12′-0.36″ (3.67m)

I had actually tried to measure the apex using the same method I performed to figure the launch height, but it would be a disservice to us all had I used the 10.5′ number that produced. Jose Bautista flips the bat in such a manner that he would have thrown it over himself STANDING on top of himself – or twice his height. In the trade of bat flipping, this is probably considered light-tower power.

Cespedes vs Bautista

Using the same method let’s look at, what we can figure to be at least a pretty similar and recent comp.

First, Cespedes’ flip.

Yoenis Cespedes’ bat flip came in the 4^th inning of game 3 of the NLDS with the score already 7 – 3 in favor of the Mets.  The tension in this game was obviously very high as the series was tied at 1 – 1, but circumstantial tension also built differently as there had been a day between this game and the game that saw the Utley v. Tejada incident.

YOENIS CESPEDES

4^th Inning – ALDS Game 3

Dodgers @ Mets

Score: 7 – 3

By the numbers, these are two fairly similar bat flips. What Cespedes’ flip lacked in height (8.5 ft; 2.6 m), it made up for in sheer distance (reference table above). But judged by context (inning, game, score), isn’t Cespedes’ bat flip actually more wrong? Of course I’m saying that with my tongue in my cheek – a bat flip is neither wrong nor right. A bat flip is really just like adding an exclamation point to a moment instead of a period. How would you write it?

Home Run.

or

Home Run!

…

Part II: (preachy commentary)

In the end, people only start talking about a bat flip in context of right or wrong if it’s offensive to a player on the opposing team. Well, it was. It was offensive to Sam Dyson, who, without coincidence, was the pitcher who had just given up the home run to Bautista that spurred the bat flip. Dyson’s reaction seemed to be more of an unhinging; a singular representation of the collective mind of the Rangers. As history now goes, the Rangers were the beneficiaries of strange fortune in the top half of the 7th, nudging them ever closer to the Championship Series. The following half inning saw the Rangers’ 167-game journey and bid for a championship suddenly unravel in a strange, beautiful, sad, and unpredictable sequencing of events. Dyson’s cortisol levels were no doubt already higher than usual, having inherited three baserunners and tasked with getting two outs against the middle of baseball’s most potent offense that features the near certain American League MVP winner and MLB’s leading home-run hitter over the better part of the last decade — oh and these would also be the first two players he would be facing. These facts about the the situation and the prowess of the hitters are somewhat minimized in a pitcher’s mind that is focusing on executing his game plan, but I felt compelled to catch a glimpse into Dyson’s psyche before it all went down.

And then it went down (refer to GIFs of Bautista above).

Dyson will have to internalize the experience, if he’s not/hasn’t already, and I don’t know what that will be like for him. But immediately following the Bautista home run was not the time for that since Dyson still needed to get one more out in the inning. In the moment, amid all the pandemonium, he needed something he thought he had some semblance of control over and he found it, eventually, supposedly, in the bat flip. In fact, the bat flip was something that would, in some strange way, vilify the hero and deflect the attention away from the fact that he just gave up the home run that would eventually be the nail in the coffin (purely from a runs standpoint) for his team’s season (of course it’s more complicated than that). I’m not saying Sam Dyson consciously thought of all this; we’re animals and we’re not always aware of, or able to keep up with the torrid pace of our physiological states – and BELIEVE that Dyson was going through some stuff. However, to believe that Dyson acted above the bat flip, or any of it, is to ignore the fact that he too reacted instinctively to the situation. He made things worse by misinterpreting gestures and pointing fingers at inconsequential things like bat flips.

