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03-31

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9

Prospectus Feature: All Spin Is Not Alike
by
Alan M. Nathan

03-27

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4

Prospectus Feature: How the Astros do Spring Training
by
Howard Megdal

03-13

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13

Prospectus Feature: Scouting With Plate Discipline
by
Jeff Moore and Andrew Koo

02-27

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9

Prospectus Feature: A.J. Preller's Offseason and the Toronto Precedent
by
Steven Jacobson

02-17

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7

Prospectus Feature: Hacking Mass Wrap
by
Wilson Karaman

02-13

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2

Prospectus Feature: The Golden Age of Immaculate Innings
by
Ian Frazer

02-12

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2

Prospectus Feature: The Genius Of Arbitration
by
Eugene Freedman

01-29

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41

Prospectus Feature: The PECOTA Release
by
Mike Gianella and Rob McQuown

01-21

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5

Prospectus Feature: Quantifying the Wobbly Chair
by
Andrew Hopen

01-13

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14

Prospectus Feature: The 2014 All Out-of-Position Team
by
Andrew Mearns

12-15

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9

Prospectus Feature: The Surprising Math Teams Use to Value a Compensation Pick
by
Jeff Quinton

12-09

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9

Prospectus Feature: How Far Did That Fly Ball Travel (Redux)?
by
Alan M. Nathan, Jeff Kensrud, Lloyd Smith and Eric Lang

12-05

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11

Prospectus Feature: The Yankees and the Toothless International Spending Limits
by
Dustin Palmateer

11-04

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6

Prospectus Feature: The #Sources Season
by
Matthew Trueblood

11-03

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32

Prospectus Feature: The Decision that Decided a World Series
by
Dustin Palmateer

10-09

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39

Prospectus Feature: Check Out This Obnoxious Cardinals Fan
by
Brian Gunn

10-08

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6

Prospectus Feature: Aaron Judge and the Question of Long-Armed Hitting Prospects
by
Jeff Moore

10-07

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1

Prospectus Feature: The Great Octoberness Rankings
by
Miles Wray

09-23

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11

Prospectus Feature: Colin Moran and the Matter of Draft Status
by
Jeff Moore

08-29

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38

Prospectus Feature: Roast A Parks
by
BP Staff

02-28

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0

Prospectus Feature: The Downfall of Denny McLain
by
Mark Armour

02-28

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0

Prospectus Feature: The Eddie Award
by
Jeff Bower

02-26

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0

Prospectus Feature: 2003 IHOF Veterans Committee Results
by
Neal Traven

02-26

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0

Prospectus Feature: The Injury Nexus: A Look at Pitcher Injuries
by
Nate Silver and Will Carroll

02-21

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0

Prospectus Feature: PECOTA At Altitude: A Review of Major League Hitters in Colorado
by
Nate Silver

02-20

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Prospectus Feature: Touring the Minors: The Pacific Coast League
by
Keith Scherer

02-19

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0

Prospectus Feature: Where Does the Money Go?: Taking a Look at Major League Payrolls
by
Doug Pappas

02-18

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0

Prospectus Feature: Could Relegation Work?
by
Derek Zumsteg

02-11

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0

Prospectus Feature: The Yankees' Seven-Man Rotation
by
Nate Silver

02-06

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0

Prospectus Feature: Playing the Armchair Arbitrator
by
Nate Silver

01-31

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0

Prospectus Feature: Top 40 Prospects Roundtable
by
Baseball Prospectus

01-28

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0

Prospectus Feature: Expanding the Playoffs: Drawing Guidance from the NBA
by
Jeff Bower

01-28

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0

Prospectus Feature: Expanding the Playoffs
by
Jeff Bower

01-24

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0

Prospectus Feature: That's the Chicago Way
by
Keith Scherer

01-23

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0

Prospectus Feature: Breaking Out
by
Nate Silver

01-22

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0

Prospectus Feature: The Midsummer Classic: Making it More Than Just an Exhibition Game
by
Doug Pappas

01-21

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0

Prospectus Feature: The Appearance of Misconduct: A Conspiracy Theory Worth Considering
by
Tim Walker