Dyson’s reaction, while not as grandiose as Bautista’s, was a reaction that was just as impulsive as Bautista’s bat flip, and yet, somehow, it seems like a lot of people deem his reaction to be more acceptable. Is it because he did his best to feign composure through it all? Do you really think he wouldn’t have approached Edwin Encarnacion in the midst of all the mayhem if the bat flip didn’t happen? I don’t. There is a Great Repression in this country, and I hate the way I phrased that, because it sounds so cheesy and adolescent, and really, what do I know? But it does feel like there is a sweeping under the rug of emotions, of feelings, and of truth. This is just how we’ve structured things; to be poised in all circumstance so that no one can see how truly horrible or beautiful we really are. Newscasters delivering horror stories; politicians admitting to affairs; talking about something you did that you’re extremely proud of but don’t want to seem too proud of — there are guidelines right down to accepted cadences, gestures, tones, and expressions for delivering each of these like they each came from an acceptable social norms textbook. Big, real emotions tend to make other people feel uncomfortable because conduct says we repress them and stay status quo. If I seem to be disgusted by it all, I’m not…as much as I used to be. But that’s probably because of anger management, finding love, and the birth of my son — three things I can talk in restricted excitement about because I’m starting to well-adjust…obviously, I’m not there yet if I’m ranting about all of this because I’m caught up in the debate of whether or not a bat flip is acceptable.

Sam Dyson said, in a post-game interview, “he (Bautista) is a huge role model for the younger generation coming up playing this game and he’s doing stuff kids do in wiffle ball games and backyard baseball, it shouldn’t be done”. First of all, Sam Dyson has been teammates with Jose Bautista, Giancarlo Stanton, and bat-flipper extraordinaire, Jose Fernandez. Do you think he was appalled at their flips when he was their teammate? Also, Sam Dyson literally just said, it’s a game, and that’s the point anyone who has ever played the game has been hammered with — “never stop having fun! Remember why you play! It’s just a game!”

I understand the game Dyson and Bautista play is also their job. I understand that to play the game professionally means having to work harder than you ever thought you could work, and that that probably has a tendency to mute and mature the game a bit — and like with anything, sometimes it’s a struggle to remember why you do it. But for Jose Bautista, everything culminated in that one swing. In that one moment after he connected with the pitch from Dyson, every swing he ever took, every time he tried out for a team, every early morning and every late night spent training made perfect sense to him. He was experiencing the moment most people, including himself up to that point, only conjure up in back yard wiffle ball games. So please, in a world where we’re forced to repress so much, don’t take the humanity out of the game, and don’t try to take away anything from Jose Bautista’s moment. Given everything in his life that led Bautista to that immensely emotional game 5, given the gravity of the situation, the no doubt distance of the home run, the do-or-die premise of the game, I’d say that bat flip was absolutely, spot-on, 100% perfect.

No this isn’t a piece for accountants so please don’t give up on it or go to sleep!  It is an MVP discussion, and there is always a lot to talk about with the MVP, the very definition of which is vague, entitling anyone to interpret it how they wish.  There are perpetual questions– is it for an outstanding player or one who can meet some criteria of clutch?  Can a pitcher be more valuable than an everyday player?  Must a candidate play on a contender?

This article lays out a framework for quantifying these issues.   As described, a definitive answer requires a little more data than we now have, but it’s possible to have this data for an interesting quantitative measure of the MVP.

Let’s start with principles:

• The objective is to win a championship. I don’t expect this to be controversial, is it?  As we’ll get into, this doesn’t mean a non-contender can’t win, but it will be more difficult for them to do so.
• Context and chances matter. We aren’t trying to pick the best player, we’re trying to pick the most valuable.  We’re not trying to forecast the future, we’re looking back at the past.  Whether a player benefits from the luck of situations or of opportunities, the player who capitalizes upon his luck seems to this author to have been more valuable than an unlucky player who doesn’t have as many such opportunities.  Dave Studeman and Dave Cameron have written well on this topic.  If you don’t agree, take it up with them.  (For future research – must an author’s first name begin with the letter “D” to believe this?)  Further, the context of a player’s team matters – clinching a pennant on the last day is more valuable based upon context than an April rout or a meaningless September game between call-ups.

Introducing CPA

Accordingly, we’ll take something old, Win Probability Added, (WPA) and dust off and tweak something else old, Championship Leverage Index (CLI) to make up a new statistic to measure value – Championship Probability Added (CPA).  Our formula is CPA = sum of all daily WPA x CLI.

The facets of WPA are discussed thoroughly in another Studeman article.  Suffice to say, it captures a hitter’s or pitcher’s contribution to the probability of his team winning a game, which we can take as a player’s value to his team in the particular game.

As for the importance of the game to the team, Studeman and Sky Andrecheck have developed a measure of the game’s importance, the Championship Leverage Index, how the outcome of a game affects a team’s championship probability, but, as Studeman pointed out in his WPA article, the new wild-card format makes calculation of CLI difficult.

Fortunately, FanGraphs has a big part of the answer in their playoff probability table, which daily measures a team’s playoff and championship probabilities.  The day to day changes in these probabilities are indicative of each game’s importance, although a full measure of a game’s importance would require running the simulations 15 more times to determine the change in probability for each game’s alternative outcome.

There are different measures of championship probability in these tables based upon projections or upon random (coin toss) probabilities for a season’s balance.  The projection-based probabilities may be more accurate, but, for our purpose, measuring the value of each game, the coin toss probabilities are more useful.  1) The projection-based probabilities are more volatile early in the season as they vary not only with the game’s outcome, but with players’ individual performance which in turn affect his team’s projections.  Thus early-season games are weighted more highly than late games.  2) A player’s individual impact can be diminished because it already has been factored into a team’s projections.

The 2015 MVP Race by CPA

For now, without the complete probabilistic simulations, we’ll try to approximate the value of a game by taking the absolute value of a daily change in a team’s championship probabilities.  We use the absolute value of the daily change since it measure’s the game’s importance whether or not a team wins.  Without this, a player would be penalized if his team loses a game, even if he has a big (valuable) game (high WPA).

For now, the daily changes must be recorded from FanGraphs by hand, so we’ll run with an illustrative example rather than a definitive analysis.  Let’s start with the top two players by WAR in each league:

In the AL, both the Angels and Jays were in contention, although, the Jays’ chances became markedly better later in the season.

While the Angels had a low probability, there was still a lot of opportunity for Mike Trout to benefit from swings in their chances in the end, but he couldn’t make up all the ground on Josh Donaldson’s high WPA during the Jays high CLI second-half run.

On the NL side, WAR leader, Bryce Harper, had his CPA affected by the Nats dropping out of playoff contention.

Harper’s early-season lead fell by the wayside as Kershaw’s performance improved from its negative start and the Dodgers remained in the championship hunt.

So, definitive MVP stat?  Not yet, but hopefully a step in that direction.  Calculating a probabilistic CLI would be a big help.  Improvements to WPA to incorporate base running and fielding would help too.

Thoughts?

Red = High swinging-strike rate (swing and a miss / total pitches)
Yellow = Medium ; Green = Low

The size of the circle also represents how high the whiff rate is

Numbers are in Feet, with -X being inside (handedness neutral) and Z being height in feet above the center of the strike zone (as per PITCHf/x strike zone top and bottom)

Some observations (and probably repetition of prior research):

1) Four-seam fastballs are great between 0.8 to 1.4 feet above the middle of the zone and between -.5 and .5 across the plate (i.e., if you want to get a swing and a miss on a four-seamer, throw it high and right down the middle). Will have similar views for GB% and HR% soon.

2) Sliders, changeups and curveballs all need to be thrown low in the zone; doesn’t appear to matter inside or outside, though changeups need to be around the plate (or they don’t get swings).

3) There is almost nowhere you can throw a two-seamer to get swings and misses, though down and in and basically high appear to be the best places to get strikes.

More to come if you think this is interesting!

Recently, Dave Cameron examined a planned back-pick by Russell Martin and the Blue Jays in Game 1 of the ALDS.  The play didn’t have a chance to happen because Delino DeShields put a 2-1 change up in play.  Not just in play, but on the ground to directly where the second baseman Ryan Goins would have been had he not been breaking for second in anticipation of the pick.  Dave wrote a great article that covered the play in depth, so feel free to go read it here.  In this article, I analyze the strategy of calling for a set pickoff attempt. What I found not only vindicates Martin and the Jays, but also questions one of my longest-held beliefs about pickoffs.