01-17

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0

Prospectus Feature: Baseball Prospectus Radio
by
Will Carroll

01-14

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0

Prospectus Feature: The 1987 Free Agent Market
by
Nate Silver

01-14

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0

Prospectus Feature: A Brief History of the Veterans Committee
by
Neal Traven

12-12

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0

Prospectus Feature: Freely Available Talent
by
Dayn Perry

12-09

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0

Prospectus Feature: 2002 STATLG-L Internet Hall of Fame
by
Neal Traven

12-04

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0

Prospectus Feature: The Forty Million Dollar Question: Building the 2003 Expos (Part Two)
by
Scot Hughes

11-26

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0

Prospectus Feature: 2002 HACKING MASS Results: All Players, By Position
by
Baseball Prospectus

11-26

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0

Prospectus Feature: 2002 HACKING MASS Results: All Players, By Name
by
Baseball Prospectus

11-26

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0

Prospectus Feature: 2002 HACKING MASS Results: All Players, By ESPN
by
Baseball Prospectus

11-22

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Prospectus Feature: The Forty Million Dollar Question: Building the 2003 Expos (Part One)
by
Scot Hughes

11-07

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Prospectus Feature: The Arizona Fall League
by
Jonah Keri

10-31

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Prospectus Feature: Evaluating the Dowd Report
by
Derek Zumsteg

10-28

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Prospectus Feature: Player Cards
by
Clay Davenport

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Separating the useful spin from the rest.

Alan M. Nathan
University of Illinois

Ever since the early days of PITCHf/x, we have had unprecedented information about the movement of pitches. We now have a precise quantitative measure of how much and in what direction a pitch moves—i.e., deviates from a straight-line path. The movement is the result of the combined forces of gravity pulling the ball downward and the so-called Magnus force on a spinning baseball. It has become conventional to remove the effect of gravity, which is easily calculable, so that the resulting movement—pfx_x and pfx_z in PITCHf/x lingo—is due only to the Magnus force. I will utilize that convention in this article. It seems sort of reasonable that there ought to be some simple relationship between the movement to the spin rate. For example, if a pitch is spinning at a higher rate, the expectation is that there will be more movement. But is that expectation correct? In fact, it is not correct because, as the title of this article suggests, all spin is not alike. And that is the issue I want to discuss here.

So why is it that all spin is not alike? The reason has to do with the vector nature of the spin: It has a magnitude and a direction. The magnitude is pretty simple, since it is just the number of revolutions per minute, or rpm. Let’s talk about the direction. The easiest way to determine the direction of the spin is to use a right-hand rule: Wrap the fingers of your right hand around the ball so that they point in the direction that the ball is turning. Your thumb will then point in the direction of the spin axis.

Here are some examples. A straight overhand fastball has pure backspin and the spin axis points to the pitcher’s right. An overhand “12-6” curveball has pure topspin and the spin axis points to the pitcher’s left. A ball thrown with pure sidespin has its spin axis pointing up or down. In all these examples, the spin axis is perpendicular to the direction of motion. On the other hand, a gyroball is a pitch thrown with the spin axis perfectly aligned along the direction of motion, much like a spiral pass in football. Indeed, it is often called “bullet spin”, since that is how a bullet will spin when shot from a rifle. All of these pitches are special cases, since in general the spin axis could be pointing in any direction whatsoever.


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How a process team handles six weeks that many analysts consider worthless.

Roaming cyborgs menace outfielders shagging fly balls. Infielders need to stop after every groundball and log it at a nearby computer. When player performance drops below a certain proprietary algorithm, a trap door opens below that player on the Osceola County Stadium field, and that one-time Astro is never heard from again.

I can confirm that this is not how spring training works for the Houston Astros.

Still, spring training is a notorious breeding ground for poor decisions made on incomplete, inaccurate or just plain useless data—the sort of bad-sample trap that should drive a Process team nuts. This isn't some progressive Astros conclusion, but a generally understood reality within the sport. I heard Mets manager Terry Collins make an umprompted argument against spring performance as a decision-driver last week, and few people have pegged Collins as some kind of hyper-sabermetric strategist. And yet: no one has moved to abolish spring training. So what does a team like the Astros, whose front office is quite aware of the limitations of spring numbers, use that time for?

For a bit of evaluation—the Astros do utilize spring performance as data, though carefully, and tacked on to what the team already knows about a player. As a significant teaching period that allows the Astros to codify coaching approach throughout the organization. And as a large dose of emotional and psychological interaction that the Astros believe will have a dramatic if still unquantifiable impact on the season.

“When we show up here, it's the one time when we have 200 players in the same place, we have 60 coaches in the same place,” Astros assistant general manager David Stearns told me as we sat in his office, a few minutes before the March 20th game between the Astros and Nationals. “It's a tremendously important time for player development. So put the evaluation aspect to the side for a moment, you think about the coach-to-player ratio during spring training, and it's about as good as it can possibly get at any time of the year. And so the amount of individual attention and specified instruction that can go on between our players and our coaches is better this time of year than anything else. For me, as I look at this for the organization as a whole, that's what gets me really excited about spring training.”

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Understanding the relationship between plate discipline in the minors and future big-league success.

Not long ago, in the empty hours that fill scouts’ time between batting practice and the first pitch, I was speaking with (read: listening intently to) to an experienced scouting director. The topic of plate discipline came up. As anyone who closely follows the BP prospect team has figured out, I fall at the “extremely important” end of the spectrum when it comes to using plate discipline to evaluate prospects and predict their future success. Because of that, it didn’t take much prodding to get me to rave about a prospect I had recently seen from this scouting director’s system. The prospect, along with many strong skills, had a fantastic eye.

The scouting director’s response surprised me. He informed me his organization values plate discipline extremely highly, to the point of actually considering it a sixth tool (something we’ve seen the old-school camp dismiss in the past). I love the concept, but was stupefied because the organization in question is not one we typically think of as sabermetrically friendly. I assumed I was at a more extreme end of the spectrum on this topic, but here my views were accepted with arms open wider than I had anticipated.

Plate discipline, of course, is not a new concept in scouting. The way we view player value has brought about the current on-base renaissance within the big-league game, and that has had a trickle-down effect into the scouting world. With a better understanding of the value of on-base ability, we have changed how we evaluate prospects in some regards, at times excusing larger holes in a hit tool, for example, so long as it comes with strong on-base skills. The ability to avoid outs with better plate discipline can make up for some flaws in one’s ability to hit his way on base.

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Is it really possible to build a great team in one winter?

By the end of the 2012 season, the Blue Jays had secured their place in baseball as the definition of middling. After their 1992-1993 heyday—the culmination of 11 straight seasons of 86 wins or more—the Jays ripped off a string of seasons that would make a centrist very happy: Only twice in the next 19 years did Toronto finish in last place in the American League East, but just once did they manage to finish within 10 games of the division winner.

Once the Rays found respectability, Toronto dropped from its usual third place, finishing in fourth each year from 2008 to 2012. This was despite a respectable 400-410 record over that span, with three seasons at or above .500.

The time had come for the Blue Jays to do something big. “I’m not going to live through what we went through this season again,” general manager Alex Anthopolous told employees in October 2012, according to Bob Elliott of the Toronto Sun.

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Revisiting the worst performers of 2014 and talking to the year's grand MASSter.

Sure, yes, the Royals returned to the World Series last year for the first time since 1985, and yes that was a big deal and all. But there was an even more important storyline of lost glory restored in 2014: HACKING MASS came back, baby! Our annual test of wills—specifically the will to identify the least-talented major-league players with the best chance of somehow, someway remaining in their teams’ starting lineup all year—returned from several years of hiatus.

For the uninitiated, our cherished rulebook is here for your reading pleasure.

Last year’s contest featured 819 players who averaged 181.2 total accumulated ESPN (that’s Exuded Stiff Points, Net). Our champions, the fightin’ Pianosa Bombardiers, paced the contest with 487 ESPN.

So without further ado, let’s begin! Ladies and gentlemen, your 2014 HACKING MASS All-Stars:

All Star Team

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Is there anything we can learn from the most random, most fleeting of exceptional baseball performances?

Baseball is no stranger to misnomers. A splitter stays in one piece; a drag bunt contacts the bat no longer than any other hit; a knuckleball is usually thrown with the fingernails. This point is even true concerning some of the game’s most notable events. A perfect game is never quite so: Spots are missed, mistakes are made, pitches are often hit extremely hard. But they result in outs all the same.

A truly perfect game, theoretically, would be composed entirely of strikeouts, with no balls thrown. Nobody has done this outside the world of video games (and probably within that world, as well). But if we shrink the scope down to a single inning, baseball history offers us a number of examples of perhaps the closest thing to true perfection that baseball offers.