My strategy for evaluating the set pickoff was to calculate the break-even point (BEP) for a pickoff attempt using Run Expectancy (RE), similar to previous analyses on bunting and stealing. To calculate the BEP for a given pickoff attempt, I calculated the RE benefit (to the defense) of an out and the weighted RE cost of a safe call or an error.  This sounds simple enough, but calculating the RE after an error involved some guesswork.

Although errors can result in multiple outcomes, I chose to pick one outcome for each base to simplify the analysis. Thus, I assumed 2 bases for all runners on an errant throw to first, 1 base for all runners on an error to second, and, after much thought, 2 bases for runners on second and 1 base for runners on the corners on an error to third. If you have data that can replace these assumptions, please let me know.  Otherwise, be cognizant of my assumptions when you attempt to make use of the findings.  For example, if there is a slow runner on second, the BEP for a pickoff attempt to a corner will be overly conservative (inflated).  Additionally, I didn’t differentiate between pickoff attempts from the pitcher and the catcher.  The pitcher has a shorter, unobstructed throw, and favorable balk rules when picking to second or third, but still has to deal with the risk of a balk, especially to first, along with the added difficulty of throwing off the mound.  Finally, while calling for a back-pick from the catcher can put a defender out of position, I chose to ignore this factor because a) I assume it is rare for a hitter to find the vacated hole, and b) the defense can choose to avoid contact.

In order to weight the cost of a failed pickoff attempt appropriately, I had to estimate what the error rate would be on attempts.  While we do have data on pitcher error rates on pickoff attempts (around 0.95%), the data are only from throws to first.  Set pickoff plays are more challenging for the defense, so the error rate should be higher than on typical attempts to first.  My solution, in lieu of empirical data from actual set pickoff attempts, was to estimate catchers’ throwing error rates from the 2015 season.  I chose this strategy for two reasons: First, catchers are one of the primary players who can attempt a set pickoff, so it made sense to sample from their performance.  And second, catchers accumulate a large portion of their assists under similar conditions to the pickoff attempt (for example, in 2015 nearly 40% of all catcher assists came from caught stealing).  Thus, I expected catcher throwing error rates to approximate the error rates we would observe on set pickoff plays.

While not a perfect method, I estimated catcher throwing error rate as Throwing Errors / Assists + Throwing Errors + Stolen Bases.  The mean throwing error rate in a sample of catchers (n = 38) who played at least 500 innings in 2015 was 3.6%.  Do you accept that set pickoff plays will result in 3.8 times more errors than typical pickoff throws to first? If not, adjust your own estimates accordingly.

Using the estimated throwing error rate for catchers, the formula for estimating the BEP on a set pickoff attempt is RE cost / (RE cost – RE benefit). In this equation, RE benefit = RE after a pickoff – RE before a pickoff; RE cost = RE before a failed attempt – RE with a failed attempt, and RE with a failed attempt = (RE of a safe call *.964) + (RE of an error *.036).  Using the RE tables found here, I generated Table 1 below.

Table 1.  Success rate required to attempt a pick at each base.

Table 1 presents the BEP for the defense of (successful pickoffs / attempts) X 100.  In other words, Table 1 provides the minimum expectation of success required for the defense to attempt a set pickoff and it be a break-even strategy. Unfortunately, it is difficult to guess how successful set pickoff attempts typically are.  In Dan Malkiel’s study of pickoffs to first, he found that righties and lefties were successful about 2% and 4% of the time, respectively.  However, Malkiel’s study sampled situations with base-stealers on first, so the stolen-base rate was between 17% and 21%.  It’s impossible to know what percentage of successful pickoffs occurred when the runner intended to steal, but it’s safe to say 2% and 4% success rates are a little high if the runner on first isn’t planning on going. Set pickoffs usually work differently than throws to first, since neither the pickoff nor the steal are always expected. Therefore, the data on picks to first can only serve as a point of reference, helping to calibrate expectations rather than serving as predictions themselves.

One way to assess if teams are over- or under-utilizing set pickoffs is to compare their pickoff to error ratios with the BEPs for that metric. Unfortunately, I could only find data for one special case of the set pickoff: a catcher back-pick to first.  In the Malkiel study, successful back-picks were 96% of back-picks plus errors.  If we assume an error puts the runner on third, the BEP for pickoffs/pickoffs + errors is 50%, suggesting that catchers have room to get much more aggressive in attempting to pick runners off first.  Without more data, it’s difficult to comment further on current MLB behaviour regarding set pickoff plays. Nevertheless, the estimates in Table 1 provide interesting insights into the risks and rewards of pickoff plays. Below, I list six lessons that can be gleaned from Table 1.  At least two of these lessons fly directly in the face of my own long-held beliefs, and maybe yours too!

Lesson 1

If, at any time, the defense notices that it has better than a 15% chance of picking off a runner, they should attempt the pickoff.

Lesson 2

Pickoff attempts require greater confidence with two outs, with three exceptions.  Often, the required success rate is over 5%, requiring a fairly egregious mistake by the runner to warrant a throw. The exceptions to this rule are with a runner on first, a runner on second, or a pick to second with runners on first and second.

Lesson 3

A runner on second with no runner ahead of him should probably be targeted frequently.  The BEPs are consistently low for attempting the pickoff to second, while the runner is motivated to be aggressive by the chance to score a run or steal third. Even failed attempts have the favorable by-product of keeping the runner close, a factor not considered in Table 1.

Lesson 4

Throwing behind the runner on first with runners on first and second or the bases loaded is dangerous.  This doesn’t mean it’s a bad play if the runner on first opens the door, but the defense should be really confident to make the throw.

Now for the lessons that go against everything I thought I knew…

Lesson 5

Pitchers should throw over to third with runners on 1^st and 3^rd in a steal situation.  Ever since the MLB outlawed the fake-to-third move, pitchers haven’t been allowed to bluff the throw in hopes of catching the runner breaking from first.  Based on Table 1, it seems strange that pitchers ever faked the throw to begin with.  With no one out, the defense would only need to pick the runner off third 8 times per 1000 attempts, or nail the runner stealing second 3 times per 100 attempts, or a combination of the two to break even.  Additionally, if the runner on first breaks for second it’s an easier throw from third than from first, which was often the result with the fake-to-third move.  While many old-school baseball people will object to throwing over to third, the common refrain “he’s not going anywhere!” doesn’t necessarily apply to the 1^st and 3^rd steal situation.  The runner could be trying to get closer to home so he can steal on the catcher’s throw to second, making it the perfect time to throw over.  Although the third baseman’s positioning will sometimes make a true pickoff attempt at third difficult, the rules do not require the pitcher to throw directly to third.  Thus, teams can make legitimate efforts to get the runner on third when the situation allows it, while other times making throws away from the base solely to catch the runner on first breaking for second.

Lesson 6

The situation that requires the lowest probability of success to attempt a pickoff is when there is a runner on third with no one out.  The defence needs to nab merely 2 runners out of every 1000 attempts to break even. And get this, the BEP on pickoff attempts to third with 0 out is lower than the BEP for typical throws to first, even with the much lower error rate on throws to first (0.95%), and even after adjusting the assumed cost of an error to one base.  Holding probability of success constant, the pickoff attempt to get a runner on third with 0 out is the least risky pickoff attempt possible. The LEAST risky.

Of course, a runner who is on third with no one out should be taking no chances.  But that doesn’t mean a pickoff will never work…

My name is Rich Rieders and I am a 2015 graduate of Rutgers Law School. Over the winter, I participated in Tulane University’s 9th Annual Baseball Arbitration Competition and we finished in 2nd place overall out of 40 teams.

In order to prepare for the competition, I created a database (going back to 2008) consisting of all arbitration awards and players who signed 1-year contracts avoiding arbitration along with their respective statistics. Using regression analysis, I was able to determine which statistics correlate most with salary. In turn, I have created a projection system that can accurately predict arbitration salaries. My projections are more accurate than the ones featured on MLBTradeRumors.