Per baseball-almanac.com, the game has seen 79 instances of these “immaculate innings.” They are more than three times as rare as no-hitters and about as much so as a cycle. But they lack the narrative momentum of those events, the build-up and climax. With a perfect game, we have 26 batters to see it coming. With a cycle, we have three (or more) at-bats. But with an immaculate inning, it’s a single inning, its significance clouded by that of the game as a whole.

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February 12, 2015 6:00 am

Prospectus Feature: The Genius Of Arbitration

2

Eugene Freedman

How baseball's unique animal pushes negotiations closer together.

In the past two weeks Mat Latos, Neil Walker, and Jarrod Parker have lost their arbitration hearings and Danny Valencia, Jerry Blevins, and Vance Worley prevailed, determining each of their salaries for the 2015 season. More than a dozen hearings remain before February 20th. Major League Baseball and the Players Association have two types of arbitration in their collective bargaining agreement. The first is grievance arbitration, a common labor-relations dispute-resolution mechanism designed to resolve disputes over the meaning of the negotiated agreement and to deal with disciplinary matters. The other is salary arbitration and it is a rather unique animal.

Salary arbitration is a creation of the collective bargaining agreement and its origin is linked to the reserve clause system. Baseball’s reserve clause is a system that ensures clubs’ unfettered right to control a player for his first six seasons. Historically, it had been much more restrictive, though. Teams could renew players for one additional year after each season, in perpetuity. Curt Flood unsuccessfully challenged the reserve clause to the Supreme Court. See Flood v Kuhn, 407 U.S. 258 (1972). Ultimately, it was upended through a grievance arbitration decision frequently referred to as Messersmith-McNally, after players Andy Messersmith and Dave McNally, who were grievants in the case. The result of Messersmith-McNally was to allow players free agency under certain circumstances. Following the decision, Major League Baseball (“the Clubs”) and the Players Association negotiated a limit to the reserve clause and a process by which players could receive market-like salaries in the years they were under team control. That process is called salary arbitration and it is contained in Article XI, E of the parties’ CBA.

The CBA provides that players with more than three and less than six years of Major League service are eligible for salary arbitration. Additionally, a class called “Super Two” players, with at least two and less than three years of Major League service, are eligible if they have at least 86 days of service during the previous season. They must also rank in the top 22 percent in total service among the players with at least 86 days of service and at least two but less than there years. These service time cutoffs are why clubs are very conscious of when they promote top prospects to the Majors. Such delayed promotions frequently are described as not letting a player’s arbitration clock start ticking.

What makes baseball salary arbitration different from grievance arbitration in the labor-management setting, or arbitration in most other settings, is that it uses a format called final offer arbitration. In most arbitration settings, the arbitrator can craft any decision she feels is appropriate, as long as it conforms to the terms of the agreement and law. In many cases, there is a belief that the arbitrator will “split the baby,” referring to Biblical tale of King Solomon. In final offer arbitration, the parties submit their final offer as their proposed remedy, and the arbitrator is bound to select one offer or the other. The arbitrator has no discretion to fashion a different remedy.

“History attests to the genius of this one-issue process,” said George Cohen, the former Director of the Federal Mediation & Conciliation Service, who served as the MLBPA outside counsel during the 1994-1995 unfair labor practice strike. Cohen said, “at the culmination of an informal, private, expedited hearing the arbitrator must award either the team’s proposed salary or that of the player. And that award is final and binding on all parties. It requires immediate decisions, with no rationale and no precedent.”

Arbitrator Richard I. Bloch, who served as baseball’s grievance arbitrator from 1983 to 1985 and heard baseball salary arbitration cases for nearly 30 years, said that it can be frustrating not to be allowed to justify the award and tell the parties why it was the right decision, but that having no written decision definitely helps with expedition.

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Tackling a few relevant topics on PECOTA day.

Welcome to PECOTA day, sponsored by DraftKings. Premium subscribers can now download the 2015 Weighted Means Spreadsheet under the Fantasy tab at the top of this page, or by clicking "manage your profile." Player pages have been updated with these projections, as have team depth charts (with projected standings) and the fantasy team tracker. Allow us to expand on a few details that might be helpful to you.

Why Does PECOTA Hate My Team?