I will be releasing my 2016 projections once the season is over and all awards are announced.

The goal of this article is to properly explain how arbitration salaries are determined and how to choose the best comparative baseball salaries (comps) as outlined in Article VI, Section E, Part 10(a) of the CBA. You can think of the comps as legal precedent. The closer the comps are to the player’s stats, the more comps you have and the more recent those comps are, the stronger your argument.

First and foremost, the purpose of the arbitration process is to compensate the player for his actual results on the field, not to give him a salary based on what we expect he will produce in the upcoming season. We concern ourselves with only the traditional stats. I know this is a complete departure from the way we normally think here on FanGraphs, but salary arbitration is a completely different animal. In essence, arbitration salaries are determined by the accumulation of traditional counting stats.

For our purposes, there are six types of players who are up for arbitration in a given offseason and each type has its own separate valuation. The six types of players are:

(1) First-year-eligible SP

(2) SP who have previously been through the arbitration process

(3) First-year-eligible RP

(4) RP who have previously been through the arbitration process

(5) First-year-eligible position player

(6) Position players who have previously been through the arbitration process.

I will explain, in detail, how to properly choose player comps for each of the six group of players. In this segment, we will focus just on the starting pitchers.

For a SP who is arbitration eligible for the first time, here are the statistics that correlate most with eventual salary:

Platform IP: 60.83%

Platform GS: 57.59%

Platform SO: 54.41%

Platform W: 53.12%

Career IP: 50.56%

Career SO: 47.45%

Career W: 42.76%

Career GS: 37.10%

When initially looking for player comps, these are statistics we are going to focus on. Keep in mind that although ERA is not listed, it is nonetheless important as ERA is still one of the default statistics during a hearing and the first basis for comparison. Note that rate stats almost always have a very low correlation since rate stats do not take into account playing time.

Let’s use Atlanta Braves starter, Shelby Miller, as an example of a first-year-eligible SP.

Shelby Miller is arbitration-eligible for the first time going into 2016 with 3 years and 30 days of service time (3.030). In his platform season (2015), Miller made 33 starts recording 6 wins, 171 SO with a 3.02 ERA in 205.1 IP. Over his career, Miller has compiled 575 IP, 32 W, 483 SO with a 3.22 ERA in 96 GS. The objective here is to find the players who avoided arbitration by signing a 1 year contract with statistics that are most similar to Miller’s. The more recent, the better. The best way to do that is to set a floor and a ceiling and then work your way towards the middle.

From Miller’s perspective, let’s look at Miguel Gonzalez’s 2014 platform season. Like Miller, Gonzalez posted a low win total despite a very strong ERA. Gonzalez made 26 starts, recorded 10 wins, 111 SO with a 3.23 ERA in 159 IP. Over his career, Gonzalez compiled 69 starts, 30 wins, 308 SO with a 3.45 ERA in 435.2 IP. Although their ERA and win totals are extremely close, Miller bests Gonzalez in all the most important categories and has significantly more playing time and strikeouts. Therefore, we can definitively state Miller should receive more than Gonzalez did. As such, Gonzalez’s 2015 salary of 3.45 million should be the floor.

From Atlanta’s perspective, let’s look at Chris Tillman’s 2014 platform season. Like Miller, Tillman pitched a similar amount of innings and games with a pretty low ERA. In his platform season, Tillman made 34 starts recording 13 wins, 150 SO and a 3.34 ERA in 207.1 IP. Over his career, Tillman compiled 45 W, 680.1 IP, 511 SO with a 4.00 ERA in 118 GS. Although Miller has the better ERA, Tillman is superior in all the other major categories. Hence, we can conclude that Miller will receive less than Tillman. We can use Tillman’s 2015 salary of $4.315 million as the ceiling.

Given the above, Shelby Miller is likely to receive somewhere between $3.45 million and $4.315 million. Now that we have a range, let’s find someone towards the middle.