Every year, fantasy owners and fans of teams ask this question, “Why Does PECOTA Hate My Team?” Last year, Deadspin compiled five dozen “(maybe) surprising player projections.” This season, there’s already been a Lineup Card with eight such surprising projections and Sam Miller did some Pebble Hunting to reveal some of the “winners” in the PECOTA pitching projections. This all raises the question of why Baseball Prospectus would keep publishing surprising projections. Shouldn’t these things be getting better with time, as the system is refined and there’s more data?

It would be disingenuous to suggest that projections never miss the mark. Sometimes by a lot. In fact, last season alone, 39 of the 362 position players for which Baseball Prospectus had projected 100 or more plate appearances actually amassed 100 or more plate appearances with very unexpected (to PECOTA) hitting performances. We looked at these players’ WARP-per-600 plate appearances, with FRAA removed (yes, FRAA is important, but it’s projected differently and is—sometimes—much more out of the player’s control than batting stats). Using this metric, 39 players missed by 3.0 or more WARP-per-600. It could almost have been called, “Craig’s List”, as Mr. Allen Craig was the no. 9 culprit with a WARP-per-600 difference of 4.6 … and as those who saw him play for Boston can attest, he was making a strong run to top this list. PECOTA had projected 1.8 WARP-sans-FRAA in 426 PA (March 22nd projections), and he ended up with -1.7 WARP-sans-FRAA in 505 PA. But Dan Uggla took the top honors, falling 5.7 WARP-per-600 short of projections. Steve Pearce was no. 3 and represented the top over-performer, bettering his WARP-per-600 projection by 5.4.

The above examples come from the most stable group of players—batters who were projected to play and who did play. Yet, some of the most surprising projections entering the 2014 season ended up being close to perfect. For example, people who saw A.J. Burnett pitch in 2013 thought PECOTA needed glasses, as it projected Burnett to have one of the 10 largest declines in 2014. It projected his ERA to be 4.24, which, considering the drop in leaguewide offense in 2014, would have been adjusted to 4.14. His FIP in 2014? 4.14. Projections for Bryce Harper and B.J. Upton, tabbed as “(maybe) surprising” in the Deadspin article, proved prescient.. Remember the reaction when Chris Davis had a .289 TAv projection (again March 22)? That number ended up being optimistic (he posted a .271), even though when he was coming off a .358 TAv season virtually everyone thought PECOTA hated the guy.

Seriously, though, PECOTA doesn’t hate any player or anyone’s team. There are no biases in it based on anything but historical track records. For completeness, it should be noted that results such as the examples herein are not just “shrugged off” – both accurate and inaccurate results are processed. So, while some projections are going to be surprising, it’s important to keep in mind that all-in-all, the results have been very accurate over the years (thank you, Nate Silver!).

Using Team Tracker

Everyone who follows baseball at all has probably dabbled in the Baseball Prospectus Team Tracker—the most powerful tool of its kind available. For a reminder of some of the various things Team Tracker can do, both on the Team Tracker pages and elsewhere on the site, please refer back to Feature Focus articles on Team Tracker, Basics and Team Tracker, Advanced. The primary reason it’s being mentioned here is that 2015 PECOTA forecasts are now available. Shown is an actual portion of the Team Tracker page for the hitters on my Scoresheet team. (A team which was much better last season than it had any right to be. I had the second-best record among 24 teams entering the final week of the season and then, um, moving on… ) It can be seen that even for a 24-team league, hard times are likely ahead in 2015, based on PECOTA projections. The excerpt from my Team Tracker display is truncated on the right side as a reminder that there are many other stats which can be selected for the reports—allowing them to be tailored to each owner’s needs.

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What makes a manager lose his job?

Last fall, the Diamondbacks, Cubs, and Red Sox all finished last in their respective divisions. The Diamondbacks dismissed manager Kirk Gibson in what was widely seen as an appropriate move given the franchise’s decline and Gibson’s grittiness-bordering-on-violence. The Cubs fired manager Rick Renteria, not because of performance but because Joe Maddon became available. Public reaction was one of uncomfortable sympathy; nobody was out for Renteria’s head, but c’mon, it’s Joe Freaking Maddon. The Red Sox retained John Farrell, whose team severely underperformed expectations. Surely he benefitted here from a wildly successful 2013.

Point being, keeping or dismissing a manager is a complicated decision, in which on-field results have to be weighed against history, context, and intangibles like leadership and respect. But of the tangible results, which types truly matter, and how much does each shade the picture? I aimed to build a model to answer that question.

The Model
For my data, I included all seasons from 1996 (first full season of the Wild Card Era) to 2013, using information I could find within or derive from the Lahman database. This includes things like win percentage, playoff appearances, year-to-year improvement, and awards won. I opted to include every opening day manager (i.e. no interim guys, whose fates are often pre-determined) and used my data to predict whether or not each would appear as manager for the same franchise next year. I chose to fit a decision-tree model with boosting. (For those interested, the final tuning parameters chosen by repeated CV were: shrinkage=0.01, #trees=350, and interaction depth=3.) I excluded the two expansion-team managers because they messed up variables that relied on previous seasons, and because I felt they deserved unique categorization but were too few to be distinguished by the model. I also excluded 1999 Astros manager Larry Dierker, whose health forced a mid-season hiatus, resulting in two separate 1999 stints in the Lahman database.


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The players who played where players like them should not play.

Baseball certainly had its share of wacky storylines in 2014. From the mystery woman in the Giants’ dugout during the wild card game to the Great Wall of Dodgers to, well, the Royals’ entire playoff run, baseball maintained its heritage of bizarre occurrences. (Ben Revere even homered! Twice!) Most importantly, the longstanding tradition of Weirdball with people playing out of position continued. Last year, I wrote about the 2013 All Out-of-Position Team, a collection of players who spent time on defense in places where they were about as appropriate as Jose Canseco on The 700 Club.

Raul Ibanez never did get to center field as I had hoped, but there was definitely an impressive showing of major-league players who simply should not be associated with the positions they played. However, every appearance they made there was a treasure, truly demonstrating the strange depths baseball can occasionally reach.

Pitcher: Adam Dunn
After 462 homers in just 14 seasons, the big lefty surprisingly decided to call it a career early, just a month before his 35th birthday. While it is a bit disappointing that fans won’t get to see Dunn moonshots anymore, he at least gave them one thrill they likely never expected to see: one inning on the mound.


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Why does the value a team places on a draft pick seem to change from situation to situation?

“The Yankees never made an offer to David Robertson; determined they’d rather sign Andrew Miller and get the draft pick [compensation] for Robertson.” – Buster Olney, via Twitter

All other factors equal, it is preferable to sign a free agent who is not attached to a qualifying offer than a free agent that is QO-attached. This is obvious. What is not obvious is by how much, or whether that “how much” is always constant from free agent to free agent for each team. First round pick protection, competitive window, payroll limit, state of one’s minor-league system, and upcoming draft class will all determine how each team costs (values) losing a draft pick. According to traditional financial, economic, whatever-you-want-to-call-it theory, weighing these factors all makes sense. But, according to traditional theory, each team would individually weigh the cost of giving up a draft pick equally across all QO-attached free agents. Example time:

Team X puts the cost of losing its first round pick at $8M. Absent the qualifying offer, Team X values Max Scherzer at six years, $150M and Ervin Santana at two years, $25M. Taking the cost of losing a first round pick into account, Team X should value Scherzer at 6 years, $142M and Santana at 2 years, $17M.

Cool, makes sense. Alas, mental accounting, which posits that “people spontaneously generate their own mental accounts, and where we place these boundaries subtly (but profoundly) influences financial decision making,” indicates that our traditional theories may be oversimplifying things here. Specifically, it notes that we create topical accounts, in that our decisions are altered by the context of the situation. Whereas most think it absurd to drive 15 minutes down the road to another car dealership to save $75 on a $25,000 car, many will stand in line for an hour in the middle of the night to save that same $75 on a $250 smart phone.

Question: What does this have to do with QO-attached free agents?

Answer: Given the use of topical accounts, we could hypothesize that if GMs categorize Scherzer as an impact player and Santana as a role player—and are less willing to give up a draft pick to get a mere role player—that teams might be either (i) undervaluing the cost of the QO when valuing top free agents (saving $75 on the car) and (ii) overvaluing the cost of the QO when valuing lower-end free agents (saving $75 on the smart phone).

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The distance a fly ball travels depends to a large degree on which lot of baseballs it came from.

How Far Did That Fly Ball Travel (Redux)?

Alan Nathan#, Jeff Kensrud*, Lloyd Smith*, Eric Lang#

#Department of Physics, University of Illinois

baseball.physics.illinois.edu

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