In 2011, Justin Masterson made 33 starts with 12 W, 158 SO, 3.21 ERA in 216 IP. Over his career he made 87 starts, with 28 W, 485 SO, 3.92 ERA in 613.2 IP. Those numbers are quite similar across the board with Miller having a better ERA, but fewer IP. Masterson’s 2012 salary was $3.825 million. Alex Cobb ($4.0 million in 2015),  Travis Wood ($3.9 million in 2014) and Steven Strasburg ($3.975 million in 2014) are all good comps as well.

As for my model, Miller projects to receive $3,859,816 +/- $145,351 which is perfectly in line with the comps above. MLBTradeRumors projects him at $4.9 million, which is not only significantly higher than the above comps, but would beat the record for a first-year player by nearly 600K.

For a player who has already been through the arbitration process before, the valuation is completely different as career statistics are no longer used the 2nd, 3rd, 4th, etc. time around (except in a few rare cases). This group of players are the most difficult to project since we use fewer variables due to the exclusion of career stats and how there are fewer SP across the league than relievers or position players. Nonetheless, we can still get a pretty good idea what their eventual salary will be.

For an SP who has previously been through the arbitration process, the stats that correlate most with eventual salary are:

(1) Platform W: 69.12%

(2) Platform RA9-WAR: 64.04%

(3) Platform SO: 60.97%

(4) Platform fWAR: 58.93%

(5) Platform IP: 58.34%

(6) Platform GS: 49.75%

For example, let’s look at Angels SP Garrett Richards who is arbitration eligible for the second time going into 2016. As a Super-2 going into 2015, Richards received a $3.2 million salary. That figure includes everything he had done in his career up to that point. Thus, when determining his 2016 salary, we don’t need to focus on previous seasons. We need only determine what his 2015 season was worth and give him a raise. In his platform season (2015), Richards made 32 starts recording 15 wins, 176 SO, 3.65 ERA, 2.5 fWAR and 2.8 RA9-WAR in 207.1 IP. We want to find the players whose stats are most similar to Richards.

First let’s discuss Matt Garza’s 2010 platform season (a bit old, but still useful) where he made 32 starts recording 15 wins, 150 SO, 3.91 ERA, 1.9 fWAR and 2.8 RA9-WAR in 204.2 IP. Other than the strikeout numbers, we have a virtually identical season. As such, Richards is likely to receive a raise higher than Garza’s $2.6 million raise going into 2011. We can consider a raise of $2.6 million to be his floor.

Next let’s look at C.J. Wilson’s 2010 platform season (again old, but useful still) where he made 33 starts recording 15 wins, 170 SO, 3.35 ERA, 4.1 fWAR and 5.1 RA9-WAR in 204 IP. Wilson has the same amount of wins and virtually the same number of SO although Wilson has a clear advantage in fWAR and RA9-WAR with a slightly better ERA so it’s pretty safe to say that Richards is likely to get a raise lower than Wilson’s $3.9 million raise. The $3.9 million should be the ceiling.

Homer Bailey’s 2012 platform season is a great final comparison. Bailey made 33 starts recording 13 wins, 168 SO, 3.68 ERA, 2.7 fWAR and 2.8 RA9-WAR in 208 IP. Both players are virtually identical statistically. Bailey received a raise of $2.925 million so Richards is likely to receive a very similar raise himself. Shaun Marcum ($3.1 million in 2011), Jordan Zimmerman ($3.050 million in 2011) and Max Scherzer ($2.975 million in 2013) are all good comps as well.

Therefore, we can be certain that Richards will receive a raise somewhere between $2.6 million and $3.9 million. As for my model, Richards projects to receive a raise of $2,923,484 for a total salary of $6,123,484+/- $336,500 and, unsurprisingly, that is perfectly in line with the comps above. MlbTradeRumors is projecting a raise of $3.6 million for a total salary of $6.8 million which I think is a bit generous given the comps we have at our disposal, but not unreasonable.

Next up: Relief Pitchers.